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A proposal concerning the application of the principle of complementarity in philosophy Copeland, Brian Dwight 1985

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A PROPOSAL CONCERNING THE APPLICATION OF THE PRINCIPLE OF COMPLEMENTARITY'IN PHILOSOPHY by BRIAN DWIGHT COPELAND B.Ed., The University of B r i t i s h Columbia, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of Philosophy) We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1985 0 Brian Dwight Cope!and, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that'the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Philosophy  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date October 1, 1985 - i t -A B S T R A C T The aim of t h i s paper i s to ou t l i n e a position concerning the unity of knowledge and to provide a model fo r the r e l a t i o n s h i p between r e a l i t y and knowledge. This paper i s based on remarks made by E.W. Beth in his Foundations of Mathematics, in which he claims a new version of realism i s needed. This realism would hold that man i s acquainted with four aspects of r e a l i t y and that the various aspects should be considered complementary. More s p e c i f i c a l l y Beth states: In my opinion, man has on account of his own l i f e experience an immediate and authentic contact with various spheres (perhaps i t would be better to say, zones, or aspects) of r e a l i t y , some of which may be enumerated; physical r e a l i t y - the world of matter -, soc i a l r e a l i t y - the world of men -, subjective r e a l i t y - the world of mind -, l o g i c a l r e a l i t y - the world of reason or discourse - , in which mathematical entites p a r t i c i p a t e . It seems reasonable however t e n t a t i v e l y to consider the various spheres of r e a l i t y as complementary. . . . (Beth, 1959, pp. 644-645) I w i l l be using the p r i n c i p l e of complementarity in i t s general form to argue f o r a c e r t a i n type of unity of knowledge. In the introduction I discuss the general need for unity of knowledge. Attempts at unity in atomic physics are examined in Chapter I, in p a r t i c u l a r the role of complementarity in unifying the theory of Quantum Mechanics. Chapter II treats complementarity as a thema in Hoi ton's sense, "an u n v e r i f i a b l e , u n f a l s i f i a b l e and yet not quite a r b i t r a r y hypothesis" that i s c r u c i a l to the development of knowledge (Hoiton, 1973, pp. 185-192). Chapter II also examines applications of complementarity in contexts other than atomic physics. Having shown the p r i n c i p l e in use in d i f f e r e n t contexts I proceed in Chapter III to develop my main thesis -that the p r i n c i p l e of complementarity represents a new model of explanation. When applied to the problem of the unity of knowledge, the p r i n c i p l e would suggest the view that knowledge i s a description of projections of the actual state, r e a l i t y , on the observer. This view i s compatible with a new version of realism. Complementarity, together with modest realism, modest foundational ism and a prospective conception of truth can be used to provide the outline of an a l t e r n a t i v e to foundational ism and coherentism. Chapter IV discusses complementarity in r e l a t i o n to other metaphysical and epistemological approaches to the monism-pluralism issue. Chapter V discusses the p o s s i b i l i t y of a r e a l i s t i c i n t e r p r e t a t i o n of knowledge in the special case of science. I conclude with a summary of the argument in t h i s paper. supervisor: - iv T A B L E O F C O N T E N T S Page ABSTRACT 11 LIST OF TABLES v i LIST OF FIGURES v i i INTRODUCTION 1 CHAPTER I THE CASE IN QUANTUM MECHANICS 7 1) The Meaning of Complementarity in Quantum Mechanics 7 2) The Impetus toward Complementarity 17 3) Instances of Physical Complementarity 20 4) Is Complementarity A n t i r e a l i s t i c ? 24 II VARIATIONS ON COMPLEMENTARITY 34 1) Complementarity in i t s General Form 35 2) Complementarity as a Thema 38 3) Ontological versus Epistemological Complementarity 40 4) Five Cases of Complementarity 42 5) Five Noncases 52 - V -CHAPTER Page III COMPLEMENTARITY AND THE CONCEPT OF REALITY 57 1) The Concept of Real i ty 58 2) A Modest Realism 61 3) The Complementary Aspects of Real i ty 64 4) Complementarity as Part of as Alternate Theory of Knowledge 77 5) A D ia lec t i ca l Epistemology 83 V COMPLEMENTARITY AND ITS RIVALS 88 1) Complementary Plural ism and the Monism-Plural ism Issue 88 2) Unity-Divers i ty in Knowledge 102 3) The Complementarity of Physical and Mathematical Knowledge (d i f fe rent a l legat ions) ,.^y,.< 127 4) The Complementarity^bf Physical and Mathematical Knowledge (both types required) 140 5) The Semantic Functors Inf(T,R) and Proj(T, B {) 144 VI COMPLEMENTARITY AND THE POSSIBILITY OF A REALISTIC INTERPRETATION OF SCIENTIFIC KNOWLEDGE 149 1) Introduction 149 2) Formulation. 149 3) C l a r i f i c a t i o n 151 4) Arguments for S c i e n t i f i c Realism. 154 5) Objections 160 SUMMARY 166 BIBLIOGRAPHY 172 - vi -LIST OF TABLES TABLE Page I Three General Conceptions of S c i e n t i f i c Explanation 137 - v i i -LIST OF FIGURES FIGURE Page 1 A Nondirectional Model of Knowledge 4 2 The Schrodinger Cat Experiment 22 3 The Necker Cube 37 4 R e l a t i v i s t i c Complementarity 43 5 The Bul l 48 6 Gestalt Complementarity 49 7 Geometric Projection 51 8 Connectiv ity, P rovab i l i t y and Truth 82 9 Real i ty and Knowledge 145 - vi i i -It i s one of the saddest features of our age that we are faced with an e n t i r e l y unnecessary dichotomy: on the one hand there are those whose devotion to i n t e l l e c t u a l c l e a n l i n e s s and rigour i s exemplary but who refuse to deal with anything but small, and often downright t r i v i a l , questions; i n the other camp are men l i k e Toynbee and some of the e x i s t e n t i a l i s t s who deal with the big and i n t e r e s t i n g questions, but i n such a manner that the p o s i t i v i s t s point to them as l i v i n g proofs that any e f f o r t of t h i s kind i s doomed to f a i l u r e . . . . (Kaufmann, 1968, p. 51) - 1 -I N T R O D U C T I O N The need for unity of knowledge i s the need to see organized information rather than a loosely connected c o l l e c t i o n of f a c t s . A coherent body of knowledge could then be taken to represent a coherent r e a l i t y . Unifying fundamental i n s i g h t , I hold, i s a metaphysical c r i t e r i o n for adequacy in regard to theories in general and our theory of r e a l i t y in p a r t i c u l a r ( i . e . they must not be ad hoc). But, I w i l l argue, despite considerable e f f o r t , i n t r a d i s c i p l i n a r y and i n t e r d i s c i p l n i a r y u n i f i c a t i o n s of knowledge have shown only l i m i t e d success at best. Some technical r e s u l t s in highly developed f i e l d s , , where the p o s s i b i l i t i e s f o r u n i f i c a t i o n would appear to be most promising, even suggest separation may be fundamental. This raises the p o s s i b i l i t y of a p l u r a l i s t i c view of r e a l i t y and a revised theory of knowledge to replace t r a d i t i o n a l foundational ism and coherentism. The model of unity I wish to support I w i l l c a l l a nonhierarchical model. It i s nonhierarchical in the sense that unity i s to be achieved not by giving b i t s of knowledge hi e r a r c h i c a l status r e l a t i v e to a ground, but by t r e a t i n g knowledge as a quasi-isotopic medium. L e v e l l i n g has had very l i m i t e d success (e.g. physical monism, as represented by Geometrodynamics, has t e n t a t i v e l y u n i f i e d only c e r t a i n r e s t r i c t e d parts of space-time physics). The h i e r a r c h i c a l proposal f a i l s because the hierarchy presupposes some a r b i t r a r y c r i t e r i o n of status. Whether the c r i t e r i o n i s immediacy, intersubjective invariance, - 2 -truth in a l l possible worlds or human usefulness each could only a r b i t r a r i l y be countenanced as the norm and pattern f o r knowledge in general. There e x i s t such d i v e r s i t i e s in the d i r e c t i o n and r e s u l t s of consideration that knowledge of the d i f f e r e n t aspects of r e a l i t y cannot be d i r e c t l y compared. The i n t e r s u b j e c t i v e invariance and ends directed approach of engineering would be appropriate in building a bridge but inappropriate in counselling a c h i l d . Concentration on subjective nuance and emotional impact might be appropriate in evaluating a painting but i r r e l e v a n t in judging the correctness of a l o g i c a l proof. The structure of knowledge i m p l i c i t in a foundational model i s often suggestive of a tree with roots, trunk and branches or a building with foundation and superstructure. I m p l i c i t in these metaphors, I think, are the following: i) at some point, d i r e c t contact with r e a l i t y i s possible, knowledge and r e a l i t y merge. At t h i s point concepts are s e l f evident and truths are absolute because knowledge and r e a l i t y are one, i i ) a l l knowleddge i s s o l i d l y connected, d i r e c t l y or i n d i r e c t l y , to the roots or foundation, i i i ) unity i s achieved through placement in the connected i n f e r e n t i a l system. I oppose t h i s metaphor on the grounds that i t i s misleading. Knowledge i s more aptly described as a bootstrap operation which leaves knowledge and r e a l i t y separated in a strong sense. This i s not a l i m i t a t i o n on knowledge but a p o s i t i v e p r i n c i p l e concerning the nature of knowledge. Knowledge i s not rooted or grounded in r e a l i t y , rather I would say that - 3 -i t i s reasonable to believe that i t r e f l e c t s in a generally r e l i a b l e manner, features of the world. I recognize that we are not i n a position to ostensibly compare r e a l i t y and knowledge. The view I o f f e r i s more modest than foundational ism. I contend we need a new g e s t a l t , a s h i f t i n perspective away from foundational ism and "the given." Both are deeply appealing, on a psychological l e v e l , but are p h i l o s o p h i c a l l y inadequate. The central place they can assume in one's thinking d i s t o r t s our view of knowledge and of the r e a l i t y i t represents. The view I suggest w i l l be a rational view which asks for knowledge which has a horizontal rather than a v e r t i c a l unity and which derives v a l i d i t y not from foundations but from i t s d i a l e c t i c a l s e l f c o r r e c t i n g operational s t y l e . The nondirectional model I am suggesting d i f f e r s from foundational ism in that; i ) we do not have knowledge that i s rooted in r e a l i t y . Knowledge i s a description of a projection of the actual state - r e a l i t y . There are no self-evident truths or concepts, i i ) there i s no absolute connection throughout our bodies of knowledge. Some accounts of aspects of r e a l i t y may be considered mutually incompatible yet complementary, i i i ) unity i s achieved through a topological r e l a t i o n of being in a one-manifold rather than a hierarchical one of stacking up in a c e r t a i n order. The appropriate physical model would be the Moebius band ( F i g . 1), not the tree or temple. I w i l l provide more detail and argument in Chapter III (sec. 4) f o r t h i s view. At t h i s - 4 -F i g . 1. A Nonhierarchical Model of Unified Knowledge. The Moebius band has no top or bottom. The band i s not "rooted" in r e a l i t y . Unity in t h i s model i s a b u i l t - i n feature of the one-dimensional manifold. point I want j u s t to indicate my general int e n t i o n . In contrast to the foundational model of the tree or the temple of knowledge I o f f e r the Moebius band. I conceive of the band as unrooted, with no foundation. The band has no bottom or top, no place to s t a r t . The domains of knowledge may be conceived of as regions, not necessarily connected, on the surface of the band. The unity of knowledge here i s modelled in the r e l a t i v e positions of the regions on the band. Unity in t h i s model i s a b u i l t in structural feature of the one dimensional manifold, not an externally imposed order on i t s parts. This i s my - 5 -(metaphysical) notion of what unity of knowledge has warrant to be in the l i g h t of the present state of our knowledge. How i s the p r i n c i p l e of complementarity involved in my discussion? In the following way. In atomic physics, physical r e a l i t y requires, f o r i t s adequate de s c r i p t i o n , both wave and p a r t i c l e accounts. The wave and p a r t i c l e accounts are mutually exclusive but complementary - in the sense of completing. An atomic en t i t y cannot e x h i b i t both i t s wave and p a r t i c l e properties simultaneously. I am suggesting that r e a l i t y in general requires four complementary modes of explanation in order to give an adequate account of i t s four complementary aspects. . .the physical, the s o c i a l , the subjective and the l o g i c a l . I am not claiming that physical complementarity can be generalized. I am claiming that complementarity i s a general p r i n c i p l e and that when we deal with i t in atomic physics we are dealing with a special statement of the general p r i n c i p l e . Situations outside of physics are not vague analogies of physical complementarity, rather the s i t u a t i o n in physics i s a r e f l e c t i o n of a wide ranging p r i n c i p l e . In the following chapters I w i l l ; i ) discuss the app l i c a t i o n of complementarity in Quantum Mechanics (Q.M.), i i ) i l l u s t r a t e the ap p l i c a t i o n of complementarity outside of Q.M., i i i ) show how the p r i n c i p l e can be applied to the questions of; - 6 -a) what type of unity of knowledge i s possible? b) what form should our concept of r e a l i t y take? - 7 -C h a p t e r I C O M P L E M E N T A R I T Y A N D I T S S I G N I F I C A N C E I N Q U A N T U M M E C H A N I C S The aim of t h i s chapter i s to discuss the s i g n i f i c a n c e of the p r i n c i p l e of complementarity in Quantum Mechanics. My discussion w i l l be organized into four parts. F i r s t I w i l l deal with the meaning of the p r i n c i p l e in Elementary Quantum Mechanics. This w i l l include some treatment of the role of the p r i n c i p l e in regard to the int e r p r e t a t i o n of the mathematical formalism of the theory. I w i l l then try to account for the impetus which would cause the necessary s h i f t i n perspective needed to countenance the adoption of such a new model of explanation. The t h i r d part of t h i s chapter concerns three applications of the p r i n c i p l e and the fourth part the issue of whether or not the use of the p r i n c i p l e of complementarity commits one to any of p o s i t i v i s m , idealism or realism. 1 ) T h e M e a n i n g o f C o m p l e m e n t a r i t y i n Q . M . i ) R e s t r i c t e d S e n s e . In Q.M. the p r i n c i p l e of complementarity has two senses, as distinguished by Niels Bohr in his Como Address of 1927. The f i r s t sense i s the r e s t r i c t e d technical sense associated with the Heisenberg - 8 -Uncertainty P r i n c i p l e which i n s i s t s that conjugate parameters l i k e position and momentum or energy and time cannot be simultaneously measured with a r b i t r a r y p r e c i s i o n . The second sense i s the more general sense associated with wave-particle d u a l i t y which declares that some experimental r e s u l t s require f o r t h e i r adequate explanation the use of two (or more) mutually exclusive but not contradictory, theories. Consider the r e s t r i c t e d sense of the p r i n c i p l e as i t concerns the position x and the momentum p of some atomic e n t i t y . The uncertainty p r i n c i p l e states that the product of the uncertainty in position x and the uncertainty in momentum p must s a t i s f y the re l a t i o n *Ax & p ^ h* where h = 6.63 x 10 ^  Jsec . For conjugate parameters, le s s uncertainty in the measurement of one parameter induces more uncertainty in the other. This uncertainty i s not the r e s u l t of imprecise measurement but because a r b i t r a r i l y high precision f o r the second parameter i s not there to be had. I w i l l elaborate on t h i s point l a t e r when I discuss the formalism. Average values of pos i t i o n and momentum are not mutually exclusive notions since both are needed to specify the state of a system and both can be measured simultaneously - in a s u f f i c i e n t l y stringent operative sense. But position and momentum are complementary observables in that they cannot simultaneously be measured with a r b i t r a r i l y high p r e c i s i o n . Bohr f i r s t introduced the p r i n c i p l e of complementarity into physics during the International Congress of Physics in September, 1927, at Como, Italy in these words; - 9 -The very nature of the quantum theory thus forces us to regard the space-time co-ordination, and the claim of c a u s a l i t y , the union of which characterize the c l a s s i c a l theory as complementary, but exclusive features of the de s c r i p t i o n , symbolizing the i d e a l i z a t i o n of observation and d e f i n i t i o n respectively. (M. Jammer, 1966, pp. 351-352). This version of complementarity i s a b i t more general than the uncertainty version i n d i c a t i n g that precise space-time descriptions of atomic e n t i t i e s cannot be given simultaneously with causal descriptions. This i s because t r a j e c t o r i e s are not single well defined paths f o r atomic e n t i t i e s but paths of p r o b a b i l i t y . Either space-time descriptions can be supplied in which case the e n t i t y jumps around a r b i t r a r i l y or causal descriptions can be given in which case the e n t i t y must be conceived of as a d i f f u s e p r o b a b i l i t y wave. But both descriptoins cannot be invoked concurrently. To be more exact about complementarity in the r e s t r i c t e d sense l e t me b r i e f l y discuss the Q.M. formalism. Any state of a dynamical system of n p a r t i c l e s with three degrees of freedom each w i l l be completely described by a normed wave function in H i l b e r t space. I w i l l consider the case of j u s t one p a r t i c l e with one degree of freedom so that the wave equation takes the form iff(f,jt). The wave function i s s i m i l a r in i t s mathematical behaviour to functions describing c l a s s i c a l p o t e n t i a l s . In p a r t i c u l a r 2 there are three c l a s s i c a l forms of f i e l d equations; i ) V<p - v * d ± z - ' - wave equation, which describes the behaviour of e l e c t r i c , l i g h t and sound waves; - 10 -i i ) i i i ) The equations of Q.M. can be brought formally into form ( i ) or ( i i ) although the emergence of complex quantities modifies the s i t u a t i o n somewhat. But the Schrodinger equation of Q.M., although arguably of c l a s s i c a l form does not represent measurements of parameters for e n t i t i e s but rather determines the p r o b a b i l i t y of obtaining c e r t a i n values when measurement i s performed. This, to some, has represented a weakening of the concept of r e a l i t y . The wave function can be A determined by solving a general eigenvalue equation of the form H Vr= E^y- where H i s the Hamiltonian operator corresponding to t o t a l energy of the system, \fr the wave function to be determined and E n allowed energies f o r the system. If-yr- includes time e x p l i c i t l y i t i s c a l l e d time dependent; i f not i t i s c a l l e d time independent and represents a stationary state of the system. V i t s e l f has no d i r e c t physical meaning but V (^vi^idd-x represents the p r o b a b i l i t y of finding the system in the element of configurational space d t between q f c and qK + dq f c. This means then that ^y^dx gives the p r o b a b i l i t y of finding the e n t i t y i n the region R. It i s required that J * cLf - 1 . alt sf*<t-x 7 d JLM ^ F V V> x> <>t - heat equation, which describes the behaviour of heat waves and thermal radiation; (ft - F _ potential equation, which describes, among other phenomena, e l e c t r o - and magnetostatics. - 11 -For every observable property A of a system there exists in the HiIbert space, a l i n e a r Hermitian operator A* such that all properties of the observable A can be determined from the mathematical A properties of the operator A, operating on ir . Furthermore each n-dimensional operator A* possesses a complete orthonormal basis of eigenvectors oC± and a corresonding set of real eigenvalues a^ such that; * - cC- i= 1,2, ^ A °ct - a. The only value i t i s possible to obtain in a measurement of observable A are the a^. In an experimental s i t u a i t o n i f a system i s in a state -y^s.t. y?s i s an eigenfunction of an operator A ( i . e . A-^=3;.^ for some i ) , then a d e f i n i t e , precise r e s u l t w i l l be obtained f o r the observable A ( i . e . a^). If i s not an eigenfunction of A* then the strongest p r e d i c t i v e statement that can be made i s that the expected 3 value of the measurement w i l l be; all s p a « e •  5 cLt ^11 space. In general the act of measuring A causes an abrupt, discontinuous change in the state vector y of the system "popping" i t into an eigenstate oC^. Complementarity can best be approached in the r e s t r i c t e d sense by way of the compatibility theorem which states that the - 12 -following three conditions are equivalent, where observables A and B A A have operators A and B respectively; i ) A and B are compatible observables, i i ) "A a n d i i possess a common eigenbasis, A A i i i ) A and B commute. Consider then the complementarity of position and momentum. The A\ A operator f o r position i s X = x and for momentum P =-i/nU_. They do not commute since, X P - - X l hot Let the position observable be A and momentum observable B. Since the operators do not commute the observables A and B are not compatible ( i . e . not simultaneously measurable with a r b i t r a r y p r e c i s i o n ) . This means that i f three rapid measurements M, and M 3 on A, M 2 on B are made so that the state vector Y does not time-evolve then M 2(B) w i l l i n t e r f e r e so that M,(A) / Mj(A). This i s due to the f a c t that measurement M #(A) s h i f t s y into an eigenstate oc^ of A. Measurement M^ (B) then s h i f t s into an eigenstate j&i of B, which w i l l not, in general, be the same as that for A (by i i ) . When M 3(A) i s made o A collapses from state p £ which i n general i s not an eigenstate of A. The measurements of position and momentum i n t e r f e r e with each other because t h e i r operators do not have a common eigenbasis. The conditions needed for an accurate description of position ( i . e . T ^ " in an eigenstate of ft), preclude in general the existence of an accurate - 13 -value of momentum ( i . e . y also in an eigenstate of B). This i s the r e s t r i c t e d sense of the p r i n c i p l e of complementarity. To give a more concrete form to the preceding f o r m a l i t i e s I w i l l now discuss a p a r t i c u l a r example of a problem that can be solved using Q.M. and I w i l l also show how the p r i n c i p l e of complementarity arises in a natural way in the i n t e r p r e t a t i o n of the s o l u t i o n . Consider the case of a p a r t i c l e confined in a one-dimensional box of length a. The potential energy outside the box i s s p e c i f i e d to be i n f i n i t e , i nside the box zero. The problem i s to give the best description of the state of t h i s system. The observable we are interested in w i l l be total energy E so the relevant Q.M. operator i s H. To findy^, the best Q.M. description of the state of the system,. A we need to solve Hv= E,,-^. It i s the case that; and n ) |_| = j - + V <A 1 T = operator f o r k i n e t i c energy , A V = operator f o r potential energy. Consider two cases a) outside the box and b) inside the box. a) Outside the box; V = <X> I G F + ^ = E * V * i l l + [ E „ - V w ] Tfc = O - 14 -But there i s no function which twice d i f f e r e n t i a t e d gives times i t s e l f except V s 0 /. j -yrz CLT = J OdT = O , a o as expected. b) Inside the box; V = 0 A solution to * i s 1^= A s i n (oc X ) where cK = <2mc"h The boundary conditions require 0 at the edges of the box. -p- (o) = ir(a) * O •yjr (o) = /A sin (j*<b)I] - /4 s/n£cT| = O , oC = ri IT n = 1 , 3 ^ 2. Z. 2 - 15 -The wave function must be normalised. a. J ( A s m „ r r * ) dx. = 1 s o A--(&y a t 2 mot £ _ = n a A 2 S m a Quantized energy l e v e l s are a natural feature of solutions obtained using the theory. To see the need f o r complementarity take the case where the p a r t i c l e i s in i t s lowest energy state n = 1. If we want to know the momentum we must use P = -ihd " V i s here c l e a r l y not an eigenfunction of P so a d e f i n i t e r e s u l t w i l l not be expected. The expected value i s ; ? „ T> , ^ - f sin rrx(-iKjr\^os irx d.x J y/, PMrt dx ^ a J T V a V a o j" yr2 dye 1 But i f the square of momentum i s considered P = -h d_ applied to -yr o t x 2 _tfdLZ A sinfirx] = f\ JL A sin I UlL \. yr /s an ei^e-n f u ^ c tion z 2 with eigenvalue = h T[_ = ^n, Et so a * - 16 -so the expected value = 0 but the eigenvalue -± \J<?Lrn E, . It can be said therefore that there i s an uncertainty in our knowledge of Sim i l a r l y with position there i s an uncertainty, in t h i s case of a. If the product i s computed ; I i ) G e n e r a l S e n s e . The second sense of complementarity was pointed out by Bohr in 1927. I t i s represented by, for example wave-particle d u a l i t y . There had been building up a range of r e s u l t s which seemed to require two d i f f e r i n g types of explanation. Some res u l t s could be explained using a wave model of l i g h t (e.g. interference) other r e s u l t s could be explained using a p a r t i c l e model (e.g. photoelectric e f f e c t ) . Attempts to reconcile the two views were a f a i l u r e . They appeared l o g i c a l l y incompatible and mutually exclusive. Bohr suggested that wave and p a r t i c l e descriptions were mutually exclusive but not l o g i c a l l y contradictory, they are complementary in that atomic 4 e n t i t i e s cannot e x h i b i t both set of properties at once. To i l l u s t r a t e l e t me discuss the double s l i t experiment. A beam of discrete photons i s directed at an opaque screen with two openings in i t . When both s l i t s are open individual photons - 17 -are detected on the screen behind the b a r r i e r , but the pattern of detection i s that of a c l a s s i c a l wave interference pattern. If one opening i s blocked a normal b e l l shaped d i s t r i b u i t o n i s obtained. Two be l l curves do not superimpose to give an interference pattern. With two s l i t s open l i g h t behaves as a wave, with one s l i t open i t behaves as a p a r t i c l e . If I can use an analogy from r e s t r i c t e d complementarity i t were as i f l i g h t were in a superposiiton state and that the experimental conditions determined into which observable state i t collapsed. The act of experimenting conditioned what was observed. Complementarity i s a departure from previous ideals of explanation. The c l a s s i c i a l ideal was that coherent, u n i f i e d descriptions and explanations of nature could be given in a l l cases. What i s being proposed here i s that in some cases i t i s possible to generate adequate explanations of physical phenomena only through the exhaustive overlay of d i f f e r e n t mutually exclusive theories. 2 ) T h e I m p e t u s T o w a r d C o m p l e m e n t a r i t y I contend that complementarity i s a general p r i n c i p l e which; i ) has applications outside of Q.M., i i ) does not depend on Q.M. f o r roots or support, and - 18 -i i i ) assumes d i f f e r e n t s p e c i f i c forms when used in other f i e l d s of study. Bohr did not invent the idea of complementarity although he pioneered i t s application in physics. Gerald Hoi ton gives at l e a s t two possible sources (Hoiton, 1982, pp. 133-149). One i s Kierkegaard, whom Bohr read. Kierkegaard stresses the role of a q u a l i t a t i v e d i a l e c t i c between d i f f e r e n t conceptions of l i f e . There i s constant c o n f l i c t between them. We cannot hope to have continuous progress i n , and as s i m i l a t i o n to these conceptions but must make choices. There i s thesis and ant i t h e s i s but no re c o n c i l i n g synthesis. Hoi ton remarks that Kierkegaard's stress on the discontinuity between incompatibles, abrupt t r a n s i t i o n s and lack of synthesis was as nonclassical in philosophy as Bohr's quantum jumps, p r o b a b i l i s t i c c a u s a l i t y and wave-particle d u a l i t y were in physic (Hoiton, 1982, p. 146). Holton also c i t e s William James, and his analysis of consciousness, whom Bohr also read. James claimed that the stream of consciousness, although u n i f i e d , i s characterized by abrupt jumps in the quali t y of experience (e.g. from introspection to anger, to objective thought, to meditation). In pathological cases the discreteness of consciousness becomes acute: It must be admitted therefore, that in c e r t a i n persons, at l e a s t , the total possible consciousness maybe s p l i t into parts which coexist but mutually ignore each other, and share the objects of knowledge between them. More remarkable they are complementary. Give an object to one of the consciousnesses and by that f a c t you remove i t from the other. Barring a c e r t a i n common fund of knowledge, l i k e the command of language, etc., what - 19 -the upper s e l f knows the under s e l f i s ignorant of and v i s a versa. (Hoiton, 1982, pp. 141-142) I am not suggesting of course that Bohr copied these notions. Just that complementarity i s a broad notion that w i l l have varying s p e c i f i c forms. Recognition of the general p r i n c i p l e f a c i l i t a t e s a p plication in p a r t i c u l a r instances. Bohr had great expectations about the role complementarity could play regarding the p o s s i b i l i t y of unifying knowledge. He attempted numerous applications in t r y i n g to r e a l i z e a unifying perspective on human knowledge (Hoiton, 1973, pp. 152-155). He suggested that thought, emotion and v o l i t i o n be considered complementary aspects of human consciousness. He t r i e d to apply the p r i n c i p l e to everyday situations remarking how love and j u s t i c e were complementary ways of r e l a t i n g to his son in d i s c i p l i n a r y s i t u a t i o n s . There i s good reason to think that Bohr conceived of complementarity as a p r i n c i p l e of broad scope and a p p l i c a t i o n (Hoiton, 1982, pp. 152-153). Complementarity represents a middle ground between coherent, u n i f i e d explanation and a s e r i a l array of data. Physics had been achieving a considerable degree of unity in the nineteenth and early twentieth century. For examle; i ) Maxwell's electrodynamics u n i f i e d e l e c t r i c i t y , magnetism and o p t i c s , i i ) Special R e l a t i v i t y u n i f i e d kinematics with electrodynamics^ and - 20 -i i i ) General R e l a t i v i t y u n i f i e d gravitataion with the structure of space-time.5 Einstein was even convinced a u n i f i e d f i e l d theory was possible in which electrodynamics and g r a v i t a t i o n would be u n i f i e d . In the face of t h i s s i t u a t i o n wave-partice d u a l i t y was a r e c a l c i t r a n t anomaly. Thesis and a n t i t h e s i s were present without any suggestion of synthesis. To Einstein t h i s was an unattractive s i t u a t i o n . Bohr, on the other hand, accepted complementarity and considered i t a p o s i t i v e p r i n c i p l e c h a racterizing an essential feature of human knowledge. What I am suggesting i s that what has proven useful in physics might likewise prove u s e f u l , in a suitable form, in philosophy, with regard to the concept of r e a l i t y and with regard to the problem of the unity of knowledge. 3 ) I n s t a n c e s o f P h y s i c a l C o m p l e m e n t a r i t y The a p p l i c a t i o n of general complementarity in Q.M. extends beyond wave-particle d u a l i t y . I have already discussed Bohr's spacetime-causality complementarity. The general idea i s that when a si t u a t i o n permits p a r t i a l explanation in a ce r t a i n set of compatible terms i t may require further completing explanation in another set of terms. To review b r i e f l y wave-particle duality in the double s l i t experiments, the physical set up seemed to condition the theoretical - 21 -d e s c r i p t i o n . P a r t i c l e descriptions of l i g h t were needed to account for individual detections. Wave descriptions are needed to account for the interference pattern with two s l i t s . But the descriptions are not required simultaneously so they are not l o g i c a l l y contradictory. Another manifestation of complementarity i s that exhibited in the Schrodinger Cat Experiment ( F i g . 2) . The cat, representing macroscopic r e a l i t y , must be e i t h e r dead or a l i v e at the end of the experiment. The radioactive atom, representing quantum r e a l i t y , need not be e i t h e r disintegrated or i n t a c t - i t can s t i l l be in a superposition state. The f a c t that the cat and the atom are in the same box c e r t a i n l y does not mean they can be described in the same way. C l a s s i c a l , thermodynamic, causal explanation of the fate of the cat i s possible. But not so with the atom. There i s no paradox here because the conditions which would allow a stochastic explanation of the atom preclude such a descripton of the cat (e.g. the cat has no function). The conditions which would allow for c l a s s i c a l description of the cat preclude such a description f o r the atom (e.g. simultaneous exact values f o r a l l parameters). Causal and quantum stochastic descriptions are complementary. They are mutually exclusive but not contradictory since they apply in d i f f e r e n t circumstances. A t h i r d manifestation of complementarity can be seen in Be l l ' s Experiment. This could be c a l l e d o b j e c t i v i t y - local c a u s a l i t y d u a l i t y . Polarized, p e r f e c t l y correlated photons are emitted in opposite d i r e c t i o n s from a common source. Each passes - 22 -F i g . 2. Schrodinger Cat Experiment. Causal evolution of a j o i n t system and stochastic evolution of a p a r t i a l subsystem are complementary properties. - 23 -through a separate p o l a r i z e r , c a l l them A and B, and i s either detected or not. Let & be the angle between the two p o l a r i z e r alignments. If 8 = 0 the number of miscorrelations or "errors" E w i l l be zero since the photons are i n the s i n g l e t state ( i . e . p e r f e c t l y c o r r e l a t e d ) . But i f A i s rotated through a nonzero angle then there w i l l be some "errors" E(0). Now also rotate B through 9 i n the opposite d i r e c t i o n so that the r e l a t i v e total angle between the p o l a r i z e r alignments i s 29. C a l l "errors" in t h i s case E(20). Considered c l a s s i c a l l y E(20) - 2E(0) since i n the ZQ case we have rotated both p o l a r i z e r s and so w i l l not pick up double errors ( i . e . no double errors are detected since by s h i f t i n g both p o l a r i z e r s there i s no standard against which comparison can be made - two "errors" cancel). The formalism of Q.M. predicts that B e l l ' s i n e q u a l i t y , E(20) - 2E(8), w i l l not always be c o r r e c t . Experimental r e s u l t s show that the Q.M. prediction i s c o r r e c t . There turns out to be too many "errors" in the 20-case compared to the O-case. It would seem that i n moving A we must have disturbed the p o l a r i z a t i o n of the photons headed for B, so producing the "extra errors" that give r i s e to the v i o l a t i o n of B e l l ' s Inequality. Complementarity can be used to explain B e l l ' s Experiment. There are at l e a s t two c r u c i a l assumptions used in developing the r e s u l t ; o b j e c t i v i t y , that photons e x i s t in a d e f i n i t e state when unobserved, and lo c a l c a u s a l i t y , that by s h i f t i n g the B p o l a r i z e r we did not influence the A p o l a r i z e r . C l a s s i c a l l y we would have to abandon one of these. But complementarity allows us to consider them - 24 -mutually exclusive but not contradictory. It does not appear that the o r i g i n a l experimental s e t t i n g e f f e c t s the r e s u l t in that the Aspect Experiment has shown that the Bell Inequality i s v i o l a t e d even i f the p o l a r i z e r s are rotated a f t e r the photons are emitted. If you i n s i s t on o b j e c t i v i t y , then r e a l i t y must be nonlocal in order to explain the observed v i o l a t i o n of the i n e q u a l i t y . Conversely i f you are set on retaining s t r i c t l o c a l c a u s a l i t y then you must give up the idea that the photons are in an objective physical state to s t a r t with. Accepting l o c a l c a u s a l i t y precludes objective description and giving an objective description precludes local c a u s a l i t y . This i s the application of the p r i n c i p l e of complementarity to B e l l ' s Experiment. 4 ) I s C o m p l e m e n t a r y A n t l r e a l i s t i c ? Q.M. could be considered a p o s i t i v i s t i c theory being a p r e d i c t i v e device for c l a s s i c a l observables. I t could be considered i d e a l i s t i c in the sense that i t appears that properties are created by the act of observation. I w i l l argue that complementarity and Q.M. are compatible with realism. F i r s t I w i l l discuss the general controversy, then deal with p o s i t i v i s m , idealism and realism in turn. The pursuit of knowledge i s an e c l e c t i c enterprise. In various contexts the pursuit of knowledge can be viewed as a r e a l i s t i c , i d e a l i s t i c or p o s i t i v i s t i c undertaking. It i s r e a l i s t i c in the sense that knowledge i s most often believed to describe a world - 25 -independent of the observer. It i s i d e a l i s t i c in so f a r as the concepts and theories seem to be free creations of the i n t e l l e c t , not l o g i c a l l y derivable form the observable. For while i t may be useful to keep in mind what i s observable there are no reports on the observable which can be true or f a l s e u n t i l there i s a conceptual apparatus in place. The pursuit of knowledge may appear p o s i t i v i s t i c i n so f a r as concepts and theories derive t h e i r warrant from t h e i r effectiveness i n organising, co-ordinating and i n t e r p r e t i n g sensory experience. It may even appear metaphysical in that c e r t a i n c r i t e r i a such as s i m p l i c i t y and unity are considered important in determining acceptable theory. I cannot prove realism correct and idealism and positivism wrong. But I do think realism i s preferable and I w i l l try to say why. Bohr considered Q.M. i n general and the-fi- function in p a r t i c u l a r j u s t a p r e d i c t i v e device. Feyerabend says Bohr held that the\fr function i t s e l f has no new conceptual content but represents merely a tool f o r predicting c l a s s i c a l observables. This view seems to be based on a c e r t a i n view of language and meaning (Feyerabend, 1958, p. 88). For Bohr compelemtarity arises because Q.M. must use c l a s s i c a l concepts to explain the r e s u l t s of Q.M. C l a s s i c a l e x p r e s s i b i l i t y requires that a l l knowledge be expressed in c l a s s i c a l terms. Such a view seems implausible to me, as d i f f i c u l t as i t may be to generate alternate schemes. But h i s t o r i c a l l y we have seen examples of alternate schemes. There has been myth, A r i s t o t e l i a n physics, Ptolemaic astronomy, R e l a t i v i t y , and Newtonian Mechanics, a l l of which - 26 -represented conceptual s h i f t s . There i s no good reason I can see to think we have reached the end of the l i n e in conceptual evolution. I contend that in the case of Q.M. we should take the theory at face value, and considering that i t i s one of the best confirmed theories of science, assume that i t has real conceptual content and actually t e l l s us about part of physical r e a l i t y , however odd or nonclassical the new knowledge may be. If Q.M. i s j u s t a p r e d i c t i v e device, there i s the question of i t s i n t e r p r e t a t i o n . In t h i s regard the p o s i t i v i s t p o sition seems unsatisfactory. The p o s i t i v i s t p o sition seems to indicate our i n t e r p r e t a t i o n does not depend on the state of our theoretical knowledge, the i n t e r p r e t a t i o n being f i x e d by the constraint of c l a s s i c a l e x p r e s s i b i l i t y . How could i t be so fixed? There seem to be two p o s s i b i l i t i e s . According to the pragmatic theory of meaning symbols acquire meaning through repeated use. But repeated use of a sign demonstrates the behaviour of an organism, not meaning. According to the phenomenological theory of meaning symbols acquire meaning from phenomena. But phenomena are nonconceptual and acquire meaning only in the l i g h t of conceptualization. Interpretations of formalisms a r i s e from and depend on theoretical understanding. Sensory experience does not s u f f i c e to explain the structure or function of knowledge. The end r e s u l t s of a p o s i t i v i s t i c view of Q.M. include being stuck in a c l a s s i c a l conceptual rut and having to s e t t l e for a l i m i t e d or even t r i v i a l conception of nature. - 27 -It might be argued that in Q.M. we create our r e a l i t y in the act of observation. Bishop Berkely's view of knowledge i s resurrected by atomic physics. In a c e r t a i n sense i t i s true that the presence of the observer conditions the r e s u l t to be obtained in Q.M. But does t h i s conditioning imply idealism? I think not. Take the case of the length of an object in the Special Theory of R e l a t i v i t y . Because the length i s a funci ton of the r e l a t i v e speed of the object and the observer that does not mean, I claim, that R e l a t i v i t y i s an i d e a l i s t i c theory. It merely indicates that some properties are observer conditioned. In f a c t i t turns out that one of the outcomes of R e l a t i v i t y i s that many more properties are observer conditioned that previously believed. Because the value we measure for an observable, according to Q.M. (e.g. momentum) can jump around i f the system i s not in an eigenstate of momentum, does that imply Q.M. i s an i d e a l i s t i c theory? No, i t indicates that c e r t a i n properties are observer conditioned. But what i f a l l properties are observer conditioned? F i r s t of a l l t h i s i s not the case fo r S.R., G.R. or Q.M. In each case there are i n v a r i a n t quantities that are the same for every observer. For S.R. these would include the v e l o c i t y of l i g h t , entropy of a closed system, r e s t mass and energy-mass of a closed system. For Q.M. the invariants would include e l e c t r i c charge, spin, Bose-Einstein/Fermi-Dirac s t a t i s t i c and the wave function of a closed system. A s c i e n t i f i c theory must also be capable of being formulated i n a way that i t s laws are covariant with respect to a certain set of admissible transformations. Intersubjective invariance i s b u i l t into - 28 -the structure of physical theory in the attempt to r e f l e c t the conviction that there i s an objective external world, nature, and that we can have knowledge of the structure and function of nature. My second point concerning observer conditioned properties i s that, counterfactually speaking, even i f a l l properties of objects or systems were observer conditioned t h i s s t i l l would not show that realism i s untenable. It would merely show something about what we c a l l a property. In addition to the above s p e c i f i c objections to idealism I have a more general objection. It would seem to replace our ordinary view of language, in which there are terms designating both thoughts and what i s thought of, by a r e s t r i c t e d new view of language in which there can be terms for only what i s thought of. And whereas the former i s adequate, in almost a l l situations the l a t t e r i s inadequate in most s i t u a t i o n s . It seems for example to t r i v i a l i z e the concept of nature, which can no longer be associated with an independent external r e a l i t y but i s at best a c e r t a i n sublass of ideas. If we have no terms which refer to external r e a l i t y but only terms which ref e r to thoughts, we cannot even r a i s e the question of idealism v. realism because we cannot speak of external r e a l i t y (even though i t may seem I j u s t d i d ) . This does not prove idealism wrong and realism r i g h t , but i t does leave the i d e a l i s t the task of explaining why we should a r b i t r a r i l y r e s t r i c t the supposed scope of our language, and by so doing, render inadequate what was previously adequate. That we cannot give an exhaustive account of the r e l a t i o n s h i p between -29 -nature and thought does not imply that e i t h e r concept should be pre-emptorily eliminated or d i s t o r t e d . ^ In defending realism I point to the necessity of having terms for thoughts and what i s thought of, for knowledge and for what i s known. I agree that the r e l a t i o n s h i p between knowledge and r e a l i t y i s not c l e a r at the present time, but i t i s preferable to grapple with whatever puzzles there are rather than rule out the problem from the s t a r t . With regard to Q.M. in p a r t i c u l a r there i s no reason to abandon realism. Q.M. and wave-particle d u a l i t y may be j u s t a l i m i t i n g case of a more general physical theory in which d u a l i t y i s removed. This seems improbable but cannot presently be ruled out. In the event that physics i s unifed by f i n d i n g a theory that u n i f i e s presently d i s j o i n t theories of space-time, p a r t i c l e dynamics, elementary p a r t i c l e c o n s t i t u t i o n , thermodynamics and cosmology there i s no t e l l i n g i n advance what features the theory w i l l have. But even i f complementarity p e r s i s t s , as i t does in l i m i t e d unifying theories such as quantum f i e l d theory, t h i s does not argue against realism because complementarity i s compatible with realism. State descriptions in terms of space-time accounts of " t r a j e c t o r i e s " are novel. But i t i s s t i l l possible to maintain that the wave function should be viewed as having real content. Q.M. i s concerned with the description of the nature of physical systems in addition to state desc r i p t i o n s . This involves among other things f i n d i n g eigenvalues of operators and f i n d i n g wave functions which are Lorentz i n v a r i a n t . I hold that the nature of the systems, as revealed in our best confirmed - 30 -theories should be considered, p r o v i s i o n a l l y , to r e f l e c t aspects of the structure of r e a l i t y . Measurement i s not concerned usually with the d i r e c t object of our i n t e r e s t but with a projection of i t . R e l a t i v i t y showed how what were considered properties of things are often j u s t properties of a p r o j e c t i o n . In p a r t i c u l a r the simultaneity of two events, the duration of an event, the length and mass of an object a l l are not i n t r i n s i c properties of objects or events but depend on the r e l a t i v e motion of the observer and the event or object. S i m i l a r l y in Q.M. many properties of systems, not in an eigenstate, are properties of projections on an experimental apparatus, which in some cases may be a human being. But invariant quantities and covariant laws are s t i l l there r e f l e c t i n g the objective aspects of r e a l i t y , and so there remains good reason to hold to the idea of an external world which embodies and u n i f i e s the projections. In some ways I would guess the a n t i r e a l i s t i c flavour of Q.M. i s due to a c e r t a i n i l l conceived view of realism. Q.M. i s not r e a l i s t i c , i t might be argued, because we already know what i s real and the kinds of things Q.M. commits us to do not f i t the b i l l . The wave function, f o r example, seems to point to a t h i r d r e a l i t y , apart from the subjective and the p h y s i c a l , a world of time evolving p r o b a b i l i t y waves. The waves develop in a law l i k e manner according to the Schrodinger wave equation. But what evolves i s p r o b a b i l i t i e s not objects, events, thoughts or other such f a m i l i a r e n t i t i e s . Operators applied to wave functions give i n d e f i n i t e r e s u l t s for - 31 -measurements whereas i t was previously believed that precise values for a l l parameters of a system were attainable, up to the l i m i t s of accuracy of the measuring instruments. In general only the p r o b a b i l i t e s of an event occurring can be given whereas previously i t was held that given the i n i t i a l conditions of a system and the physical laws that govern i t the system could be p r e c i s e l y and determinately characterized at a l l l a t e r times. Measuring one observable can a f f e c t , in Q.M. theory, the value attainable for a d i f f e r e n t observable whereas i t was previously believed that measurable values for a l l observables existed independently. Various quantities were thought to be capable of continuously assuming any value whatsoever (e.g. v e l o c i t y , momentum, total energy) but Q.M. requires that only c e r t a i n discrete eigenvalues are possible. These re s u l t s are a l l "unreal" i t could be claimed. But the view of realism I hold finds nothing "unreal" here. The f a c t that a theory modifies what we consider real i s to be expected. To be a r e a l i s t with respect to theories requires that you believe that a c o n s i s t e n t l y interpreted well confirmed theory gives you at l e a s t probable knowledge about some aspect of r e a l i t y . If S.R. t e l l s you the length of an object varies with the r e l a t i v e v e l o c i t y of the observer and the observed, then believe t h i s and c o r r e c t the previous misconception about absolute length. The conservative approach of a Lorentz in attempting to give a Newtonian i n t e r p r e t a t i o n of the Michelson Morley experiment merits consideration i n i t i a l l y , but i n l i g h t of repeated confirmation of S.R. and repeated an hoc adjustments to N.M., considerations of s i m p l i c i t y - 32 -weigh heavily in favour of considering the S.R. view of the world r e a l . S i m i l a r l y with Q.M. and complementarity. If Q.M. t e l l s me that position and momentum are not simultaneously measurable with a r b i t r a r y precision then take t h i s f o r knowledge about r e a l i t y , e s p e c i a l l y as theory becomes better confirmed. Q.M. i s now one of the best confirmed physical theories we have. For a r e a l i s t then Q.M. provides some of the most probable knowledge we have concerning the structure and behaviour of the relevant aspects of physical r e a l i t y . • • • • Mathematical formalisms, as uninterpreted c a l c u l i , t e l l us nothing. But the c a l c u l i are b u i l t on ideas and the ideas can be used to describe the world. The ideas involved in Q.M. are d i f f e r e n t from those we were accustomed to. But they solved problems in physics where other ideas have f a i l e d . The ideas are compatible with realism, a view which I would be prepared to give up only in extreme conditions. And the ideas are suggestive of application in varying contexts. I think they can be applied to give an up to date description of a warranted concept of r e a l i t y and to suggest a model for the unity of knowledge. - 33 -N O T E S For energy and time, i f A t i s the time a v a i l a b l e for the energy measurement there i s an inherent uncertainty ^ E in the energy s . t . A E A t £ h. Where 0(x,y,z,t) i s a f i l e d quantity, F a function of x, y,z,t,#, v = v e l o c i t y , D a constant. 3 C l e a r l y i f \jr i s an eigenfunction t h i s reduces to J ifr-s * j Vr* ax a a. S vfdr _ a. y as expected. / -^f- dL-x J ^ 2 d.x 4 Physical phenomena can be described using p a r t i c l e notions momentum p and energy E, or wave notions wavelength A and frequency y . The descriptions are related by the equations p = h/\ and E = hv where h- Planck's constant. 5 S.R. Minkowski space-time and i t s symmetry group, the Lorentz transformations, preserve the laws of kinematics and electromagnetism whereas N.M. Newtonian space and time do not. S.R. i s consistent with Michel son-Moriey; N.M. i s not. 6 I n that the e f f e c t s of gravity are i d e n t i f i e d with the i n t r i n s i c curvature of space-time as induced by the stress energy d i s t r i b u t i o n i n a region. ^Friedman also makes the point that only realism can give an adequate account of how theories can be confirmed. Only the r e a l i s t can appeal to the referents of unifying theoretical e n t i t i e s in explaining the practise of conjoining independently supported theories and using subsequent observational r e s u l t s to give repeated boosts of confirmation to a l l the subtheories (Friedman, 1983, pp. 236-250). - 34 -C h a p t e r I I V A R I A T I O N S O N C O M P L E M E N T A R I T Y One of my main theses in t h i s paper i s that the p r i n c i p l e of complementarity i s useful in a t t a i n i n g a ce r t a i n type of unity of knowledge. In t h i s Chapter I would l i k e to give a general version of the p r i n c i p l e and discuss i t as a thema in Gerald Hoi ton's sense of one of those u n v e r i f i a b l e , u n f a l s i f i a b l e yet not quite a r b i t r a r y hypotheses which set out the methodological framework from which substantive theory derives. I w i l l argue that complementarity as a de s c r i p t i v e , rather than normative p r i n c i p l e , has both an ontological and epistemological version. I then discuss f i v e cases of complementarity outside of Q.M. This w i l l e s t a b l i s h the general relevance of the p r i n c i p l e and i l l u s t r a t e some of the d i f f e r i n g forms the p r i n c i p l e assumes in d i f f e r e n t contexts. In the following chapter, using the preceding discussion as a springboard, I w i l l argue for i t s s p e c i f i c application to the analysis of the concept of r e a l i t y and to the problem of saying what type of unity can be ascribed to knowledge. Following the f i v e p o s i t i v e cases I discuss some instances of n o n a p p l i c a b i l i t y . This i s necessary in part to show that the p r i n c i p l e i s not some attempt at a shallow syncretism of the form everything i s somehow related to everything e l s e . I w i l l argue - 35 -against t h i s possible c r i t i c i s m and e s t a b l i s h complementarity as a nont r i v i a l p r i n c i p l e . 1 ) T h e G e n e r a l P r i n c i p l e o f C o m p l e m e n t a r i t y Complementarity i s a l o g i c a l notion that e x i s t s independently of Q.M. It derives from completeness and refers to two or more parts completing a whole. In mathematics, for example, two angles A and B are complementary i f f . m Z A + m Z B = 90, measure 90 being considered a complete angle. In colour theory two colours X and Y are complementary i f f . X + Y-* white, white being considered a complete colour. In music, i n t e r v a l s M and N are complementary i f f . M N forms an octave, eight notes being considered a complete set of notes. In the case of descriptions of objects or events two descriptions A and B are complementary (Compl(A,B)), i f f . they complete a d e s c r i p t i o n . More s p e c i f i c a l l y the descriptions must meet the following conditions; i) they must purport to have a common referent, i i ) they must make d i f f e r e n t a l l e g a t i o n s and, i i i ) they must both be j u s t i f i a b l e descriptions in that each must express something about the common referent - 36 -not expressible, f o r various reasons, in the framework of the other d e s c r i p t i o n . The most common reason f o r the i n e x p r e s s i b l i t y i s a difference in l o g i c a l categories employed in the two desc r i p t i v e system. This set of conditions i s met by the wave and p a r t i c l e descriptions of the double s l i t experiment for example. The common referent i s the beam of l i g h t and i t s behaviour in the experimental set up. The p a r t i c l e account would describe l i g h t in terms of photons. The photons must pass through one s l i t or another and are detected i n d i v i d u a l l y . But the p a r t i c l e account must leave out of account the pattern of detection with two s l i t s , since interference i s incompatible with p a r t i c l e behaviour. The wave account would describe l i g h t as an electromagnetic wave leaving the source, waves passing through the s l i t s and i n t e r f e r i n g . But the wave account would be unable to explain the individual detections, since l i g h t i s not l o c a l i z e d in di s c r e t e units in a wave theory. The wave and p a r t i c l e descriptions are incompatible. But they are not l o g i c a l l y contradictory since i t i s not being claimed that the descriptions apply simultaneously but that they apply under d i f f e r e n t circumstances to the common referent ( i . e . conditions which make one description appropriate r u l e out the appropriateness of the other). To take an example outside of physics consider the Necker cube ( F i g . 3). One des c r i p t i o n , c a l l i t I, would be that there i s a cube with face "a" toward us and face "c" on the bottom. Description II would be that we are looking up at face "c" and face "a" i s into - 37 -F i g . 3. The Necker Cube. Description I: a i s toward us, c at the bottom. Description I I : we are looking up at c and a i s a at the back, into the page. Descriptions I and II are complementary. - 38 -the page. There i s a common referent and I and II make d i f f e r e n t statements. The g e s t a l t that gives I rules out II and visa versa. I and II are complementary descriptions of the cube i n F i g . 3. It i s the recognition of t h i s p l u r a l i t y of description with unity of referent that I think i s relevant to the concept of r e a l i t y and the unity of knowledge. 2 ) C o m p l e m e n t a r i t y a s a T h e m a o f K n o w l e d g e Gerald Hoi ton has argued that a theory should be considered as e x i s t i n g i n a three dimensional vector space. Each component of a theory has projections on the three orthonormal basis vectors, which span the space; the a n a l y t i c - h e u r i s t i c , the phenomic and the thematic components of theory (Hoiton, 1958, pp. 185-194). In t h i s section I w i l l argue that complementarity i s a thematic p r i n c i p l e in Hoi ton's sense. Some examples of thematic p r i n c i p l e s w i l l be discussed, f o r comparative purposes, and the case for complementarity being of th i s type w i l l be presented. Any theory, including Q.M. and G.R. for examples, need three sorts of elements. They need r e l a t i v e l y e a s i l y determined phenomic elements that can be accorded the status of observable f a c t s . This would include meter readings and perceptual events. Theories need a n a l y t i c - h e u r i s t i c devices such as, in Q.M., H i l b e r t space, and the operator calculus or in G.R. nonEuclidean space-time and the tensor - 39 -c a l c u l u s . Theories need thematic devices that, while not a n a l y t i c do stake out firm but not f i n a l commitment to c e r t a i n conceptual and methodological metapositions. In the case of Q.M. a central thema i s that of complementarity (as i s d i s c o n t i n u i t y ) . Complementarity provides f o r the consistent i n t e r p r e t a i t o n of the Heisenberg Uncertainty P r i n c i p l e AxAp^ht and d i s c o n t i n u i t y for the i n t e r p r e t a t i o n of Planck's Law E=hv as examples. G.R. has i t s themata al s o , including determinism, contiguity and c l a s s i c a l u n i f i e d explanation. Let me now take the case of a theory with a prominent thematic element and examine the r o l e of the thema there. Later I can compare the r o l e of complementarity in Q.M. The p r i n c i p l e of general covariance in G.R. s t i p u l a t e s that the laws of physics must be covariant with respect to any continuous transformation of the co-ordinization of the space-time manifold. There are at l e a s t four important features of the p r i n c i p l e cannot be stated within G.R. in the tensor c a l c u l u s . I t i s completely general and cannot be f a l s i f i e d in the usual empirical manner since i f i t comes to deciding between some empirical law and covariance the former i s more l i k e l y to be rejected since the l a t t e r i s adopted for the purpose of selecting proper laws of nature. The p r i n c i p l e could be withdrawn, however, i f i t proves u n f r u i t f u l in the long run as f a r as a s s i s t i n g in the generation of useful theory. Insofar as i t deanthropomorphizes physics by deemphasizing the role of the individual observer, covariance represents a commitment to new c r i t e r i a of o b j e c t i v i t y and real i t y . - 40 -Complementarity i s a thematic p r i n c i p l e of Q.M. The p r i n c i p l e states that complementary descriptions of phenomena w i l l sometimes be necessary f o r adequate theoretical accounts of Q.M. objects and events. Insofar as theories are d e s c r i p t i v e the p r i n c i p l e i s suggestive of a new model of explanation. In place of monolithic reductive explanation a piecemeal p l u r a l i s t i c explanation i s mandated in c e r t a i n cases. Complementarity cannot be stated in the formalism of Q.M. but functions as a metatheoretic p r i n c i p l e f o r i n t e r p r e t i n g the formalism. It i s a commitment to a c e r t a i n type of explanation, as i s covariance. Also l i k e general covariance, complementarity poses new problems concerning the nature of o b j e c t i v i t y and r e a l i t y as discussed in Chapter I. G.R., by way of comparison, found o b j e c t i v i t y and r e a l i t y in tensor i n v a r i a n t s . I w i l l argue that Q.M. also points to an o b j e c t i v i t y and r e a l i t y of an abstract mathematical nature, in the form of i n v a r i a n t s . But t h i s i s not to say that t h i s exhausts the notion of r e a l i t y nor would i t provide a basis f o r a reductive unity of knowledge. The s i m i l a r i t i e s between G.R. and Q.M. would simply represent the shared approach of the s c i e n t i f i c method. 3 ) O n t o l o g i c a l v s . E p i s t e r o l o g i c a l C o m p l e m e n t a r i t y I wish to d i s t i n g u i s h two types of complementarity, ontological and epistemological. In the case of the Necker cube ( F i g . 3) i t seems that some coherent account can be given, a l b e i t at a d i f f e r e n t explanatory l e v e l , that takes away the complementarity. - 41 -Problems with description a r i s e with the cube because a three dimensional object has been projected onto a two dimensional surface, by a sort of t r i c k e r y , and the t r i c k e r y has back-fired. In the neutral three dimensional s i t u a t i o n l i n e " i " w i l l be ei t h e r in front of or behind the l i n e "i" so making only one of descriptions I or II corr e c t . In t h i s case there i s an epistemological but not an ontological complementarity. In Q.M. the p o s s i b i l i t y of removing the complementarity i s in doubt, i t may be a permanent feature. No neutral ground has been found from which the complementarity can be seen to vanish. In the case of the r e s t r i c t e d p r i n c i p l e i t has been shown that f o r conjugate parameters l i k e spin-x and spin-y the assignment of exact value to one parameter l o g i c a l l y precludes any assignment of value to the other, thereby seemingly r u l i n g out the p o s s i b i l i t y of a consistent neutral ground. This would represent a case of ontological complementarity in that i t seems to a r i s e not j u s t from l i m i t s of de s c r i p t i v e a b i l i t y but from the p o s s i b i l i t y of d e s c r i p t i o n . In the case of the general p r i n c i p l e there i s no proof that neutral ground i s not possible, as for the r e s t r i c t e d p r i n c i p l e . But Q.M. i s presently a well confirmed and v i r t u a l l y unchallenged theory of micro-dynamics. The psi-function has both wave l i k e and p a r t i c l e l i k e features. It i s a superpositon of the two models. H i l b e r t space was chosen to represent Q.M. phenomena prec i s e l y because i t can mimic d u a l i t y . At present, i f a r e a l i s t view of theories i s adopted, we would be warranted i n believing we have a case of ontological complementarity here. - 42 -4 ) F i v e C a s e s o f C o m p l e m e n t a r i t y The aim of t h i s section i s to discuss f i v e cases of complementarity. These examples show the p r i n c i p l e in use in d i f f e r e n t contexts. I repeat the d e f i n i t i o n in the general case; Compl(A,B,) i f f . A and B are two descriptions s.t.; i ) they purport to have a common referent, i i ) they make d i f f e r e n t allegations and i i i ) they are both j u s t i f i a b l e and needed i n that each gives expression to some truths not expressible in the other descriptive system. a ) R e l a t i v i s t i c C o m p l e m e n t a r y D e s c r i p t i o n s Consider a rocket and two observers A and B, c o l l i near as in F i g . 4. The rocket has r e s t length 100 m. From A's point of view the rocket i s approaching at 150,000,000 m/sec from one side and B i s approaching at 200,000,000 m/sec from the other. From A's view the rocket has length ; -y "£2 r 1 (3. Ox IO*)Z W - 43 -200,000,000 m/sec 150,000,000 m/sec observer B observer A Rocket ( rest length 100m) F i g . 4. R e l a t i v i s t i c Complementarity. ^~^^>^_Parameter Desription *-"*-»-^_ Veloc i ty Length A 150,000,000 m/sec 87m B 263,000,000 m/sec 48m - 44 -B, from his point of view w i l l describe the rocket as approaching at a ve l o c i t y c * 9 * to'* ^ y.33 The length of the rocket according to B w i l l be; = .4&L„= 43m. Each of ,the two descriptions have i ) the same referent, i . e . the rocket; i i ) d i f f e r e n t allegations to make and i i i ) are j u s t i f i a b l e because they express something not expressed in the other d e s c r i p t i o n . It i s a feature of S.R. that c e r t a i n properties are describable in d i f f e r e n t ways depending on the state of the observer. I am not claiming that Einstein thought in these terms, I am simply arguing that the p r i n c i p l e of complementarity c l a r i f i e s the relationship betwen description "A" and description "B". b ) C a t e g o r i c a l C o m p l e m e n t a r i t y Consider the following descriptions of Beethoven's F i f t h Symphony: i) the informal account of the experience of a 1istener, i i ) the musical score, - 45 -i i i ) the physical account of frequencies, amplitudes, sound durations and beat patterns. There seems to be a common referent here - the music of the F i f t h Symphony. Each description makes c a t e g o r i c a l l y d i f f e r e n t allegations yet each expresses something about the music that the other two descriptions must necessarily, because of t h e i r categorical l i m i t s , leave out. This, I claim, i s r e f l e c t i v e of the incompleteness of description from c e r t a i n points of view. Both Einstein and Born have turned to the example of music used here in explaining that science cannot provide a complete account of r e a l i t y . E i n s t e i n i s quoted as having the following discussion: Do you believe that absolutely everything can be expressed s c i e n t i f i c a l l y ? Yes he re p l i e d i t would be possible but i t would make no sense. It would be description without meaning - as i f you described a Beethoven symphony as a v a r i a t i o n in wave pressure. ( c i t e d in Clarke, 1971, p. 243) What Einstein has i d e n t i f i e d here, I think, i s the need for mutually exclusive yet (completing) complementary d e s c r i p t i o n s . 1 If I may be permitted a small digression I would l i k e to comment on some remarks made by W.V. Quine, in t h i s regard, in his 2 review of Nelson Goodman s Ways of World Making. According to Quine, Goodman claims that there are no neutral descriptions of the world and that there are in f a c t many actual worlds corresponding to the many ways which are avai l a b l e f o r making them. Some of these worlds include the world of common sense, the world of an a r t i s t (e.g. Picasso), and the world of physical theory. There i s no reasonable way of excluding alternate ways of world making. But Quine counters - 46 -that only physical theory has the scope needed to span r e a l i t y in that nothing happens in the world "without some r e d i s t r i b u t i o n of microphysical states." Quine claims i t i s reasonable to consider the physical world as the world - he i s committed to at l e a s t a nonreductive, nontranslatory version of physical ism. I take i t then Quine would say that description " i i i " i s the c o r r e c t description of the Beethoven Symphony. I f i n d t h i s account of things inadequate in that other, what seem to me legitimate, descriptions are j u s t l e f t dangling and unaccounted f o r . It i s inadequate both with regard to the question of a minimal unity of knowledge and with regard to an defensible position concerning our concept of r e a l i t y . Physical ism may be a useful hypothesis but at present i t prejudges an open question. c ) C o m p l e m e n t a r i t y i n A r t Science emphasizes d e s c r i p t i o n , a r t emphasizes depiction. There i s a continuity between the two methodologies. But even within ar t there i s room for complementary depictions, a r i s i n g from the choice of diverse creative p o s s i b i l i t i e s r e a l i z e d through; i ) supression of the " i r r e l e v a n t " , i i ) treatment of broad forms, i i i ) method of dealing with c o n t i n u i t y - d i s c o n t i n u i t y , iv) rounding out, s i m p l i f y i n g . - 47 -A p r i m i t i v i s t deals with a common sense r e a l i t y of objects as they are thought to e x i s t in themselves. The a r t i s t paints not as he sees things but as they are supposed to be. Realism in a r t depicts a physical r e a l i t y abstracted from common sense but seen from a p a r t i c u l a r point of view. Impressionism i s concerned with the depiction of the world of appearance. Futurism i s the a r t of fr e e l y created images, produced using the w i l l , fantasies and c r e a t i v i t y of the a r t i s t . The a r t i s t t r i e s through d i f f e r e n t s t y l e s to depict r e a l i t y . But i t would be a r b i t r a r y to value one form to the exclusion of the others. The depictions should be considered complementary depictions (which in turn are complementary to descriptions) of a non-uniform r e a l i t y . Picasso, i t seems to me, has provided an a r t i s t i c depiction of complementarity in The Bull ( F i g . 5). Is i t a b i c y c l e seat with handle bars on top? Or i s i t a b u l l ' s head as the t i t l e says i t is? Or i s i t some sort of superposition of the two? I claim The Bull depicts the issue of complementary depictions. d ) G e s t a l t C o m p l e m e n t a r i t y The g e s t a l t of the candle holder and the faces ( F i g . 6) i l l u s t r a t e s complementarity in another context. Two descriptions seem - 48 -F i g . 5. The B u l l . Description I - a b u l l ' s head. Description II - a b i c y c l e seat with handle bars on top. Descriptions I and II are complementary. - 49 -F i g . 6. Gestalt Complementarity. Description I - l i g h t candle holder on dark background. Description II - two dark faces on l i g h t background. Descriptions I and II are complementary. - 50 -equally c o r r e c t but both cannot be given simultaneously because i t seems that the perception of one g e s t a l t precludes the perception of the other g e s t a l t . We see ei t h e r a l i g h t candle holder with dark background or two dark faces with a l i g h t background, but not both. Only one description can be corr e c t at a given time. The descriptions probably a r i s e from some hard wired information processing systems i n the human perceptual apparatus. The apparatus processes input to form a figure and a ground. The choice of certan data to form ground preclude i t from forming figure and visa versa. Complementary descriptions of ( F i g . 6) are needed because of the p l u r a l i t y inherent in the item. e ) G e o m e t r i c P r o j e c t i o n Consider the e l l i p s e A with major axis a and minor axis b and the geometric projections of A onto the x and y axes giving C and D ( F i g . 7). Consider descriptions of C and D as i n d i r e c t descrip-tions of A, since every point p € A has an image point p'e. C - 51 -F i g . 7. Geometric Projection. Descriptions of A, using the information at C and D, are complementary. The complementarity ar i s e s from the geometric reduction of a two-dimensional object to a one-dimensional object. - 52 -and p'kD. Then descriptions using the information at C and D are complementary and the complementarity arises from the geometric reduction of a two-dimensional object to a one-dimensional object. This s i t u a t i o n (projection) might be viewed as a physical analogue of the way i n which knowledge i s the description of projections of objective r e a l i t y on d i f f e r e n t states of the observer. 5 ) N o n c a s e s o f C o m p l e m e n t a r i t y It may be tempting to c r i t i c i z e the princple of complementarity as t r i v i a l - claiming that everything i s loosely connected to everything e l s e . I w i l l show that t h i s i s not the case, that the p r i n c i p l e i s well defined and not vacuous. A second point that needs to be dealt with i s that concerning the possible overzealous a p p l i c a t i o n of the p r i n c i p l e . I claim that there are legitimate and i l l e g i t i m a t e uses of the p r i n c i p l e . I o f f e r the following as conditions that rule out the i l l e g i t i m a t e uses of complementarity: - 53 -a ) L a c k o f C o m m o n R e f e r e n t If there i s no common referent then descriptions are simply unrelated. For example i ) the paper on which t h i s essay i s written i s white and i i ) the l i n e s of p r i n t on t h i s paper are 20 in number, are not complementary. b ) C o n t r a d i c t i o n Descriptions, to be complementary, must both be j u s t i f i a b l e , although not simultaneously so. Contradictory descriptions f a i l in thi s regard so that i ) the paper on which t h i s essay i s written i s black and i i ) the paper on which t h i s essay i s written i s white, are not complementary. c ) L a c k o f D i f f e r e n t S t a t e m e n t The statements of description must make d i f f e r e n t assertions not j u s t take on d i f f e r e n t syntactic form. The following sentences are d i f f e r e n t but they make the same statement and so cannot express complementary descriptions: i ) The paper on which t h i s essay i s written i s white, i i ) White i s the colour of the paper on which t h i s essay i s written, - 54 -i i i ) Le Papier sur l e q u e l l e cette essai est e c r i t e est blanc. d ) L a c k o f I n P r i n c i p l e E x c l u s i v i t y A c h a i r cannot be observed from a l l physical perspectives at once. The descriptions of various space-slices or time-slices of the chair I do not want to c a l l complementary because we are dealing in each description with nonequivalnet set of information. Complementarity applies only in s i t u a t i o n s where equivalent information i s available f o r both descriptions yet mutually exclusive accounts r e s u l t . The complementarity r e s u l t s not from lack of information but from some p r i n c i p l e involved in the a c q u i s i t i o n of knowledge and/or i t s expression. Bohr was given to saying that the molecular and behavioural aspects of biology were complementary desriptions of organisms. He argued that the f a c t that a l i v i n g organism usually had to be k i l l e d to get molecular information made simultaneous behavioural and molecular accounts impossible. But t h i s claim i s i n c o r r e c t . Information can be obtained from d i f f e r e n t organisms at d i f f e r e n t times. The e x c l u s i v i t y i s not one of p r i n c i p l e but j u s t of operative f a c i l i t y . Suppose a man has a malignancy in his foot that can be observed only by using surgery, a s i t u a t i o n which i s p h y s i c a l l y incompatible with observing the man using his feet to walk. Having a - 55 -pedal malignancy i s not a complementary property to walking since the incompatibility i s not one of p r i n c i p l e . e ) P r e s e n c e o f S i n g u l a r A d e q u a c y If two accounts are conventional they are not complementary. Conventional accounts are mutually exclusive but s i n g u l a r l y adequate. Euclidean and noneuclidean geometries are conventional descriptions of space i n that e i t h e r provides a corr e c t description of space by 3 i t s e l f . One theory i s s u f f i c i e n t , i t i s claimed. Wave and p a r t i c l e theories are complementary in that they are mutually exclusive but neither i s adequate in i t s e l f to account f o r the r e a l i t y in question. • • • • What I have argued in t h i s chapter i s that complementarity i s a general p r i n c i p l e only one of whose applications i s in Q.M. I have given some examples of applications of the p r i n c i p l e in d i f f e r e n t contexts. In the f i n a l chapter I w i l l apply the p r i n c i p l e to the concept of r e a l i t y and to the problem of the unity of knowledge. - 56 -N O T E S Feigl has said, i n a s i m i l a r vein. . . "while I think that a world description (a l a Minkowski) can be given that i s -necessarily - devoid of indexical terms, such a world description can neither be f u l l y understood nor p r a c t i c a l l y used without being linked - with the help of indexical terms - to the experience of a sentient and sapient ( i . e . human) being (Feigl 1967, p. 147). The New York Review, November 23, 1978, p. 25. Conventionalism i t s e l f may be untenable. Consider i t for the sake of argument. Friedman argues for example that ( i ) G.R. uses "a p e r f e c t l y determinate and objective spatial and spatio-temporal physical geometry and that ( i i ) there are good methodological reasons to c a l l G.R. a better theory than i t s r i v a l s because (a) i t s r e a l i s t i c treatment of space-time allows f o r repeated boosts in confirmation of subtheories; (b) i t gives determinate content to a l l the laws of motion ( i t i s parsimonious); (c) i t has the theoretical structure to unify space-time theories (Friedman, 1983, Chapter 7). - 57 -C h a p t e r I I I C O M P L E M E N T A R I T Y , T H E C O N C E P T O F R E A L I T Y A N D T H E U N I T Y O F K N O W L E D G E The thesis of t h i s paper i s that the p r i n c i p l e of complementarity represents a new model of explanation and that when applied to the problem of the unity of knowledge leads to the view that i t i s a u n i f i e d description of projections of the actual state -r e a l i t y . My argument w i l l be divided into f i v e parts. I w i l l argue: i) that the concept of r e a l i t y i s ambiguous and that the ambiguity can be resolved by adopting the view that r e a l i t y has at l e a s t four complementary aspects, i i ) that a modest version of realism can be defended which asserts, among other things, that there i s an external world and that well confirmed theories give at l e a s t probable knowledge about t h i s world, i i i ) that some preliminary, although perhaps sketchy characterization of the nature of the complementarity involved here can be given and that an a t l e a s t p l a u s i b l e i n t u i t i v e idea can be offered as to the content of the complementary aspects of r e a l i t y , iv) that using a modest version of realism, a modest foundationalist epistemology and the p r i n c i p l e of complementarity an al t e r n a t i v e theory of knowledge (to t r a d i t i o n a l foundational ism and coherentism) and model of explanation can be developed, v) and f i n a l l y that the d i a l e c t i c a l s e l f c orrecting conception of knowledge which - 58 -emerges from the above considerations i s preferable to "absolute" truth or coherence as a rationale f o r warranted b e l i e f . 1 ) T h e C o n c e p t o f R e a l i t y The concept of r e a l i t y and of what i s real i s ambiguous. Dif f e r e n t senses of the term are used i n d i f f e r e n t contexts. I w i l l discuss f i v e possible senses here. What i s immediately perceived i s often considered real in that i t i s not a f a b r i c a t i o n or construction of an i n d i v i d u a l ' s i n t e l l e c t but j u s t unadulterated raw experience -"the given." I t might be argued in t h i s regard that the content of my specious present i s real because i t i s j u s t f a c t , not yet muddled by r a t i o n a l i z a t i o n , prejudice and assumption. If I can be sure of anything, suggests t h i s p o s i t i o n , I can be sure of t h i s subjective r e a l i t y and so i t i s r e a l . Material objects and physical processes are often considered real because they represent i n t e r s u b j e c t i v e l y i n v a r i a n t , objective knowledge. Whereas knowledge of subjective r e a l i t y i s c h a r a c t e r i s t i c a l l y l o g i c a l y unstable and l i m i t e d in i t s explanatory and p r e d i c t i v e power, knowledge of physical r e a l i t y has the opposite features. The s u b j e c t i v i s t would argue that physical conception of the world i s a big c o u n t e r f e i t with frequencies, f i e l d s , stress tensors and wave functions i n place of the more emotive and "Christmasy" characterizations used in the subjective domain. But i t could be countered that while "raw thinks and f e e l s " represent a - 59 -c e r t a i n type of contact with r e a l i t y t h i s contact i s no less a construct that the physical d e s c r i p t i o n , both necessarily involving conceptualization, and that the physical i s superior because i t i s invariant with respect to transformations of the observational base. You are reporting here on objective r e a l i t y not on the idiosyncracies of how i t i n t e r a c t s with c e r t a i n organisms. You are dealing with the hard and tangible world of physical r e a l i t y . What i s real i s the p r a c t i c a l , e f f e c t i v e world of action not the i l l u s i o n s of the subjective or the abstractions of physical theory. The world i s a world of action and of being shaped by, and in turn shaping, other men. Reality i s revealed in the course of man's concrete involvement in his social milieu not in withdrawal to a world of ivory tower abstractions. Social r e a l i t y embodies the real in i t s formulations of the actual r e s u l t s of humanities' i n t e r a c t i o n with i t s e l f and the world. The idea of r e a l i t y , i t could be argued i s best exemplified i n refined, well confirmed physical theories l i k e Special R e l a t i v i t y . What i s real in such a theory are quantities and laws that have the same value and form respectively for any admissible observational basis. Only that which i s the same for any "possible observer" i s r e a l . Other knowledge i s knowledge about projections of the actual r e a l i t y on the observer and such knowledge underdetermines the actual state. This, usually mathematical, world of in v a r i a n t quantities and covariant laws represents another conception of r e a l i t y . - 60 -Reality embodies an extreme ideal of permanence i t could be contended. Subjective, physical and social r e a l i t y a l l e x h i b i t too much changeability. Only l o g i c a l r e a l i t y , which deals with the most general features of t h i s world, features which would have to be present in any world, has the degree of permanence required to merit the designaiton r e a l . A p l u r a l i s t i c notion of the concept of r e a l i t y i s necessary because there i s a p l u r a l i t y of c r i t e r i a f o r what i s r e a l . In f a c t for knowledge to be expressed always requires some d e f i n i t e conceptual and methodological commitments.* The content of each p a r t i c u l a r f i e l d of knowledge i s determined by these commitments, in p a r t i c u l a r by the forms of judgment and of questions from which knowledge issues. Roughly the subjective emphasizes the "immediate," the physical emphasizes the i n t e r s u b j e c t i v e l y i n v a r i a n t , the social emphasizes the p r a c t i c a l - e f f e c t i v e and the l o g i c a l emphasizes the necessary. I w i l l not clam that t h i s i s an exhaustive l i s t of complementary aspects, the ethic a l and aesthetic may represent f i f t h and sixth aspects. I do want to e s t a b l i s h or at l e a s t render p l a u s i b l e the idea that r e a l i t y i s not a uniform monolithic e n t i t y , according to what we are warranted in believing at present. - 61 -2 ) A M o d e s t R e a l i s m I f i n d both idealism and positivism implausible. I cannot prove e i t h e r wrong but I prefer realism. The version of realism I adopt must be compatible with the p r i n c i p l e of complementarity. The version I w i l l defend may be c a l l e d modest realism. It holds that there i s an external world independent of the observer but does not claim we have " d i r e c t " access to i t . It holds that our knowledge t e l l s us what the world i s probably l i k e . There i s a boundary between objective states of a f f a i r s and states of the observer, but we might (often) be mistaken about the exact location of the boundary (e.g. the notion of the physical length of an o b j e c t ) . In f a c t a considerable amount of our knowledge might be of a r e l a t i o n a l nature. But t h i s in i t s e l f does not rule out realism, i t j u s t narrows the c l a s s of objective properties. The difference between knowledge and i l l u s i o n i s the presence of invariants which point outward to something objective and r e a l . Modest realism recognizes the separation of the external and the internal worlds and the authentic character of each, and wishes to explain away neither. To be real i s not to be interpreted as known in a l l d e t a i l . Knowledge i s a s a l u t a t i o n , not an embrace. Knowledge cannot become the r e a l i t y i t represents. We cannot even get outside of knowledge to compare knowledge and r e a l i t y so the correspondence theory of truth i s inadequate. But neither i s knowledge j u s t dangling loose from r e a l i t y . The a p p l i c a t i o n of human knowledge to understand and modify - 62 -world, f o r example, i s j u s t one f a c t that argues f o r t h e i r at l e a s t tenuous as s o c i a t i o n . Coherentism i s also inadequate then for t h i s reason. Pragmatism's characterization of truth as what i s useful to believe i s too vague and open to s e l f deception to be operative. I cannot give a statement as to what truth i s but I w i l l indicate l a t e r what a "prospective" conception of truth has to o f f e r . Although the external world i s separate from the internal world i t i s s t i l l possible to a t t a i n knowledge. Reality does not consi s t of unknowable "things in themselves." The internal-external separation sets out a parameter of knowledge. Although we do not have access to s e l f evident concepts or absolute truths, knowledge i s s t i l l possible, although necessairly a guess. The answer to the blinding skeptic who argues here that separation implies a complete dis j o i n t n e s s , i s that his requirement of symbiosis between knowledge and r e a l i t y i s simply not there to be had. And in f a c t the skeptic's insistence on absolute evidence and truth, the lack of which appears i n i t i a l l y so disappointing, should be viewed as s e t t i n g unacceptable expectations to s t a r t with. Lack of absolute evidence or truths should not be considered a l i m i t i n g condition on knowledge but rather a p o s i t i v e p r i n c i p l e that must be taken into account in the development and j u s t i f i c a t i o n of such knowledge. The nonuniform structure of r e a l i t y i s r e f l e c t e d in the f a c t that i t requires complementary, l o g i c a l l y incompatible theories f o r i t s d e s c r i p t i o n . This i s not to preclude the p o s s i b i l i t y of a u n i f i e d coherent theory but to r e f l e c t the current state of our knowledge. - 63 -For a r e a l i s t holds that the best way to f i n d out about r e a l i t y i s to see what our best theories have to say. And what they have to say, i t seems to me, i s that i t takes subjective, physical, social and l o g i c a l accounts, each with t h e i r c h a r a c t e r i s t i c concepts, p r i n c i p l e s and forms of question and judgment, to span the concept of r e a l i t y . I w i l l take t h i s opportunity to remark that the d i s t i n c t i o n between observational and theoretical terms i s independent of the l o g i c a l status as outlined above I hold that a l l knowledge i s propositional and of a kind in t h i s regard. The subjective aspect has no claim to "the given." And indeed we may on occasion make reports on physical objects that are as d i r e c t as subjective reports. Knowledge has "bootstrapped" i t s e l f out of the world. At no point i s i t s t r i c t l y a copy of the world. What i s observational and theoretical i s an accidental feature of the bootstrap operation, a l l traces of which have dissolved. But being a r e a l i s t amounts primarily to holding that the best confirmed theories in our body of knowledge t e l l us about the external world, even though we do not understand the bootstrap process and even though the same knowledge can be bootstrapped into existence s t a r t i n g from many d i f f e r e n t observational-theoretical bases. I do not claim to be able to prove that modest realism i s correct and positivism or idealism wrong. What i s at issue here i s not a factual matter - i t i s an issue between d i f f e r e n t ideals of explanation, and of knowledge. Idealism wishes to substitute a s i t u a t i o n which i s inadequate in most regards, because i t - 64 -severely r e s t r i c t s our ontology, f o r a s i t u a t i o n which i s adequate in most regards. Positivism o f f e r s a cataloguing of experience in a p r e d i c t i v e scheme assuming that a p r e d i c t i v e scheme can be meaningful without an i n t e r p r e t a t i o n . This would constitute organization without understanding f o r me. Both idealism and positivism t r y to s e t t l e the issues of what there i s by f i a t . Realism has an openness to i t by v i r t u e of recommending that we accept the account(s) of r e a l i t y supplied by our best confirmed theories. This i s not to say that idealism and positivism do not have legitimate points to make but j u s t to say that a s u i t a b l y , c a r e f u l l y stated version of realism can and should be maintained. 3 ) T h e C o m p l e m e n t a r y A s p e c t s o f R e a l i t y My discussion here w i l l be along the following l i n e s . What we can s t a r t with, "neutral ground" in an analysis of knowledge, i s an undifferentiated mass of data. The data i s undifferentiated with respect to l o g i c a l type, immediateness and other c r i t e r i a . Unity of knowledge i s embodied in the unity of t h i s manifold of data. The appropriate analogy here would be the topological unity of the surface of a Moebious band, which derives from the one-dimensional nature of the s t r i p . P l u r a l i t y of knowledge arises in the attempt to c l a s s i f y and sort t h i s information according to c e r t a i n c r i t e r i a . The analogy could then be extended to a Moebious band with d i s j o i n t regions. - 65 -Reality makes i t s e l f manifest by way of projections onto observers. Complementarity i s a response to the u n i t y - p l u r a l i t y d i a l e c t i c that i s acting i t s e l f out here. I conclude t h i s section by discussing some of the c h a r a c t e r i s t i c s of the aspects of r e a l i t y . There i s an established tendency to i d e n t i f y the real with the referent of a c e r t a i n p r i v i l e g e d type of knowledge. For the p o s i t i v i s t t h i s i s usually reports on sensations, some so r t of immediately given experience. Reports are often considered i n c o r r i g i b l e . For the m a t e r i a l i s t ("physicalist") the p r i v i l e g e d reports concern physical objects. Such reports have both the empirical content and the inte r s u b j e c t i v e invariance needed to consider them reports on the r e a l . From the social perspective reports on knowledge r e a l i z e d in the course of p r a c t i c a l endeavour represent contact with r e a l i t y rather than the "ivory tower abstractions." To the r a t i o n a l i s t , p r i v i l e g e d knowledge i s the demonstrably true, in the sense - necessitated by reason. But I hold that there are no p r i v i l e g e d reports without prejudging the issue of what i s r e a l . What we can leg i t i m a t e l y s t a r t our analysis of knowledge from i s a complex unanalyzed mixture of crudely interpeted experience. The unity of our concept of r e a l i t y derives from t h i s pr i m i t i v e unity. But knowledge also exhibits a p l u r a l i t y of forms and our concept of r e a l i t y should r e f l e c t t h i s - i f we are to hold to the r e a l i s t p o s i t i o n that our best confirmed knowledge gives at l e a s t probable information about r e a l i t y . - 66 -The view of r e a l i t y I hold i s that we do not have access to r e a l i t y as such but that knowledge constitutes reports on and descriptions of projections of the actual state of a f f a i r s on a system of reference. This would be formally analogous to the way in S.R. that length or mass i s a projection on the observer or to the manner in Q.M. that the measurement of an observable l i k e p o sition i s construed as determining the projection of the wave function for the system onto the eigenbasis for the position operator. The formal equivalence can be summarized by saying that the instrument of observation records projections of the actual state. The maximal complete theory of r e a l i t y can be obtained by accumulating descriptions of an a r b i t r a r i l y large number of independent projections. The use of mutually exclusive descriptions i s i n d i c a t i v e of complementarity. But the f i n a l r e s u l t of complementarty descriptions i s a set of invariants that point to stable structures. In S.R. the invariants include the i n t e r v a l , v e l o c i t y of l i g h t and energy-mass of a closed system. In Q.M. they include e l e c t r i c charge, re s t mass and spin. When we determine these quantities we decide that we have access to a d e f i n i t e object or process. The observer i s needed and i n t e r f e r e s but t h i s does not rule out the p o s s i b i l i t y of obtaining a c e r t a i n r e s t r i c t e d but well defined c l a s s of information which i s independent of the observer in the sense that i t i s invariant with respect to c e r t a i n transformations of the observational base. In the case of subjective r e a l i t y the admissible transformations are the q u a l i t a t i v e changes in individual consciousness and the invariant concepts are mind and s e l f . - 67 -For physical r e a l i t y the admissible transformations are the space-time r e l a t i o n s of reference frame and the invariants are matter-energy and i t s manifestations. Social r e a l i t y admits transformations from people to other people and the invariant i s man. And l o g i c a l r e a l i t y admits transformations across possible worlds and the invariant i s reason. Understanding r e a l i t y involves being presented with a host of phenomena which w i l l appear random and chaotic unless c e r t a i n c r i t e r i a are applied to s e l e c t s i g n i f i c a n t events, suppress others and abstract and i d e a l i z e the s i t u a t i o n . This w i l l emphasize the d e t a i l s of c e r t a i n projections. What we are acquainted with are messages -messages that cannot be understood without the a p p l i c a t i o n of a symbolic function. This s i t u a t i o n could be viewed as a more general case of visual message processing where a figure-ground sorting must take place and auditory message processing where a message-noise sorting occurs. But the symbolic function i s not absolute so that in the same "raw" material what i s "noise" in one view i s the r e a l i t y of another view. This view of knowledge presupposes that there i s a free choice to be made among various competing complementary conceptions of r e a l i t y . Some aspects of r e a l i t y may await discovery through the use of d i f f e r e n t figure-ground mixes. The concept of r e a l i t y I am proposing i s that r e a l i t y be construed as the concept that integrates and u n i f i e s the descriptions of the projections of the actual state of the world on the observer, as reconstructed by the various symbolic functions. Being a r e a l i s t with respect to theories, the state of our knowledge should dictate our view of r e a l i t y . The state of our - 68 -knowledge i s that i t consists of a set of d i s j o i n t y e t suggestively 2 i n t e r a c t i v e theories. Our conception of r e a l i t y should r e f l e c t such a unity amidst d i v e r s i t y . The application of complementarity seems to be to hold the most promise of success in t h i s regard. I do not know i f complementarity i s a feature of knowledge to be l a t e r explained away. I do hold that i t i s relevant and important to the explanation of knowledge and i t s r e l a t i o n to the world as we presently have warrant to conceive of the issue. In the remainder of t h i s part of the paper I want to argue for Beth's contention that we may conceive of r e a l i t y as having at l e a s t four complementary aspects. In p a r t i c u l a r Beth states that he thinks a new version of realism i s possible based on the idea that . . .man has on account of his own l i f e experience an immediate and authentic contact with various spheres (perhaps i t would be better to say, zones, or aspects) of r e a l i t y , some of which may be enumerated; physical r e a l i t y - the world of matter - social r e a l i t y - the world of men - and subjective r e a l i t y - the world of mind - l o g i c a l r e a l i t y - the world of reason or discourse - in which mathematical e n t i t i e s p a r t i c i p a t e . It seems reasonable however t e n t a t i v e l y to consider the various sphere of r e a l i t y as complementary aspects of one and the same substratum, in the same sense we have recently been taught to speak of the complementary aspects of physcial r e a l i t y . (Beth, 1959, pp. 644-645) Before I begin to argue f o r Beth's complementary aspects of r e a l i t y I would l i k e to make six points by way of introduction. 1) My remarks w i l l be avowedly inadequate in a c e r t a i n 4 sense. I cannot prove my case and i t i s not an a n a l y t i c truth - 69 -that r e a l i t y has four or more complementary aspects. I am suggesting the application of a c e r t a i n form of explanation. The j u s t i f i c a t i o n of t h i s extension would include seeing i f i t f i t s and checking the success of a program involving i t s use throughout a u n i f i e d theory of knowledge. In view of the f a i l u r e of monolithic explanation in general and s p e c i f i c cases, I claim that i t i s prudent and warranted to retain and use a l l the viable a l t e r n a t i v e s . 2) Beth uses the phrase "some of which may be enumerated." I take i t t h i s would mean the l i s t of aspects may not be exhaustive. The ethi c a l and the aesthetic would be two candidates that come to mind. But the issue here i s j u s t that one sphere i s not enough. 3) Each sphere of r e a l i t y has subaspects but does not form a h i e r a r c h i c a l l y ordered deductive system. Certain concepts and pr i n c i p l e s may be shared across the d i s c i p l i n e s (e.g. force in physics, chemistry and biology) which study a given aspect of r e a l i t y , but the concepts and p r i n c i p l e s have idiosyncracies p a r t i c u l a r to the f i e l d . There i s a dominant methodology within a sphere but with adaptation to p a r t i c u l a r circumstances (e.g. the s c i e n t i f i c method in the physical sciences). There i s an invariant central idea (matter-energy in the physical sciences) but the idea takes on connotations peculiar to p a r t i c u l a r d i s c i p l i n e s . And there i s a common general form to questions asked and judgments made although again with s p e c i a l i z a t i o n s . Complementarity does not explain the - 70 -nature of the intra-aspects "unity." This i s to be achieved by the s p e c i a l i z e d research within the p a r t i c u l a r d i s c i p l i n e s . Complementarity i s j u s t an accurate method of characterizing an evolving epistemological s i t u a t i o n . Each sphere i s b u i l t around invariant concepts and c h a r a c t e r i s t i c transformations; physical r e a l i t y , matter-energy and the space-time transformations; social r e a l i t y , man and the cross-person transformations, "putting yourself i n someone elses shoes"; subjective r e a l i t y , mind and the changes of conscious and unconscious content; and l o g i c a l r e a l i t y , reason and the transformations across l o g i c a l l y possible worlds. But i t i s c h a r a c t e r i s t i c of the development of knowledge that i n i t i a l core ideas are best studied as part of a broader system of concepts and p r i n c i p l e s . So that in the case of a well developed body of knowledge considerable refinement of i n i t i a l ideas i s usually present and there i s usually a unifying idea c l u s t e r in place. Once again i t would seem only prudent to leave any statement concerning the precise connections here to the individual d i s c i p l i n e s while entertaining complementarity as a possible unifying thematic supposition. 5) On the d i v e r s i t y side of the u n i t y - d i v e r s i t y d i a l e c t i c c e r t a i n accounts and descriptions are l o g i c a l l y incompatible with other accounts and descriptions. For example subjective descriptions, with t h e i r indexical features, are incompatible with p h y s i c a l i s t i c descriptions with t h e i r i n t e r s u b j e c t i v e l y invariant forms of concepts - 71 -and p r i n c i p l e s . So f o r example "I am hungry" and "I have a blood sugar of .005 and an H-neuron complex f i r i n g across sections of my brain" are l o g i c a l l y incompatible because they are statements formed in d i f f e r e n t conceptual systems with d i f f e r e n t c r i t e r i a f o r v a l i d questioning and judgment. This type of l o g i c a l i ncompatibility would include l o g i c a l and psychological desriptions as well as l o g i c a l and physical d e s c r i p t i o n s . The d i r e c t i o n of inquiry in each case i s so d i f f e r e n t that comparison does not seem possible in p r i n c i p l e . 6) The foregoing considerations might lead to the question, does t h i s mean that there are four or more aspects of r e a l i t y or j u s t four or more ways of providing descriptions of i t ? I do not have a categorical answer. What I claim i s that we have warrant to characterize r e a l i t y i n the way suggested by our best confirmed theories. If our theories are disconnected with suggestions of a complementary type of unity then t h i s should be the characterization of our concept of r e a l i t y . If our theories were completely unconnected then our concept of r e a l i t y should r e f l e c t t h i s . If at some time our theories showed some type of strong monolithic coherence so should our concept of r e a l i t y . To the question I respond - one sort of r e a l i t y with four complementary aspects AND four ways of providing descriptions of i t . The answer sounds odd because the question was put in a p r e j u d i c i a l manner to s t a r t with. I can only answer the question by p a r t i a l l y r e d i r e c t i n g i t . - 72 -Our concept of r e a l i t y emerges then in at l e a s t four ways depending on the complementary "figure-ground" extractor used to inter p r e t the message from r e a l i t y . I am l e f t the task, in t h i s section of the paper, of discussing the aspects of r e a l i t y revealed in th i s enterprise. I o f f e r the following, avowedly b r i e f and unsatisfactory, account. The subjective aspect of r e a l i t y emerges as a reductum from a more general set of experiences. What emerges i n i t i a l l y i s a sense of the e x i s t e n t i a l l y poignant here and now. This gradually forms an authentic sense of s e l f and of my sensations, my thoughts, f e e l i n g s and actions. This i s a world of my "thinks," " f e e l s " and "dos." It i s a world described with the "Christmasy" emotive language suggested by terms l i k e t h i r s t y , t i r e d , hungry, itchy and sad. The extreme l i m i t of subjectivism i s solipsism. And t h i s view i s not l o g i c a l l y contradictory. The solitude of the s e l f i s an ir r e d u c i b l e dimension of human l i f e . But solipsism i s incomplete. It i s incomplete in that i t leaves out of account the experience of other people and the existence of an objective external world. Solipsism and subjectivism are both incomplete as theories of r e a l i t y . Using either alone would be l i k e t r y i n g to make sense of quantum r e a l i t y with only wave views.** There are a number of approaches to the study of subjective r e a l i t y including introspection, a phenomenological analysis of consciousness and a r t . I think a r t merits a special remark here. Art and science, f o r example, should be conceived of as complementary, not h o s t i l e modes of des c r i p t i o n . Each embody procedural, conceptual and - 73 -methodological devices p a r t i c u l a r l y suited to the study of c e r t a i n of the aspects of r e a l i t y . The s p e c i f i c value of a r t for man i s that i t can get c l o s e r to subjective experience than science. It can e l i c i t the emotive content of l i f e and present i t in a r e l a t i v e l y immediate, u n i n t e l l e c t u a l i z e d depictive way. The shortcomings of a r t are r e f l e c t i v e of the shortcoming!'ngs of the subjective mode of description - l o g i c a l i n s t a b i l i t y , i m p l i c i t inconsistency and l i m i t e d explanatory power. But these are feature inherent in t h i s aspect of r e a l i t y . Whereas science i s dominated by reason, o b j e c t i v i t y and i n t e l l e c t u a l reconstructions, and so i s a c o n s t r i c t i n g a c t i v i t y , a r t i s dominated by emotion and v o l i t i o n , by the mind and the individual s e l f and by an authentic contact with the flow of conscious existence, and so i s an expansive a c t i v i t y . But a r t also points outside the world of the s e l f . Representative realism in a r t depicts the world from a c e r t a i n point of view. Perspective, f o r example i s important. Unlike primitivism or impressionalism, representative realism conceives of knowledge as being of something external and so capable of d i f f e r e n t formulations depending on the point of view of the observer. The social aspect of r e a l i t y emerges in the social m ilieu of l i m i t e d knowledge, the imperative to act, and the f a c t of l i f e and r e a l i t y being other people. It i s the world of motivation, power and s a t i s f a c t i o n as acted out in the s o c i a l context - people c o n t r o l l i n g and being c o n t r o l l e d by other people. Other forms of knowledge have neither the character of authenticity nor the degree of certainty - 74 -which are usually ascribed to them because they are a l l at l e a s t partly d e r i v a t i v e with respect to our knowledge of other people and of t h e i r reactions to our behaviour. This makes the knowledge suspect because of the possible moral, conceptual or emotional bias responsible f o r i t being implanted in us. The legacy of language, b e l i e f s , behavioural d i s p o s i t i o n s and emotional tendencies mixes f a c t , opinion, d e c e i t , fantasy and "noise" i n a kaleidoscopic array. As yet i t i s d i f f i c u l t to say what social r e a l i t y i s in s p e c i f i c d e t a i l . There are as yet no well established theories.'' What theories there are lack the universal assent given to theories in some of the physical sciences. There are s p e c i a l i z e d d i s c i p l i n e s -psychology, sociology, h i s t o r y , economics, p o l i t i a l science, and some shared concepts but well confirmed theories are absent. Knowledge in t h i s domain often reduces to the views held by s u f f i c i e n t l y powerful people. Knowledge and truth become the social product of a c u l t u r e . I l l u s i o n , b l u f f , guess and fantasy are a l l facts of s o c i a l r e a l i t y . My characterization of social r e a l i t y may have sounded demeaning. I intend no such imputation. I merely wish to show that the r e a l i t y of acting where there i s l i m i t e d knowledge, motivating where reason i s not enough and getting things done in conditions where almost everything i s possible and being recommended i s a quantum leap upward i n awkwardness from predicting which way a b i l l i a r d b a l l w i l l bounce when struck by another. Acceptable accounts of economic - 75 -c y c l e s , h i s t o r i c a l trends, stock markets and other preferences await new and perhaps odd-sounding types of explanation. Physical r e a l i t y emerges from experience by the application of s c i e n t i f i c method. Physical description attempts to b u i l d i n t e r s u b j e c t i v e l y invariant theory, theory that i s b u i l t on concepts and p r i n c i p l e s that can be o b j e c t i v e l y used because they can be seen to be used to generate measurable r e s u l t s . What "data" serve as the observables does not matter because the meaning of physical concepts i s i n v ariant with respect to sensual source (e.g. v i s u a l , auditory e t c . ) . Theories should also not change form when formulated from other space-time frames. We have a world of frequencies, amplitudes, wave functions and tensors replacing the " f r i e n d l y " world of regular sights and sounds. But science gains a large measure of l o g i c a l s t a b i l i t y , consistency and p r e d i c t a b i l i t y in the process. One of the prices i t pays i s closeness, another i s the scope of what i s objective since as the covariance of laws and invariance of quantities i s expanded over a large and larger c l a s s of admissible transformations of observational base the class of objective e n t i t i e s gets smaller, to the extreme case of G.R. in which a l l that i s objective i s space-time proximity of local events and c e r t a i n tensor laws. While a Minkowski diagram of r e a l i t y may t e l l a l o t about the world, i t would be incomplete, nevertheless, in ce r t a i n regards. It could probably not account f o r the presence of mathematical knowledge for example. A wave account of a Beethoven sonata, although cor r e c t , would s t i l l leave something out ( i . e . aesthetic - 76 -considerations), or at l e a s t there i s no good reason to think the account could be complete. And I think science could not deal with a question as to what constitutes a good l i f e , although I take the question to be meaningful. The l o g i c a l aspects of r e a l i t y emerges as the subjective, social and physical aspects of experience are suppressed. What emerges then could be conceived of as general features of the world and of a consistent world. The concept of r e a l i t y or of an object are not obtained in the way the concept of pain, v e l o c i t y or family are. Each derives from an authentic contact or i n t e r a t i o n with a fourth aspects of r e a l i t y . I c a l l t h i s the l o g i c a l aspect of r e a l i t y , but i t should be taken to include not j u s t the domain of l o g i c but mathematics and philosophy a l s o . I do hold a r e a l i s t i c view with regard to a l l three d i s c i p l i n e s in that I maintain that the meaning and purpose of a l l three does not l i e in the series of l o g i c a l l y r elated c o l l e c t i o n of symbols but in what these c o l l e c t i o n s have to t e l l us, i n t h e i r respective ways, about the world. The u n i t y - d i v e r s i t y d i a l e c t i c assumes an acute form here with the supposed reduction of mathematics to l o g i c . But unity does not win out absolutely because t r a d i t i o n a l l y and c h a r a c t e r i s t i c a l l y mathematical axioms are s t i l l needed (e.g. the axiom of i n f i n i t y ) . - 77 -4 ) C o m p l e m e n t a r i t y a s P a r t o f a n A l t e r n a t e T h e o r y o f  K n o w l e d g e I believe that a modest r e a l i s t ontology, a modest foundationalist epistemology and the use of the p r i n c i p l e of complementarity can provide an a l t e r n a t i v e to foundational ism, as a theory of knowledge. It has the v i r t u e of stopping short of coherentism. Foundational ism i s inadequate because i t r e l i e s on absolute evidence, absolute truth and "the given" - none of which can be produced f o r inspection. The general idea of foundational ism has proven to be psychologically a t t r a c t i v e but i n c o r r e c t . Coherent!'sm leads to blin d i n g skepticism in that there i s no connection between r e a l i t y and knowledge. The f a c t that propositions cohere does not increase t h e i r c r e d i b i l i t y unless at l e a s t some of the propositions have i n t r i n s i c c r e d i b i l i t y , however small, to s t a r t with. In t h i s section of the paper I f i r s t of a l l outline a version of foundational ism and indicate why i t f a i l s as a general description of the symbolic function ( i . e . the mapping that takes messages from r e a l i t y and maps them into symbols that express knowledge). I then present my a l t e r n a t i v e and di s t i n g u i s h i t from both foundational ism and coherentism. Let me di s t i n g u i s h three fundamentally d i f f e r e n t symbolic functions; the mythical, common sense, and the r e l a t i o n a l . Within each symbolic function p a r t i c u l a r concepts, p r i n c i p l e s and methodologies are used. Although the same name may be used in d i f f e r e n t symbolic characterizations of r e a l i t y the meaning i s - 78 -d i f f e r e n t (e.g. supernatural force in myth, the common sense push or pull and in science the distance rate of change of work. The question of the true r e a l i t y does not a r i s e here because the complex we c a l l r e a l i t y i s an unavoidably m u l t i v a r i a t e , but not amorphous, e n t i t y . the expressive mode which dominates the mythical function fuses the sign with i t s s i g n i f i c a n c e . The thunder i s the anger of a god. The smile i s a kind i n t e n t i o n . Appearance and r e a l i t y are one. The i n t u i t i v e mode, which dominates common sense distinguishes between appearance and r e a l i t y d i f f e r e n t i a t i n g the world i n t o ; i ) space and time, i i ) r e lated material objects or substances, and i i i ) properties or a t t r i b u t e s which adhere to the substances. It i s usually claimed that we can have d i r e c t contact with r e a l i t y through s e l f - e v i d e n t concepts and absolute truths. Knowledge at the foundational level could be conceived of as a copy of r e a l i t y . The conceptual mode, which dominates science, i s a system of r e a l t i o n s as opposed to a system of substances with a t t r i b u t e s . There i s no absolute esence with which to have d i r e c t contact but there are varioua diverse manifestations of r e a l i t y to report on i n various diverse manners. Knowledge i s not rooted or grounded in r e a l i t y but does have probable connections with i t . Within the conceptual mode I wish to di s t i n g u i s h four submodes - the subjective, the physical, the social and the l o g i c a l . These are symbolic submodes used to reveal the four complementary aspects of r e a l i t y . - 79 -Foundational ism would maintain that a l l knowledge i s acquired by means of inference form a c e r t a i n number of immedaite, i r r e d u c i b l e , self-evidence t r u t h s . In p a r t i c u l a r i t would hold that f o r any group of sentences S to form a v a l i d theory T; the following conditions msut be met; i ) Reality - any sentence in S must r e f e r to real e n t i t i e s (essences or t h e i r adhering a t t r i b u t e s ) , i i ) Truth - any sentence belonging to S must be true, i i i ) Connection - any i n f e r e n t i a l consequences of a sentence in S must be in T, iv) Evidence - there are in S (a) s e l f evident terms (b) definable terms and none other, v) Evidence - there are in S (a) s e l f evident truths (b) truths derivable from s e l f evident truths and none other There are problems with each assertion. The r e a l i t y condition assumes we can get at essences and report on them. It would be possible to maintain through that we report on projections of r e a l i t y on the recoridng instrument ( i . e . us). Essences are problematic. The truth and connection conditions amount to truth being considered a decidable notion 8 ( a l g o r i t h m i c a l l y computable) or a constructive notion (provable in a formal system) neither of which i s true in general. S e l f evident terms and truths are also problematical in that despite much e f f o r t there are no unobjectionable insances of e i t h e r . - 80 -My alternate proposal i s based on a re v i s i o n of each of the above f i v e conditions concerning r e a l i t y , t r u t h , conneciton and evidence. For the f i r s t condition I propose that any sentence of S must re f e r to projections of r e a l i t y on an observer, some of which may be invariant with respect to a set of transformations. This does not mean that knowledge i s subjective though because the projection takes place in a 9 law-like, repeatable manner. Appearance i s an objective property of r e a l i t y . There are three fundamental symbolic functions in use so fa r (there could be many more). They are the mythical, the ocmrnon sense, and the r e l a t i o n a l . The r e a l t i o n a l has four submodes (at least) the subjective, the s o c i a l , the physical and the l o g i c a l . For the second condition I propose that any sentnce belonging to S must be probable. We are not in a position to say of a sentence that i t i s true, period. For aside from simple error there i s always the p o s s i b i l i t y of meaning change, due to conceptual s h i f t s , which would r a d i c a l l y a l t e r the di r e c t i o n and conditions of inquiry. For th t h i r d condition I propose the princple of complementarity whereby, monolithic deductively u n i f i e d thoeries are replaced as ideals by mutually exclusive but complementary theories. The development of modern l o g i c has shown that the notion of provable in a formal system i s a weaker notion than t r u t h . Whereas i t was once possible to believe that a l l and only true propositions are provable and that a l l and only f a l s e propositions are disprovable, i t i s now probable that in most theories there w i l l be unprovable truths and nondisprovable falsehoods. A looser connetivity i s needed. I am of f e r i n g complementarity as providing the relevant model of the way in - 81 -which theories span an information manifold. In t h i s view truth has neither a decidable or constructive character but what I w i l l c a l l a prospective character. Truth can be approximated through a d i a l e c t i c a l refinement, s t a r t i n g from i n i t i a l l y , s l i g h t y c r e d i b l e propositions, but never attained completely. For the fourth and f i f t h conditions I o f f e r the view that there are no s e l f evident concepts or absolute truths but only concepts and propositoins with some p l a u s i b i l i t y . The i n t r i n s i c c r e d i b i l i t y of c e r t a i n propositions i s a p r i m i t i v e f a c t f o r me, or perhaps i t would be more accurate to say a thematic princple in Hoi ton's sense, which i s adopted to account for the f a c t of the existence of knowledge. But i n t r i n s i c c r e d i b i l i t y i s not confined to any one aspect of knowledge - subjective, s o c i a l , physical or l o g i c a l . We can increase the p r o b a b i l i t y propositions have in a d i a l e c t i a l process of s e l f c o r r e c t i o n . For example "I am writing these words on a piece of white paper" has some i n t r i n s i c c r e d i b i l i t y f o r me as I write t h i s paper. I can increase i t s c r e d i b i l t y i n a number of ways, for example; i ) check, by using memory, my i n i t i a l experience, i i ) look again at the paper, i i i ) ask other people about the colour of the paepr, iv) have a spectroscopic analysis made of the l i g h t emitted by the paper, - 82 -Tfu + nS Fa Ue hood.5 T KeoremS Nc^a+'ohs of T h e o r e m s The structures of the truth and p r o v a b i l i t y spaces do not coincide as assumed above. It now seems that (due to Godel); ( i ) p r o v a b i l i t y i s a weaker notion that truth; ( i i ) there are truths unreachable in a given theory...but a complementary theory may account for such truths, i . e . i t takes more than one theory to span the space; ( i i i ) the d i v i d i n g l i n e between truth and f a l s i t y i s not simple but i n f i n t e l y complex and d e t a i l s . Truth cannot be described in a f i n i t e way (e.g. e f f e c t i v e l y or c o n s t r u c t i v e l y ) . But there remains a prospective notion of t r u t h . F i g . 8. Connectivity, P r o v a b i l i t y and Truth - 83 -v) analyze what i s meant by an object having a colour to check on the proposition's v e r f i a b i l i t y . But there i s no absolute t e s t , only a d i a l e c t i c a l s e l f correcting process of approximation s t a r t i n g from some "data" which have some i n i t i a l , i n t r i n s i c c r e d i b i l i t y . What i s wrong with coherentism i s the b e l i e f that i t i s possible to s t a r t with an i s o l a t e d statement with no c r e d i b i l i t y and generate c r e d i b l e statements form i t . From zero c r e d i b i l i t y , zero c r e d i b i l i t y i s obtained, and a l l knowledge f l o a t s a d r i f t from r e a l i t y , t o t a l l y i n c r e d i b l e . What i s wrong with foundational ism i s the other exterme - thinking that knowledge i s fi x e d or rooted in r e a l i t y . Knowledge has neither roots or foudnations. The lack of absolute evidence, truth and unity msut be made over from implying a negative l i m i t a i t o n on knowledge to suggesting a p o s i t i v e p r i n c i p l e governing the j u s t i f i c a t i o n of knowledge. 5 ) D i a l e c t i c a l E p i s t e r o l o g y The view of knowledge I am endorsing, using modest realism, modest foundational ism and the princple of complementarity represents a s h i f t from a uniform s t a t i c model of explanation to a p l u r a l i s t i c dynamic - 84 -model of explanation. A uniform account of knowledge i s not possible at present, so being a r e a l i s t , I believe that r e a l i t y i s not uniform but p l u r a l i s t i c . And since there are no absolute ocncepts or truths I must content myself with knowledge of varying p r o b a b i l i t y . Knowledge evolves under the influence of c e r t a i n opposing constraints, some of which include; i ) i n t u i t i v e evidence vs. formal rigour, i i ) utmost generality vs. obvious i d f f e r e n t i a t i o n s , i i i ) conservation of t h e o r e t i c a l base vs. radical conceptual s h i f t , iv) abstraction vs. p r a c t i c a l a p p l i c a t i o n , v) conformity to experience vs. u n i f i c a t i o n . D i a l e c t i c a l , s e l f correcting knowledge approaches higher degrees of p r o b a b i l i t y but only within the framework of c e r t a i n fundamental d i r e c t i o n s and methodologies. So even i f the p r o b a b i l i t y of a body of knowledge increases and approaches unity i t does so only with a framework. There i s always the p o s s i b i l i t y of a fundamental s h i f t , in the conditions of equilibrium, that would necessitate a reassessment of knowledge. - 85 -N O T E S i This represents the reconstruct ton of r e a l i t y from i t s projections. 2 Given e n t i t i e s of types A and B (e.g. physical and mental in the mind-body problem, material and geometric in the geometrization of G.R. waves and p a r t i c l e s in Q.M.) postulated by theories T and T there are at l e a s t nine types of r e l a t i o n s that could e x i s t ; ( i ) A reductionism - The A are real and the B's are j u s t v a r i e t i e s or combinations of the A's, ( i i ) B reductionism - The B are real and the A's are j u s t v a r i e t i e s or combinations of the B's, ( i i i ) A-B p a r a l l e l i s m - A's and B's simply coexist i n harmony with no further explanation possible, (iv) Coordination r e l a t i o n - there e x i s t s a correspondence rule specifying how to translate talk about one level back and f o r t h into the other. This says nothing about the ontological status of the A and B. (v) A-B interactioniism - A and B i n t e r a c t in a causal way, (vi) A-epiphenomenalism - B i s an epiphenomenon of A, ( v i i ) B-epiphenomenal ism - A i s an epiphenomenon of B, ( v i i i ) Hidden variable vTew - A and B are not fundamental e n t i t i e s but spin o f f s from a more basic e n t i t y , as yet unspecified, (ix) A-B complementarity - A's and B's are each involved in separate, legitimate theoretical structures and should be taken as real and as having aspects of the real s i t u a t i o n . 3 Paragraph adapted from remarks in Jauch, 1973, pp. 63-64. th e s i s . 4 The inadequacy I would hope to remedy in a future Ph.D. 5 In mathematics for example number i s studied using generalizations l i k e function, transformation, operator, group...in physics matter i s studied using tensor f i e l d , wave function.... 6 Mere consistency of a view does not guarantee i t s v a l i d i t y as a description of the world. 7 The reason being, claims Hoi ton, that the social sciences have f a i l e d to develop the thematic component of theory, confining themselves j u s t to the phenomenic and a n a l y t i c (Hoiton, 19763, p. 13). 8 That i s truth i s absolutely determinable and i s coincident with p r o v a b i l i t y . 9 This i s to say I take i t to be reasonable to think that the world i s understandable. 10 I owe some of the idea here to Hofstadter, 1979, p. 71. - 86 -Bohr, as an expansionist, believed that physics can be helpful in understanding the most essential question of existence - human values.... He granted a universal scope to the r e g u l a r i t i e s of physics, so that they could be extended to human behaviour as well as to inanimate objects...but that scope included within i t a concept of contradictory and complementary aspects of t r u t h . . . . Bohr believed that science and r e l i g i o n were complementary aspects of the same r e a l i t y , but that both were necessary f o r an understanding of that r e a l i t y , j u s t as wavelike and cor p u s c l e l i k e models are necessary f o r an understanding of atomic physics. (Graham, 1981, pp. 64-65) - 87 -In my opinion, man has on account of his own l i f e experience an immediate and authentic contact with various spheres (perhaps i t would be better to say, zones, or aspects) of r e a l i t y , some of which may be enumerated: physical r e a l i t y - the world of matter -, social r e a l i t y - the world of men -, subjective r e a l i t y - the world of mind -, l o g i c a l r e a l i t y - the world of reason or discourse -, in which mathematical e n t i t i e s p a r t i c i p a t e . ... It seems reasonable however t e n t a t i v e l y to consider the various spheres of r e a l i t y as complementary aspects of one and the same substratum, in the same sense as we have recently been taught to speak of complementary aspects o f physical r e a l i t y . . . . (Beth, 1959, pp. 644-645) - 88 -C h a p t e r I I I C O M P L E M E N T A R I T Y A N D I T S R I V A L S I wish to toss complementarity into the ring as a candidate f o r consideration in the monism-pluralism debate. Complementarity in general i s the view that simultaneously mutually exclusive y e t completing explanations are required to get a maximally consistent account of certain phenomena. In Chapter II I have discussed some of the uses of complementarity. In t h i s chapter I w i l l attempt to pos i t i o n i t amongst i t s r i v a l s and argue f o r i t s legitimacy in one p a r t i c u l a r case - the complementarity of physical and mathematical accounts of r e a l i t y . I also discuss the type of unity of knowledge which complementarity helps expl i c a t e . * * * * * * * 1 ) C o m p l e m e n t a r y P l u r a l i s m a n d t h e M o n i s m - P l u r a l i s m I s s u e Consider two general questions; (i ) How many types of independent e n t i t i e s are there in r e a l i t y ? and, ( i i ) How many i r r e d u c i b l e types of knowledge are there? To the f i r s t , metaphysical, question there could be at l e a s t three sorts of answers; - 89 -(Mi) r e j e c t the question, and metaphysics in general, arguing that we have access only to knowledge, (Mii) give the common sense answer, many, since i t i s prima f a c i e obvious there are many things i n the world, e.g. c h a i r s , people, numbers, fe e l i n g s , sets, values ( M i i i ) argue that there i s only one independent e n t i t y , r e a l i t y as a whole, since only the world as a whole could be considered independent. To the second, epistemological question, there could be at l e a s t three sorts of answers; (Ei) r e j e c t the question, and rational knowledge in general, arguing that we have no warranted knowledge, ( E i i ) give the common sense answer, many, since i t i s prima f a c i e obvious that there are many ir r e d u c i b l e types of knowledge in the world, e.g. aesthetic, e t h i c a l , mathematical...., E ( i i i ) argue that there i s r e a l l y only one type of knowledge in that others can be reduced to one foundational l e v e l , e.g. to phenomenal knowledge or physical knowledge. Let me give these positions names as follows; M(i) metaphysical skepticism, M(ii) metaphysical pluralism, M ( i i i ) metaphysical monism, E ( i ) epistemological skepticism, E ( i i ) epistemological pluralism, E ( i i i ) epistemological monism. - 90 -Positions on the monism-pluralism issue involve combinations of the possible metaphysical and epistemological views. There are nine possible combinations. I w i l l discuss each position b r i e f l y and give an example of a philosopher who takes up such a p o s i t i o n . I w i l l then proceed to locate complementary pluralism in context. (1) (2) (3) (4) (5) (6) (7) (8) (9) METAPHYSICAL M3 (monism) M3 (monism) M(3) (monism) M(2) pluralism M(2) pluralism Ml (skepticism) Ml (skepticism) Ml (skepticism) M2 (pluralism) EPISTEMOLOGICAL E2 (pluralism) E3 (monism) El (skepticism) E(2) pluralism E(3) monism E3 (monism) E(2) (pluralism) E(l) (skepticism) E ( l ) (skepticism) EXAMPLE Spinoza Hegel Bergson Descartes Russel1 Carnap ( l o g i c a l positivism) Von Mises skepticism hypothetical POSITION ( 1 ) . Spinoza and Hegel argued on the basis of the doctrine of internal r e l a t i o n s . This doctrine holds that; (a) nothing but the world as a whole i s t r u l y independent, and (b) everything i s in i t s real nature e s s e n t i a l l y related so everything must be known to know anything. - 91 -In Spinoza's case he argued that to understand and get knowledge of an e n t i t y i s to know i t s causes. But these are external to the e n t i t y , so we must look beyond the e n t i t y . It e s s e n t i a l l y depends on other e n t i t i e s . There can therefore be only one independent, s e l f subsisting, s e l f explanatory thing, diversely known as God or Nature. There i s not mind and body, each i s but one side or aspect of the real process; Thinking substance and extended substance are one and the same thing, comprehended now through t h i s , now through that a t t r i b u t e . (Spinoza, 1927, sec. 17) But there are d i f f e r e n t kinds of knowledge. Types include; ( i ) hearsay knowledge, ( i i ) vague empirical acquaintance, ( i n t u i t i v e knowledge); ( i i i ) immediate deduction, sciencs); (iv) a fourth form which combines immediate deduction and d i r e c t perception, mathematics. POSITION 2 . Spinoza i s open to the objection that his argument for metaphysical monism, based on causation, assumes r e a l i t y must be a strongly connected causal system. But perhaps i t i s j u s t a disconnected - 92 -brute f a c t . To counter t h i s objective Hegel argues that reason, not cause, i s the proper category to use in t h i s argument. Only the world as a whole, the absolute, i s an independent, s e l f s u bsisting, s e l f explanatory e n t i t y because; ( i ) the reason f o r a thing, unlike the cause, has an internal l o g i c a l connection with i t , but, ( i i ) only thoughts stand in l o g i c a l r e l a t i o n s h i p s with one another so, ( i i i ) the absolute i s a l o g i c a l l y a r t i c u l a t e d system of thoughts e x i s t i n g in an absolute mind. For Hegel the movement of thought p a r a l l e l s the movement of the world -in each there i s d i a l e c t i c a l progression. The Absolute i s one completely coherent system. Both Spinoza's and Hegel's position seem to set an ideal of understanding that cannot be attained since to understand anything properly the whole must be comprehended. Inquiry into the nature of the world seems an impossible dream. Their positions seem to require the completion of inquiry and the termination of the pursuit of knowledge. But i t seems we can make piece-meal, provisional progress and att a i n imperfect knowledge. - 93 -POSITIONS 3 * 9 . These two positions I w i l l deal with together, both under the name of Bergson. While there i s a r e a l i t y and while physics, mathematics and rational knowledge in general may be necessary and s u f f i c i e n t for the comprehension of part of i t , an a d d i t i o n a l , i r r a t i o n a l " i n t u i t i o n " i s necessary in accounting for l i f e and consciousness. In some cases an a r a t i o n a l , d i r e c t perception of the thing i t s e l f i s required; A true empiricism i s one that sets i t s e l f the task of getting as close as possible to the o r i g i n a l , of sounding the depths of l i f e , of f e e l i n g the pulse of i t s s p i r i t by a sort of i n t e l l e c t u a l auscultation. (Bergson, 1949 p. 4) In t h i s view the world i s to be discovered a r a t i o n a l l y . POSITION 4 . Descartes held that there were two substances, body and soul. The essence of body was extension and of soul thought. They were independent e n t i t i e s although they could i n t e r a c t (through the pineal gland). Descartes would allow a p a r t i a l monism within each category. Epistemologically Descartes was also p l u r a l i s t . He held that there was introspective knowledge, such as my awareness that I am now thinking, and there was innate ideas, such as the notion of God and of corporeal and s p i r i t u a l substance. - 94 -Kant, I think also, i s a p l u r a l i s t in both senses. Metaphysically there are the phenoemna and the noumena. There are l e v e l s of understanding; ( i ) perception - coordinating sense impressions into an image, the manifest image, ( i i ) experience - coordinating perceptions by means of the categories of understanding - we get experience of the natural world, ( i i i ) knowledge - coordinating judgments of experience by means of general p r i n c i p l e s (ideas) we have knowledge of the metaphysical world, (iv) over and above t h i s we have p r a c t i c a l knowledge based on the b e l i e f in the p o s s i b i l i t y of r a t i o n a l l y guided action in a realm of freedom, the world of ethi c a l conduct. POSITION 5 . Berkeley held that material substance, as explained by Descartes and Locke, i s an u n i n t e l l i g i b l e nonentity. It could not resemble or cause the ideas of sensation, on which a l l knowledge i s based, since by hypothesis i t could not be independently observed and compared to sensation. Material things are j u s t orderly regular systems of sense experiences. To be i s to be perceived. The only consistent theory of r e a l i t y rests on the view that what i s real i s what i s perceived by God and perhaps by some human mind. There are many ideas, the substances of the world, but ultimately only one form of knowledge, immediate perception. - 95 -Neutral monism holds to a neutral nonidealist version of t h i s p o s i t i o n . There i s , i t i s argued a subjectless, neutral "given." Out of t h i s neutral s t u f f material objects and mental phenomenon can be constructed. Russell held t h i s epistemological position with metaphysical pluralism; ...the most fundamental of my i n t e l l e c t u a l b e l i e f s i s that t h i s [the proposition that the world i s a unit] i s rubbish. I think the universe i s a l l spots and jumps, without unity, without continuity, without coherence or orderliness or any of the other properties that governesses love. (Ru s s e l l , 1931, p. 98) POSITION 6 . Hume pointed out that the resolution of the Berkeley-Locke controversey leads to metaphysical skepticism; Philosophers begin to be reconciled to the p r i n c i p l e , that we have no idea of external substance, d i s t i n c t from the ideas of p a r t i c u l a r q u a l i t i e s . This must pave the way for a l i k e p r i n c i p l e with regard to the mind, that we have no notion of i t , d i s t i n c t from the p a r t i c u l a r perceptions. (Hume, 1967, p. 218) Kant's attempt to save substance rested on the d i s t i n c t i o n between phenomena and noumena. Kant interprets the notion of substance, making i t applicable to the phenomenal rather than as Locke d i d , to the real world. God, the soul, things-in-themselves belong to the real world, which i s the object of f a i t h , not of knowledge. The real world, though - 96 -unknowlable, i s a necessary assumption. As Locke's separation of idea and thing generated Berkeley's idealism so Kant's d i s t i n c t i o n between appearance and r e a l i t y generated the c r i t i c i s m s of positivism and pragmatism, in p a r t i c u l a r t h e i r r e j e c t i o n of metaphysics. Machian positivism wanted to reduce knowledge to economically organized sensation. Metaphysical speculation was to be eliminated. Such speculation would include, f o r example, Newtonian absolute space and time, which had been standing in the way of progress in physics u n t i l Einstein developed S.R. Metaphysics was senseless. Philosophy i s only a science, in the c l a s s i c statement by the Viennese C i r c l e in the Wissenschaffliche Weitauffasung of 1929; The metaphysicians and theologians, misinterpreting t h e i r own sentences, believe that t h e i r sentences assert something, represent some state of a f f a i r s . Nevertheless, analysis shows that these sentences do not say anything, being instead only an expression of some emotional a t t i t u d e . To express t h i s may c e r t a i n l y be a s i g n i f i c a n t task. However, the adequate means for i t s expression i s a r t , for example l y r i c poetry or music. (in Von Mises, 1951, p. 400) - 97 -Metaphysics was ruled out in positivism and there was a tendency to phenomenalism i n i t i a l l y . Schlick (1925-35) reinterpreted the Kantian form-content d i s t i n c t i o n as the theory-observaiton d i s t i n c t i o n . Kant's idea of necessary categories of cognition determining knowledge was replaced by theoretical conventions determining knowledge (Friedman, 1982, Introduction). Theories were a r b i t r a r y devices used to systematize phenomena. Schlick argued, wrongly, that G.R. showed the complete r e l a t i v i t y of form. As the group of admissible transformations of the observational base widened, he argued, objective content lessened. In the l i m i t as a l l continuous transformation were permitted the only features of the world that remained invariant, p h y s i c a l l y objective, were, t o p o l o g i c a l l y speaking, space-time proximities, i . e . observations where observer-observed world l i n e s meet - phenomena. Carnap in his early work Per Logische Aufbau der welt (1928) attempted to show how the concepts of various s c i e n t i f i c d i s c i p l i n e s could be construed as l o g i c a l constructions, erected on the basis of neutral concepts that r e f e r to elements and r e l a t i o n s of a subjectless raw material of experience. Later Carnap was to replace the concepts describing raw material of experience as the base with the concepts of intersubjective science (Logical Foundations of Unified Science, 1938). These then are two forms that the r e j e c t i o n of metaphysics, coupled with epistemological monism, can take. POSITION 7. Positivism in i t s early stages turned out to be too harsh. The need for metaphysical p r i n c i p l e s in science and the - 98 -meaningful content of ethical and aesthetic judgments made adjustment necessary. Von Mises, in his 1950 book Positivism, summarizes t h i s new positivism; i ) language must be c r i t i c a l l y used, i i ) there are protocol sentences, minimally i n f e r e n t i a l simple statements, to which a l l meaningfully assertions must be connected, i i i ) the goal of knowledge i s to b u i l d axiomatized theories that systematize knowledge, iv) c a u s a l i t y and p r o b a b i l i t y are natural methods of explanation and alone stand a c r i t i c a l l i n q u i s t i c examination, v) the idea that there i s a fundamental unbridgeable difference in method between natural sciences and humanities i s untenable, vi) metaphysical propositions, characterized by s t r i c t l y l i m i t e d c o n n e c t a b i l i t y , are s t i l l needed, but research leads away from them toward science. But von Mises cautions; A s c i e n t i f i c theory, as well as a work of a r t , i s always only a one-sided hint to possible experiences, never t h e i r complete exhaustion. (Von Mises, 1950, p. 370) v i i ) An ever increasing s c i e n t i f i c knowledge w i l l gradually guide l i f e and the conduct of men. (Von Mises, 1950, pp. 368-370) I o f f e r Von Mises as a p o s i t i v i s t who rejects metaphysics in general but allows that d i f f e r e n t forms of knowledge may be required to obtain an exhaustive account of r e a l i t y . - 99 -POSITION 8. It might be argued, by way of an extreme form of skepticism, that a l l knowledge beyond that of elementary perception i s impossible. Taken as an objection against the v a l i d i t y of science and the s c i e n t i f i c method one might argue (a) from h i s t o r i c a l change or (b) against any method. (a) History i s strewn with theories that were once believed true but now are believed f a l s e , e.g. phlogiston theory, c a l o r i c theory, aether theory, impetus theory. There i s no assurance that what we now take to be true won't be accepted as f a l s e at some l a t e r time. S c i e n t i f i c theories don't t e l l about r e a l i t y but j u s t enable people to give explanations and make predictions. Better ones may come along. They don't r e f e r to r e a l i t y and are neither true or f a l s e . (b) How can any method of obtaining knowledge be known to be correct? If we can never be c e r t a i n our knowledge and method of inquiry are v a l i d we have no r i g h t to c a l l r e s u l t s knowledge. I have discussed nine possible positions regarding the monism-pluralism issue. I wish now to discuss the p r i n c i p l e of complementarity and i t s use in e x p l i c a t i n g the position I favour -position #1 - metaphysical monism with epistemological pluralism. My exposition of position #1 uses a general version of Bohr's p r i n c i p l e of complementarity. Bohr found in Q.M. that to make sense of, for example, the double s l i t experiment a set of simultaneously mutually exclusive conceptual pictures are needed. Photons have both wave and p a r t i c l e - 1 0 0 -properties (see Cope!and, Chapt. 2). The way to resolve the problem here i s ; (i) to accept both explanations and ( i i ) the reality is to be understood as completely described by the exhaustive overlay of competing partial explanations. I define Compl (T,,T Z), two mutually incompatible theories are complementary, i f and only i f ; (i) they have a common referent, ( i i ) they make different allegations, and ( i i i ) they are both required to obtain a maximally complete account of the phenomena. I hold with regard to reality in general, and our knowledge of i t , that; (a) Experience is chaotic without a free choice being made of some explanatory system(s), (b) We often deal with projections of the actual state-reality, (c) There are some quantities invariant under projection, (d) The actual state is inferrable, from projections, by exhaustive overlay of the different accounts of the projections, (e) Various irreducible types of knowledge are needed to span human information space; these include physical, social, subjective, logical, ethical and aesthetic, (f) None of the types of knowledge is foundational, (g) Position # 1 , interpreted using complementarity, is a plausible candidate for a solution to the monism-pluralism problem. - 101 -...any adequate theory of science must take into account at l e a s t (four p r i n c i p l e s claims Gonseth); (1) the p r i n c i p l e of r e v i s i b i l i t y ; (2) the p r i n c i p l e of t e c h n i c i t y ; (3) the p r i n c i p l e of duality - neither rationalism nor empiricism are s u f f i c i e n t as a basis f o r a theory of science; (4) the p r i n c i p l e of i n t e g r a l i t y , according to which science is* a whole the parts of which are not autonomous.... I would venture to question the convenience of the fourth, the p r i n c i p l e of i n t e g r a l i t y . This p r i n c i p l e had been accepted by the Vienna C i r c l e as one of t h e i r main theses. The thesis of the unity of science, however, was seen by the lo g i c i a n s of the school to be hardly tenable on account of the necessity of separating l o g i c from metalogic and microphysics from macrophysics. Hence i t seems appropriate to replace the unitary conception of science by a p l u r a l i s t one, based on the notion of complementarity.... (Beth, 1959, pp. 624-625) - 102 -2 ) U n i t y - D i v e r s i t y o f K n o w l e d g e In Part I of t h i s essay I discussed the a p p l i c a b i l i t y of the p r i n c i p l e of complementarity to the monism pluralism issue. I wish now to discuss i t s a p p l i c a b i l i t y to the unity of r e a l i t y and of knowledge -metaphysical unity and epistemological unity. With regard to metaphysical unity I w i l l discusss eight positions; ( i ) materialism; ( i i ) idealism; ( i i i ) p a r a l l e l i s m ; (iv) interaction!'sm; (v) epi phenomenal ism; (vi) emergent!"sm; ( v i i ) reductionism; ( v i i i ) complementarity. With regard to epistemological unity I w i l l discuss six p o s i t i o n ; ( i ) conventionalism; ( i i ) i d e n t i t y ; ( i i i ) reductionism; (iv) nonreducitonism; ( p a r t i a l monism); (v) emergentism; (vi) complementary. ( A ) M e t a p h y s i c a l U n i t y . POSITION 1 . Sklar claims that the nineteenth century notion of unity of science was based on the metaphysical thesis of crude material ism (Sklar, 1974, pp. 536). This view developed gradually from Democritus and his assertion that only atoms and the void are r e a l , through Hobbes1 view that the e n t i r e world was body and "...hath the dimensions of magnitude, namely length, breadth, and depth" and Ludwig Buchner's - 103 -summary of the case for nineteenth century materialism in Force and  Matter: ...the words mind, s p i r i t , thought, s e n s i b i l i t y , v o l i t i o n , l i f e , designate no e n t i t i e s and no things r e a l , but only properties, c a p a c i t i e s , actions of the l i v i n g substance, or r e s u l t s of e n t i t i e s , which are based upon the material form of existence. (Buchner, 1884, pp. 242-43) Metaphysical unity took the form of a law-like deterministic material universe as described by Laplace in A Philosophical Essay on  P r o b a b i l i t i e s . POSITION 2 . Berkeley argued that material substance as propounded by Descartes and Locke could not be fundamental - that to be i s to perceived - so what i s r e a l , must be mental in character. I d e a l i s t s argued for o b j e c t i v i t y as: (a) s t a b i l i t y in the mind of God, for Berkeley or (b) the l o g i c a l l y necessary unfolding of thoughts of an absolute mind, for Hegel. While idealism seemed p l a u s i b l e , as part of a Kantian philosophy of mathematics for example, i t f a i l e d to achieve very much success as a philosophy of science. The unity i t proposes i s a metaphysical unity of the world, the world being a group of mental e n t i t i e s . POSITION 3 . P a r a l l e l i s m i s a form of metaphysical pluralism which asserts that there are at l e a s t two i r r e d u c i b l e substances in the world - 104 -and that they have a p a r a l l e l but noninteractive existence, although they may be coordinated. There may, for example, be material, brain events and mental, mind events, both independent e n t i t i e s , i r r e d u c i b l e to one another, e x i s t i n g side by side. Let me now introduce a b r i e f account of G.R., which w i l l provide further material for the discussion of these metaphysical positions. John Graves claims that the " c r u c i a l conceptual innovation in G.R." i s the i d e n t i f i c a t i o n of what had previously been considered c a t e g o r i c a l l y d i f f e r e n t e n t i t i e s , the curvatures and the TuV physical stresses (Graves, 1971, p. 147). In setting up a law of gravitation in G.R. Einstein proceeded in four steps. F i r s t he set up the metric; d s = 21 g^.x> ** x M *• w n e r e t n e g= $• (x, , x,t, xs , ) - $ some continuous function. Second define a ten component tensor $^OLV i f i r s t d erivative of | u v » second derivative of . This tensor s p e c i f i e s the geometry of the space. Third, in a four dimensional space, specify the stress functions on each of four non coplanar surface elements p a r a l l e l to the coordinate planes. Call the stress functions 7^ , 7^ , 7 ^ Tx with components TXif, T 2, T ^  ,T ^T^, 7 ^ , Tft) TilC J^T^T^, TtyL, ~T T T T<1 T V which - 105 -spe c i f i e s the physical stress in the space - ( reduces to a ten component tensor since i t i s symmetrical, i . e . - T^- ). Einstein's i n i t i a l idea was that space-time was a structural quality of the f i e l d so that the T t t J / should determine the <gMv . The should then be proportional to the ; 'RMJ, - ±-^v R, = <3T<£ T ^ , where - ^"J^v i s a factor introduced so both sides obey the conservation of energy p r i n c i p l e and &ir& i s the proportionality cz constant. The int e r p r e t a t i o n of t h i s i d e n t i t y has many candidates, including; ( i ) physicalism, the T ^ ^ stresses are alone real - the 1 ^ being j u s t ways of loose t a l k , ( i i ) idealism, j u s t the , mathematical objects created by our imagination, are independent - the Tuv being j u s t organized c o l l e c t i o n s of these elements of thought ( i i i ) materio-geometric p a r a l l e l i s m , geometry and physical stress simply coexist in harmony with no further explanation possible (a d u a l i s t p o s i t i o n ) , and other p o s s i b i l i t i e s . POSITION 4 . Interactionism would involve a pluralism with a causal, or some other, transfer of information and energy from one realm to another. In the mind-body problem i t would hold that the brain a f f e c t s thoughts and/or that the mind can produce changes in the brain. In the case of G.R. i t would hold that space-time and physical stress mutually i n t e r a c t in a causal way. J.A. wheeler has made a remark that seems suggestive of t h i s dynamic, as opposed to s t a t i c , view of space-time, to the e f f e c t that space-time t e l l s matter how to move and matter t e l l s space-time how to curve. Psycho-physical interactionism might be - 106 -characterized analogously to the e f f e c t that mind t e l l s brain what program to execute and brain t e l l s mind how, programmatically, to think. A metaphysical unity can be r e a l i z e d here by way of ( i ) a p a r t i a l monism within one realm and; ( i i ) the i n t e r a c t i v e unity of the parts to the system. POSITION 5 . Epiphenomenal ism may be understood as the hypothesis of (i ) a one-one r e l a t i o n of a's to some but not a l l b's and ( i i ) dangling nomological r e l a t i o n s connecting the a's and b's. In our two cases under consideration - in the mind-body problem m a t e r i a l i s t i c epiphenomenal ism seems s c i e n t i f i c a l l y most problable; that there i s a one-one r e l a t i o n of mental states to some but not a l l physical states and there are some "dangling nomological r e l a t i o n s connecting the mental and physial states. S i m i l a r l y for G.R. m a t e r i a l i s t i c epiphenomenal ism would hold that space-time i s an epihenomenon of matter. This could be the characterization of Einstein's early view of G.R.: There i s no such thing as an empty space, i . e . a space without f i e l d . Space-time does not claim existence on i t s own but only as a structural quality of the f i e l d . . . . ( E i n s t e i n , 1973, p. 365) Unity i s achieved here by vir t u e of the foundational unifying role of the phenomena with regard to the epiphenomena. - 107 -P O S I T I O N 6 . Emergent!sm holds that c e r t a i n e n t i t i e s spring discontinuous!/ into existence from others. The new whole transcends i t s parts. There would be a cer t a i n h i s t o r i c a l unity of o r i g i n at l e a s t . Mind may be emergent from matter, i . e . derivative from i t , but now not j u s t matter, but matter at-a-new-level-of-complexity. In G.R. an emergent i n t e r p r e t a t i o n would involve the view that say matter i s emergent from space-time v o r t i c e s . I am not aware of any defenders of t h i s view. Emergentism i s a variety of pluralism but achieves metaphysical unity through appeal to h i s t o r i c a l - e v o l u t i o n a r y antecedence. P O S I T I O N 7. Metaphysical reduction!'sm holds that a c e r t a i n e n t i t y or event A i s numerically i d e n t i c a l with a set of e n t i t i e s or events £ 15, , 3^ , S 3 .. . 3n ^ . T n j s r e a l l y then i s j u s t the position that the same ent i t y or event has been i d e n t i f i e d under d i f f e r e n t conditions. The morning star i s the evening star, HO i s water. It would maintain that the brain and the mind are j u s t the same entity encountered in two d i f f e r e n t contexts or that space-time and matter-energy are j u s t the same e n t i t y approached from d i f f e r e n t perspectives. P O S I T I O N 8. Metaphysical complementarity arises in Q.M. According to the Heisenberg Uncertainty P r i n c i p l e any sequential measurement of position (x) and momentum (p) on a closed system can r e s u l t in values of - 108 -(x) and (p) only with a necessary uncertainty. This uncertainty i s not due to experimental error, rather i t i s due to the fundamental status of p o t e n t i a l i t y in nature. If Z\ x—*0 then /\p —* c o and p has no d e f i n i t e value whatsoever. The e n t i t i e s x and p are bound in a r e l a t i o n which sees the one vanish as the other becomes completely c e r t a i n . I am not aware of uses of metaphysical complementarity outside Q.M. but mention i t j u s t to point out another unitary r e l a t i o n s h i p between e n t i t i e s . ( B ) U n i t y - D i v e r s i t y i n G e n e r a l . I have mentioned these eight positions concerning metaphysical unity in order to say now that the use of complementarity that I am advocating i s nonmetaphysical. I am concerned with i t s epistemological use. Let me digress concerning the unity of knowledge. Taking the example of science, l e t me d i s t i n g u i s h three approaches to unity; ( i ) theoretical unity, ( i i ) unity of method, ( i i i ) l o g i c a l reduction. Logical reduction aims to achieve unity in the d e f i n a b i l i t y of a l l terms in a domain in terms of some foundational domain, e.g. s e n s a t i o n a l i s t i c predicates or predicates r e f e r r i n g to the observable properties of physical things. Unity of method aims at unity in the sense of common standards of explanation, s i g n i f i c a n c e , evidence etc. Von Mises in Positivism f o r example, claims: The idea that there exists a fundamental unbridgeable difference in method or even in kind of "understanding" between the natural sciences and the humanities i s untenable. In history and the social sciences, too, one deals with observations, inductive generalizations, - 109 -hence theories, and with the f i r s t approaches to tautological systems; every r e s u l t i s , in the l a s t analysis, a proposition v e r i f i a b l e in experience. (von Mises, 1951, p. 369) Theoretical unity refers to a number of strategies which involve the empirical reduction of one d i s c i p l i n e to another. There are three versions: (1) Conceptual reduction, in which a l l the terms of one d i s c i p l i n e are reduced to the terms of some one d i s c i p l i n e (e.g. physics). This reduction might involve biconditional d e f i n i t i o n s , a n a l y t i c "true in vir t u e of the meanings of the terms involved" d e f i n i t i o n s , or some less r e s t r i c t i v e type of equivalence; (2) Unity of laws i s attained to the extent to which the laws of one domain of knowledge become reduced to those of another. This would require conceptual reduction and some method of deriving the reduced laws from the reducing laws. Realization would mean an all-comprehensive explanatory system had been achieved; (3) Strong unity i s r e a l i z e d i f a l l laws are not only reduced to one level but the laws of that d i s c i p l i n e are connected. Maxwell's theory of electromagnetism u n i f i e s electromagnetism and l i g h t by showing they f a l l under the scope of the same four d i f f e r e n t i a l equations. S.R. un i f i e d kinematics and electromagnetism by showing the laws of each are subject to the same transformation rules - the Lorentz transformations. - 110 -Supergravity, by way of a t h i r d example of strong unity, aims at unifying gravity, electromagnetism, weak forces and strong forces in one comprehensive theory. A l l forces and p a r t i c l e s would be derived as projections from a super p a r t i c l e - f i e l d of eleven dimensions. D i f f e r e n t projections produce d i f f e r e n t f i e l d s , e n t i t i e s and laws but a l l are uni f i e d in the s u p e r f i e l d . And t h i s i s not j u s t metaphysical in that conditions in a black hole may produce situations in which the superfield speculation may be empirically t e s t a b l e . I mention the forms of unity in science from weakest to strongest to contrast them with complementarity which seeks to achieve a weak form of unity. Sklar characterizes our present picture of unity of science as; (i ) i t must be an e m p i r i c i a l , not a l o g i a l task, to avoid vacuity, ( i i ) i t w i l l be a concatentation of reductions with unity being obtained by the ultimate, perhaps i n d i r e c t , reduction of a l l theory to some basic theory. Sklar characterizes t h i s s i t u a t i o n as an imperialism (probably of physics) rather than a federalism of sciences (Sklar, 1974, p. 530); ( i i i ) basic theories w i l l explain less basic theories, with at any time some basic unexplained explainer at the bottom of the hierarchy. Complementarity aims at more of a federalism than an imperialism. Imperial ism may well apply within a d i s c i p l i n e l i k e science. But with regard to knowledge as a whole I think a weaker view i s equally defensible. At l e a s t i t deserves i t s place in the ring as a contender. Between the simple conjunction of several branches of knowledge, which does not e f f e c t a unity, and the super unity exemplied by Supergravity, there are halfway houses. Complementarity, I wish to argue, i s one of them. What general statement of such a federalism among - I l l -d i s c i p l i n e s might be offered? I f i n d E. Cassirer's view expressed in Einstein's Theory of R e l a t i v i t y Considered from the Epistemological  Standpoint persuasive; If we understand...(how)...the affirmation of r e l a t i v i t y develops with inner consequence and necessity out of the very form of physics, a c e r t a i n c r i t i c a l l i m i t a t i o n of t h i s affirmation also appears. The postulate of r e l a t i v i t y may be the purest, most universal and sharpest expression of the physical concept of o b j e c t i v i t y , but t h i s concept of the physical object does not coincide, from the standpoint of the general c r i t i c i s m of knowledge, with r e a l i t y absolutely. The progress of epistemological analysis as shown in the assumption of the s i m p l i c i t y and oneness of the concepts of r e a l i t y i s recognized more and more as an i l l u s i o n . Each of the o r i g i n a l d i r e c t i o n s of knowledge, each i n t e r p r e t a t i o n , which i t makes of phenomena to combine them into the unity of a theoretical connection or into a d e f i n i t e unity of meaning, involves a special understanding and formulation of the concept of r e a l i t y . These r e s u l t s have not only the c h a r a c t e r i s t i c differences of meaning in the objects of science, the d i s t i n c i t o n of the "mathematical" object from the "physical object," the "physical" from the "chemical," the "chemical" from the " b i o l o g i c a l , " but there occur also, over against the whole of theoretical s c i e n t i f i c knowledge, other forms and meanings of independent type and laws, such as the e t h i c a l , the aesthetic "form." It appears as the task of a t r u l y universal c r i t i c i s m of knowledge not to level t h i s manifold, t h i s wealth and variety of forms of knowledge and understanding of the world and compreess them into a purely abstract unity, but to leave them standing as such.... No individual form can indeed claim to grasp absolute " r e a l i t y " as such and to give i t complete and adequate expression. (Cassirer, 1953, p. 446) ( C ) E p i s t e m o l o g i c a l U n i t y . I w i l l discuss six positions concerning the unity of knowledge with the view i n mind of comparing and contrasting them with complementarity. By "theory" I mean, very broadly, any hypothesis, generalization or law (deterministic or s t a t i s t i c a l ) , or any conjunction of these; by "phenomena" I mean either p a r t i c u l a r occurrences - 112 -or t h e o r e t i c a l l y formulated general patterns (Oppenheim and Hempel, 1948, 135-175). Call two theories T, ,T 2 complementary, i . e . Compl (T T J i f f ; ( i ) they have a common referent, ( i i ) they make d i f f e r e n t a l l e g a t i o n s , but ( i i i ) they are both needed to give a complete account of the phenomena. Combinations .of meeting ( ) or f a i l i n g to meet (x) these conditions generaate eight p o s i t i o n s ; Condition Position ( i ) ( i i ) ( i i i ) 1 7 7 S" 2 3 4 * 5 * 6 x x * 7 x * " 8 • • V I think some of these p o s s i b i l i t i e s represent recognizable r e l a t i o n s h i p s betweeen theories. These are (1) conventionalism; (2) i d e n t i t y ; (3) conceptual reduction; (4) i r r e d u c i b i l i t y ; and (8) complementarity. Positions (5), and (7) are uninteresting cases as far as I can see. Position (5) seems l i k e nonsense in that i t seems r i d i c u l o u s for two theories to have d i f f e r e n t referents yet make the same a l l e g a t i o n s . Position (7) suffers from the same problem as position (5) in that I do not see how theories which have d i f f e r e n t referents can make the same alle g a t i o n s . Let me now consider the viable positions. P O S I T I O N 1 . Conv(T ( ,p i f f ; ( i ) they have a common referent, ( i i ) they make d i f f e r e n t a l l e g a t i o n s , - 113 -( i i i ) only one of them i s needed to give a complete account of the phenomena. Let me use the Poincare parable as an example of conventionalism. The common referent, the phenomenon i s a two-dimensional disk heated to a o certain temperature while the circumference i s at 0 K. The temperature a distance r from the centre i s were R i s the radius of the disk. The temperature of the center then i s and at the edge - O . The index of the medium of transmission of l i g h t on the disk at any point r from the centre i s i ~r~i ~I . Two-dimensional inhabitants of the world are equipped with r i g i d rods, l i g h t rays etc. The rods a l l contract uniformly with diminishing temperature and in proportion to the drop in temperature, with length = 0 when temperature i s 0 K. Consider two theories of the i n t r i n s i c geometry of the world: T, : assuming the rods are r i g i d the residents w i l l conclude that t h e i r world i s a Lobachevskian plane of i n f i n i t e extent. Geodesies are not s t r a i g h t l i n e s but Lobachevskian geodesies and the r a t i o of circumference to radius of a c i r c l e i s always greater than 2Tf. Using l i g h t rays, assuming the l i g h t t r a v e l s along geodesies and that the index of r e f r a c t i o n of the vacuum i s constant, they w i l l once again f a l s e l y i n f e r that t h e i r plane is Lobachevskian, unbounded and i n f i n i t e . T 2: the rods shrink and the l i g h t bends, perhaps due to some f i e l d s . The world i s a two-dimensional Euclidean disk bounded and - 114 -f i n i t e . T, and T 2 have a common referent, the world of Poincare's parable. They make d i f f e r e n t a l l e g a t i o n s , of a Lobachevskian and Euclidean s o r t . But each i s adequate by i t s e l f to explain the phenomena. The problem here of course i s which one to pick, i f a choice i s to be made. POSITION 2 . Id(T,,T 2) i f f : (i ) they have a common referent, ( i i ) they make the same al l e g a t i o n s , ( i i i ) only one of the theories i s required to give an adequate account of the phenomena. What we have here then i s the same object i d e n t i f i e d in d i f f e r e n t contexts. Consider the following example. (a) In quantum mechanics the state of a physical system can be described using the Schrodinger or the Heisenberg representation. In the Schrodinger representation (wave mechanics) the wave function -\(r i s regarded as a function of position and time. A system i s in an eigenstate i f f H yr- = ^-'f" • The momentum appearing in the Hamiltonian i s represented by the operator ~ ^^-^ . In the Heisenberg representation (matrix mechanics) a dynamical variable such as momentum position etc. i s represented by means of matrix, the time rate of change of the variable X - 115 -being given by i / i X - X M - H X , where H i s the Hamiltonian of the system. Dynamical variables which cannot be measured simultaneously with a r b i t r a r y precision are represented by matrices or more generally operators, which may not commute. A system in state y-has a d e f i n i t e value for the dynamical variable A, in wave mechanics, v, i f i s an eigenfunction of the operator A, i . e . A yr - a ^fr (a = constant). In the Heisenberg representation a dynamic variable has a precise value i f f i t s matrix s a t i s f i e s the commutation r e l a t i o n XH = HX. The eigenvalues and p r o b a b i l i t i e s are i d e n t i c a l in both representations. Lawrence Sklar summarizes the s i t u a t i o n as follows; ...the development of quantum mechanics...the u n i v e r s a l l y accepted position that the Heisenberg and Schrodinger versions of the theory constitute not two a l t e r n a t i v e theories between which we must choose but rather two a l t e r n a t i v e representations of one and the same theory.... In the Schrodinger representation the state of a system i s i n i t i a l l y f ixed by the preparation of the system. But as time elapses the state changes according to a dynamical law and the internal c o n s t i t u t i o n of the system. The mathematical representatives of the observables are operators, constant in time. So the changing p r o b a b i l i t i e s of outcomes as the system dynamically evolves are attribu t e d to i t s time-dependent state. In the Heisenberg picture the state of a system i s characterized by i t s preparation, and i s represented by a temporally unchanging mathematical form, the unchanging state-vector for the prepared system. The operations for each observable, on the other hand, time-dependent mathematical structures, and the changing p r o b a b i l i t i e s of outcomes are now captured in the dynamical evolution of the operators. (Sklar, 1974, pp. 144-145) POSITION 3 . Red(T,,"g ? T, i s reduced to Jz , i f f ; - 116 -( i ) they have a common referent, ( i i ) they do not make d i f f e r e n t a llegations (when suitably t r anslated), ( i i i ) they are both needed to give a complete (intensional and extensional) account of phenomena. Reduction serves to explain the r e l a t i o n of le s s comprehensive to more comprehensive theory. There are two general versions of reduction, conceptual and t h e o r e t i c a l . In conceptual reduction the vocabulary of T i s reducible to the vocabulary of 1L . B i o l o g i c a l terms for example may be reducible to physio-chemical terms. Theoretical reduction involves the reduction of the laws, hence vocabulary also, of T, to T 2 . Kemeny and Oppenheim formalize reduction as follows; RedfT^Tj) , T reduces to T , i f f ; (1) The vocabulary of T, contains terms not in the vocabulary of T 2 ; (2) Any observational data explainable by T, i s explainable by T z and; (3) T 2 i s at l e a s t as well systematised as T, , i.S T a i s more e f f i c i e n t , in terms of explanatory power than T, . The reduction r e l a t i o n i s nonreflexive and non symmetric but t r a n s i t i v e . T ( does not reduce T^ since there i s no improvement in explanatory power. Reduction i s non symmetric, i . e . Red(T, f T 2) does not imply Red(T 2, T, ) since i f T 2 i s more comprehensive than T, , T, i s not more comprehensive than Jz . But i t i s t r a n s i t i v e in that i f Red(T, , T^) and Red (T,,T 3) then i t i s probable that Red (T, ,T 3) in that a chain of vocabulary and law reductions seem p l a u s i l e , with T 3 at the bottom of a comprehensive explanatory scheme. - 117 -Reductions take place between two theories only under the assumption of cer t a i n a u x i l i a r y assumptions that provide bridging information (Yoshida, 1977, pp. 70-72). The object of a reduction i s to show that one can derive the less from the more comprehensive theory with the help of the a u x i l i a r y , bridging assumptions. Assuming suitably r e s t r i c t e d a u x i l i a r y assumptions three types of theoretical reductions are possible; ( i ) Theoretical transformation; that T ( becomes id e n t i c a l with T j in c e r t a i n l i m i t i n g conditions. The subject matter of T, i s a subset of T 2 . Special r e l a t i v i t y reduces to c l a s s i c a l mechanics in the l i m i t as u << c . I n the l i m i t as \r —» o the Lorentz factor | > x r F ~ tends to j - - J and r e l a t i v i s t i c e f f e c t s become n e g l i g i b l e . Analagously Q.M. in the l i m i t that values for variables /v , transforms to the certainty of c l a s s i c a l l i m i t s since the uncertainty expressed in the Heisenberg r e l a t i o n , e.g. for position and momentum A x A p ^  ^ i s neg l i g i b l e , i.e u n : « r t a i r \ + y f o r a b a - s c b a l l si-zed. object^ is ( i i ) Theoretical reduction proper concerns, unlike transformation, theories with prima f a c i e d i f f e r e n t subject matter, e.g. (a) l i g h t and electromagnetic radiation or (b) temperature and mean k i n e t i c energy. T i s reduced to T £ with the aid of a u x i l i a r y assumptions and a theoretical i d e n t i f i c a t i o n i f T can be deduced from T^ . Physical optics has been reduced to electromagnetic theory (Maxwell's) under the assumption l i g h t - electromagnetic radiation and - 118 -thermodynamics has been reduced to s t a t i s t i c a l mechanics under the assumption temperature - mean k ine t i c energy Yoshida, 1977, pp. 70-72). ( i i i ) Theoretical explimination aims at e l iminat ing T and i t s vocabulary. Subject matter of T and T a i s assumed d i f fe rent and i t i s supposed there i s good reason to think T f a l se . Explimination aims at el iminat ing T , in that T can explain the success and fa i l u re s of T . Lavo i s i e r ' s theory of combustion, based on the concept of ox idat ion, expliminates the phlogiston theory in showing that phlogiston i s nothing but negative oxygen and that the quant itat ive resu l t s of combustion can be explained using ox idat ion. The tough cases in unity of knowledge are cases where there are prima fac ie d i f fe rent subject matters. I t could be granted that there may be a pa r t i a l epistemologial monism in physical science for example, while holding out for plural ism with regard to e th ic s , aesthetics etc. Reduction (proper) and expl iminat ion, in Yoshida's sense, hinge on theoret ica l i d e n t i f i c a t i o n which as Sklar points out "opens a Pandora's box": ...Pandora's Box has been opened and the dark s p i r i t s of metaphysics are a f l u t t e r about the room, mocking our empi r i c i s t predispos i t ions. What i s an i den t i f i ca t i on ? What i s a lawl ike i den t i f i ca t i on ? How do you t e l l when two classes of en t i t i e s are merely correlated and when there i s , properly speaking, only one class previously encountered under two aspects or two descriptions? Why don 't i den t i f i c a t i on s require explanation? Is i t because they are not discovered but simply ' invented ' ? Is the difference between a cor re la t ion and an i d e n t i f i c a t i o n a difference in fact? Or a decision? Or a convention?. . . (Sklar, 1974, p. 541) - 119 -POSITION 4 & 6 . Irred(T,,TA) T T, is irreducible to Tz,$J+i (i) they have different referents, ( i i ) they make different allegations, ( i i i ) they are both needed to account for different subject matter in case (6) or only one is needed in which case they are rivals or conventions. Position 6 describes theories that are independent of one another. If all there was available was position 6 the best we could do for unity of knowledge would be a conjunction of independent theories. Position 4 describes theories which are independent but which, I claim, might be related in an emergent fashion as suggested, but not necessarily defended by Meehl and Sellars in The Concept of Emergence. Irreducibility i f conceived of as antireductionism has at least three methods of defense. Fir s t of a l l there is a prima facie case for pluralism of knowledge - there seem to be different types of knowledge (e.g. s c i e n t i f i c , mathematical, subjective). Second the antireductionist could withhold assent to the theoretical identification needed to make theoretical reduction and theoretical explimination go. As Meehl and Sellars point out, the fact that, for example, the ideal of natural science may be to derive a l l laws from a certain limited number of laws or principles and in so doing convert science into mathematics, this does not translate into identity. For the existence of a mathematical relation relating values of two variables "does not mean that the entity to which the value x appertains is being equated with the - 120 -s i t u a t i o n to which the value of Y appertains any more than the discovery of a functional r e l a t i o n between a person's height and weight would require us to suppose that somehow a person's height i s the same thing as his weight (Meehl and S e l l a r s , MSPSI, p. 251) A t h i r d a n t i r e d u c t i o n i s t approach involves appeal to cases of f a i l e d reduction. Take a case from biology for example. Suppose that i t i s hypothetically granted that " l i o n s hunt zebras" designates a si t u a t i o n which i s numerically i d e n t i c a l with a c e r t a i n sequence of physiochemical events. It may s t i l l be the case that the concept "hunting" i s not definable in physiochemical terms. "Hunting" may be definable only in intentional language, using categories such as thinking, wanting and be l i e v i n g . Feigl t a l k s about a housewife, who saying "the soup i s hot now," does not r e a l i z e she i s t a l k i n g i n d i r e c t l y about the mean ki n e t i c energy of some molecules. But, intentional language i s c a t e g o r i c a l l y d i f f e r e n t from extensional, p h y s i c a l i s t i c language j u s t as object language and metalanguage are in l o g i c , d i s p o s i t i o n and occurrence language or emotive and cognitive language are in everyday discourse. The n a t u r a l i s t i c f a l l a c y " i s - language" and "ought-language" i s another example. Feigl says; I s t i l l agree, of course with Wilfred S e l l a r s , Roderick Chisholm, Stephan Korner, and others, in considering c l e a r l y intensional ( i n Brentano's sense) features as i r r e d u c i b l e to a p h y s i c a l i s t i c d e s c r i p t i o n . But as I have indicated in t h i s long essay, t h i s does not seem to me a serious flaw in physical ism. According to S e l l a r ' s decisive a n a l y s i s , t h i s i r r e d u c i b i l i t y i s on a par ( i f not a special case of) the i r r e d u c i b i l i t y of l o g i c a l categories to psychological or physiological ones. Logical categories, and p r i n c i p l e s formulated in terms of them, are indeed " c a t e g o r i c a l l y " d i f f e r e n t from those - 121 -of the factual sciences. Logic (syntax and semantics) i s , of course, indispensable in the object language or the metalanguage of a l l sciences (formal or f a c t u a l ) ; but the difference between l o g i c and psychology i s j u s t as fundamental as that between, say, l o g i c and physics. To disregard the difference amounts to making one of the most glaring category mistakes. ( F e i g l , 1969, p. 150) I mention as an aside here that Feigl l a t e r (p. 156) mentions "complementarity" and dismisses i t in a few l i n e s as a weak but suggestive analogy concerning the phenomenal and physical language. I am arguing, of course, that i t i s better than t h i s . Michael Scriven in his a r t i c l e D e f i n i t i o n s , Explanations and  Theories argues for an a n t i r e d u c t i o n i s t p o s i t i o n . He claims that; . . . i t i s an essential feature of theoretical terms that they are not reducible by d e f i n i t i o n or empirical c o r r e l a t i o n to an observation base and a f o r t i o r i not reducible to the theoretical terms of another d i s c i p l i n e . (Scriven, 1967, p. 103) The d e f i n a b i l i t y of terms from one d i s c i p l i n e in terms of another Scriven attacks using the example of " l i g h t " and "electromagnetic r a d i a t i o n . " He argues: (1) there i s a prima f a c i e obvious difference in ordinary language, - 122 -(2) i f l i g h t = electromagnetic radiation i s a formal substitution rule i t may be the case that a Doppler s h i f t may s h i f t the r e l a t i o n between " l i g h t " and "electromagnetic r a d i a t i o n , " we may see in a d i f f e r e n t band. But t h i s i s an material not a formal condition, v i o l a t i n g the formality of s u b s t i t u t i o n , (3) Light = electromagnetic radiation as a biconditional c o r r e l a t i o n does not e f f e c t a reduction - i t does not get i d e n t i t y . Scriven continues that reduction might then be interpreted as r e d e f i n a b i l i t y within the context of a completed science rather than d e f i n a b i l i t y . But Scriven claims that there i s no coherent notion of a "complete d e s c r i p t i o n " (p. 127) except within a s t i p u l a t e d context. And even i f there were, i . e . a l l questions were answered, a l l concepts and t h e i r r e l a t i o n s being known, there would be no sense in defining away th e i r intensional (contextual) features. POSITION 8. Compl (T f ,T^) i f f ; ( i ) they have a common referent, ( i i ) they make d i f f e r e n t a l l e g a t i o n s , ( i i i ) they are s t i l l both needed to give a complete account of the phenomena. - 123 -I w i l l not be arguing that Complementarity i s correct and other i n t e r t h e o r e t i c r e l a t i o n s wrong. Just that complementarity deserves to be in the ring competing with other views. I argue that the best view of r e a l i t y we have ava i l a b l e i s that afforded by well-confirmed theories and that r e a l i t y should be conceived of as the generator of the projections which well confirmed theories describe. In section III I w i l l argue in de t a i l for physical and mathematical knowledge making d i f f e r e n t allegations and in section IV for both modalities of cognition being needed to give a maximal consistent theory of r e a l i t y . I think complementarity f a l l s best into the group with i d e n t i t y and reductionism as involving metaphysical monism - that d i f f e r e n t theories have a common referent. But the referent in complementarity i s an invariant superposition of states described by the well confirmed theories. It i s a n t i r e d u c t i o n i s t in the sense that i t does not use theoretical i d e n t i t y to argue for d e f i n a b i l i t y or t r a n s l a t a b i l i t y . It combines metaphysical monism with epistemological pluralism. Reductionism i s an a n t i r e f l e x i v e , antisymmetric, t r a n s i t i v e r e l a t i o n . But complementarity, while a n t i r e f l e x i v e , T £ not complementary to Jz since they make the same a l l e g a t i o n s , i s not antisymmetric. The asymmetry of reduction gives an inverted pyramid shape to unity of knowledge, with a narrow base supporting a wider top. Complementarity i s a symmetric r e l a t i o n in that i f T completes the account of T 2, Jz completes the account of T, . The unity of knowledge i s not modelled then by a long h i e r a r c h i c a l chain or inverted pyramid. But both reduction and complementarity form a network since they are t r a n s i t i v e , - 124 -j o i n i n g theories to theories, by reduction and complementarity respectively. Complementarity i s not however j u s t antiredutionism or emergence. Unity of knowledge would not consist in the simple conjunction of independent theories but would consist of t h e i r mutual i n t e r r e l a t i o n s h i p s , l i m i t s of a p p l i c a b i l i t y and i n t e r a c t i o n in providing a maximal consistent view of r e a l i t y . Reality, in making i t s e l f known, generates a plethora of intensional contexts and the p o s s i b i l i t y of d i f f e r e n t forms of knowledge of r e a l i t y . Complementarity, furthermore, i s d i s t i n c t from emergence. Let me use Hempel and Oppenheim's d e f i n i t i o n of emergence to explain; The occurrence of a c h a r a c t e r i s t i c W in an object w i s emergent r e l a t i v e to a theory T, a part r e l a t i o n Pt, and a class G of a t t r i b u t e s i f that occurrence cannot be deduced by means of T from a characterization of the Pt-parts of w with respect to a l l the a t t r i b u t e s in G. (Hempel and Oppenheim, 1967 p. 336) They go on to say by way of example that t h i s translates roughly to the view, for the mind body problem, that "no explanation, in terms of micro-structure theories, i s availabe at present for large classes of phenomena studied in biology and psychology" ( I b i d . , pp. 336-37). A theory would be emergent, I take i t , i f f . i t s concepts, c h a r a c t e r i s t i c s and laws are not deducible in the sense above. There i s i m p l i c i t in - 125 -emergence the notion of a foundational level and a supervenient l e v e l . The supervenient level abruptly and discontinuously jumps into existence from the foundational l e v e l . This i s i m p l i c i t in the Pt r e l a t i o n which locates the supervenient level as an discontiuous part of a larger unconditional whole, e.g. mind as a supervenient type of matter. But complementarity, in the case of mathematics and science, argues against the Pt r e l a t i o n . It mathematics a part of science? Is science a part of mathematics? Neither I argue; there i s a reciprocal complementary r e l a t i o n between the two. I shall elaborate l a t e r (pp. 127-142). * * * * * * * - 126 -With respect to the other spheres or zones, each sphere of r e a l i t y has a considerable degree of autonomy. This seems to be evident from the f a c t that the attempts to reduce any of the spheres of r e a l i t y to any of the others has given r i s e to no conclusive r e s u l t s . This may be said of the e f f o r t s of m a t e r i a l i s t s to reduce everything to physical r e a l i t y , but also of the alleged reduction of the t o t a l i t y of human experience to subjective r e a l i t y (psychical monism, phenomenology, Mach's positivism) or to l o g i c a l r e a l i t y (Plato, Hegel). E s p e c i a l l y s i g n i f i c a n t in t h i s respect are the negative r e s u l t s of s i m i l a r attempts within the l i m i t e d domain of cer t a i n s p e c i f i c sciences (Brouwer, Carnap, Mannoury). Also the assumption of a hierarchical order (Nicolas Hartmann), a common o r i g i n (doctrines of emanation), or a causal i n t e r a c t i o n (Descartes) of the various spheres of r e a l i t y seems to be hardly admissible from a s c i e n t i f i c point of view. For i t involves the appl i c a t i o n of ce r t a i n notions - l i k e the notions of value, o r i g i n , and cause - outside that sphere of r e a l i t y where t h e i r a p p l i c a t i o n i s legitimate. (Beth, 1959, pp. 644-645) \ - 127 -3 ) T h e C o m p l e m e n t a r i t y o f P h y s i c a l a n d M a t h e m a t i c a l K n o w l e d g e . . .  M a k i n g D i f f e r e n t A l l e g a t i o n s Under the metaphysical assumption that mathematics and science both refer to r e a l i t y I want to argue that ( i ) they make d i f f e r e n t allegations but ( i i ) are both needed to give a maximally complete account of r e a l i t y . F i r s t of a l l there i s a prima f a c i e case that they make d i f f e r e n t a l l e g a t i o n s . Physical knowledge i s about the material, spatio-temporal world governed by causal laws. But science aims at the reduction of knowledge to mathematical terms using measurement (E i n s t e i n , The Fundaments of Theoretical Physics). A case in point i s the geometrization of physics in which matter i s i d e n t i f i e d with certain 4 geometric features of the numerical R continuum (Friedman, 1983, Chpt. 7). Cassirer claims that the resolution of the natural object and a l l sensuous and i n t u i t i v e heterogeneity into pure mathematical r e l a t i o n s of measurements "constitutes the kernel of physical procedure, the fundamental cognitive function of physics" (Cassirer, 1923, pp. 446-488). I w i l l argue f o r mathematical knowledge and physical knowledge making d i f f e r e n t allegations with regard to f i v e considerations; ( i ) questions asked and form of judgment, ( i i ) methodology, ( i i i ) theory construction, (iv) content, (v) explanation. - 128 -( i ) Q u e s t i o n s a s k e d a n d f o r m o f j u d g m e n t There e x i s t between mathematics and science d i v e r s i t i e s in fundamental d i r e c t i o n of consideration to the extent that I submit that the r e s u l t s of consideration cannot be compared. There i s a whole system of symbolic forms, the application of which produces for us the concept of an ordered r e a l i t y . The view of mathematics and science I am o f f e r i n g i s of two d i f f e r e n t sorts of knowledge each of which retains meaning only with reference to the conditions under i t which obtains. Physical knowledge i s concerned with the content of the external material world and i t s causal structure. Empirical evidence i s relevant to i t s t r u t h . Although c e r t a i n thematic suppositions are necessary, science attempts to project questions onto a contigent plane with only phenomic and a n a l y t i c elements (Hoiton, 1973, Chpt. 1). This i s the e f f o r t to make nature measurable (Cassirer, 1923, p. 358). In the case of physical knowledge we form our ideas on the basis of something which i s observable. In mathematics we also form ideas on i n t u i t i v e elements but they are not sensations. It i s c l e a r that something besides sensations i s i n t u i t i v e l y present from the f a c t , f o r example, that we have an idea of objects. The i n t u i t i v e elements of mathematics are c l o s e l y related to "the abstract elements contained in our empirical ideas" (Godel, 1947, pp. 271-72). They need not be j u s t subjective e n t i t i e s , forms of cognition in a Kantian sense. Godel goes on to claim: Rather they, too, may represent an aspect of objective r e a l i t y , but, as opposed to the sensations, t h e i r presence in us may be due to another kind of r e l a t i o n s h i p between ourselves and r e a l i t y . (Godel, 1947, p. 272) - 129 -Mathematical knowledge and physical knowledge are often i n t e r r e l a t e d but they are d i s t i n c t . For example, c e r t a i n d i f f e r e n t i a l equations may be used to formulate a theory giving an instant by instant description to every p a r t i c l e in a system under the influence of gravity. But these equations would contain nothing that can be properly c a l l e d material causation, the transfer of information. Mathematical knowledge and physical knowledge operate at d i f f e r e n t , not necessarily h i e r a r c h i c a l , l e v e l s . Consider the following exmaples. (1) 2 ^ of water plus zX of ethyl alcohol does not, empirically speaking, give 4 X of solution but 2+2 s t i l l equals 4. (2) 2 photons added to 2 photons can give 0 photons but 2+2 = 4. (3) 2+2 = 1 (mod 3) but 2+2 = 4. (4) i f the v e l o c i t y of l i g h t i s 4 u/s and two observers are approaching each other at 2 u/s they measure t h e i r r e l a t i v e v e l o c i t i e s to be ~^ 4 ^ & but 2+2 = 4. V- $ ^ Examples l i k e those above suggest, I think that mathematics and science are on d i f f e r e n t tracks. We can always f i n d physical interpretations that reconcile the mathematical i n t u i t i o n with the physical f a c t s , e.g., Case (1) straightforward physical explanation - smaller molecules (H a0) f i t in the spaces between the larger ones (C_H_0H), - 130 -Case (2) energy-mass i n t e r c o n v e r t a b i l i t y , Case (3) meaning change, Case (4) addition not the correct d e s c r i p t i v e r e l a t i o n s h i p . ( i i ) M e t h o d o l o g y Science aims at knowledge of the world as i t i s materially constituted. Mathematics aims at consistent knowledge of the world ir r e s p e c t i v e of how i t i s materially constituted. Russell puts the point t h i s way; A world in which there were no such individ u a l s (as Socrates and Plato) would s t i l l be a world in which one and one are two). It i s not open to us, as pure mathematicians or l o g i c i a n s , to mention anything at a l l , because, i f we do so, we introduce something i r r e l e v a n t and not formal. (Russ e l l , 1919, p. 37) S c i e n t i f i c methodology invovles measurement, observation, speculation, v e r i f i c a t i o n . Mathematics i s independent of the sensual perception of the material world. The p o s i t i v i s t s tended to think that only s c i e n t i f i c method could r e s u l t in knowledge. But part of s c i e n t i f i c method rests on mathematical method - the p o s s i b i l i t y of quantifying nature and using mathematical theory to describe and predict the behaviour of nature. - 131 -Rather than science being the f i n a l c o r r e c t method for achieving results Feyerabend claims that i t i s j u s t one among many: Science has done many things, but so have other ideologies...Science i s j u s t one of the many ideologies that propel society and i t should be treated as such.... Ideologies are marvellous when used in the company of other ideologies. They become boring and d o c t r i n a i r e as soon as t h e i r merits lead to the removal of t h e i r opponents. (Feyerabend, 1958 pp. 162-163) Mathematics and science are not opponents but they do employ d i f f e r e n t methodologies to a r r i v e at an understanding of r e a l i t y . ( i i i ) T h e o r y c o n s t r u c t i o n . Gerald Hoi ton describes how s c i e n t i f i c theories can be viewed as vectors in a 3 dimensional space. The orthogonal bases of the space consists of thematic, phenomenic and a n a l y t i c - h e u r i s t i c vectors. In th i s view mathematics i s required for the construction of s c i e n t i f i c theory as are projecting thematic assumptions (covariance with r e l a t i v i t y , complementary in Q.M.). The ematic elements of theory function as metaprinciples needed to inte r p r e t the theory and project i t via a measurement function into the contingent phenomic-analytic plane). In th i s view mathamtics would be one component of physical theory. In the case of G.R. for example the tensor calculus i s needed to express laws in a coordinate free form, in the case of Q.M. operator calculus and H i l b e r t - 132 -space are needed to model the projection of the function (onto the eigenbasis) which give values of observables. It seems reasonable to hold that a developed physical theory has at l e a s t f i v e independent components; (1) a formalism, or deductive machinery, without an i n t e r p r e t a i t o n , a wave equation in Q.M. or a tensor equation in G.R. for example, (2) an intended i n t e r p r e t a i t o n of the above calculus which usually refers to unobservable theoretical e n t i t i e s , a theory of l i g h t as an inte r p r e t a t i o n of Maxwell's formalism for electrodynamics, (3) correspondence rules - which l i n k some, but not necessarily a l l , terms of either the formal calculus or i t s intended in t e r p r e t a t i o n to terms which designate observables. The rules in e f f e c t project the theory into Holton's contingent phenomic-analytic plane. The rules render propositions empirically testable through measurement, (4) experimental laws which are deductive consequences of; ( i ) the formal calculus and the correspondence rules taken together or, ( i i ) the intendended inte r p r e t a t i o n and the correspondence rules, and which are confirmed by observable instances. In the ideal gas theory for example Charle's law and Boyle's law are experimental laws, - 133 -(5) models which are d i f f e r e n t from the intended inter p r e t a t i o n and which use material analogy to e x h i b i t the structure and behaviour of features of the intended i n t e r p r e t a t i o n , e.g. small p e l l e t s as a model of atoms in the ideal gas theory or waves conceived of as o s c i l l a t i o n s of the p a r t i c l e s of a material ether as a model of 1ight. In t h i s view physical theory does not seem to be a source of mathematical theory but rather to presume i t . It might be argued that mathematical knowledge i s r e a l l y a l l there i s , that physical knowledge i s j u s t a variety of mathematical knowledge. John Graves claims that the c r u c i a l conceptual innovation in G.R. i s the i n t e r p r e t a t i o n of magnitudes l i k e physical s t r e s s , that had previously been considered physical, in terms of magnitudes l i k e space-time curvature that are geometrical (Graves, 1971, p. 147). In p a r t i c u l a r the tensors used to express the fundamental physical laws must be derived from, or equated to, tensors which have a purely geometric s i g n i f i c a n c e . This i s the philosophical import of the f i e l d law: This would in e f f e c t achieve the geometrization of physics. Geometrodynamics, GMD, as an i n t e r p r e t a t i o n of GR o f f e r s a monism in which there i s no i r r e d u c i b l e e n t i t y of any other kind. There i s j u s t a single thing, Riemanian space-time. In i t s metrical and topological richness i t can account for everything e l s e . Graves says the following have been reduced to the monistic l e v e l ; ( i ) g r a v i t a t i o n , ( i i ) - 134 -electromagnet!sm, ( i i i ) charge, (iv) measuring rods and clocks, (v) physical constants, (vi) equations of motion, ( v i i ) mass, ( v i i i ) , transmutations; (ix) f i e l d equations, (x) boundary conditions and i f a quantum GMD can be developed (xi) elementary p a r t i c l e s and ( x i i ) observers (Graves, 1971). G.M.D. i s a thoroughgoing monism in which a l l a t t r i b u t e s are e s s e n t i a l l y geometrical and capable of in t e r a c t i n g with one another. This i s d i f f e r e n t from Spinoza's monism in which r a d i c a l l y d i f f e r e n t a t t r i b u t e s can e x i s t in p a r a l l e l but never i n t e r a c t with each other (e.g. God and nature). It also d i f f e r s from a Hegelian monism in that i t does not contain any f i n a l mysterious state, the absolute, which harmonizes a l l contradictions of previous stages in a new synthesis. It introduces no new conceptual features into the completed t o t a l i t y . It r e a l i z e s the determinstic goal of the whole structure being predictable, in a law l i k e fashion, from information at a single instant. But G.M.D. i s j u s t one in t e r p r e t a t i o n of G.R. and the i d e n t i t y of the T^MV with the T ^ . y can be interpreted in ways other than geometrical monism. These include; ( i ) physical monism: the T V L y are real and the are j u s t loose ways of speaking. I think Einstein once held t h i s view, he said: Space-time does not claim existence on i t s own, but only as a structural quality of the f i e l d . I t requires the idea of the f i e l d as the representative of r e a l i t y in combiantion with the general p r i n c i p l e of r e l a t i v i t y to show the true sense of Descartes' idea that there exists no space empty of f i e l d . ( E i n s t e i n , 1954, p. 365) - 135 -( i i ) materio-geometric p a r a l l e l i s m : geometry and physical stress simply coexist in harmony with no further explanation possible, ( i i i ) coordination r e l a t i o n : the basic g r a v i t a t i o n a l f i e l d law i s not in f a c t a statement in the theory but a correspondence rule specifying how to translate one l e v e l , the macroscopic phenomenal physical properties of matter back and forth into another l e v e l , the curvature of space-time. I t could become a geometric re d u c t i o n i s t position i f the geometry i s considered a micro reducing theory. (iv) materio-geometric interactionism: space-time and physical stress mutually i n t e r a c t in a causal way. Wheeler has made a remark that seems suggestive of t h i s position to the e f f e c t that space-time t e l l s matter how to move and matter t e l l s space-time how to curve, (v) m a t e r i a l i s t i c epiphenomenalism: space-time i s an epiphenomenon of matter, (vi) geometric epiphenomenalism: matter i s an epiphenomenon of space-time, (vi) hidden variable view: matter and space-time are not fundamental notions but spin o f f s from a basic l e v e l , as yet unspecified. - 136 -Positions one and three occupied E i n s t i n ' s attention at d i f f e r e n t times. Position two i s a view common to p r a c t i s i n g p h y s i c i s t s (Graves, 1971, pp. 182-184). But the nature of the ? T**v " i d e n t i t y " remains an ontological and epistemological puzzle. I hold that there i s no compelling reason to think that mathematical and physical knowledge make the same assertions in view of the f a c t that: (a) there i s a prima f a c i e difference and (b) there i s no compelling argument defending a s i m i l a r i t y behind the scenes. iv ) C o n t e n t . Donald Hi 11 man in On Grammars and Category-Mistakes argues that; (a) i t makes sense to talk of the systematic c l a s s i f i c a t i o n of the d i f f e r e n t grammatical forms of language, (b) that the germ of the category-mistake idea i s that c e r t a i n expressions for proposition-factors (names) can be improperly coupled, (c) Chomsky's system in Syntactic Structures can be used to generate a number of d i f f e r e n t l e v e l s of sentences. Category difference between expressions for proposition factors A are B i s then described as A completing a sentential environment E giving a sentence at level a in the grammatical scale but B completing E to give a sentence at level b, a = b. Let A = "helium atom" and B = "2". Consider the sentenential -35" environment "the mass of a i s greater than 10 kg." Substituting "helium atom" gives a meaning s c i e n t i f i c utterance. Substituting "2" gives an utterance that i s prima f a c i e , and in Chomsky's system, n o n s c i e n t i f i c . The utterance i s deviant in the sense that i t deviates in some way from the standard ways in which sentences containing the symbol "2" are used. That i s to say mathematical sentences and - 137 -s c i e n t i f i c sentences exist on different grammetical levels and make different assertions. ( v ) Explanation in mathematics and science are different. To explain why 8 is an even number is a different type of task than explaining why sodium usually emits yellow light when appropriately ele c t r i c a l l y stimulated. Wesley Salmon has summarized three general conceptions of sci e n t i f i c explanation; epistemic, modal and ontic, each with two subtypes, deterministic and indeterministic. Each offers a type of explanation within the context of determinism and indeterminism. Subtype Explanatory Type Determinism Indetermini sm Epi stemic possible in principle to give deductive explanation explanandum logically necessary relative to explanans explinandum high prob ab i l i t y relative to explanans Modal certain events had to happen given others nomological necessity statis t i c a l explana-tion Ontic explain by show how events f i t into patterns found in the world f i t into patterns structured by fixed causal laws f i t into patterns structured by prob-a b i l i s t i c causal relations Table I. Three general conceptions of scie n t i f i c explanations. - 138 -Mathematical propositions do not make causal assertions. They depend on formal (immaterial) r e l a t i o n s between mathematical objects. Whereas in science i t makes sense to understand c a u s a l i t y as providing "the channels of communication by which the physical world transmits information about i t s own structure" (Salmon, 1982, p. 178), i t makes no such sense in mathematics, although of course mathematics can be used as an aid in e x p l i c a t i n g causal s c i e n t i f i c theories. Salmon puts s c i e n t i f i c explanation in the ontic group. Although not intended to include mathematical explanation Salmon's scheme would probably put mathematical explanation in the epistemic group. For although Godel has shown, in the incompleteness of arithemtic, that we don't want to confuse d e r i v a b i l i t y and t r u t h , an explanation of a mathematical truth depends on deductively r e l a t i n g i t to other accepted mathematical truths. Mathematical objects do not e x i s t in time so do not evolve.. H i s t o r i c a l explanation i s i r r e l e v a n t in mathematics whereas i t i s essential in science. I see differences in ( i ) questions asked and form of judgment; ( i i ) methodology; ( i i i ) theory construction; (iv) content; (v) explanation. I see not so much contradiction as d i f f e r e n t modalities of cognition, which apply in d i f f e r e n t conditions. They make c a t e g o r i c a l l y d i f f e r e n t a l l e g a t i o n s but the concept of projection can be used to explain the sense in which they are both needed to give a complete account of r e a l i t y . - 139 -. . . i t must of course be conceded that the d i f f e r e n t spheres of r e a l i t y are not e n t i r e l y disconnected; the circumstance that human knowledge penetrates various zones of r e a l i t y i s in i t s e l f conclusive evidence of t h i s . Moreover we are aware of a c e r t a i n p a r a l l e l i s m , i f only p a r t i a l and approximate, between d i f f e r e n t aspects of r e a l i t y , which has even given r i s e to the e f f o r t s . . . t o reduce the various spheres to each other.... (Beth, 1959, p. 645) - 140 -4 ) T h e C o m p l e m e n t a r i t y o f P h y s i c a l a n d M a t h e m a t i c a l K n o w l e d g e . . .  b o t h r e q u i r e d t o g i v e a m a x i m a l c o m p l e t e a c c o u n t o f r e a l i t y Hesse's and Hoi ton's analyses of s c i e n t i f i c theories both suggest that they have separate cognitive components, including what could be c a l l e d subjective (phenomenal), l o g i c a l (mathematical) and material (embodied in the intended inter p r e t a t i o n and perhaps the model). Attempts to eliminate these have f a i l e d . I include here; (1) Mach's attempt to do j u s t with organized sensation, (2) Carnap's attempt to reduce s c i e n t i f i c statements to a protocol language concerning phenomena (Carnap, 1928), (3) Carnaps attempt at physical ism (Carnap, 1938). A l l three types of knowledge are needed but each serves a function the others cannot. The subjective provides a more immediate manifest image of the world. While i t may be l o g i c a l l y unstable, containing i m p l i c i t inconsistencies and be l i m i t e d in explanatory and predictive powers, i t connects the world to the knower i n a minimally i n f e r e n t i a l way. So even i f a Minkowski l i k e description of the world were possible, such a world view would be neither understood or useful unless connected to the experience of a sentient sapient being. The material view provides i n t e r s u b j e c t i v e l y confirmable knowledge of the world. Physical knowledge i s invariant with respect to transformations - 141 -of the observation base and as such i s more l o g i c a l l y stable. Because i t i s a l l i e d with mathematics i t i s p r e d i c t i v e l y and explanatorily powerful. Logic and mathematics provide the formal components of theory but s t i l l should not be viewed as subjective in the Kantian sense. Rather formally and materially motivated elements in theories should be viewed respectively as elements introduced ( i ) to give form ( s i m p l i c i t y etc.) and ( i i ) account for the f a c t s . But material elements are found in mathematical theories. A material motivation i s found in mathematics in so far as mathematical terms and p r i n c i p l e s refer to very general c h a r a c t e r i s t i c s of r e a l i t y . This i s what makes them so u s e f u l . How to see the material element? Consider the syntactical connections in a formal mathematical system. It cannot be denied that a numerical connection i s a matter of f a c t . But when an expression U can be derived within a formal system S, then on account of the arithmetization of syntax, the d e r i v a b i l i t y constitutes a c e r t a i n numerical connection. The same interdependence shows i t s e l f with regard to propositional implication P => Q. Formally a truth table summary of the conditions under which P 3 Q i s true and f a l s e i s enough. But i t leaves out a material sense of implication that would consider odd a l o g i c a l l y true proposition such as - (2+2 = 5) >^ (I am hungry r i g h t now). This issue i s a r e f l e c t i o n of the need for both formal and material elements of theory. Logic also has a subjective component. One of the implications of the Lowenheim Skolem theorem i s that "pure l o g i c " i s impossible. F i r s t order theories always have denumerable models, even theories of - 142 -the real numbers. The only way to solve t h i s i s to appeal to i n t u i t i o n s about the meaning of c e r t a i n of the formal primitive terms, to rule out nonstandard i n t e r p r e t a t i o n s . The view I am defending advocates not s e l e c t i n g , from among the d i f f e r e n t sorts of knowledge, one to act as a foundation. Rather the philosophical task at hand consists in defining each sort with reference to the others in utmost distinctness and c l a r i t y . So f o r example with regard to the concept of r e a l i t y (which i s the true r e a l i t y the subjective, the physical, the mathematical?), I advocate the reply that in the complex we c a l l "world" they a l l enter as equal, unavoidable forms of knowledge. The f u l l import of the forms of knowledge resides in the r e a l i z a t i o n that what r e a l i t y t r u l y i s , in the comprehensive philosophical sense, can be approached only i f we can succeed in capturing the nuances of various meanings under a formal law which they obey. Complementarity i s an attempt at setting out such a formal condition. - 143 -Eventually, the phenomena and factors j u s t have to be placed alongside each other in a pattern. Lawlike explanations and micro-reductions provide a u n i f i e d patterning, but other modes of u n i f i e d patterning also provide understanding. These other modes go alongside laws and reductions to form a s a l i e n t pattern together, one of s a l i e n t patterning and unifying • • • Yet a f t e r everything has been seen from each dimension's perspective, we s t i l l w i l l want a l l these pictures to be woven together into one u n i f i e d patterning. If monism of ultimates does not obtain, then i t i s such a patterning of the d i f f e r e n t ultimates that w i l l provide overall i n t e l l i g i b i l i t y . By i t s placement of each in r e l a t i o n to the others, the patterning w i l l straddle the d i f f e r e n t dimensions, unifying them by simultaneously showing the meaning of each, and the value (organic unity) of the whole in the larg e s t overall patterning and so the widest explanatory p i c t u r e . * (Nozick, 1980, p. 641) Complementarity (author) - 144 -5 ) T h e S e m a n t i c F u n c t o r s I n f ( T , R ) , P r o j ( T B t ) It may seem oversimplified to claim that there are six kinds of knowledge. Epistemological pluralism can be formulated in a more sophisticated way using two semantic functors; (1) Inf(T,C), the amount of information a theory T gives about an e n t i t y C. If C = R we formulate Inf(T,R); (2) Proj(T,B^), the amount of information a theory T has of type D\- . Then consider the mapping k:R-*-K from r e a l i t y to the information space we c a l l knowledge, k i s into but not onto K. I hold t h i s because I believe there may be overlapping of theories due to the intentional contextual) features of knowledge. I am claiming K i s six dimensional and that our concept of r e a l i t y i s a superposition of vectors in the six dimensional space. The space has an orthogonal basis consisting of 6\ = -[physical, s o c i a l , l o g i c a l , e t h i c a l , subjective and aesthetic forms of knowledge^. Any actual T « K has components given by Proj(T, physical r e a l i t y ) , Proj(T, social r e a l i t y ) , ....Proj(T, aesthetic r e a l i t y ) . - 145 -- 146 -In d i s t i n c t i o n from complementarity, reduction would hold that K i s 1 dimensional - that a l l theories have only one form and type of content. Antireductionism, while admitting K may be more than one dimensional seems to me to involve the view that the Je K are one form or the other. They l i e on the axes of the basis vectors only. Complementary pluralism allows them to e x i s t anywhere in the space and to have components in a l l bases. Complementary pluralism furthermore provides an explanation, using the model, of the evolution of theories, they move in the six dimensional space, in accordance with the evolution of our conceptual schemes. In d i s t i n c t i o n from positivism and pragmatism complementary pluralism holds that theories r e f e r to r e a l i t y (via k ' ). How i s r e a l i t y to be conceived? Reality i s to be understood by - i using k = Inf(T,R). R i s the referent of the Superposition of the T - for a l l well confirmed T^ . R = k ' [Sup T^ ]. There i s one r e a l i t y but d i f f e r e n t forms of knowledge of i t . That i s to say a theory of r e a l i t y in general derives from a six dimensional information space. Any view of an aspect of r e a l i t y may be clo s e r to one axis than any others but usually a l l six components w i l l be present. Although Feigl rejects complementarity he has made a remark that i s close to my pos i t i o n , as j u s t outlined; There are not two d i f f e r e n t sorts of r e a l i t y , but there are two ways of providing a conceptual frame for i t s d e s c r i p t i o n . In f a c t , at l e a s t so i t seems to me, there are a great many "perspectives" or frames - the extremes being the purely egocentric as the "lower l i m i t " and the completely physical account as the "upper l i m i t . " In between are the many halfway (or part-way) houses of the possible manifest images. It i s good exercise for an a l y t i c philosophers to make e x p l i c i t , in special reconstructions, the conceptual frame of each of these perpsectives. ( F e i g l , 1968, p. 138) - 147 -I don't think there i s anything lower about the egocentric or subjective as I term i t , or anything "higher" about the p h y s i c a l . Rather I agree with Cassirer that the philosophical task here i s not to level or rank these forms of knowledge but to leave them standing as such. Our conception of r e a l i t y w i l l emerge from the comprehensive and exhaustive overlay of these complementary views j u s t l i k e an understanding of atomic physics requires wavelike and p a r t i c l e l i k e models. There i s unity of knowledge in the sense that the d i f f e r e n t forms, physical, s o c i a l , l o g i c a l , subjective, e t h i c a l , aesthetic are a l l required to span the information space as i t presently e x i s t s and so are a l l required to generate our warranted conception of r e a l i t y . I would hold to the view that of course the choice of basis vectors here i s ultimately a r b i t r a r y . The d i v i s i o n of knowledge up into physical, s o c i a l , l o g i c a l , subjective, e t h i c a l and aesthetic i s an important feature of human knowledge. But the knowledge could, in p r i n c i p l e , be divided up other ways. Better s t i l l i t could be conceived of in "coordinate free form." Our conception of r e a l i t y would then be objective in the sense of free of an a r b i t r a r y choice of coordinates in which to represent i t . In t h i s sense the boundaries between the various domains of knowledge may be considered metaphysically a r b i t r a r y although epistemologically necessary. - 148 -It would not become physical science to see in i t s s e l f created, changeable, economical t o o l s , molecules and atoms, r e a l i t i e s behind phenomena - the atom must remain a tool for representing phenomena, l i k e functions of mathematics ... ( I t i s wrong to impute to science) the power of opening unfathomable abysses of nature, to which the senses cannot penetrate. (Mach, in Hoi ton, 1973, p. 227) If the p h y s i c i s t wishes to further his science, he must be a R e a l i s t not an Economist ( i n the sense of Mach's princple of economy); that i s , i n the flux of appearance he must above a l l search for and unveil that which p e r s i s t s , i s not transient, and i s independent of human senses. (Planck, 251) in Hoi ton, 1973, p. - 149 -C h a p t e r V C O M P L E M E N T A R I T Y A N D T H E P O S S I B I L I T Y O F A R E A L I S T I C I N T E R P R E T A T I O N O F S C I E N T I F I C K N O W L E D G E 1 ) I n t r o d u c t i o n I w i l l argue in t h i s essay that the best reason to accept s c i e n t i f i c realism as an adequate philosophy of science i s that s c i e n t i f i c realism can given an adequate account of diverse aspects of s c i e n t i f i c theory, as a good metatheory should, whereas i t r i v a l s cannot. F i r s t I w i l l formulate a minimal s c i e n t i f i c realism in terms of f i v e basic b e l i e f s . Second I w i l l c l a r i f y s c i e n t i f i c realsim with regard to i ) i t s v a r i a t i o n s ; i n t e r n a l - e x t e r n a l , general-particular, t h e o r i e s - e n t i t i e s , i i ) i t s r e l a t i o n to i t s r i v a l s and i i i ) i t s antiskeptical-prometaphysical bent. I w i l l be defending a f u l l blown general external s c i e n t i f i c realism of theories and e n t i t i e s . I then discuss nine possible reasons fo r accepting s c i e n t i f i c realism as an adequate philosophy of science. I conclude by discussing some possible objections that might be l e v e l l e d at s c i e n t i f i c realism. 2 ) F o r m u l a t i o n S c i e n t i f i c realism, as a f i r s t approximation, embodies the two views that i ) at l e a s t some terms of well confirmed s c i e n t i f i c theories refer to independently e x i s t i n g e n t i t l e s and i i ) propositions of well - 150 -confirmed theories are ei t h e r true or f a l s e in vir t u e of t h e i r reference to cert a i n states of a f f a i r s in the world. A minimal s c i e n t i f i c realism seems to me to involve holding to the following f i v e basic b e l i e f s (adapted from Graves, 1971, pp. 1-4). i) external world...that there e x i s t s an external world independent of the human perception of i t . In Einstein's words: The b e l i e f in an external world independent of the perceiving subject i s the basis of a l l natural science. ( E i n s t e i n , in Hoi ton, p. 241) i i ) canonical b e l i e f . . . t h e external world may have e n t i t i e s or properites r a d i c a l l y d i f f e r e n t and remote from those held to e x i s t in canonical b e l i e f systems such as i n t u i t i o n , " d i r e c t perception" or common sense, i i i ) access...although there i s a gulf created by modal transformations i t i s s t i l l possible to obtain p a r t i a l , probable knowledge of external r e a l i t y . This may invovle metaphysical speculation as a necessary part, iv) sensation...sense perception may be considered to r e l i a b l y report on external r e a l i t y at l e a s t in some nonproblematic situations ( i . e . there are observables) and, - 151 -v) theoretical e n t i t i e s . . . t h e r e i s some c o r r e l a t i o n between terms, laws and theories on the one hand and e n t i t i e s , r e g u l a r i t i e s and patterns on the other. 3 ) C l a r i f i c a t i o n I wish to c l a r i f y here a number of points concerning s c i e n t i f i c realism. I w i l l be ta l k i n g about a s c i e n t i f i c realism as a philosophy of the physical sciences. Other forms of realism may invovle d i f f e r e n t issues and arguments ( i . e . social realism, e t h i c a l realism, aesthetic realism, phenomenological realism, mathematical realism, l o g i c a l realism). I hold to external realism, not to Putnam's internal realism, which seems to me a realism in name only. This paper concerns general realism about the truth of theories and the reference of theoretical terms. P a r t i c u l a r disputes about the r e a l i t y of t h i s or that e n t i t y within the established empirical parameters of some d i s c i p l i n e are not at issue here. I speak for a f u l l realism of theories and e n t i t i e s , t h i s for two reasons. F i r s t I hold that at l e a s t some terms of theories r e f e r to independently e x i s t i n g e n t i t i e s , in agreement with Hacking and Cartwright for example. But I also agree with Friedman, contrary to Hacking and Cartwright, that theories are about the structure of r e a l i t y and as such are true or f a l s e in v i r t u e of the account they give of c e r t a i n objective states of a f f a i r s in the world. I am arguing for the acceptance of a general, external, comprehensive, metaphysical s c i e n t i f i c realism. - 152 -S c i e n t i f i c realism i s concerned b a s i c a l l y with what theory gives us warrant to believe e x i s t s . Because theory changes and because experience underdetermines theory there may be a number of empirically adequate theories available at any one time. S c i e n t i f i c realism must address the question of which represents r e a l i t y . Idealism would say that only human ideas e x i s t , that there i s no external r e a l i t y . John Wheeler and others have remarked how Q.M. suggests that the "world" may not be j u s t s i t t i n g out there. Positivism usually resorts to phenomenalism. Terms, laws and theories are j u s t " s e l f created, changeable, economical tools." Pragmatism in t e r p r e t s the issue of the real in terms of long term assent of the community and use in p r a c t i c a l intervention in the world. Hacking remarks; My own view, that realism i s more a matter of intervention in the world than of representing i t in words and thought, surely owes much to Dewey. (Hacking, 1983, p. 62) Realism d i f f e r s from i t s r i v a l s in being antiskeptism and prometaphysics. Its r i v a l s want to l i m i t the range of knowledge to what each thinks can be " d i r e c t l y known" or reduced to such, e.g. ideas, sensations, community agreements. Realism i s w i l l i n g to concede that the real outer world i s not d i r e c t l y knowable (what is?) but that there i s s t i l l an objective r e a l i t y , of which knowledge i s possible. Metaphysics w i l l even play an essential role in the s c i e n t i f i c enterprise of understanding the external world. We need a f u l l y stocked arsenal of - 153 -i n t e l l e c t u a l weapons to launch an attack on r e a l i t y i f we are to comprehend i t . Let me give here three quotes to back up my contention that r e a l i s t s do not shy away from metaphysics because of any overriding sense of skepticism; i ) ...we need a nonobservational source for i n t e r p r e t a t i o n s . Such a source i s provided by (metaphysical) speculation which i s thus shown to play an important r o l e within realism. (Feyerabend, 1958, p. 169) i i ) ...a science i s never in a position completely and exhaustively to solve the problem i t has to face. We must accept t h i s as a hard and f a s t , i r r e f u t a b l e f a c t , and t h i s f a c t cannot be removed by a theory which r e s t r i c t s the scope of science from the s t a r t . Therefore, we see the task of science a r i s i n g before us as an incessant struggle toward a goal which w i l l never be reached, because by i t s very nature i t i s unreachable. It i s of a metaphysical character, and, as such, i s always again and again beyond our achievement. (M. Planck, in Holton, 1973, p. 244) i i i ) Physics i s the attempt at the conceptual construction of a model of the real world and of i t s lawful structure. To be sure i t (physics) must present exactly the empirical r e l a t i o n s between those sense experiences to which we are open; but only in t h i s way i s i t chained to them.... In short, I suffer under the (unsharp) separation of Reality of Experience and Reality of Being.... You w i l l be astonished about the "metaphysicist" E i n s t e i n . But every four and two-legged animal i s de facto in t h i s sense metaphysicists. (A. E i n s t e i n , in Holton, 1973, p. 243) - 154 -4 ) A r g u m e n t s f o r S c i e n t i f i c R e a l i s m A R G . l . T h e o r e t i c a l A d e q u a c y A r g u m e n t With regard to positivism Feyerabend points out that; i) thought and sensation cannot be distinguished since thought i s j u s t economically organized sensation and i i ) subjectivism wins out over o b j e c t i v i t y since a l l e n t i t i e s and r e l a t i o n s are conceived of r e l a t i v e to an observer. A r e a l i s t i c account of theory would involve f i v e r e l a t i v e l y independent parts; the formalism, the intended i n t e r p r e t a t i o n , correspondence rules between theoretical e n t i t i e s and observables, measureable or observable r e g u l a r i t i e s and models. Parts 1 and 2 are observer independent. Realism i s superior to positivism i n that; a) there i s a boundary between the objective and the subjective state - we may, i t i s granted, be on occasion mistaken about where the l i n e i s drawn, b) reports on sensation are not i n c o r r i g i b l e , c) no dogmatic theory i s implied by the " f a c t s , " rather speculations are rendered testable in science, d) argumentation extends to a l l f i v e metatheoretical areas. These considerations do not s e t t l e the issue between positivism and realism but do suggest to me that realism i s better able to account for what goes - 155 -on in a s c i e n t i f i c theory than i s positivism (based on Feyerabend, 1958, pp. 160-170). A R G . 2 . M a t t e r o f I n t e r v e n t i o n A r g u m e n t Hacking contends that the question of what there i s can be s e t t l e d only with reference to how we act, not to how we t a l k . This i s not d i s s i m i l a r to Feyerabend's remark that the choice between positivism and realism " i s a p r a c t i c a l act which cannot follow from any theoretical consideration, although i t may be motivated by theoretical considerations" (Feyerabend, 1958, p. 170). Hacking claims that the act of experimentation, to which science i s committed as a methological t o o l , requires that we count as real whatever we use to intervene in and change the world. Hacking summarizes; Now how does on a l t e r the charge on the niobium b a l l ? Well, at that stage, said my f r i e n d , " we spray i t with positrons to increase the charge or with electrons to decrease the charge." From that day forth I've been a s c i e n t i f i c r e a l i s t . So f a r as I'm concerned, i f you can spray them then they're r e a l . (Hacking, 1983, p. 23) A R G . 3 . T a i l - D o g A r g u m e n t . The object of a philosophy of science i s to o f f e r a p l a u s i b l e account of s c i e n t i f i c theory not to redefine i t . If i t f a i l s to capture - 156 -c r i t i c a l features of science i t i s an inadequate metatheory. I agree with Graves when he states; Most philosophers of science have considered themselves e m p i r i c i s t s , often rather se l f - c o n s c i o u s l y . My recommendation, then, i s that they practise in philosophy what they preach to science. As I see i t , the task of the philosophy of science should be t h i s : to study actual s c i e n t i f i c theories to see both how and why they have evolved and how they are presently understood by t h e i r users. (Graves, 1971, p. 4) Central to science i s the concept of nature, the independently e x i s t i n g external world ( E i n s t e i n , p. 1). Positivism and idealism t r i v i l i z e the concept of nature. D'Espagnat argues in his The Quantum Theory and Reality that a refusal to seek underlying causes of observed r e g u l a r i t i e s t r i v i a l i z e s the s c i e n t i f i c enterprise and the concept of nature which i t attempts to c l a r i f y and develop. He states; One can imagine a physics grounded on p o s i t i v i s t i c p r i n c i p l e s that would predi c t a l l possible c o r r e l a t i o n s of events and s t i l l leave the world t o t a l l y incomprehensible. (d'Espagnat, 1979, p. 177) Positivism and idealism f a i l to capture the intent of science and in fa c t try to redefine i t . This i s the t a i l (philosophy) wagging the dog (science). - 157 -A R G . 4 . N o v e l P r e d i c t i o n A r g u m e n t It i s possible to argue that i f a theory makes an unexpected novel prediction which i s accurate then the terms in the theory must refer to an actual real e n t i t y . This view has some i n i t i a l i n t u i t i v e appeal. But i t has been shown to be not generally true. The c a l o r i c was used by Laplace to predict the speed of sound but the c a l o r i c was l a t e r abandoned as a p h y s i c a l l y vacuous concept (Hacking, 1983, p. 86). A R G . 5 . C o s m i c A c c i d e n t A r g u m e n t If some theoretical e n t i t y (e.g. Avogadro's number) can be calculated some twenty d i f f e r e n t ways and they a l l agree i t would have to be some extraordinary accident unless they a l l were in f a c t measurements of some real physical e n t i t y . There i s very good reason to look for a most probable common cause of the repeated experimental "coincidences." A R G . 6 . Q u a l i t y - M o d a l i t y I n v a r i a n c e A r g u m e n t S c i e n t i f i c theory i s formulated in invariant terms. Concepts are given an i n t e r s u b j e c t i v e , measurable form so that "the same" e n t i t y i s i d e n t i f i e d i r r e s p e c t i v e of the observational base (e.g. temperature and mass). Realism has a natural account to o f f e r for t h i s quality-modality invariance, namely reference to an objective external r e a l i t y . For idealism and positivism i t i s j u s t an odd feature of physical theory. See H. F e i g l , the p o s t s c r i p t to The Mental and the Physical. - 158 -A R G . 7 . C o v a r i a n t L a w - I n v a r i a n t Q u a n t i t y A r g u m e n t Mature theories (e.g. N.M., S.R., G.R., Q.M.) can a l l be formulated so that the laws are covariant ( i . e . the law i s i n v a r i a n t with respect to any of a group of admissible transformations of the reference frame). Each theory also has invariant quantities (e.g. interval in S.R., spin in Q.M.) which have the same value when measured in any of an admissible set of reference frames. Realism would a t t r i b u t e invariance and covariance to an objective r e a l i t y . Positivism, idealism and pragmatism have no c l e a r account to o f f e r here. A R G . 8 . C o m m o n S e n s e A r g u m e n t We know what i s real because we can see i t or at l e a s t i t causally influences the observable. So, for example, atoms are real because they have a causal influence on chairs which are real because we can see them. I am more i n c l i n e d to think that r e a l i t y i s something we grow into so that conciliance with common sense i s of marginal value in these philosophical issues. A r g . 9 . C o n f i r m a t i o n - U n i t y A r g u m e n t Michael Friedman argues in his Foundations of Space-Time Theories that only realism can account f o r confirmation in science and for the unity of science. With regard to e n t i t i e s he claims that the practise of taking the confirmation of e n t i t i e s in one theory as confirmation f o r "the same" - 159 -type of e n t i t y in other theories can be j u s t i f i e d only by using a r e a l i s t i c philosophy of science. For example confirmation of one theory involving atoms i s confirmation for atoms as postulated e n t i t i e s in other theories. Only the r e a l i s t can appeal to the referents of unifying theoretical entites in explaining the practise of conjoining independently supported theories and using subsequent observational results to give repeated boosts of confirmation to a l l the subtheories (see Friedman, 1983, pp. 236-250). This reverts back to the t a i l - d o g argument i n the end, I think. If science accepts t h i s process of confirmation i s philosphy to be the t a i l that wags the dog? I would hold not. With regard to theories Friedmen argues that conventionalism i s i n c o r r e c t . Take the case of covariantly formulated N.M. and G.R. as theories of gravity. Friedman argues that G.R. i s better than N.M. even i f they are both empirically adequate in that there are metatheoretic c r i t e r i a that would require the selection of G.R. as the correct theory. G.R. i s better than N.M. because; i ) i t s r e a l i s t i c treatment of space-time allows for repeated boosts of confirmation to subtheories, i i ) i t gives determinate content to a l l the laws of motion ( i . e . i t i s parsimonious), i i i ) i t has the theoretical structure to unify space-time theories (e.g. a determinate and objective spatio-temporal geometry (Friedman, 1983, Chapter 7). Theories r e f e r to objective r e a l i t y in a - 160 -manner analogous to that in which theoretical terms so r e f e r . Friedman argues for a f u l l theory-entity realism (Friedman, p. 63). Of the arguments above I f i n d 1, 2, 3, 6, 7, 9 persuasive. I would prefer to answer the question "what i s the best reason to accept s c i e n t i f i c realism as an adequate philosophy of science?" not by picking any of the above as the best but by o f f e r i n g what they have in common as the best reason to accept s c i e n t i f i c realism. S c i e n t i f i c realism can of f e r an account of so many features of s c i e n t i f i c theory where i t s r i v a l s have nothing persuasive to say. S c i e n t i f i c theory points inexorably outward to an objective external r e a l i t y . Realism accepts, preserves and explains t h i s feature, as an acceptable metatheory should. Positivism, idealism, and pragmatism d e f l e c t , r e i n t e r p r e t or ignore t h i s feature, which an acceptable metatheory must not. 5 ) P o s s i b l e O b j e c t i o n s O B J . l . C r a i g ' s T h e o r e m O b j e c t i o n Craig's theorem, i t might be argued, showed that a l l theoretical e n t i t i e s in a formalized theory can be defined in terms of observables. But the elimination i s vacuous since; i ) an i n f i n i t e number of axioms i s required and i i ) these axioms are j u s t reformulations of a l l the true observation statements entailed by the theory. Theoretical terms have - 161 -surplus meaning beyond present observation. This i s needed, among other things, to give room for conceptual growth and f o r u n i f i c a t i o n . O B J . 2 . C o r r e s p o n d e n c e T h e o r y o f T r u t h O b j e c t i o n This i s a straw man. S c i e n t i f i c realism i s not stuck with a correspondence theory of tr u t h , whereby knowledge i s a copy of r e a l i t y . Terms refer to e n t i t i e s and theories to processes and patterns but neither of the former need be copies of the l a t t e r . O B J . 3 . Q . M . O b j e c t i o n s It might be claimed that Q.M. with i t s collapse of the wave function and essential indeterminacy brings the observer back into physics and Berkeleyan idealism back into science. But I think not. S.R. showed that there are both observer conditioned properties and invariants (length and interval r e s p e c t i v e l y ) . Q.M. i s the same in t h i s regard. Some properties of the electron, for example, are observer dependent, in the collapse of the wave function from the superposition state to an eigenvalue, but others are in v a r i a n t s . Max Born in his paper Physical  Reality argues f o r a r e a l i s t i c i n t e r p r e t a t i o n of Q.M. as follows; i ) ...some quantity which may be regarded as the property of a thing i s in f a c t only the property of a projection of the actual state, - 162 -i i ) ...the idea of invariant i s the clue to a rational concept of r e a l i t y , not only in physics but in every aspect of the world. i i i ) ...with regard to p a r t i c l e experiments a number of projections of the actual state may be required to approach maximum knowledge. But the f i n a l r e s u l t of complementary experiments i s a set of invar i a n t s , c h a r a c t e r i s t i c of the e n t i t y . The main invariants are c a l l e d charge, rest mass, spin etc. In every instance, when we are. able to determine these quantities we decide we have to do with a d e f i n i t e p a r t i c l e . I maintain that we are j u s t i f i e d in regarding these p a r t i c l e s as real in a sense not e s s e n t i a l l y d i f f e r e n t from the usual meaning of the word. iv) ...the feature which suggests r e a l i t y i s always some kind of invariance of a structure independent of the aspect, the projection. (paraphrased from Born, 1953, pp. 141-143) Abner Shimony argues in his paper Metaphysical Problems in the  Foundations of Q.M. that E.P.R. may motivate some sobering r e f l e c t i o n on the r e a l i s t i c p o s i t i o n , but that i t can s t i l l be maintained. In p a r t i c u l a r the v i o l a t i o n of the Bell Inequality would seem to c a l l up f o r scrutiny; i ) realism; i i ) induction; i i i ) s e p a r a b i l i t y (D'Espagnat, 1979, p. 158). D'Espagnat, f o r one, i s not w i l l i n g to give up on realism because, he says, t h i s would t r i v i l i z e the s c i e n t i f i c exploration of nature ( i b i d . , p. 177). Shimony states that E.P.R. i s compatible with realism i f we are w i l l i n g to accept that; - 163 -i) ...the i n t r i n s i c properties of the world are very strange indeed, or i i ) s c i e n t i f i c theories say much less about the i n t r i n s i c properties of things than s c i e n t i s t s have commonly assumed. (Shimony, 1982, p. 2) But realism as outlined in points i-v on pp. 170-171 i s pe r f e c t l y at home with these two po s i t i o n s , " i i " states that the i n t r i n s i c properties of the world may be highly noncanonical. Reality i s a concept that we must be prepared to grow i n t o , not specify by f i a t to s t a r t with. And S.R. has already prepared us f o r the r e a l i z a t i o n that many concepts of c l a s s i c a l physics were not i n t r i n s i c , e.g. mass, length, v e l o c i t y , simultaneity, duration e t c . Realism makes no claim about there being a large number of i n t r i n s i c properties. O B J . 4 . P o s i t i v i s t i c E l i m i n a t i o n O b j e c t i o n This i s also a straw man but merits reply none the l e s s . Friedman remarks how p o s i t i v i s t s l i k e Schlick argue that as the allowable transformations of the reference frame are increased in the pursuit of o b j e c t i v i t y the number of invariants decreases. In the l i m i t i n g case of G.R. there should be no external r e a l i t y l e f t . But Friedman counters that although good methodology in physics does in f a c t lead us to r e j e c t absolute space, absolute v e l o c i t y , absolute simultaneity, absolute - 164 -gravitational acceleration and so on the process of r e j e c t i o n does not continue i n d e f i n i t e l y . He answers; ...parsimony i s i t s e l f constrained by the process of the o r e t i c a l u n i f i c a t i o n e n t i t i e s - can be eliminated i f and only i f no loss of unifying power r e s u l t s . (Friedman, 1983, p. 336) The p r i n c i p l e of parsimony puts an upper l i m i t on the postualtion of theoretical e n t i t i e s - the need f o r theoretical u n i f i c a t i o n a lower l i m i t . O B J . 5 . S o W h a t i s t h e R e a l . . ? O b j e c t i o n What then i s the real chair then i t might be asked. Is i t ; i ) the array of p r o b a b i l i t y waves of Q.M., i i ) the c o l l e c t i o n of atoms or molecules, i i i ) wood f i b r e s , iv) the perceptual presentation to consciousness or what causes t h i s , v) the cause of Gaugin's impressionistic depiction of i t , vi) what I'm s i t t i n g on now? I hold to a monistic realism of things and a p l u r a l i s t i c realism of kinds of things. R e a l i t y , the world, i s the only t r u l y independently e x i s t i n g - 165 -e n t i t y in that i t alone i s i n c l u s i v e and complete with regard to explanation. But there are at l e a s t six i r r e d u c i b l y d i f f e r e n t kinds of knowledge or experience - the p h y s i c a l , s o c i a l , subjective, l o g i c a l , ethi c a l and aesthetic. The " r e a l " c h a i r i s a superposition of the complementary projections of i t . But t h i s i s highly noncanonical i t might be objected. Agreed but realism guarantees no match with i n t u i t i o n . Theoretical u n i f i c a t i o n , in the pursuit of a comprehensive theory of r e a l i t y , may commit us to highly n o n i n t u i t i v e , abstract conceptual structure - S.R. and G.R. two good cases in point. - 166 -S U M M A R Y I have argued in t h i s paper for the following: (1) Unity i s a fundamental consideration in the development, evolution and j u s t i f i c a t i o n of knowledge. (2) The p r i n c i p l e of complementarity i s employed in Q.M. to ( i ) resolve the problem of incompatible descriptions, and, ( i i ) provide an explanation for incompatible observables. (3) Complementarity i s a thematic p r i n c i p l e of wide application outside of physics. I have discussed examples of what I term ( i ) r e l a t i v i s t i c , ( i i ) c a t e g o r i c a l , ( i i i ) a r t i s t i c ( d e p i c t i v e ) , (iv) g e s t a l t and (v) projective complementarity. These would be examples in addition to physical complementarity mentioned in (2) above. (4) (a) Our best confirmed theories give us probable knowledge about r e a l i t y . (b) Knowledge consists of descriptions of projections of the actual state of a f f a i r s - r e a l i t y - on the observer. (c) It i s reasonable to think that we have an authentic, although i n d i r e c t and p r o b a b i l i s t i c , contact with at l e a s t four aspects of - 167 -reality, each of which may be considered complementary to the others. We reconstruct reality from i t s projections using a symbolic function. (d) Modest realism, modest foundational ism and the principle of complementarity can together provide an alternative to foundational ism and coherentism. This view involves: (i) knowledge consists of descriptions of projections of the actual state on the observer; ( i i ) probable statements; ( i i i ) prospective truth; (iv) complementary theories to span the information manifold and (v) relative rather than absolute evidence and truth. (5) (a) With regard to eight possible positions concerning combinations of metaphysical and epistemological monism and pluralism, a metaphysical monism together with an epistemological pluralism is a viable position which can be explicated using the principle of complementarity. (b)(i) Eight positions concerning metaphysical unity include a metaphysical version of complementarity. But this is not central to my position. ( i i ) Complementarity can be used to provide a model for unity of knowledge that is weaker than types of reductionism but stronger than an antireductionist concatenation of irreducible theoretical units. ( i i i ) The three conditions defining complementarity can be used as a basis for discussing eight possible theoretical - 168 -in t e r r e l a t i o n s h i p s , six of which are s i g n i f i c a n t . Complementarity can be seen to be d i s t i n c t from conventionalism, i d e n t i t y , reductionism, i r r e d u c i b i l i t y and emergence. (c) Mathematical and physical knowledge, for example, are complementary in that; ( i ) they have a common referent - r e a l i t y , ( i i ) they make d i f f e r e n t a l l e g a t i o n s , ( i i i ) they both express something true about r e a l i t y not expressible, for various reasons, in the framework of the other mode of de s c r i p t i o n . (d) The semantic functors Inf(T,R) and Proj(T,B£) can be used to explain how; (i ) reductionism and antireductionism are special cases of complementarity ( i i ) metaphysical monism i s compatible with epistemological pluralism. (6) There are good reasons to think that complementarity i s compatible with realism, at l e a s t concerning s c i e n t i f i c knowledge. What has c a l l i n g two descriptions, accounts or theories, T and T 2 , complementary, accomplished? I t has established three conditions r e l a t i n g the two theories; - 169 -( i ) they have a common referent but, ( i i ) they make d i f f e r e n t allegations and ( i i i ) each expresses something true about the referent not expressible, for various reasons, in terms of the other mode of d e s c r i p t i o n . Complementarity i s a n o n t r i v i a l r e l a t i o n . It does not apply to mistakes. If one person describes item X as " I t ' s a b i r d " and a second as "It's a plane" conditions ( i i i ) w i l l not be met since, in truth, X i s one or the other. On the other hand consider an electron. One person describes i t as " I t ' s a p a r t i c l e " and a second as " I t ' s a wave." Both are r i g h t . Complementarity gives expression not to the idea that d i f f e r e n t people (or the same person) can mistakenly given d i f f e r e n t accounts of the same thing but that d i f f e r e n t people (or the same person) can c o r r e c l t y give c a t e g o r i c a l l y d i f f e r e n t accounts of the same thing (e.g. e l e c t r o n ) . The descriptions are i r r e d u c i b l e but completing in t h e i r accounts of the electron. Complementarity renders p l a u s i b l e a metaphysical monism joined with an epistemological pluralism. There would be a natural tendency I think to superimpose complementary theories T, and T^ to get T^ and I think t h i s i s what we should look f o r . I suspect theories w i l l be superpositions of subjective, physical, s o c i a l , l o g i c a l , e t h i c a l and aesthetic accounts. S c i e n t i f i c theories f o r example have components in the; (a) subjective; elements of experience, (b) physical; intersubjective concepts, measurement, - 170 -(c) s o c i a l ; the assent of the relevant community of experts, (d) l o g i c a l ; formal mathematical elements, (e) e t h i c a l ; value imposed on theory, (f) aesthetic; beauty used as a research tool in sel e c t i n g equations to t r y . What would be a reasonable theory as to what Beethoven's F i f t h Symphony is? I think a plausible candidate for a theory would have to include; ( i ) physical accounts of wave pressures, amplitudes, frequences, ( i i ) subjective accounts of f e e l i n g s , emotions, aroused, ( i i i ) s ocial account of relevant c r i t i c i s m , a nalysis, (i.v) l o g i c a l account of mathematical structure, (v) e t h i c a l associations and values aroused, (vi) aesthetic component. One of the saddest features of our age, as Kaufman terms i t in the introductory quote at the beginning of my paper, i s not to be remedied by choosing e i t h e r side of the dichotomy. Rather the remedy l i e s in developing the conceptual and methodological apparatus needed to f a c i l i t a t e m u l t i d i s c i piinary thinking. Complementarity, in mandating multiple accounts in c e r t a i n cases, encourages t h i s . It also thereby forces - 171 -attention on the conditions under which ce r t a i n theoretical accounts do or do not apply. And f i n a l l y , i t seems to me to embody the kind of unity amidst d i v e r s i t y that could foster the development of human knowledge out of the stage in which i t presently e x i s t s - out of the stage characterized in part by t h i s unnecessary dichotomy i d e n t i f i e d by Kaufman. In t h i s way I can understand why Bohr had such great expectations about the future role of complementarity in discovering and explaining i n t e r - r e l a t i o n s h i p s among d i f f e r e n t areas of knowledge and in so doing providing us with a model of unity of knowledge a quantum leap beyond Machian positivism in p l a u s i b i l i t y . - l?a -B I B L I O G R A P H Y Bergson, H. Introduction to Metaphysics. Translated by T.E. Hulme, New Yor\T: Liberal Arts Press, 1955. Berkeley, G. A Treatise Concerning the P r i n c i p l e s of Human Knowledge. New York"! Bobbs-Merrill, 1957. Beth, E.W. The Foundations of Mathematics. New York: Harper Torchbooks, Born, M. "Physical Reality." Philosophical Quarterly 3, 1953, pp. 143-154. Buchner, L. Force and Matter. New York: MacMillan, 1950. Reprint of the fourth English e d i t i o n (London, 1884). Carnap, R. Per Logische Aufbau da welt, Weltkreis, B e r l i n , 1928. Carnap, R. 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