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An evaluation of Charles Peirce's concept of retoduction Remnant, Peter 1948

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Mir IJJ^ An E v a l u a t i o n of C h a r l e s P e i r c e ' s Concept of R e t r o d u c t i o h hy P e t e r Remnant A Thes is Submitted i n P a r t i a l F u l f i l m e n t of the Requirements f o r t h e Degree o f MASTER OF ARTS i n the Department of PHILOSOPHY The U n i v e r s i t y of B r i t i s h Columbia September, 1948 A B S T R A C T A n E v a l u a t i o n o f C h a r l e s P e i r c e ' s C o n c e p t o f R e t r o d u c t i o n P e i r c e ' s t h e o r y o f r e t r o d u c t i o n , o r t h e f o r m a t i o n o f h y p o t h e s e s , d e s c r i b e s , a s a f o r m o f i n f e r e n c e , t h e p r o c e s s o f r e a s o n i n g b y w h i c h h y p o t h e s e s t o e x p l a i n u n e x p e c t e d e v e n t s a r e a r r i v e d a t . I n g e n e r a l , r e t r o d u c t i o n c o n s i s t s i n t h e s u g -g e s t i o n o f a k n o w n c l a s s o f e v e n t s o f w h i c h t h e e v e n t t o b e e x p l a i n e d may p o s s i b l y b e a p a r t i c u l a r c a s e . On t h e o t h e r h a n d , P e i r c e s o m e t i m e s s p e a k s o f r e t r o d u c t i o n a s p o s i t i n g a n u n o b s e r v e d e n t i t y t o e x p l a i n o b s e r v e d p h e n o m e n a . I t h a s b e e n a r g u e d , h o w e v e r , t h a t t h i s s e c o n d d e f i n i t i o n o f r e t r o d u c t i o n c o n s t i t u t e s a s p e c i a l c a s e o f t h e f i r s t . T h e t h e o r y o f r e t r o d u c t i o n i s p r e s e n t e d i n t w o d i f -f e r e n t f o r m s , t h e e a r l i e r a n d t h e l a t e r , w i t h a t r a n s i t i o n p e r i o d b e t w e e n t h e t w o f o r m s f a l l i n g i n t h e y e a r s f r o m 1 8 8 5 t o 1 9 0 0 . T h e e a r l y t h e o r y s t r e s s e s t h e f o r m a l s t r u c t u r e o f t h e r e t r o d u c t i v e f o r m o f i n f e r e n c e , a n d p r e s e n t s r e t r o d u c t i o n a n d i n d u c t i o n a s p a r a l l e l f o r m s o f r e a s o n i n g , d i f f e r i n g i n t h a t t h e f o r m e r i n f e r s f r o m o b s e r v e d f a c t s o t h e r f a c t s d i f -f e r e n t f r o m t h o s e o b s e r v e d , w h i l e t h e l a t t e r i n f e r s f a c t s t h e seme a s t h o s e o b s e r v e d b u t o f . g r e a t e r g e n e r a l i t y . H y p o -t h e s e s a n d i n d u c t i o n s a r e c o n s i d e r e d a s o f c o m p a r a b l e s t a b i l i t y . I n t h e l a t e r t h e o r y r e t r o d u c t i o n o r i g i n a t e s a l l n e w i d e a s , i n t h e f o r m o f s u g g e s t e d h y p o t h e s e s , w h i c h t h e m --selves are l i t t l e more than intelligent guesses, hut qualify-as forms of inference in that unlike perceptions to which they are analogous they may be subjected to criticism as to their adequacy^ in explaining the events under question. Induction in the later theory i s the process of testing hypo-theses by deduction of experiential predictions from them and comparison of observed fact with those predictions. The criterion for the acceptance of hypotheses for inductive testing i s purely one of economy. The validity of retroduction consists, not in any objective probability of i t s conclusions, but in the fact that only by retroduction can any new ideas be originated, and hence in the fact that together with inductive testing i t constitutes the only method of arriving at true statements about the real world. The whole series of mental performances between the notice of the wonderful phenomenon and the acceptance of the hypo-thesis, during which the usually docile understanding seems to hold the bit between i t s teeth and to have us at i t s mercy, the search for pertinent circumstances and the laying hold of them, sometimes without our cognizance, the scrutiny of them, the dark laboring, the bursting out of the startling conjecture, the remarking of i t s smooth f i t -ting to the anomaly, as i t i s turned back and forth like a key in a lock, and the fi n a l estimation of i t s Plausibility, I reckon as composing the First Stage of In-quiry. Its characteristic formula of reasoning I term Retroduction . . . . (6.469). C. S. Peirce Contents Introduction i i i Chapter: I. The Early Theory -- 1867-1877 . . . 1 II. The Early Theory 1878-1882 . . . 13 III. The Early Theory — 1883-1895 . . . 26 IV. The Later Theory — 1896-1910 . . . 43 Bibliography • • 66 - i i i -Introduction It i s hard to believe that a f u l l century has elapsed since the birth of Charles Peirce, and that during that time the great influence which he has had upon modern thought has derived almost entirely from the crumbs of his philosophic system. To a large extent this may be accounted for by the fragmentary and cryptic nature of his writings and by the uncompromising originality of his views, but even now, in the flurry of excitement caused by the publication of the f i r s t six volumes of his collected papers, the tendency of commentators has been to skim his surface for palatable morsels, rather than to seek the core of his thought. One result of this tendency has been the overemphasis placed on the variety and disorder in Peiree's writings, to the neglect of the unified and coherent system underlying these writings. It i s the purpose of this study to follow a single concept in Peiree's system in a l l the detail of i t s presen-tation from i t s f i r s t appearance until the end of Peiree's philosophie activity. It i s hoped that the results w i l l be twofold: that not only w i l l the f u l l complexity of his views on that concept be revealed, but that a key may be discovered to the whole massive structure of Peiree's philosophy. The success or failure of this second aim w i l l become apparent only in work subsequent to the present paper. The concept to be so investigated i s that of retro-- i v -auction, or the formation of hypotheses, a concept f e l t worthy of investigation both for the importance accorded i t by Peirce as the f i r s t stage of inquiry and the sole subject matter of pragmatism, and for i t s comparative neglect by other philo-sophers. The term retroduction i s only one of the four terms used by Peirce to describe the process of hypothesis formation, and has been rather arbitrarily selected from among i t s three rivals, hypothesis, abduction and presumption, in accordance with Peirce's use of i t in his f i n a l and in many ways most mature papers. The term hypothesis has been restricted where-ver possible to denoting the conclusion of a retroduction. "In view of the aim of this study, the plan of presen-tation w i l l follow the chronological order of Peirce's writings, with the f i r s t three chapters focussed upon the three main sets of papers prior to 1895 and the fourth chapter devoted to the period from 1896 to 1910. The year 1895 has been taken to represent the dividing point between Peirce's early theory of retroduction, considered in the f i r s t three chapters, and his later theory, covered in the f i n a l chapter, although, in fact, the whole period after 1883 until the turn of the cen-tury appears to have been one of transition. The close inter-relationship between the various aspects of Peirce's thought has made i t necessary to precide, to use Peirce's own term, the theory of retroduction from the many theories impinging upon i t . The sources for Peirce's writings referred to in this paper have been listed in the bibliography, with an ad-d i t i o n a l r e f e r e n c e t o M o r r i s C o h e n ' s e x c e l l e n t b i b l i o g r a p h y o f t h e m i s c e l l a n e o u s s c i e n t i f i c a n d p h i l o s o p h i c a r t i c l e s a n d r e v i e w s c o n t r i b u t e d t o a n u m b e r o f p e r i o d i c a l s , t o b e f o u n d i n " C h a n c e , L o v e a n d L o g i c " . T h e b i b l i o g r a p h y t o t h i s p a p e r w i l l b e f o u n d t o c o n t a i n a l s o a l i s t o f c o m m e n t a r i e s o n t h e p h i l o s o p h y o f C h a r l e s P e i r c e , w h i c h , w i t h o u t p r e t e n d i n g t o b e e x h a u s t i v e , i n c l u d e s a l l t h e t i t l e s w h i c h h a v e come t o h a n d . O n l y a s m a l l p r o p o r t i o n o f t h e s e p a p e r s w i l l b e f o u n d r e l e v a n t t o t h e q u e s t i o n o f r e t r o d u c t i o n , t h e m a j o r i t y h a v i n g b e e n l i s t e d a s a n a i d t o t h e f u r t h e r s t u d y o f P e i r c e . I w i s h t o a c k n o w l e d g e w i t h g r a t i t u d e t h e a s s i s t a n c e a n d e n c o u r a g e m e n t w h i c h I h a v e r e c e i v e d f r o m D r . B a r n e t t S a v e r y , D r . A . P . M a s l o w , a n d M r . Edmund M a c d o n a l d , i n t h e p r e p a r a t i o n o f t h i s p a p e r , a s w e l l a s t o e x p r e s s my a p p r e -c i a t i o n o f t h e i n f l u e n c e o f D r . T . G . H e n d e r s o n i n f i r s t t u r n i n g me t o w a r d p h i l o s o p h y . - 1 -An Evaluation of Charles Peirce'3  Concept of Retroduction Chapter I The Early Theory — 1867-1877 The early-theory of retroduction is set forth by Charles Peirce in papers dating from his f i r s t published work in 1867, until the mid 1890's, at which time his thought on this subject underwent the pronounced change to the later theory, f i r s t presented in the papers of 1901. Although the writings during the early period show some considerable de-velopment from the earliest to the latest, the fact that a l l the important papers of this pe riod were edited by Peirce in 1893 for inclusion in a work on s c i e n t i f i c reasoning, "The Search for a Method," without the introduction of significant changes, suggests that he found a l l the accounts of retro-duction satisfactory. It i s quite clear, however, that the account of retroduction given in the last of these important papers of the early period, "The Theory of Probable Inference" of 1883, represents Peirce 1s fullest and most developed de-scription of the early theory. In view of the pronounced variations between the main statements of the early period, i t w i l l be most convenient to present Peirce*s early theory in three chapters, correspon-ding to the three main sets of papers written during this - 2 -period,* and including the less important remarks on retro-duction made in papers of the same years. This f i r s t chapter w i l l cover the theory of retroduction as set forth in Peiree's f i r s t group of papers, published in the Proceedings of the American Academy of Arts and Sciences for 1867. In the f i r s t of the papers of 1867 (2.461-2.516)'!" following an exposition of the forms of deductive reasoning, Peirce shows hypothetic and inductive forms of reasoning to follow from rearrangements of the premisses of a valid syllogism in Barbara. No verbal definition of "hypothesis" or "induction" i s offered unti l the end of the paper, and the syllogistic forms are l e f t to speak for themselves. Given the syllogism (2.509): Any M i s 77*P* Any S i s M . *oAny S is 77'P' - where 77'P' denotes the conjunction of a l l the characters of M, we pass to the form of reasoning from definition: Any M i s 77'Pf Any S i s 77'P' .'. Any S i s M - which constitutes what Peirce calls formal hypothesis. The fallacy in terms of traditional logic, here exemplified, i s claimed to be justified in a later passage (2.514) where, taking an identical proposition: M i s p«p"P"' i t i s argued that: 1. Charles Hartshorne and Paul Weiss, ed., The Collected  Papers of Charles Sanders Peirce, vol. 2, para. 461-516. •All citations of the collected Works w i l l be by volume and paragraph number as above. - 3 -Whatever is P'P" and P f M i s p»p«P"t andwhatever is P'P" and P"' i s M Hence i f S i s p«p«pw' Then S i s M. It i s d i f f i c u l t to see, however, how this f u l l e r explanation does anything more than repeat the fallacy of the f i r s t statement, and the actual justification seems to hang on the fact that M i s p»p«p"' i s an identical proposition by definition: the same being true of M i s 77'P* i f the implioit assumption that a subject i s identical with the conjunction of a l l i t s predicates be granted.,'1 Turning again to the formal hypothesis, i f , for^'P', we substitute a group of characters of M, p t p n p n t etc., we ar-rive at-the form of probable hypothesis or retroduction: Any M i s p'p«p"» etc. S i s p»p«ptt» etc. .'. S i s probably M. Since the major premiss i s no longer identical, and cannot therefore be validly converted without limitation, S can no longer be categorically stated to be M. Peirce advances an ingenious argument to support the probability of M's predication of S (2.510). Since every proposition has a contradictory, one half of a l l pos-sible propositions are true. Moreover, for every true parti-cular proposition there i s a true universal proposition, and for every true negative proposition there i s a true affirmative 1. ..There seems to be a clear link between this assumption ahd the pragmatic principle of 1878 - 'consider what effects that might conceivably have practical bearings we conceive the object of our conception to have- then our conception of these effects i s the whole of our conception of the objectl (5.402). ( - 4 -proposition. Hence of a l l possible propositions of the form M i s 77 'P' one ha l f are true. In every untrue proposition of t h i s form,, some f i n i t e r a t i o of the P's are untrue. Hence, of a l l pro-positions of t h i s form which are p a r t l y true, some f i n i t e r a t i o more than one half are wholly true. That i s , since of a l l possible propositions M i s 77 fP» one h a l f are wholly true, of the other h a l f — the fa l s e h a l f — a f i n i t e r a t i o are wholly f a l s e , and a f i n i t e r a t i o are f a l s e with some of the characters P, true. Consequently, since retroduction deals with propositions known to be p a r t l y true — t h i s w i l l be enlarged upon — the wholly f a l s e set may be ignored, and i t then follows, that of a l l possible propositions arrived at by retroduction, more w i l l be wholly true than f a l s e . Hence, he claims, i f P' be substituted for TPP' we obtain a formula of probable hypothesis which, although i t gives no determinate p r o b a b i l i t y to the inference, w i l l , however weak at f i r s t , by repeated use lead us to the establishment of more and more secure hypotheses. A further problem i n the int e r p r e t a t i o n of Peiree's statement l i e s i n the fact that although t h i s statement i s made i n terms of propositions of the form M i s T i ' P 1 i t apparently applies to the conclusion of the retroduction which i s i n the form S i s probably M - 5 -I t w i l l be convenient to r e s t a t e the r e t r o d u c t i o n : M i s p ' p « p m e t c . S i s p » p « p " ' e t c . . \ S i s probably M That i s , S and M are both ptpnpnt e t c , and M i s by d e f i n i t i o n 7 71pi — although we do not know, and cannot s p e c i f y every c h a r a c t e r o f M. Hence, when we say t h a t ' s i s pro b a b l y M, we are a c t u a l l y p r e d i c t i n g t h a t whatever c h a r a c t e r s o f M can be found, w i l l be p r e d i c a b l e o f S, t h a t i s t h a t S i s p r o b a b l y 77*P* Since we know from the premisses t h a t S and M have some o f the c h a r a c t e r s contained i n 7 7 t p f ^ n common — namely p « p « p « » e t c . — we are j u s t i f i e d i n the statement t h a t r e t r o d u c t i o n d e a l s w i t h p r o p o s i t i o n s which are at l e a s t p a r t l y t r u e . £ s e e above]}. Ingenious as t h i s argument appears, i f t h i s i n t e r -p r e t a t i o n i s c o r r e c t i t would seem t o be based on a confu-s i o n between l o g i c a l t r u t h and m a t e r i a l t r u t h , which i s not apparent u n t i l P e i r c e ' s statement i s f u l l y s e t f o r t h . When P e i r c e speaks of a t r u e h y p o t h e s i s t h i s is-presumably i n terms approximating the d e f i n i t i o n : " T r u t h c o n s i s t s i n the ex i s t e n c e o f a r e a l f a c t corresponding t o the t r u e propo-s i t i o n , " (2.652). T h i s i s a d e f i n i t i o n of m a t e r i a l t r u t h , and w h ile i t i s by no means c l e a r i n what the correspondence between f a c t and p r o p o s i t i o n s c o n s i s t s , i t c e r t a i n l y appears i n a p p l i c a b l e to 'one h a l f o f a l l p o s s i b l e p r o p o s i t i o n s . ' The sense i n which, of two c o n t r a d i c t o r y p r o p o s i t i o n s , one i s t r u e and the other i s f a l s e , i s q u i t e d i f f e r e n t from - 6 -m a t e r i a l t r u t h and f a l s i t y , s i n c e i n terms of the d e f i n i t i o n given, unless there i s a f a c t corresponding to one of the two c o n t r a d i c t o r y p r o p o s i t i o n s , both must be s a i d e i t h e r to be m a t e r i a l l y f a l s e , or t o be meaningless. L o g i c a l t r u t h can be brought i n t o harmony w i t h m a t e r i a l t r u t h by saying t h a t of two c o n t r a d i c t o r y p r o p o s i t i o n s , i f one be t r u e , the other must be f a l s e and v i c e v e r s a . I t may be, however, th a t t h i s i s t o m i s i n t e r p r e t P e i r c e , and that by • p o s s i b l e p r o p o s i t i o n s ' he i s r e f e r r i n g to m a t e r i a l r a t h e r than l o g i c a l p o s s i b i l i t y . I f so, assuming tha t the remainder of the i n t e r p r e t a t i o n i s c o r r e c t , he ap-pears to be saying that of a l l the statements t h a t could be made about the w o r l d , i f those which are known to be f a l s e on the b a s i s of present knowledge are excluded, the remainder w i l l c o n t a i n s l i g h t l y more t r u e p r o p o s i t i o n s than f a l s e ones. Then i f any p r o p o s i t i o n be s e l e c t e d at random i t w i l l have a p r o b a b i l i t y of being t r u e determined by the p r o p o r t i o n of t r u e p r o p o s i t i o n s t o the whole c o l l e c t i o n , and t h i s proba-b i l i t y , although unknown, can be known to be g r e a t e r than This, i s probably c l o s e r to what P e i r c e meant; but without ques t i o n i n g the v a l i d i t y of t h i s second i n t e r p r e t a t i o n , i t must seem d o u b t f u l how much i s added thereby to our under-standing of the success of the experimental method. Our hypotheses are not drawn at random from the c l a s s of a l l p o s s i b l e p r o p o s i t i o n s , but from a narrower c l a s s whose boundaries are set by previous s c i e n t i f i c work, and, ac-cording to P e i r c e , by c e r t a i n c h a r a c t e r i s t i c s of the human mind. The probability attaching to the general class of a l l possible propositions has no effect upon the probability of the truth of propositions taken from this narrower class, and i t is not clear how the amount of this latter probability can be arrived at except from the relative successes and failures of the propositions selected and tested. On this basis Peirce claims that the probability of any hypothesis so selected being true i s very high. A more significant factor in the success of amplia-tive inference — both retroductive and inductive -- i s repeatedly stressed by Peirce throughout his subsequent writings. This i s the self corrective nature of experimental method, such that, however erroneous be i t s results at any point, "the further application of the same method must cor-rect the error" (5.145 cf. 5.348-352). Thus the success of this method is independent of the probability of any of i t s particular premisses. Toward the end (2.515) of the paper under con- • sideration, Peirce defines hypothesis as "an argument which assumes that a term which necessarily involves a certain number of characters, which have been lighted upon as they occurred, and have not been picked out, may be predicated of any object which has a l l these characters." Retroduction thus appears to be the placing of objects within previously defined classes — or the predica-tion, of a given object, of a class name, which name has been defined by a sampling process. In terms of the formal syllogism, by reason of the common characters p'p"p«» etc. the object S i s placed in the class of objects M, and sup-posed to share a l l the characters of M. This interpretation i s supported by another passage of the same year (2.425), where, from similar premisses to those used above, the conclu-sion: S i s a l l that M i s is derived, and our knowledge of S i s said to be potentially increased, in that i f there are any more characters common to the class .M, and i f we discover these characters, they w i l l either be predicable of S, or w i l l exclude S from the class M. A description of retroduction given in 1868, sup-ports the same interpretation by speaking of i t as dealing with an absence of knowledge as to whether, besides the characters attributed to an object by the premisses, other characters belong to i t — by proceeding nas though a l l the characters requisite to the determination of a certain object or class of objects were known." In this case M i s spoken of as either a class of objects or another object(5.272). In this same paper the function of retroduction i s described as being "to substitute for a great series of predicates forming no unity in themselves, a single one (or small number) which involves them a l l , together (perhaps) with an indefinite number of others. w (2.576) This i s an advance on the previous descriptions, in that the S i s no longer spoken of as i f a l -ready named, although in many cases i t may be, but becomes a 'this', a complex of characters as yet unclassified, and the process of retroduction i s extended to include the recognition of events experienced. In keeping with this restatement the form of retroduction i s given as: i f A then B B .'. A - where B represents a complex of characters, and might well be replaced by p»p"p«» etc. This form involves a logical fallacy analagous to that of the other form of retroduction discussed above, with the result that again the premisses suggest, rather than necessitate, the conclusion. This same form, although with a slightly different application, is used by Peirce to describe retroduction in the "Lectures on Pragmatism" of 1903, where (5.189): The surprising fact, C, i s observed; but i f A were true, C would be a matter of course. Hence, there i s reason to suspect that A i s true. It i s in this sense that retroduction i s spoken of as "reasoning from consequent to antecedent" (5.£76). Five rules are given, to which retroduction must conform in order to arrive at a valid hypothesis (2.511): 1. the deductive syllogism from which the retroductive argu-ment derives must be valid, or, as Peirce says in the course of a footnote to these rules — " i f i t i s granted that hypotheses are inferred . . . observed facts must follow apodictically from the hypothesis without the aid of subsidiary hypotheses." - 10 -This rule appears to be more a primary test for formed hypo-theses than a guide for their formation. 2. the conclusion of the retroduction is not to be held as absolutely true and i s to be rejected, i f and when i t i s found "thatP' was taken from some higher class than M" — 'higher' presumably meaning "of broader extension." 3. following from rule 2, the predicate of the premisses must be a conjunction of predicates — that i s , of characters. 4. this aggregate must be of different qualities and not of mere names. 5. the only principle upon which the instanced predicates can be selected i s that of belonging to M. The footnote to these rules, referred to above, is a rejection of a possible sixth rule, the principle which Peirce attributes to the positivists, that "no hypothesis i s admissible which is not capable of verification by direct observation." Por Peirce retroduction i s a form of logical inference, valid, although uncertain, because arguing from certain premisses according to a formal process of reasoning. Peirce points out that to accept the p o s i t i v i s t i c principle seriously is to rule out the whole body of accepted historic fact, a l l of which i s dependent on retroductive reasoning, and completely out of reach of direct observation. It must be noted that this early theory of hypothe-sis involves a division of a l l reasoning into explicative or deductive, and ampliative; and of ampliative reasoning into hypothesis and induction (2.709). These two forms of reason-ing are then developed side by side, the one paralleling the other such that each statement about the one can, by the sub-- 11 -stitution of 'subject* for 'predicate' or 'S' for 'P», be made applicable to the other. Induction i s described in terms of i t s derivation from a syllogism in Barbara — i t s form being £ ' S' i s P S' is M * 1 M i s P where £.' S' denotes the sum of a l l classes coming under M; i t is subject to the five rules and.to the statement regarding probability — a l l made applicable by the minor adjustments described; and is f i n a l l y defined as an "argument which as-sumes that a whole collection from which a number of instances have been taken at random has a l l the common characters of those instances" (2..515).' It i s necessary to emphasize this parallel rela-tionship of hypothesis and induction; the f i r s t reasoning from certain characters of an object to the total nature of the object; the second, from instances of a collection to the nature of the whole collection, in order to bring out clearly the position of retroduction in the early theory as compared with i t s position in the later theory. Retroduction, in this earliest statement, has been put forward as a form of inference, starting from premisses established according to certain rules, and reaching a con-clusion asserting the probable inclusion of an object in a class of objects, or the similarity of an object to another object. It has been argued that what has been called formal hypothesis rests upon the assumption that a subject i s identi-- 12 -t i c a l w i t h the c o n j u n c t i o n of a l l i t s p r e d i c a t e s ; and t h a t the t r u t h of h y p o t h e s i s i s p o s s i b l e r a t h e r t h a n p r o b a b l e . 13 -Chapter I I The Ea r l y Theory — 1878-1882 The second main statement of the early theory of retroduction i s to be found i n the l a s t of the s i x papers on the " I l l u s t r a t i o n s of the Logic of Science" published i n the Popular Science Monthly f o r 1878 (2.619-644). This paper, although d i f f e r i n g considerably from the papers considered i n Chapter I, was also edited without a l t e r a t i o n for "The Search for a Method." I t i s possible, according to Peirce, to speak of every deductive syllogism i n Barbara as the derivation of a r e s u l t , the conclusion, from the ap p l i c a t i o n of a (rul-^Tx yjfi stated i n the major premiss, to a case under that rule, stated i n the minor premiss(2.620).. "This d e f i n i t i o n , of course, applies . . . only to the f i r s t f i g u r e . " By truie) 1 \ Peirce refers to what he frequently c a l l s a 'leading p r i n - ^ ciple,- f according to which we pass from a premiss — the case to a conclusion — the res u l t (cf. 3.162-172). Such a leading p r i n c i p l e i s l o g i c a l l y good i f i t never, or i n probable i n -ference, seldom, leads us from a true case to a false r e s u l t . Thus: A l l men are mortal — Rule Socrates i s a man — Case Socrates i s mortal — Result. A l l three forms of inference — deduction, induction and retroduction — can be described and d i f f e r e n t i a t e d i n terms 1. C. S. Peirce, "Syllogism," i n J". M. Baldwin, ed., D i c t i o - nary of Philosophy and Psychology, v o l . 2, p. 630. - 14 -of these three classes of propositions: 1. A l l deduction i s the application of general rules to particular cases, with a consequent result. This is not always evident, hut, by reducing any deduction to Barbara, w i l l be found always to be so (2.620). 2. A l l induction i s the conclusion of "A rule from the observation of a result in a certain case" (2.622): These beans were in this bag — Case These beans are white — Result A l l the beans in the bag were white — Rule 2. A l l retroduction i s the conclusion of a case from.a rule and a result (2.623): A l l the beans from this bag are white — Rule These beans are w h i t e — Result .'. These beans are from this bag — Case. The conclusion in induction and retroduction i s not, of course, claimed to follow deductively from the premisses. An alternative formulation of retroduction and in -duction, given in this same paper, i s based upon the deri-vation of syllogisms in Baroco and Bocardo by denying the conclusion and one or other of the premisses of a syllogism in Barbara (2.626). If the conclusion and the case be denied, and the rule be admitted in: A l l men are mortal Socrates i s a man Socrates i s mortal the result.is a Barooo syllogism: Socrates i s not mortal A l l men are mortal • Socrates i s not a man The conclusion of this syllogism i s of the nature, according to Peirce, of a very weak hypothesis — "so timid as to lose - 15 -i t s amplifiative character entirely" (2.630). Similarly, by denying the rule and admitting' the case, the resulting Bocardo syllogism has for i t s conclusion a weak induction. In either case, the conclusion f a i l s to achieve ampliative status in that i t expresses merely a lack of knowledge, rather than leaping boldly into the unknown to suggest an explanation for the premisses, either in the form of a new case, or a new rule — the f i r s t of these constituting a hypothesis, the second, an induction. If we apply the same treatment to what Peirce calls a probable deduction in Barbara, we arrive, he claims, at a valid hypothesis or induction (2.627). Thus by denying the result and accepting the rule of the probable deduction: Most of the beans in this bag are white This handful of beans i s from this bag .'.Probably, most of this handful i s white we arrive at the form of retroduction: Pew beans of this handful are white Most beans in this bag are white Probably, these beans were taken from another bag. Similarly, by denying the result and accepting the case, of the deduction, we get the induction: Probably, few beans in the bag are white. A consideration of Peirce 1s use of probability with regard to hypotheses w i l l be postponed until the next chapter, when the whole period during which Peirce spoke of retro-duction as a form of probable inference w i l l have been covered. It should be mentioned in passing, however, that the example of probable deduction from which he derives the examples of - 16 -retroduction and induction, above, i s not of the form of simple probable deduction: I B i s C A i s B .'.Probability i s £ that A i s C (cf. 2.695) but i s a case of s t a t i s t i c a l deduction (cf. 2.700). A second point to be mentioned concerns the hypo-thesis arrived at in the example of retroduction given above: Probably these beans were taken from another bag. This i s actually a free interpretation of the more accurate conclusion: Probably these beans are not from this bag. This corrected conclusion is no more an ampliative hypo-thesis than Is the conclusion of the Baroco syllogism given above. Whether the syllogism from which the retroduction is derived be apodictic or probable, the formation of a positive hypothesis involves a step beyond the logically valid con-clusion of the given premisses. Two descriptions of the nature of retroduction are given in this paper of 1878 by Peirce (2.624): a. Finding that two objects have a strong resemblance in certain respects, we infer that they resemble one another strongly in other respects. This i s fundamentally the form taken by retroduction in Chapter I, although, with the exception of one passage (5.272), the iufgrenbe (Is) ^j*-***** from an object to a class of objects, rather than from one object to another. This statement can, however, be 17 -made compatible w i t h t h a t g i v e n i n the p r e s e n t chapter: u s i n g the example g i v e n above, from d i s c o v e r i n g t h a t two c o l l e c t i o n s o f beans resemble each o t h e r s t r o n g l y as t o c o l o u r , we i n f e r t h a t they resemble each o t h e r i n having both been fo r m e r l y o f the same c o l l e c t i o n . The weakness of the hypothesis so d e s c r i b e d a r i s e s r a t h e r from the weakness of the example i t s e l f , than from any i n - a p p l i c a -b i l i t y of t h i s d e s c r i p t i o n o f hy p o t h e s i s to the example, b. F i n d i n g some c u r i o u s circumstance, e x p l a i n a b l e by the s u p p o s i t i o n t h a t i t i s a case o f a c e r t a i n g e n e r a l r u l e , we adopt t h a t s u p p o s i t i o n . T h i s statement i s more i n keeping w i t h the viewpoint o f the paper at prese n t under i n v e s t i g a t i o n , although i t i s not wh o l l y a t odds w i t h t h a t of Chapter I , where r e t r o d u c t i o n i s d e s c r i b e d as t h e i n -fe r e n c e of a minor premiss from t h e major premiss and the c o n c l u s i o n o f a s y l l o g i s m . The d i f f e r e n c e a r i s e s mainly from the r e s t r i c t i o n , i n the f i r s t papers, o f p r e -misses t o those p r e d i c a t i n g q u a l i t i e s , which r e s t r i c t i o n i s - not r e t a i n e d i n the prese n t paper; and from the s p e c i f i c a -t i o n of the p r o p o s i t i o n s i n a Barbara s y l l o g i s m as r u l e , case and r e s u l t . A new c o m p l i c a t i o n i s i n t r o d u c e d , however, by the examples g i v e n by P e i r c e t o i l l u s t r a t e what he means by r e t r o -d u c t i o n , the c l e a r e s t o f which may be quoted i n f u l l : Numberless documents and monuments r e f e r t o a con-queror c a l l e d Napoleon Bonaparte. Though we have not.seen the man yet we cannot e x p l a i n what we have seen, namely, a l l these documents and monuments, without supposing t h a t he r e a l l y e x i s t e d (2.625). - 18 -This l s a new form of hypothesis, i n which an e n t i t y or event, by i t s very nature immune from d i r e c t o bservation, i s p o s i t e d to e x p l a i n observable evidence. As w e l l as a l l h i s t o r i c a l f a c t , such s c i e n t i f i c e n t i t i e s as 'atoms' f a l l i n t o t h i s c l a s s . This view of r e t r o d u c t i o n i s formulated a b s t r a c t l y l a t e r i n the same paper, where i t i s s a i d t h a t "by hypothesis, we conclude the existence of a f a c t q u i t e d i f f e r e n t from any-t h i n g observed, from which, according to known laws, some-t h i n g observed would n e c e s s a r i l y r e s u l t " (2.636). R e t r o d u c t i o n c o n s i s t s i n reasoning 'from e f f e c t t o cause', as opposed to i n d u c t i o n , which passes from p a r t i c u l a r s to a general law. The f u n c t i o n of r e t r o d u c t i o n i s to e x p l a i n ; of i n d u c t i o n , t o c l a s s i f y . Justus BuchlerJ- i n d i s c u s s i n g P e i r c e ' s theory of r e t r o d u c t i o n , objects to the i n c l u s i o n , i n the above quota-t i o n , of the words 'according to known laws', on the grounds t h a t , when, to e x p l a i n a circumstance C, we p o s i t A, because i f A were t r u e , C would f o l l o w as a matter of course, w h i l e i n some cases t h i s law may be a l r e a d y known, i n many the law ' i s a c t u a l l y part of the hypothesis or s u p p o s i t i o n A*. There seems at f i r s t glance j u s t i f i c a t i o n f o r such c r i t i c i s m ; the s c i e n t i f i c hypotheses by which atoms or molecules are pro-posed appear to be c l e a r l y of t h i s nature and t o take the form: given the s u r p r i s i n g f a c t C -(then there i s an A of such a nature as t o b r i n g about a C and A has occurred) 1. Charles P e i r c e ' s Empiricism, p. 133 n• - 19 -- of which the whole bracketed portion i s the hypothesis. What has been done is to infer a law of such a nature that i f i t were to be acted upon, C would result. A i s nothing more than an occasion of a law. If this i s to assert the primacy of laws over the events which take place according to those laws, i t w i l l be quite in accordance with Peiree's concept of the reality of law. On the other hand, although i t may be true that such a hypothetical entity A has ascribed to i t , as part of i t s character, the laws of i t s activity, these laws being such that C would follow from the occurrence of A, unless the description of A's action i s in terms of .known laws i t can hardly be claimed that C has been explained. Hence i t i s Peiree's conviction that "progress in science depends upon the observation of the right facts by minds furnished " with appropriate ideas" (6.604, cf. S.75E). If i t be claimed that necessity for previously known laws to underlie every hypothesis involves an inf i n i t e regression, this i s countered by the fact that Peirce bases a l l retroduction ultimately on 'instinctive' knowledge of mechanical and social principles. "It seems incontestable . . . that the mind of man i s strongly adapted to the comprehension of the world . . •, that certain conceptions, highly important for such a comprehension natu-r a l l y arise in his mind; and that without such a tendency, the mind could never have had any development at a l l " (6.417). A l l science i s ultimately nothing but the outgrowth from these instincts (6.500). No attempt i s made by P e i r c e i n the p r e s e n t paper to b r i n g the view of r e t r o d u c t i o n as r e a s o n i n g from e f f e c t to cause i n t o harmony wi t h the two other views g i v e n above — of r e t r o d u c t i o n as i n f e r e n c e of the s i m i l a r i t y of o b j e c t s i n a l l r e s p e c t s , from t h e i r observed s i m i l a r i t y i n some r e s p e c t s , and of r e t r o d u c t i o n as i n f e r e n c e of a case from a r u l e and a r e s u l t . A f o u r t h d e s c r i p t i o n of r e t r o d u c t i o n — t h i s the most g e n e r a l of a l l — i s g i v e n toward the end of the paper under c o n s i d e r a t i o n (2.642), i n which r e t r o d u c t i o n i s spoken of as i n f e r e n c e 'from f a c t s of one kind t o f a c t s of another', as opposed to i n d u c t i o n which i n f e r s 'from one set of f a c t s another set of s i m i l a r f a c t s ' . T h i s statement suggests t h a t P e i r c e may have looked upon r e t r o d u c t i o n as c o v e r i n g a wide number of types of a m p l i a t i v e i n f e r e n c e ; t h i s would e x p l a i n both the d i v e r s i t y of d e f i n i t i o n s and the v a r i e t y of s y l l o g i s -t i c forms g i v e n f o r r e t r o d u c t i o n . Although P e i r c e speaks o f r e t r o d u c t i o n as e x p l a i n i n g events i n terms o f known laws, he warns a g a i n s t the i d e a t h a t the v a l i d i t y of the h y p o t h e t i c method i s dependent u l t i m a t e l y upon a /n^rdejc^of nature (2.633). P a r t i c u l a r hypotheses are a r r i v e d at and strengthened as a r e s u l t of our knowledge of v a r i o u s r e g u l a r i t i e s and laws i n nature, but to r e s t the v a l i d i t y o f h y p o t h e t i c method as a whole upon any such order c o n s t i t u t e s an attempt to reduce a m p l i a t i v e r e a s o n i n g to a form of deduction. P e i r c e c o n s i d e r s t h i s q u e s t i o n more f u l l y - 21 -with regard to induction in another paper from the same series of 1878 (6.410-413), where he argues that the validity of induction — and the same may be said of the parallel, though weaker, retroduction — depends on i t s self corrective nature, such that, i f continued in long enough i t w i l l lead inevitably to truer and truer statements about real facts. The theory ^j\f^ that ampliative reasoning depends for i t s validity on an ^rdeg? of nature, that i s , upon the principle that what occurs under certain circumstances must occur under similar circumstances, leads to a number of inadequacies: 1. i t f a i l s to account for those ampliative conclusions in which the event i s only stated to occur in a certain proportion of cases, under the given circumstances (6.411). .2. i t forbids the drawing of ampliative conclusions with re-gard to any character about whose constancy we know no-thing (6.412). 3. i t overlooks the conditions actually necessary for valid synthetic reasoning — namely, predesignation of the character concerned and random sampling from the whole class of objects under consideration (6.413). 4. i f the validity of synthetic reasoning were dependent on the order of nature, i t is conceivable that there could be a universe in which such reasoning would .be invalid (5.345)1 Peiree's arguments have been given very cryptically-==^1 he presents many more, and enlarges upon them considerably, but space does not allow careful consideration of this question. - 22 -Throughout the presentations of the early theory of retroduction Peirce places his emphasis upon the logical form of the reasoning involved, with only scant consideration of what i s ordinarily regarded as the more important problem — that of testing hypotheses. He does devote a paragraph (2.634), i however, to setting up certain principles for valid testing: 1. since i t i s possible, given two objects or classes of objects, to find any number of resemblances between them, 'a hypothesis should be distinctly put as a question, before making the observations which are to test i t s truth . . . . We,must try to see what the result of pre-dictions from the hypothesis w i l l be". That i s , predictions must be deduced from the hypothesis i t s e l f , and the facts observed to see If such predictions are exemplified under the conditions specified in the hypothesis. 2. ''the respect i n regard to which resemblances are noted must be taken at random". Presumably by 'noted' he means •predicted and observed', because he goes on to say: "We must not take a particular kind of predictions, for which the hypothesis i s known to be good." 3. "the failures as well as the successes of the predictions must be honestly noted. The whole proceeding must be f a i r and unbiased." For Peirce, scientific reasoning, as opposed to deductive reasoning, i s largely dependent for i t s validity upon the courage and high principle of the reasoner: "The logic which observational science - 23 -uses is not, like the logic that the books teach, quite i n -dependent of the motive and the s p i r i t of the reasoner. There is an ethics indissolubly bound up with i t ' — an ethics of fairness and impartiality" (6.3, cf. 1.576). In the expression of these rules Peirce i s refer-ring specifically to hypotheses concerning the similarity of objects and classes of objects — in principle, however, these rules are applicable to a l l hypothetic inference. The careful distinction maintained by Peirce be-tween induction and retroduction has been stressed several times and constitutes one of the main characteristics of the" early theory of ampliative reasoning. Peirce argues further, in opposition to persons unnamed, that not only are the pro-cesses of induction and retroduction quite distinct, but that hypotheses so arrived at, can never, since by their nature they reason from facts of one kind to facts of another, be replaced by inductions, which are limited to inference from facts to other facts of a similar kind (2.642). The third important argument advanced to. justify the distinction between retroduction and induction i s based on their a f f i n i t y to two physiological processes of ap-prehending facts (2.643). This aspect of Peiree's theory of retroduction can be br i e f l y summarized here. Hypothesis,-he claims, "produces the sensuous element of thought, and induction the habitual element." Just as in a hypothesis a single conception is substituted for a tangle of predicates, - 24 -so "when our nervous system i s excited in a complicated way, there being a relation between the elements of the excita-tion, the result is a single harmonious disturbance which I cal l an emotion." This emotion which i s substituted for the complex of excitation i s "essentially the same thing as a hypothetic inference." Peirce draws no sharp distinction between sensation and emotion, and in the present quotations i s using the term emotion to cover both. Induction, being the inference of a rule, since "the belief of a rule is a habit" (2.643) and "a habit i s a rule active in us", " i s the logical formula which expresses the physiological process of formation of a habit." Deduction, i t may be added, i s of the nature of volition and of the concentration of attention on a fact. A fourth merit of the distinction between induction and retroduction l i e s in i t s relevancy to the division of the sciences into the classificatory sciences, which are,, according to Peirce, purely inductive; the sciences of theory, such as pure physics; and the sciences of hypothesis — in which he includes "geology, biology, etc" (2.644). In spite, however, of his careful bifurcation of ampliative reasoning into induction and retroduction, Peirce admits a certain mingling of the two processes in the forma-tion of most theories. Insofar as any induction i s extended quite beyond the limits of our observation, It partakes to some degree of the nature of a hypothesis, and must be sup-ported by i t s efficacy in explaining observable facts (2.640). - 25 -The difference, however, between such an induction, and what Peirce would c a l l a pure induction, limited to the ultimately observable, seems negligible as far as the reasoning involved in their formation i s concerned. Any ampliative induction, as opposed to an induction based on exhaustive enumeration, is at the time of i t s formation a prediction about facts as yet unobserved. Whether or not such facts are ultimately observable has a great deal to do with the weight of the i n -duction, but very l i t t l e , i t would appear, to do with the process of reasoning by which i t was•attained. Furthermore, unless Peirce i s redefining retroduction as the process of reasoning involved in the formation of a l l statements about unobservable facts, i n terms of the various definitions of retroduction given, i t i s not clear how the inductions re-ferred to can in any way be said to .be in part retroductions. - 26 -Chapter III The Early Theory — 1883-1895 In 1883 Peirce edited the Johns Hopkins "Studies in Logic", to which he contributed "A Theory of Probable Inference" (2.694-754), a paper setting out a theory of pro-bable deduction, induction and retroduction. This paper, like those already considered, was edited in 1893 for inclu-sion in "The Search for a Method", without alteration of text. An example has been given in Chapter II of what Peirce came to c a l l simple probable deduction, and i t was stated at that time that i t i s from the syllogism of s t a t i -s t i c a l deduction rather than from this simple deduction that ampliative inference i s derived. Peirce makes this point clear in the present paper, and introduces a further refine-ment by distinguishing between s t a t i s t i c a l deduction, and a variation which he calls s t a t i s t i c a l deduction in depth. Stat i s t i c a l deduction (2.700) i s of the form: "^-proportion r of the M's are P's S'S^"' etc. are a numerous set, taken at random from the M's .'.probably about the proportion r of the S's are P's. Deduction in depth relates to the degree of resemblance be-tween objects or classes of objects, in terms of a compari-son of their characteristics. S t a t i s t i c a l deduction in - 27 -depth takes the form (2.705): every M has the numerous marks p»p«p*" etc. S has an r-likeness to the M's /.probably and approximately, S has proportion r of the marks P'P"P"' etc. - where "r-likeness" i s a measure of resemblance, with a scale of numbers from zero, denoting total dissimilarity, to unity, denoting identity (2.704). the probable deductive syllogism, by denial of the conclusion the inductive or hypothetical conclusion w i l l be positive, rather than negative as was the case in Chapter II. Given the premiss of the s t a t i s t i c a l deduction: proportion r of the M's are P's the proportion denoted by r may be any value between 1 and 0. For every value of r there is a ratio p, which i s the logical negative of r, and which admits of every value which r excludes and excludes every value of which r Then, i f the major premiss and conclusion of the s t a t i s t i c a l deduction be denied and transposed, the form for induction is obtained: S'S"S"' etc. are a numerous random sample of the M's proportion p of the S's are P's .'.probably about proportion p of the M's are P's Peirce points out that 'probably about' must be regarded as the modality with which the conclusion is drawn in deduction and induction, and not as a part of the proposition, in which case the deduction would be necessary, and i t s inversion an instance of Bocardo (2.720 n.). The derivation of induction and retroduction from 7 admits (2.720). - 28 -In the same way, by denying and transposing the minor premiss and the conclusion, of the s t a t i s t i c a l deduction in depth, the form for retroduction.is arrived at (2.721): every M has the numerous marks p»p«p«» etc. S has proportion p of the marks P ,P , fP n' etc. .'.probably and approximately, S has a p-likeness ^ to the class of Mfs. < According to Peirce, however, i t is^©"t^tric^ly nece^sar^r that the s t a t i s t i c a l deduction be inverted by denial of the conclusion and a premiss. This denial i s neces-sary in the case of ordinary syllogism, which i s based on a relation of containing and contained; and i t has been carried over therefrom into the inversion of s t a t i s t i c a l deduction. The s t a t i s t i c a l deduction, however, involves an assumption of an approximate equality between the ratio of P's in the whole class and in the sample, and this relation of equality i s convertible (2.718). Retroduction can be, and has by other writers been spoken of as induction of characters, rather than of objects. Instead of taking a random sampling of the objects in a class, the characters of an object or class of objects are sampled, and induction proceeds from the degree of similarity discove-red between the characters sampled from the two objects. The great difference between induction and retroduction depend on the di f f i c u l t y of counting characters rather than things, and upon the fact that an inference from certain resemblances between objects to the overall resemblance between the two objects i s far weaker than the inference of induction proper. "There is no greater nor more frequent mistake in practical logic than th suppose that things which resemble one another strongly in some respects are any the more l i k e l y for that to be alike in others" (£.634).. Hypotheses must be formed on the basis of significant resemblances and be tested by prediction of further resemblances, under the conditions of testing des-cribed in Chapter II. What Peirce means by significant re-semblances is not made perfectly clear, but may in part be explained by his discussion of our knowledge of special uni-formities in nature, by which we are aware of the tendency of certain types of characters to be constant throughout a class (£.743). Another possibly more important factor in this problem of the significance of certain data i s Peirce*s theory, briefly mentioned in Chapter II, concerning man's tendency to guess right regarding principles of mechanics and the moral sciences (£.753). Then i f man has such a ten-dency, certain facts leading to f r u i t f u l guesses would appear more significant than other facts. Two factors thus inter-act in the formation of hypotheses; in addition to the "well established proposition that a l l knowledge i s based on ex-perience . . . we have to place this other equally important truth, that a l l human knowledge, up to the highest flights of science, is but the development of our inborn animal instincts" (£.754). Peirce accepts the "well established" definition of a hypothesis as "a proposition believed in because i t s consequences agree with experience" (£.707), as being in accordance with his own use of the term, and gives Kepler's - 30 -hypothesis as to the orbit of Mars as an example of this use. Kepler "traced out the miscellaneous consequences of the sup-position that Mars moved in an ellipse, with the sun at the focus, and showed that both the longitudes and the latitudes resulting from this theory were such as agreed with obser-vation." On the other hand, the suggestion in ordinary use of the term hypothesis, "of uncertainty, and of something to be superseded" (2.708) is quite foreign to Peirce*s use of i t . In the same passage Peirce mentions Newton's use of the term, where Newton claims to give a general formula for the motions of heavenly bodies, but makes no hypotheses to explain the causes of their motions, and this again Peirce accepts as coinciding with his own usage. Now unless Peirce i s taking into account Kepler's peculiar theory of mathe-matics as/in some way of causal eff_icjicy, i t would appear that Kepler was giving a general formula for the motion of Mars, rather than suggesting the cause of such motion. Kepler appears to be doing what Peirce i s referring to when he speaks of retroduction as the process of bringing a "con-fused concatenation of predicates" into order under "a synthetizing predicate" (2.712). This, rather than Newton's use of hypotheses as suggesting causes, seems to represent Peirce's customary use of the term. However, in this same paper (2.713), Peirce does speak of men as looking upon Nature, from their anthropo-morphic position, as continually making deductions in Barbara, - 31 -i n which laws of nature c o n s t i t u t e major premisses, and the occurrence of causes under those laws b r i n g e f f e c t s as con-c l u s i o n s . Then the f u n c t i o n of r e t r o d u c t i o n i s the d i s c o v e r y o f such causes. T h i s use o f h y p o t h e s i s i s not u n l i k e t h a t i n P e i r e e ' s example of our i n f e r e n c e of the e x i s t e n c e of Napoleon to e x p l a i n c e r t a i n evidence; nor i s i t u n l i k e the i n f e r e n c e of e n t i t i e s , such as atoms and e l e c t r o n s , t o e x p l a i n observed phenomena. I t i s p o s s i b l e , however, t h a t a l l these types of r e t r o d u c t i o n can be considered as s p e c i a l cases of a more general form of reasoning by which order i s i n t r o d u c e d i n t o a confused c o n c a t e n a t i o n of p r e d i c a t e s . In the case of K e p l e r ' s r e t r o d u c t i o n an i d e a l o r b i t i s suggested, and i t i s found t h a t c e r t a i n of the p o s i t i o n s of a body moving i n t h a t o r b i t would c o i n c i d e w i t h the observed p o s i t i o n s o f Mars. In the same way r e t r o d u c t i o n might suggest a c e r t a i n i d e a l s e r i e s of events i n time, f o l l o w i n g one another i n terms of known laws, and c u l m i n a t i n g i n an event or events c o i n c i d i n g w i t h observed f a c t . Then i t might be assumed t h a t t h e i d e a l s e r i e s of events c o n s t i t u t e d an e x p l a n a t i o n of the f a c t s observed. What may be two u n r e c o n c i l e d t e n d e n c i e s i n P e i r e e ' s view on t h i s matter are w e l l i l l u s t r a t e d by two statements from the two s e c t i o n s o f h i s review of W i l l i a m James' " P r i n -c i p l e s of Psychology." I n the f i r s t o f t h e s e , he speaks o f "the g e n e r a l c h a r a c t e r of s c i e n t i f i c hypotheses" as w e l l expressed by James 1 d e s c r i p t i o n of them as "attempts to - 32 -explain phenomenally given elements as products of deeper 1 lying entities." in the second he says, "To explain any process not understood i s simply to show that i t i s a special case of a wider description of process which i s more i n t e l l i g -2 i b l e . " Peirce holds the theory that a l l valid reasoning: consists in constructing a diagram according to a general precept, in observing certain relations between parts of that diagram not explicitly required by the precept, showing that these relations w i l l hold for a l l such diagrams, and in formulating this conclusion in general terms (1.54) Although in one passage he specifically includes the process of constructing the diagram "from the state of things asser-ted in the premisses" under deduction (1.66), the process ^-^J7i% appears fundamentally the same as that by which hypotheses A Ifi are constructed from a collection of data. A section from a paper of 1890 seems to support this suggestion, where he " speaks of "the highest kind of synthesis" as being.that which "the mind is compelled to make in the interest of intelli-9f\Pe~ ,lf,t<**' g i b i l i t y . . . this i t does by introducing an idea not con- ' tained in the data, which gives connections which they would not otherwise have had" (1.383). In order to understand Peirce's theory of amplia-tive inference i t is necessary to clarify his uses of the con-cept of probability in these early papers. A general distinc-tion between necessary and probable forms of reasoning i s drawn as follows: 1. The Nation, vol. 53, 1891, p. 15. 2. Ibid., p. 33. - 33 -The difference between necessary and probable reasoning i s that in the one case we conceive that such facts as are expressed by the premis-ses are never, in the whole range of possibility, true, without another fact, related to them as our conclusion i s to our premisses, being true likewise; while in the other case we merely con-ceive that, in reasoning as we do, we are f o l -lowing a general maxim that w i l l usually lead us to truth (2.696). The distinction made in Chapter II, between simple probable deduction, of the form: i B i s C A i s B .'.probability i s £ that A i s C, and s t a t i s t i c a l deduction: the S's are a numerous random sample of the M'' s proportion r of'the M's are P's .'.probably about the proportion r of the S's are P's illustrates a certain ambiguity in Peiree's use of the con-cept of probability! A qualification of the general des-cription of probable inference given above defines the type of inference in simple probable deduction: To say then, that a proposition has the probability p means that to infer i t to be true would be to follow an argument such as would carry truth with It in the . ratio of frequency p (2.697). This, briefly, i s Peiree's frequency theory of probability. Buchler brings s t a t i s t i c a l deduction into confor-mity with the frequency theory by restating the above example as follows: If the proportion p of a class M has the property P, i t follows with probability p that a member of a sub-class S, chosen at random from M w i l l have the property P. 2. 1. cf. Buchler: Charles Peiree's Empiricism, pp. 241-54 for a detailed but confused treatment of this ambiguity. 2. Ibid., p. 245 Not only, however, does he thereby destroy the identify of ^ s t a t i s t i c a l deduction, but, since he leaves induction in the( form given by Peirce, he does away with the link between in- I duction and deduction without resolving the equivocality in 1 the use of the probability concept. It i s more expedient to leave s t a t i s t i c a l deduction in i t s original form and to i n -clude i t with ampliative inference as making use of a dif-ferent type of probability from that found in simple probable deduction. It is in this second type of probability, exclu-ded from the frequency theory, but in conformity with the .more general description of probable inference as reasoning "following a general maxim that w i l l usually lead us to the truth" ( E . 6 9 6 ) , in which we are here interested. The f i r s t suggestion of this equivocal sense of probability appears in a paper of 1878, "The probability of Induction," where Peirce makes the statement that "in the case of analytic inference we know the probability of our conclusion ( i f the premisses are true^probability here being used in the frequency sense"]], but in the case of synthetic inferences we only know the degree of trustworthiness of'our proceedings" ( 2 . 6 9 3 ) . This distinction must be extended to include s t a t i s t i c a l deduction as well as ampliative inference the significance of the term "probably" in the conclusion of each of these forms of inference referring to the tendency of the method of inference, i f continued in, to yield a true proposition from true premisses. . -• 35 • There i s , however, a further distinction along these lines, between the conclusion of a s t a t i s t i c a l deduction and that of an ampliative inference. The possible f a l s i t y of any particular conclusion from true premisses in a statis-t i c a l deduction arises from the fact that "the S's constitute a numerous random sample of the M's", so that the truth of the conclusion depends on the truth of the assumption that the S's are a representative sample of the M's. If i t be found that the conclusion of any particular s t a t i s t i c a l deduction from true premisses is false, further sampling w i l l tend to vindicate the ratio stated in the conclusion (E.703 cf. 709,722). The conclusion may be false for any given set of samples, but for a truly representative sample the conclusion must hold good. As Ernest Nagel points out, in the case of any s t a t i s t i c a l deduction, either i t i s known that the sampling is represen-tative, or i t Is hypothetized to be so, and this hypothesis is to be verified." 1" In ampliative inference the truth of the conclusion from true premisses is similarly dependent on the represen-tativeness of the sampling, with the difference that in this case the ratio stated in the conclusion is derived from the samples taken, rather than from knowledge of the ratio in the whole collection. Here again, i f the sampling was not representative of the whole collection, the conclusion w i l l be false, but in this case further sampling w i l l so modify the ratio as to lead to a closer approximation to that ratio true of the whole collection. "The probability of i t s 1. "Charles Peiree's Guesses at the Riddle", J. Philos. vol. 30, 1933, p. 382 - 36'-[the inductive process^ conclusion only consists in the fact that i f the true value of the ratio sought has not been reached, an extension of the inductive process w i l l lead to a closer approximation" (2.730). The derivation of the ampliative forms of inference from s t a t i s t i c a l deduction gives the primary rule for the vali d i t y of induction and retroduction, which is that the deductions of which they are the inversions must be valid and strong. Even though valid, probable deductions vary in strength, this term denoting the probable error of the concluded ratio. The probable error can be arrived at by > the formula: 0.477 1 2r(l-r) y n where r i s the given ratio and n i s the number of indepen-dent instances sampled. In most cases,'in deduction, r w i l l be indefinite, so that only a maximum and minimum figure can be given for the probable error. In the case of induc-tion and hypothesis, "r being wholly indeterminate, the minimum value i s zero, and the maximum i s obtained by putting r = §" (2.724). It i s not at a l l clear what Peirce means when he says that the concluded ratio r i s wholly indeter-minate for ampliative inference, since particularly in the case of induction a very definite ratio i s obtained by sampling. It should be noted that when Peirce speaks of retroductions and inductions as derived from deductions - 37 -he must mean that i t i s the formulae, or the syllogistic forms, for these types of inference that are so derived, and not the particular inferences themselves. It i s only after the ampliative inference has been made that both premisses of the deductive syllogism are known. Consequently, although Peirce himself may not have recognized the fact, i t would ap-pear that this primary rule for the validity of ampliative inferences, that the deductions of which they are the inver-sions must be valid and strong, i s not a rule for the formation of any particular inference, but a criterion for the validity of inferences already formed. An important rule for securing valid inferences i s that the sampling of things, in induction, and of characters, in retroduction, should constitute a f a i r choice from the class sampled. Each sample must be drawn at random from the whole lot, and independently of a l l other samples taken. "The sample must be taken according to a precept or method, which, being applied over and over again indefinitely, would in the long run result in the drawing of any one set of i n -stances as often as any other set of the same number,"(S.726). Not only i s s t r i c t honesty on the part of the investigator essential for good sampling, but also, in most cases, some mechanical contrivance is necessary to avoid any unconscious bias in the selection of samples. Another indispensable precept with regard to samp-ling i s the rule of predesignation. Before any instances - 38 -are drawn from the class under consideration, the character for which the class i s being sampled must have been settled upon (2.736). That i s , in any s t a t i s t i c a l deduction of the form given above, the major premiss: proportion r of the M's-are P's must have been laid down, before the sampling specified in the minor premiss: the S's are a numerous random sample of the M's has been carried out. Then the inference has been made a l -ready, that the proportion r of the S's w i l l be P's, and i t is only necessary to draw the samples. If, on the other hand, the sampling i s done f i r s t , before stating the major premiss, and then on the basis of the sampling the major premiss i s decided upon, clearly the inference w i l l not be a valid s t a t i s t i c a l deduction. Similarly in s t a t i s t i c a l induction in depth, the term S, of the proposition: S has an r-likeness to the M's » must be predesignated prior to sampling. This principle holds" good for Induction, just as" i t does for deduction. In sampling a class M, both the character P which is being sampled for and the number of samples to be drawn must be predesignated. The inference has then been made prior to sampling, that the ratio of P's in the sample w i l l hold good for" the whole class M. Samples may then be drawn and the ratio noted. If, on the other hand, the character P i s not predesignated, but i s decided - 39 -upon by inspection of the sample, i t i s possible to find, in any set of instances of a class, any number of particular regularities which w i l l not hold good for the whole class. Such regularities, i f particularly striking may suggest a question, but have no place in valid induction (2.737). In keeping with the parallel treatment which he gives induction and retroduction in most discussions of ampliative inference, Peirce speaks of predesignation as applying in the same way to retroduction, i t being the term S of the proposition: S has proportion p of the marks P'P MP , M etc. which must be predesignated. Since, however, i t i s the un-expected appearance of S, in retroduction, which initiates reasoning to explain i t by the formation of a hypothesis, i t i s not clear where predesignation i s involved. Peirce him-self c l a r i f i e s this matter somewhat in a later passage (2.739), where the rule.of predesignation for retroduction i s said to be merely a restatement of the rule "that a hypothesis can only be received upon the ground of i t s having been verified by a successful prediction", with the exception that " i t i s not at a l l requisite that the r a t i c p should be given in advance of the examination of the samples." This may be interpreted as meaning that given S to explain, and having formed a crude hypothesis that S i s l i k e M, consequences of M may be predicted and compared with the data involved in the event S, and the degree of their resemblance noted. This - 40-is comparable with. Kepler's retroduction regarding the orbit of Mars, previously discussed. Peirce interprets the rule that a hypothesis should be simple as meaning that the objects reasoned about, and their relationship to each other, should be familiar to the reasoner, since, in such a case the hypothesis regarding their degree of similarity i s based on a knowledge of a great number of their characteristics (£.740). In addition to this aspect of fami-l i a r i t y there i s also Peiree's theory, already mentioned, of the'tendency of the human mind to make true guesses, and of the mind's af f i n i t y to those types of natural laws related to mechanics and to other l i v i n g beings, so that by following the.guide of familiarity and simplicity the mind i s actually following i t s instinctive bent (S.753-4). Another aspect . again of -the principle of simplicity relates to the testing of hypotheses. In most cases the simpler a hypothesis i s , . , the easier i t i s to test and discard i f found to be false (1.68). This last aspect of simplicity i s related to considerations of economy in the acceptance of hypotheses, rather than of their comparative strengths, but is.none the less important. The principle of simplicity i s not to be confused with Ockham's principle — that entities are not to be un-necessarily multiplied — which Peirce also holds to be valid in the formation of hypotheses (4.35), this latter constitu-ting for Peirce a purely methodological maxim without the metaphysical ramifications of the principle of simplicity. - 41 -Peirce's views on the theory of ampliative inference as dependent upon an order of nature have been discussed in Chapter II. He repeats his rejection of this theory in the present paper (2.749), but considers at the same time the ef-fect of our knowledge of special uniformities, upon ampliative inferences. Four such types of special uniformity are li s t e d , which may be so strong as to turn the ampliative inference into a deduction from the known uniformity, but which in most cases merely function to increase or decrease the strength of an in-duction or retroduction (2.743): 1. members of a class may present a greater or less general resemblance as regards a cer-tain line of characters. If we find a certain metal to have certain characters of cer-tain types i t i s a strong induction that a l l other samples of that metal w i l l show the same characters. 2. a character may have a greater or less tendency to be present or absent throughout • ithe whole of whatever classes of certain kinds. In biology generic and specific characters show such greater and less tendency to be present or absent throughout a genus. 3. a certain set of characters may be more or less intimately connected, so as to be probably either present or absent together in certain kinds of objects. Then i f two objects show some of these characters in common, a hypothesis concerning the similarity of these objects w i l l be strengthened. 4. an object may have more or less tendency to pos-sess the whole of certain sets of characters when i$ possesses any of them. - 42 -Both 3 and 4 clearly relate to the construction of hypotheses, while 1 and 2 relate to inductions. This paper of 1883 i s the final systematic presen-tation of the early theory of retroduction, although that theory must have been held by Peirce at least until 1893, when the papers for "The Search for a Method" were edited. The scattered references to retroduction, to be found in subsequent papers, included in the early period, have been considered in the present chapter, but add nothing sig-nificant to the early theory. - 43 -Chapter IV The Later Theory — 1896-1910 The f i n a l , and most complete, statement of Peiree's early theory of retroduction was made in the "Theory of Pro-bable Inference", of 1883. No further writings on retroduc-tion, of any length, appear un t i l 1901, but since papers of the early period, written from 1867 to 1883, were edited in 1893 for a projected work, the "Search for a Method", i t may be assumed that the early theory was held until that year. The f i r s t remarks on retroduction which appear to belong to the later theory occur in a manuscript of 1896, and are f o l -lowed by similar statements in 1898, but no explicit renun-ciation or revision of the early theory i s to be found prior to the papers and letters written in 1901 on Hume's refutation of miracles. 1 Important statements appear in 1902, in the manuscript of an uncompleted work, "The Minute Logic" and in the articles on logic contributed by Peirce to Baldwin's Dictionary of Philosophy and Psychology. In 1903 the "Lectures on Pragmatism", given by Peirce under the auspices of Harvard University, restate the later theory with emphasis on the relation between pragmatism and retroduction. Nothing of great importance on the subject appears after 1903 with the exception of Peiree's "Neglected Argument for the Reality of God" which was published in the Hibbert Journal of 1908. 1. P. P. Wiener ed. "The Peirce-Langley Correspondence -Hume and the Laws of Nature", Amer. Philos. Soc. Proc, vol. 91 #2, 1947 pp. 201-28. - 44 -In view of the fact that, unlike the early theory, the later theory i s presented for the most part in a large number of short passages in papers written within a few years of each other, i t is possible to state i t as a systematic whole, rather than in chronological order of development. In several passages in these papers of the later period Peirce presents a rough outline-of the occasion calling forth a hypothesis, the retroduction involved, and the inductive testing of the accepted hypothesis. Such an outline gives the approximate contents of the later theory. A l l inquiry whatsoever arises from our observation of some event, unexpected and unexplainable in terms of formulated theory, which i t i s the purpose of that inquiry to explain. Such inquiry Peirce divides into three stages, the f i r s t stage being retroduction, by which upon careful scrutiny of the observed facts some explanatory hypothesis i s brought to mind. Since, however, such a hypothesis i s merely a sug-gested explanation without guarantee or probability as to i t s truth, i t must be tested by comparison with fact. The second stage of inquiry consists i n the deduction from the hypothe-sis of a wide variety of experiential consequences which would follow from i t s truth. The third stage, known as In-duction, ascertains to what degree these predicted conse-quences actually accord with experience, and on the basis of these findings judges as to the truth or f a l s i t y of the hypothesis. One point with regard to Peirce's terminology - 45 -should be noted, and that i s that although he terms the second stage of inquiry deduction, and the third stage, in-duction, on several occasions he speaks of both the second and the third stage as induction, meaning by this use of the term, the whole testing procedure following retroduction. The period of transition from the early theory to the later theory outlined above, f e l l as has been stated between the years 1895 and 1901. During this time remarks on retroduction in. Peirce fs writings are scarce,.but show gradual deviation from the position held in the paper of 1883. Pronounced departure from the early theory is most evident in a manuscript of 1896, in which Peirce speaks of retroduction as the "provisional adoption of a hypothesis -because every possible consequence of i t i s capable of experimen-t a l verification . . . ." (1.68), and of a. hypothesis as "practically no more than a question" (1.120), of which the best hypothesis i s that "which can be most readily refuted i f i t is false" (1.120). The idea of a hypothesis as an i n -telligent guess, with the emphasis in scientific method on procedures of testing clearly belongs to the later theory, as opposed to the early theory concept of hypotheses as the stable conclusions of syllogistic reasoning. , The reasons for this transition are not altogether clear, and Peirce himself makes only the barest mention of his change of thought. One such passage occurs in a paper of 1902, wherein he speaks of a "slight positive error" in the theory of 1883, and of*a capital error on the negative side, - 46 -in that "the reasoning with which I was there dealing could •not be the reasoning by which we are led to adopt a hypo-thesis" (2.102). A second passage appears in the Peirce-Langley correspondence of 1901, in which Peirce speaks of a new doctrine of the logic of hypothesis, following from the pragmatic principle, which doctrine he has held for the past five or six years and i s now ready to publish. 1 This second statement i s In keeping with A.W. Burks1, suggestion that the transition from the early to the later theory may have followed from Peiree's attempt to bring the various aspects of his thought into a coherent system.2 It is Burks.* opinion that the theory of retroduction was amended to bring i t into conformity with Peiree's pragmatism and tychism; Peirce himself suggests a link between retroduc-tion and the doctrine of categories (2.102) but does not en-large on the point. Another influence in the change of theory may have been the analogy which Peirce draws, from his earliest papers on, between retroduction and the act of perception. That retroduction should be the source of a l l new ideas, and that induction should at a l l time's be subsequent to some retroduction are more consistent with the processes of per-ception and habit formation than are the doctrines of the early theory. The changed relationship between retroduction and induction Is probably the most obvious difference intro-duced by the later theory. In the early theory synthetic i n -ference was bifurcated into retroduction, the reasoning from 1. P. P. Wiener ed. "Peirce-Langley Correspondence-Hume and the Laws of Nature", Amer. Philos. Soc. Proc.,vol.91, #2,1947, p.205 2. "Peiree's Theory of Abduction", Philos. Soi. vol. 13,1946, p.302 characters of one kind to characters of another, and induction, the generalizing from facts to other facts of similar kind. In the later theory induction i s a process of testing predic-tions from hypotheses against experienced facts; a l l synthetic inference f a l l s under retroduction. "Presumption £an alter-native term for retroductionjj i s the only kind of reasoning which supplies new ideas, the only kind which i s , in this sense synthetic" (2.777). What was formerly called induction, Peirce speaks of as being "a mixture of deduction and presump-tion" (2.775). To some extent this change i s merely one of terminology, but not only does i t solve the tendency, in the early theory, for retroduction and induction to overlap in spite of the careful distinction drawn between them, but i t also accords with the new emphasis, in the later theory, on • the testing procedure. Retroduction, as described in the later theory, is a process of adding to the observed facts a statement, termed a hypothesis, which explains those facts In terms of other facts and makes "them applicable . . . to other c i r -cumstances than those under which they were observed" (6.524). "Any supposed truth from which would result such facts as have been observed" (6.525) constitutes for Peirce a hypothesis explanatory of those facts. The term 'result* is used in i t s logical rather than material sense. That i s , the relation-ship referred to i s not specifically one of cause and effect but such that the facts observed may be seen to be particular cases of a wider class of facts, of a nature either the same - 48" -as or different from those observed. In another passage Peirce speaks of the observed facts*as constituting a'likeness' of those represented in the hypothesis, and again gives Kepler's hypothesis as to the orbit of Mars as an example, in that the observed positions of Mars constituted a likeness of those of a body moving in the orbit described in the hypo-thesis (2.96). This i s in keeping with Peiree's concept of explanation, referred to in Chapter III, as consisting in the demonstration that the process or event to be explained is a special case of a more general and better known class of processes. Emphasis in the early theory was thrown very heavily on the process of reasoning underlying the formation of hypo-theses and inductions, to the comparative neglect of methods of testing hypotheses. In opposition to what Peirce calls, the positivist position, hypotheses were regarded as in no way uncertain and "something to be superseded" (2.707), but as conclusions comparable in strength to the conclusions of induction. In the later theory, on the other hand, where testing rather than formation of hypotheses becomes the crucial process in the logic of discovery, hypotheses are no longer regarded as stable or reliable. They are accepted . merely as possible explanations of the facts noted, as "practically no more than a question" (1.121). They are guesses or conjectures suggested by the premisses and "ac-cepted as having some chance of being true" (2.786) and as having a form such as to suggest experiments which w i l l test -.49 -the degree of their truth. The justification for the enter-tainment of such uncertain conjectures as having any possi-b i l i t y of truth at a l l i s that " i f we are ever to learn anything or to understand phenomena at a l l , i t must be by abduction [an alternative term for retroduction^ that this is to be brought about" (5.171). Only by retroduction can ideas be originated. In keeping with the extremely provisional status of hypotheses, one of the important c r i t e r i a of their accep-tance i s that they be easily and speedily testable; "the best hypothesis . . . i s the one which can be the most readily re-futed i f i t is false" (1.120). A third break which Peirce makes with the early theory in these later writings concerns the probability of hypotheses. In the early theory conclusions, from induction and retroduction were spoken of as being probable, not in the sense, of the frequency theory of probability, but in the sense of being arrived at by a method, which, i f continued in long enough, must lead eventually to a true statement of the facts. Although Peirce does hot declare as much, his use of the term probability for these two widely different concepts suggests that he may have considered the two forms of pro-bability as ultimately reducible to a single form. In the later theory Peirce distinguishes these two concepts most clearly and divorces a l l idea of probability from retroduc-tive conclusions. In doing so he distinguishes between four concepts frequently confused: probability, validity, l i k e l i -hood, and pl a u s i b i l i t y . Probability Peirce now limits to - 50 -•objective probability* which i s "the ratio of frequency of a specific to a generic event in the ordinary course of experience" (2.777). At no time, in either early or later writings, does Peirce claim this form of probability for pure hypotheses, although insofar as hypotheses are supported by deductions from known uniformities, as discussed in Chapter III, he seems in the later theory to class them as in this sense probable (cf. 6.527, 6.534). His remarks on this point are extremely brief, but clear as far as they go. "There are facts which . . . necessitate the truth, or the f a l s i t y , or the probability in some definite degree, of the hypothesis" (6.527). It would appear, however, that only a hypothesis whose character can be arrived at deductively may be spoken of as probable — such a hypothesis, for instance, as that on a particular throw of a die a particular face would show, in which case the probability would be one sixth. This, however, is scarcely a hypothesis in Peiree's general use of that term. Apart from this special case., hypotheses, however*; strongly supported by known facts, can hardly be spoken of as being probable in the accepted sense of that word. Validity, as Peirce uses i t , i s that characteristic of any inference by which i t has "that sort of efficiency in leading to the truth, which i t professes to have" (2.779). The characteristics of validity differ for each type of infe-rence, the validity of each instance of inference depending upon i t s having the characteristics of i t s type. That charac-- 51 -t e r i s t i c of the inductive method, formerly spoken of as i t s probability, by which i f persisted in i t must eventually lead to truth, i s now spoken of as i t s validity (2.781). Similarly, a retroduction i s valid i f i t s conclusion be such "that i t s consequences are capable of being tested by experimentation" and "that the observed facts would follow from i t as neces-sary conclusions" (2.781). These are the only c r i t e r i a of a valid hypothesis; such_a hypothesis, however, may be hope-lessly weak since strength and validity are unrelated concepts. Likelihood, as defined by Peirce, i s a characteris-t i c of theories unproved, as are in varying degrees a l l scien-t i f i c theories, but "supported by such evidence, that i f the rest of the conceivably possible evidence should turn out upon examination.to be of a similar character, the theory would be conclusively proved" (2.663). Likelihood, although Peirce does not specifically relate i t to retroduction, would presumably apply to hypotheses, both insofar as they have been partly proved and, i t would seem, insofar as they are suppor-ted by known facts. Plausibility, however, of a l i four concepts, i s the one most particularly related to hypotheses. Peirce defines i t as that characteristic of an untested theory which i f true would so explain the given facts "as to recommend i t for further examination" (£.662). Unfortunately this statement hardly describes what i t i s in the theory or hypothesis, apart from i t s affording an explanation, that recommends i t for further examination. It cannot be anything of the nature of - 52 -objective facts found to support the hypothesis, since these are accounted for under probability or likelihood, but ap-pears to be what he calls elsewhere "subjective probabili-ties, or likelihoods, which express nothing but the conformity of a new suggestion to our prepossessions" (2.777)i It may be that plau s i b i l i t y is intended to cover not only the prin-ciple of the consistency of new hypotheses to accepted theories, but the principles of simplicity and familiarity as well, -both of which are aspects of our prepossessions and principles of some weight in Peiree's system. Like plausibility, the concept of the strength of hypotheses is never clearly set forth, and Peirce himself admits i t to be vague (2.780). Strength appears, however, to rest on a combination of plausibility and likelihood; that i s , upon the conformity of the hypothesis'to our preposses-sions' and upon the objective evidence supporting the hypo-thesis. In the matter of the formation of hypotheses i t has already been suggested that Peirce in the later theory discarded the systematic derivation, • from the deductive syllogism, of the form of retroduction, and came to look upon the hypothesis as suggested by more or less unconscious inter-action between objective facts and the mind of the observer. He distinguishes between argument and argumentation, the f i r s t being "any process of thought reasonably tending to produce a definite belief" and the second, "an Argument proceeding upon definitely formulated premisses" (6.456), and G l a s s e s - 53 -retroduction as argument rather than argumentation (6.469). The process of thought in a retroduction consists in the colligation, or gathering together, of a l l available facts related to the subject under consideration, followed by an act of observation which in this case consists in "the d e l i -berate yielding of ourselves" to the force of the facts, from which the hypothesis results (5.581). More exp l i c i t l y , Peirce describes this process of observation as one in which, upon examining the features of an unexpected occurrence, we notice "some remarkable character or relation among them" which we at once recognize "as being characteristic of some conception" already familiar to us (£.776). This process of reasoning i s not unlike that of the f i r s t statements of the early theory in which: M i s ptp«p«» etc. • • S is P'P"P"» etc. .'.S is like M the main difference being that Peirce now considers "syllogis-t i c forms and the doctrine of logical extension and compre-hension "as of secondary importance in the retroductive process (8.10£). The gist of his meaning seems to be that while every retroduction f i t s , by reason of the conformity of mental activity to syllogistic patterns, into the patterns so carefully described in the early theory, the actual for-, mation of hypotheses is not made possible or aided by the knowledge of these patterns. Retroduction, in short, i s an argument, but not an argumentation. If the syllogistic form emphasized in the early - 54 -theory i s only cf' secondary importance, and i f , as Peirce further claims, retroduction consists in mere suggestion of conjectures for which no reason can he given (5.171), can i t he classed as a type of inference? R. B. Braithwaite 1 con-siders that i t cannot and regards Peiree's classification as verbal, on the grounds that a theory that comes to mind as a flash of insight can hardly be claimed to be the product of a reasoning process deserving the name of inference. Peirce himself appears to support this judgment when he says that " i f one does not at a l l know how one's belief comes about, i t cannot be called even by the name of inference" (6.497). Inference, for Peirce, involves by definition an element of control; for there to be control i t i s necessary that the reasoner be aware that he is making an inference, although he may be unaware of the actual mental processes involved. Inference proper i s thus distinguished from those mental processes which Peirce, with customary perversity, calls 'unconscious inference', such inference being unconscious, not because the subject i s Ignorant of the processes involved, 2 but because he is unaware that any inference has been made. ' Inference i s defined as "a process in which the reasoner i s conscious that a judgment, the conclusion, i s de-termined by other judgment or judgments, the premisses, 1. Review of Collected Papers, Vols. I - IV. Mind. N.S. vol. 43, 1934 p. 510. 2. cf. C. S. Peirce, Review of Wm. James' "Principles of Psychology" Pt. II. The Nation, vol. 53, 1891, p. 33. - 55 -according to a general habit of thought, which he may not be able precisely to formulate, but which he approves as con-ducive to true knowledge" (2.773). If these statements on the nature of inference seem at f i r s t glance to support Braithwaite's contention that retroduction cannot be classed as inference, more careful consideration w i l l show that they provide adequate support for Peirce's own classification. Peirce himself applies the above distinction, between inference and 'unconscious inference', to retroduction and the non-inferential process, analogous to retroduction, involved in the formation of percepts. The similarity which Peirce claims to exist between the proces-ses of formation of hypotheses and percepts has already been outlined; the difference between them l i e s in the fact that percepts "are absolutely beyond criticism" (5.182), and are •unconscious inferences'. We may, by psychological analysis, discover percepts to be the product of mental processes of the same form as retroduction, but they are differentiated • from hypotheses by the fact that while the hypothesis i s "something whose truth can be questioned or even denied", we cannot form the least conception of what i t would be to deny the perceptual judgment" (5.186). Possibly, without distorting Peirce's meaning, i t can be added that we are able to question or to deny the hypothesis because we are aware that i t i s the product of a mental process, (or else, that we are aware that i t i s the product of a mental process because we can question or deny i t . ) For a conclusion to be classed as an inference - 56 -we must be able to "go back and c r i t i c i z e the premisses and the principles that guide the drawing of the conclusion" (6.497). For such a conclusion to be admissible as a hypo-thesis, criticism of. the reasoning involved must show "that i t would account for the facts or some of them" (5.189), the form of such inference being: The surprising fact C i s observed But i f A were true, C would be a matter of course Hence, there i s reason to suspect that A i s true (5.189). Since this form of reasoning i s invalid as deductive infe-rence the premisses do not compel the conclusion but advance i t as a suggestion and, in the face of criticism, support i t as plausible. Since, however, pla u s i b i l i t y constitutes a recommendation that the hypothesis be tested, the conclusion "should be such that definite consequences can be plenti-f u l l y deduced from i t of a kind which can be checked by ob-servation" (E.786).1 The f i r s t principle of the acceptance of hypotheses — that they account for the given facts — Is essential; on the second principle, that they suggest experiments by which they may be tested, Peirce seems to be less sure. Although in 1902 he speaks of testability as the 'principal rule' in the acceptance of hypotheses (2.786), he makes a distinction in a paper of 1898 between hypotheses upon which verifiable predictions can be based, and those which while unverifiable are held "as a mere convenient vehicle of thought — a mere matter of form" (5.599). 1. On the question of the classification of retroduction as a form of inference: cf. A. W. Burks, Peiree's Theory of Abduction, Philos. Soi.. vol. 13, 1946, pp. 301-6. - 57 -Again, in 1908, he advocates acceptance of the hypothesis of G-od's reality, "whose ultimate test must be in it s value in the self-controlled growth of man's conduct of l i f e " (6.480), and yet, in the same paper, speaks of the necessity of testing hypotheses by prediction and v e r i f i c a -tion (6.470 f f . ) . It may be that Peirce i s drawing a dis-tinction between those hypotheses which are to be added, i f verified, to the body of existing theory, and those which are to be relied upon in the conduct of l i f e . Judging from the 1898 statement.the latter have their function even in the conduct of sci e n t i f i c thought, but must, like catalysts, be cleared away before the theoretic product i s f u l l y revealed. Such a distinction between theory and practice is one that becomes more and more evident in Peirce's writings as he grows older. Peirce states the principles governing the acceptance of hypotheses for testing in another way in the "Lectures on Pragmatism" of 1903, where he claims not only that the prag-matic maxim is the only rule necessary for the admissibility of hypotheses, but that this is a l l that, the pragmatic maxim actually i s . The maxim as Peirce gives i t in this particular passage i s , in fact, only one of many statements which he derives from the principle of pragmatism and is as follows: a conception can have no logical effect or impact differing from that of a second conception except insofar as, taken in connection with other con-ceptions and intentions, i t might conceivably modify our practical conduct differently from that second conception (5.196). - 58 -If the pragmatic principle may be distinguished from the maxims derived from i t , i t would seem best summarized in the statement "that the possible practical consequences of a concept constitute the sum total of the concept" (5.25), in which form i t is rather less cumbersome than in the form given above, and apparently more relevant to the matter in hand. The two functions of pragmatism, or "whatever the true doctrine of the Logic of Abduction may be", are f i r s t , "to give us an expeditious riddance of a l l ideas essentially unclear" and second, "to lend support [toj| and help to render distinct, ideas essentially clear, but more or less d i f f i c u l t of apprehension . . . . (5.206). From these quotations i t may be seen that Peiree's pragmatism is a doctrine of meaning, rather than of truth. Since "pragmatism is the doctrine that every conception i s a conception of conceivable practical ef-fects" (5.196), the pragmatic maxim legislates on the ac-cep t i b i l i t y of hypotheses in terms of whether or not their conceivable practical effects account for the phenomena under consideration. On no other grounds than the adequacy of their conceivable effects to explain the phenomena, are hypotheses to be accepted for testing, or rejected as in-admissible. That this Is the whole function of the pragmatic • principle follows from the fact that both induction and de-duction are formal processes carried on independently of their content in any particular instance. Pragmatism affects their content, in that a l l content i s originally derived from retro-- 59 -auction but with the formal, process of induction and deduction i t has nothing to do. In the event of there being a number of plausible hypotheses to explain the phenomenon under investigation, the basis upon which hypotheses are accorded priority for testing is one of economy — "Economy of money, time, thought and energy" (5.599). Peirce at one point goes so far as to c a l l this the 'leading consideration' in retroduction (5.599). Without attempting to supply an exhaustive or systematic set of rules, Peirce suggests a number of precepts as aids in the economical selection of hypotheses for testing. 1. If there i s a large number of. acceptable hypotheses, then the most economical procedure is to find, i f possible, some observable result which would follow from one half of the hypotheses and not from the other half, and to test for this result. By repetition of this method a large number of hypo-theses can very quickly be reduced to that small remainder which can no longer be halved and must be tested one by one (6.529). 2. Among any set of possible hypotheses, those which appear simplest to the human mind should be tested f i r s t . Two reasons exist for this rule: a. The simpler a hypothesis i s , the easier in most cases i s i t to deduce i t s consequences and test for them. Such a hypo-thesis, If false, can.be readily eliminated (6.533). b. Since i t i s Peirce's belief that the possibility of any sci e n t i f i c truth whatsoever depends on a human faculty of - 60 -guessing correctly, and since such a faculty i s based on the existence of a harmony between the human mind and nature, i t is his contention that the simplicity of hypotheses w i l l in some cases be an indication of this harmony, and hence a sugges-tion of their possible truth (6.530-2, cf. 6.477). 3. Any hypothesis which for any reason may be more easily and more quickly tested than the other plausible hypotheses should for this reason be considered f i r s t (6.533). 4. Any hypothesis strongly supported by an objective fact, of the nature of a deduction from known principles, should be given an early t r i a l (6.534). -5. Any hypothesis "which suggests an experiment whose d i f -ferent possible results appear to be, as nearly as possible, equally l i k e l y " (2.786), should always be preferred. This precept does not appear to be in harmony with that immediately preceding i t , and the reason for i t i s not clear. Peirce doe's not offer any explanation, but i t may be that he considers such a hypothesis more crucial than any other. 6. Ockham's razor i s offered as a sound economic principle for the selection of hypotheses — Peirce calls i t "the very roadbed of science" — but i t i s accorded nothing, more than methodological status and does not give the simpler hypo-thesis any objective probability (4.1, 6.535). 7. No hypothesis should be abandoned too readily, but should be maintained u n t i l clearly unacceptable. 1 The testing of any hypothesis involves two stages 1. "Scientific Method" in Dictionary of Philosophy and  Psychology, vol. 2, p. 501. - 61 -of inquiry: f i r s t , the deduction from the hypothesis of a large number of facts which would be observable under speci-fied conditions i f the hypothesis were true, and second, the inductive process of discovering whether or not such facts actually do occur as stated. The Second Stage o f Inquiry, the deductive, consists in an explication of the hypothesis by logical analysis, such that i t i s rendered as distinct as possible, followed by a demonstration or deduction' of conse-quences from the explicated hypothesis (6.471). The Third Stage of Inquiry, the inductive, ascertains "how far those consequents accord with'Experience" (6.472) and on this basis pronounces on the truth of the hypothesis. Induction invol-ves three sub-stages, the classificatory, "by which general Ideas are attached to objects of Experience" (6.472), the Probational, the actual testing by experiment, and the Senten-t i a l , in which the results of the probations are weighed, and judgment passed on the hypothesis. Probation is of two forms, Crude Induction and Gradual Induction, of which the latter is again divisible into qualitative and quantitative. Crude Induction "is the only Induction which concludes a Logically Universal Propo-sit i o n " (6.473); i t involves an assumption that since a l l events of a certain class have had a certain characteristic, a l l future events of that class, w i l l show the same characte-r i s t i c (2.756), that since a l l men up to the present have been mortal, ' a l l men are mortal. 1 Such an induction is extremely weak, and i s subject to refutation at any moment. - 62 -Gradual induction "makes a new estimate of the proportion of truth in the hypothesis with every new Instance" (6.473), thereby gradually correcting any error in i t s just evaluation of the hypothesis (5.145). Quantitative gradual induction investigates the deduction from a hypothesis, that a class of objects w i l l have a certain character, by sampling that class and noting the occurrence of the character predesignated, the assumption being that the sample is representative of the whole class (2.758). Qualitative induction, or abductory induction as Peirce sometimes calls i t , consists in deducing a wide variety of characters from the hypothesis, such that the discovery, of the existence of each of these characters .. w i l l add weight to the hypothesis, and the discovery of a l l w i l l constitute proof (2.759). Peirce gives as an example the hypothesis that a certain man i s a Catholic priest, from which i t would follow that upon investigation he would be found to possess certain characteristics. If the hypothesis i s , in fact, correct, then examination w i l l reveal one by one, each of these characteristics (6.526). Qualitative induction i s weaker than quantitative induction, since depen-dant upon our estimation of the weight of the evidence gathered in support of the hypothesis, but of greater u t i l i t y (2.759). In the division of gradual induction into quali-tative and quantitative induction Peirce appears to introduce equivocal meanings of the term Induction. Induction, in the later theory, i s on several occasions used to describe the - 63 -whole process of testing hypotheses, which meaning may be seen to coincide with that given for qualitative induction, in spite of Peirce*s classification of i t as a form of Pro-bation. As has been stated, qualitative induction involves the deduction of a number of consequences from a hypothesis, and the investigation of those consequences. This, in brief, is the general procedure of testing hypotheses (cf. 6.526). Quantitative induction, on the other hand, is a procedure by which the truth of any particular deduction from a hypo-thesis is tested, and does occur in the probational stage of qualitative induction. It i s , in fact, the process of reasoning called induction in the early theory, but described in the later theory as "a mixture of deduction and presump-tion** (2.776). It is only in terms of this classification, and by using the term induction to denote the whole testing process, that Buchler*s claim with regard to the later theory, that "the conclusion of an induction . . . i s always some hypo-thesis previously abduced",1 can be justified. This state-ment does not apply to 'quantitative inductions* which con-clude only single deductions from hypotheses. The details of the later theory have been compared point by point with those of the early theory, in the course of this chapter. It remains to compare the two theories in general, both as to the extent to which they actually differ, and as to the comparative merits of the two theories.' 1. Charles Peirce's Empiricism, p. 135. - 6 4 -Comparison of Peiree's theories of retroduction with those ad-vanced by other philosophers i s beyond the scope of t h i s paper. In spite of the pronounced differences to be noted between the early and l a t e r theory, i t has been suggested throughout the present chapter that many of the changes i n -troduced i n Peiree's l a t e r writings go no deeper than matters of terminology and emphasis. The terms retroduction and i n -duction are redefined i n the l a t e r theory, and as a result come to bear a relationship to each other quite d i f f e r e n t from that holding i n the early theory, but i n spite of t h i s change the actual sequence of processes remains much the same. Synthetic inference, bifurcated i n the early theory into retroduction and induction, becomes i n the l a t e r theory wholly the province of retroduction, with the inductive inference of the early theory analysed into a combination of deduction and retroduction. The term induction i s carried over- into the l a t e r theory to comprise the process of testing the con-clusions of retroduction, a process b r i e f l y described but •-l e f t unnamed i n the early theory. The s y l l o g i s t i c form of retroduction, taken i n the early theory as the actual process of reasoning involved i n the formation of hypotheses, and f o r that reason developed and described i n great d e t a i l , i s re-cognized i n the.later theory as being merely a description of the reasoning, i n terms of evidence, known theory and r e s u l -tant hypothesis, and i s consequently relegated to a p o s i t i o n of secondary importance. Hypotheses are no longer, in-the l a t e r - 65 -theory, spoken of as probable, but the change i s in fact wholly one of terminology in order to avoid confusion with the frequency theory of probability. Finally, the function of retroduction, as the explanation of startling phenomena in terms of known laws remains the same throughout both theories. This is not, however, to say that there are not differences-between the two theories, nor that the change of emphasis does not in i t s e l f constitute a very real change. It i s f e l t that in these differences the later theory represents a pronounced improvement over the early theory, in that i t is' thereby enabled to present a clearer and more balanced descrip-tion of the logic of discovery. By his reallocation of the terms retroduction and induction, Peirce has been able to describe the sequence of reasoning from the appearance of the unexpected event which institutes inquiry, to the accep-tance of a verified explanatory hypothesis, in such a manner that retroduction and induction, probation and deduction appear in in£er-relation as stages in sci e n t i f i c procedure, rather than as independent and unrelated types of inference. The change of emphasis in the later theory, together with the abandonment of the syllogistic form as an important factor In retroduction, makes i t possible to avoid the disproportio-nate picture given in the early theory of the relative impor-tance of retroduction and the techniques of testing, and to consider many of the probtos of verification ignored by the early theory. • - 66 -Bibliography Hartshorne, Charles and Weiss, Paul, ed., Collected Papers of  Charles Sanders Peirce. (1866-1911), Cambridge, Harvard University Press, 1931-1935, 6 vols. Peirce, C. S., Papers on Logic in, Baldwin, J. M., ed., Dic- tionary of Philosophy and Psychology. New York, Maomillan, 190£, 2 vols. Peirce, C. S., Peirce-James correspondence, in Perry, R.B., The Thought and Character of Wm. James, Boston", L i t t l e , Brown and Co., 1935, 2 vols. Peirce, C. S., "The Peirce-Langley Correspondence—Hume and the Laws of Nature" (1901), ed. P. P. Wiener, Amer. Philos. Soc. Proc., 91 #2: 201-228, 1947. Peirce, C. S., Review of Wm. James Principles of Psychology, The Nation, 53: 15, 32-33, 1891. For the most complete bibliography of Peirce's published writings, including those not as yet printed in the Collected Papers, see: Cohen, M. R., Chance, Love and Logic, New York, Hareourt, Brace, 1923. - 67 -Anderson, P. R. .and Fisch, M. H . , Philosophy in Amerioa. New York, Appleton-Century, 1939. Armstrong, A. C , "The Evolution of Pragmatism", J. Philos.. 5: 645-650, 1908. Braithwaite, R. B., Review of Collected Papers, vols. 1-4, Mind. N. S.. 43: 487-511, 1934. Britton, Karl, "Introduction to the Metaphysics and Theology of Charles Sanders Peirce", Ethics. 49: 435-465, 1938-39. Britton, Karl, Review of Collected Papers, vol. 6, Mind, N. S. , 46: 394-399, 1937. Buchler, Justus, "The Accidents of Peiree's System", J. Philos., 37: 264-269, 1940. Buchler, Justus, Charles Peiree's Empiricism, London, Kegan Paul, 1939. Burks, A. W., "Peiree's Conception of Logic as a Normative Science", Philos. Rev., 52: 187-193, 1943. Burks, A. W., "Peiree's Theory of Abduction", Philos. Sci.. 13: 301-306, 1946. Carpenter, P. I., "Charles Sanders Peirce, Pragmatic Trans-cend entalist", New England Quarterly, 14: 34-48, 1941. Carus, Paul, "The Founder of Tychism", Monist, 3: 571-622, 1893. Carus, Paul, "The Idea of Necessity", Monist, 3: 68-96, 1892. Carus, Paul, "Mr. Charles S. Peiree's Onslaught on the Doc-trine of Necessity", Monist, 2: 560-582, 1892. Cohen, M. R., Introduction to Chance, Love and Logic, New York, Harcourt, Brace, 1923. Cohen, M. R., "Charles S. Peirce and a Tentative Bibliography of his Published Writings? J. Philos., 13: 726-737, 1916. Cohen, M. R., "The Founder of Pragmatism", The Nation, 135: 368-370, 1932. Creegan, R. F., "Radical Empiricism and Radical Historicism", J. Philos., 41: 126-131, 1944. Dewey, John, "Charles Sanders Peirce", New Republic, 89: 415-416, 1937. - 68 -Dewey, John, "The Pragmatism of Peirce", J. Philos., 13: 709-715, 1916. . ; Dewey, John, "Peirce's Theory of Linguistic Signs, Thought and Meaning", J.. Philos., 43: 85-95, 1946. Dewey, John, "Peirce's Theory of Quality — a Reply to Goudge", J. Philos.. 32: 701-708, 1935. Feibleman, J. K., "Esthetics of Peirce',' Personalist, 22: 263--273, 1941. Feibleman, J. K., "Individual Psychology and the Ethics of Peirce", J. Gen. Psychol., 31: 293-295, 1944. Feibleman, J. K., "Influence o.f Peirce on Dewey's Logic'' Educa., 66: 18-24, 1945. Feibleman, J. -K., An Introduction to Peiroe's Philosophy, New York, Harper, 1946. Feibleman, J. K., "Peiroe's Phaneroscopy", Phil, and Pheno- menological Research, 1: 208-216, 1940. Feibleman, J. K., "Peiroe's Use of Kant", J. Philos., 42: 365-377, 1945. , Feibleman, J. K., "The Relation of Peirce to New England Culture", American Journal of Economics and Sociology.. 4: 99-107, 1945. . • Feibleman, J. K., "Systematic Presentation of Peirce's-Ethics", Ethics, 53: 98-109, 1943-. Freeman, Eugene, The Categories of Charles Peirce, Chicago, Open Court,.1934. Gallie, W. B., "The Metaphysics of C. S. Peirce", Aristotelian  Soc. Proo., N. S.. 47: 27-62, 1946-47. Gentry, George, "Peiroe's Early and Later Theory of Cognition and Meaning", Philos. R., 55: 634-650, 1946. Goudge, T. A., "Conflict of Naturalism and Transcendentalism in Peirce", J. Philos., 44: 365-374, 1947. Goudge, T. A., "Peiroe's Treatment of Induction", Philos. Sci., 7: 56-68, 1940. Goudge, T. A., "Views of Charles Peirce on the Given in Experience", J. Philos., 32: 533-544, 1935, 33: 289-295, 1936. "~ - 69 -Hall, G. S., "Philosophy in the United States", Mind, 4: 89--, 105, 1879. Hamblin, F. M., "Comment on Peiree's Tyohism", J. Philos.. 43: 378-383, 1945. Hartshorne, Charles, "Charles Sanders Peiree's Metaphysics of • Evolution", New England Quarterly. 14: 49-63, 1941. Hartshorne, Charles, "Continuity, the Form of Forms, in Charles Peirce", Monist, 39: 521-534. Hartshorne, Charles, "Critique of Peiree's Idea of God", Philos.. R., 50: 516-523, 1941. Jastrow, J., "Charles S. Peirce as a Teacher", J. Philos., 13: 723-726, 1916. Ladd-Franklin, C , "Charles S. Peirce at the Johns Hopkins", J. Philos., 13: 715-722, 1916. Leonard, H. S., "The Pragmatism and Scientific Metaphysics' of C. S. Peirce", Philos. Sci., 4: 109-121, 1937. Lewis, C. I., A Survey of Symbolic Logic, Berkeley, U. of Calif., 1918. Lovejoy, A. 0., "A Note on Peiree's Evolutionism", J. Hist. Ideas, 7: 351-354, 1946. McCrie, G. M., "The Issues of Synechism", Monist, 3: 380-401, 1893. Morris, C. W., "Peirce, Mead and Pragmatism", Philos. R., 47: 109-127, 1938. Muirhead, J. H., "Peiree's Place in American Philosophy", Philos. R., 37: 460-481, 1928. Nagel, E., "Charles Sanders Peiree's Guesses at the Riddle", J. Philos., 30: 365-386, 1933. Nagel, E., "Charles Sanders Peirce, Pioneer of Modern Empiri-cism", Philos. Soi., 7: 69-80, 1940. Ramsey, F. P., Foundations of Mathematics, London, Kegan Pauli 1911. Royce, J. and Kernan, F., "Charles Sanders Peirce", J. Philos., 13: 701-709, 1916. Russell, F. C , "Hints for the Elucidation of Peiree's Logical Work", Monist. 18: 406-415, 1908. - 70 -Russell, F. C , "In Memorlam -- Charles S. Peirce", Mpnist, 24: 469-472, 1914. Schilpp, P. A., ed., The Philosophy of John Dewey, Evanston and Chicago, Northwestern U., 1939. Schneider, H. W., History of American Philosophy, New York, Columbia U., 1946. Schroeder, Ernst, Der Vorlesungen iiber die Algebra der Logik, Leipzig, Teubner, 1895. Sidgwick, Alfred, Review of Collected Papers, vol. 5, Mind, N. S.« 44: 223-230, 1935. Townsend, H. G., Philosophical Ideas in the United States, New York-, American Book Co., 1934. Townsend, H. G., "Pragmatism of Peirce and Hegel" Philos. R., 37: 297-303, 1928. Townsend, H. G., "Sources and Early Meanings of American Prag-matism", J. Philos. 32: 181-187, 1935. Weiss,. Paul, "Charles Sanders Peirce, Founder of Pragmatism", Sewanee R., 50: 184-192, 1942. Weiss, Paul, "The Essence of Peiroe's System", J. Philos., • 37; 253-264, 1940. Weiss, Paul, "Peirce, Charles Sanders", Dictionary of Ameri-can Biography, 14: 398-403, 1934. Weiss, Paul and Burks, A. W., "Peiroe's Sixty-six Signs", • J. Philos., 42: 383-388, 1945. Wiener, P. P., "Evolutionism and Pragmaticism of Peirce",-J. Hist.. Ideas, 7: 321-350, 1946. Wiener, P. P., "Peirce's Metaphysical Club and the Genesis of Pragmatism", J. Hist. Ideas, 7: 218-233, 1946. 

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