UBC Theses and Dissertations

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UBC Theses and Dissertations

The variables of logicality Morris, Harold C. 1983

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THE VARIABLES OF LOGICALITY by HAROLD C. MORRIS A.B., U n i v e r s i t y o f Miami, 1975 J.D., U n i v e r s i t y o f Idaho C o l l e g e o f Law, 1978 M'.Ai, Washington S t a t e U n i v e r s i t y , 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the F a c u l t y o f Graduate S t u d i e s Department o f P s y c h o l o g y We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d : THE UNIVERSITY OF BRITISH COLUMBIA September, 1983 © H a r o l d Campbell M o r r i s , 1983 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s f o r scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date OCM<A JS, im DE-6 (3/81) ABSTRACT This t h e s i s i s concerned w i t h the a n a l y s i s , e x p l i c a t i o n and measurement of the p s y c h o l o g i c a l c o n s t r u c t of l o g i c a l i t y . L o g i c a l i t y i s d e f i n e d i n terms of an a b i l i t y to work w i t h l o g i c a l form a t a f a i r l y e x p l i c i t l e v e l of awareness. L o g i c a l form, a concept borrowed from formal l o g i c , i s desc r i b e d and shown to have p r o p e r t i e s corresponding to d i f f e r e n t l o g i c a l a c t i v i t i e s : (1) l o g i c a l forms can be v a l i d or i n v a l i d , and so can be judged as such; (2) p a r t i c u l a r l o g i c a l forms can be i d e n t i c a l , i n s p i t e of d i f f e r i n g c ontent, and so can be matched as such; and (3) a s e t of l o g i c a l l y s t r u c t u r e d givens can be extended to permit d i s c l o s u r e o f some i n f e r e n c e or answer, and so s o l u t i o n s to deductive problems can be found. To each of these l o g i c a l a c t i v i t i e s there corresponds an a b i l i t y to perform the a c t i v i t y , and i t i s by t h i s route that the three components of l o g i c a l i t y are a r r i v e d a t . They are i d e n t i f i e d as the f o l l o w i n g : (1) l o g i c a l judgment, i n which an argument's form i s ev a l u a t e d f o r v a l i d i t y ; (2) l o g i c a l i n t u i t i o n , i n which arguments are matched f o r i d e n t i t y of form; and (3) deductive problem s o l v i n g , i i i c o n c e i v e d o f as a d e r i v a t i o n - l i k e c o g n i t i v e p r o c e s s i n which an i n f e r e n c e i s drawn from a s e t o f l o g i c a l l y s t r u c t u r e d g i v e n s . I n r e v i e w i n g the p s y c h o l o g i c a l l i t e r a t u r e p e r t a i n i n g to each o f t h e s e p r o p o s e d v a r i a b l e s i t i s n o t e d t h a t t h e s e a s p e c t s o f l o g i c a l i t y have always been s t u d i e d i n i s o l a t i o n from one a n o t h e r . An i m p o r t a n t q u e s t i o n though i s whether or t o what e x t e n t l o g i c a l i t y i s a u n i t a r y t r a i t . One a p p roach to a n s w e r i n g t h i s q u e s t i o n i s to d e t e r m i n e t h e degree o f i n t e r c o r r e l a t i o n e x h i b i t e d by the v a r i a b l e s . With t h i s t e s t o f the u n i t a r i n e s s o f l o g i c a l i t y i n mind o p e r a t i o n a l d e f i n i t i o n s o f the t h r e e v a r i a b l e s a r e d e v e l o p e d . S u b j e c t s drawn from a p o p u l a t i o n o f u n i v e r s i t y s t u d e n t s o f d i v e r s e majors (1) e v a l u a t e d argument forms as t o t h e i r v a l i d i t y , t o a s s e s s l o g i c a l judgment; (2) matched argument forms t o a s s e s s l o g i c a l i n t u i t i o n ; and (3) answered v a r i o u s q u e s t i o n s r e l a t i n g t o d e d u c t i v e s t o r y problems t o a s s e s s d e d u c t i v e p r o b l e m s o l v i n g a b i l i t y . A s i g n i f i c a n t c o r r e l a t i o n was found between measures o f l o g i c a l judgment and l o g i c a l i n t u i t i o n , a l t h o u g h the magnitude o f t h i s c o r r e l a t i o n (,r= +.38) was n o t g r e a t . D e d u c t i v e p r o b l e m s o l v i n g was n o t c o r r e l a t e d w i t h e i t h e r l o g i c a l judgment o r l o g i c a l i n t u i t i o n . The u n i t a r i n e s s o f l o g i c a l i t y i s d i s c u s s e d i n l i g h t o f t h e s e f i n d i n g s , w i t h the c o n c l u s i o n drawn t h a t th e v a r i a b l e s a p p e a r as r e l a t i v e l y i n d e p e n d e n t i n m a n i f e s t a t i o n , p erhaps b e c a u s e o f d i f f e r e n t i a l p r e v i o u s p r a c t i c e by s u b j e c t s . The i m p l i c a t i o n s o f t h e p r e s e n t a n a l y s i s o f l o g i c a l i t y and o f the e m p i r i c a l f i n d i n g s on t h e i n t e r c o r r e l a t i o n o f the v a r i a b l e s a r e d i s c u s s e d and s u g g e s t i o n s f o r f u t u r e r e s e a r c h o f f e r e d . ACKNOWLEDGEMENT A p p r e c i a t i o n i s e x t e n d e d h e r e t o my t h e s i s s u p e r v i s o r , M erry B u l l o c k , w i t h o u t whose u n s t i n t i n g h e l p t h i s t h e s i s c o u l d n o t have been begun, l e t a l o n e c o m p l e t e d ; t o my committee members, Ray C o r t e e n and L a r r y W a l k e r , e v e r t o l e r a n t as I p r e s s e d e v e r y d e a d l i n e ; and t o my w i f e M a r i a n n a M o r r i s , who managed t o put up w i t h my l a t e n i g h t absences t h r o u g h t h e w r i t i n g o f t h i s opus. vi TABLE OF CONTENTS Page ABSTRACT i i ACKNOWLEDGEMENT v L I S T OF FIGURES v i i i L I S T OF TABLES ' i x LI S T OF APPENDICES x I . INTRODUCTION 1 I n f e r e n c e , R e a s o n i n g , and L o g i c a l C o g n i t i o n 2 Types o f I n f e r e n c e 2 L e v e l s o f I n f e r e n t i a l P r o c e s s 5 The V a r i a b l e s o f L o g i c a l i t y 9 Is L o g i c a l i t y U n i t a r y ? 9 L o g i c a l Form 10 P i a g e t on the R e a l i z a t i o n o f L o g i c a l Form 12 L o g i c a l Form and t h e V a r i a b l e s o f L o g i c a l i t y 14 I I . ISSUES AND PRECEDENTS IN THE PSYCHOLOGICAL LITERATURE PERTAINING TO LOGICALITY 19 U n d e r s t a n d i n g and L o g i c a l i t y 19 P i a g e t ' s S t r u c t u r a l i s t Approach 24 The S t r u c t u r e 25 The INRC Group Model 26 A C r i t i q u e o f the S t r u c t u r a l i s t Program 28 The Genevan C o n c e p t i o n o f L o g i c a l i t y 31 The V a r i a b l e s o f L o g i c a l i t y i n the P s y c h o l o g i c a l L i t e r a t u r e 32 L o g i c a l Judgment 32 D e d u c t i v e P r o b l e m S o l v i n g 38 A n a l o g i c a l R e a s o n i n g and F o r m a l Problems 41 C o n c l u s i o n s 44 v i i I I I . LOGICAL ACTIVITIES - 45 You Be the Judge 46 L o g i c a l Judgment vs. Deductive Problem S o l v i n g 48 D e r i v a t i o n 51 L o g i c a l Wayfinding i n D e r i v a t i o n 55 I n s i g h t 57 Assumption-based Str a t e g y i n Wayfinding 58 D e r i v a t i o n , L o g i c a l Judgment, and Deductive Problem S o l v i n g 62 L o g i c a l I n t u i t i o n 68 Conclusions on the U n i t a r i n e s s of L o g i c a l i t y 11 IV. METHOD 74 Tasks and M a t e r i a l s 74 L o g i c a l Judgment 75 L o g i c a l I n t u i t i o n 76 Deductive Problem S o l v i n g 76 Subjects 77 Procedure 78 V. RESULTS AND DISCUSSION 80 How Subjects Performed 80 L o g i c a l Judgment 80 L o g i c a l I n t u i t i o n 82 Deductive Problem S o l v i n g 83 The V a r i a b l e I n t e r r e l a t i o n s h i p s 87 Comparing the C o r r e l a t i o n s 89 General D i s c u s s i o n 92 Some Research I m p l i c a t i o n s 96 REFERENCES 9 8 APPENDICES 102 v i i i L I S T OF FIGURES Page F i g u r e 1 C o n f i d e n c e I n t e r v a l s f o r t h e P e a r s o n _r c o r r e l a t i o n s between v a r i a b l e s o f l o g i c a l i t y . 89 i x L I S T OF TABLES Page T a b l e 1 A f o r m a l p r o b l e m , "You Be t h e Judge", w i t h q u e s t i o n s 47 T a b l e 2 An example o f a d e r i v a t i o n , i n t h e n o t a t i o n o f s y m b o l i c l o g i c 52 T a b l e 3 The c o r r e l a t i o n m a t r i x f o r the t h r e e l o g i c a l v a r i a b l e s 88 X LIST OF APPENDICES Page Appendix I The S u b j e c t Consent Form 102 Appendix I I L o g i c a l Judgment M a t e r i a l s 104 A p p e n d i x I I I L o g i c a l I n t u i t i o n M a t e r i a l s 112 A p p e n d i x IV D e d u c t i v e P r o b l e m S o l v i n g M a t e r i a l s 11/ Appendix V K e n d a l l ' s T a u — A n A l t e r n a t i v e C o r r e l a t i o n a l S t a t i s t i c 123 1 I . INTRODUCTION The purpose o f t h i s t h e s i s i s to e x p l i c a t e and measure a c e r t a i n p s y c h o l o g i c a l c o n s t r u c t : l o g i c a l i t y . A t t h e o u t s e t l o g i c a l i t y can be d e f i n e d as one's c a p a c i t y f o r l o g i c a l thought and a c t i o n . T h i s d e f i n i t i o n w i l l be e l a b o r a t e d on i n t h i s i n t r o d u c t i o n , however, b e g i n n i n g w i t h some s t i p u l a t i o n as to what q u a l i f i e s as " l o g i c a l " c o g n i t i o n . The n o t i o n o f l o g i c a l form, borrowed from f o r m a l l o g i c , p r o v e s h e l p f u l s u b s e q u e n t l y i n the endeavor t o d i s t i n g u i s h the s e v e r a l l o g i c a l l y d i r e c t e d c o g n i t i v e a c t i v i t i e s . F i n a l l y , as t h e r e c o r r e s p o n d s t o each such a c t i v i t y an a b i l i t y t o p e r f o r m the a c t i v i t y , t h e a n a l y s i s a r r i v e s a t t h r e e a b i l i t i e s t h a t c o n s t i t u t e the components o f l o g i c a l i t y . L o o k i n g f u r t h e r ahead, a s u r v e y o f the p e r t i n e n t p s y c h o l o g i c a l l i t e r a t u r e makes up c h a p t e r I I , and an i d e a l i z e d s o r t o f l o g i c a l a c t i v i t y — t h e d e r i v a t i o n worked f o r a f o r m a l p r o b l e m — i s examined i n C h a p t e r I I I , b o t h i n o r d e r to c o n c r e t i z e the more a b s t r a c t f o r m u l a t i o n s g i v e n i n p r e v i o u s s e c t i o n s , and to s e t the s t a g e f o r the e m p i r i c a l q u e s t i o n o f t h i s t h e s i s , w hich i n q u i r e s i n t o the m a n i f e s t u n i t a r i n e s s o f l o g i c a l i t y . 2 The Method c h a p t e r ( I I I ) o f t h i s t h e s i s d e v e l o p s measures o f t h e t h r e e v a r i a b l e s d e f i n e d p r e v i o u s l y ( l o g i c a l judgment, l o g i c a l i n t u i t i o n , and d e d u c t i v e p r o b l e m s o l v i n g ) and s p e c i f i e s a p r o c e d u r e by which the l o g i c a l i t y o f a p o p u l a t i o n o f f o r m a l l y u n t r a i n e d a d u l t s can be a s s e s s e d . R e p o r t o f t h a t assessment appears i n c h a p t e r V, a l o n g w i t h d i s c u s s i o n o f the i m p l i c a t i o n s o f the f i n d i n g s . I n f e r e n c e , R e a s o n i n g , and L o g i c a l C o g n i t i o n Types o f I n f e r e n c e . F o r the l o g i c i a n , l o g i c a l a c t i v i t y c o n s i s t s i n the i d e n t i f i c a t i o n o f arguments and the d e t e r m i n a t i o n o f t h e v a l i d i t y o f t h e i r forms. L o g i c a l i t y , however, i s a p s y c h o l o g i c a l , n o t a l o g i c a l c o n s t r u c t , and p s y c h o l o g i s t s t e n d t o have a much b r o a d e r n o t i o n o f what i t i s to a c t o r t h i n k l o g i c a l l y . P i a g e t , f o r example, d e v o t e d much o f h i s l o n g c a r e e r to the s t u d y o f what he c o n s i d e r e d to be l o g i c a l i t y , b u t showed l i t t l e i n t e r e s t i n argument i d e n t i f i c a t i o n o r asse s s m e n t . P r o b a b l y many p s y c h o l o g i s t s would be tempted to equate l o g i c a l c o g n i t i o n w i t h i n f e r e n c e d r a w i n g . I t might be w e l l t h e n t o b e g i n r e f i n i n g o u r d e f i n i t i o n o f what i t i s to be l o g i c a l by c o n s i d e r i n g j u s t what k i n d o r k i n d s o f i n f e r e n c e might be i n v o l v e d i n l o g i c a l t h i n k i n g . 3 C S . P e i r c e , the American l o g i c i a n , c l a s s i f i e d i n f e r e n c e s as b e i n g e i t h e r e x p l i c a t i v e o r a m p l i a t i v e . (K.T. Fann, 1970, p r o v i d e s a good a c c o u n t o f P e i r c e on the forms o f i n f e r e n c e ) . I n e x p l i c a t i v e i n f e r e n c e , the c o n c l u s i o n n e c e s s a r i l y f o l l o w s from t h e p r e m i s e s , w h i l e i n a m p l i a t i v e i n f e r e n c e t h e c o n c l u s i o n does n o t ; the c o n c l u s i o n a m p l i f i e s r a t h e r than m e r e l y conveys what i s s t a t e d i n the p r e m i s e s . E x p l i c a t i v e i n f e r e n c e i n v o l v e s making e x p l i c i t what was i m p l i c i t to b e g i n w i t h . D e d u c t i o n , where a c o n c l u s i o n n e c e s s a r i l y f o l l o w s from some grounds, i s e x p l i c a t i v e . P e i r c e r e c o g n i z e d two s o r t s o f a m p l i a t i v e i n f e r e n c e : a b d u c t i v e and i n d u c t i v e . A b d u c t i v e and i n d u c t i v e i n f e r e n c e s a r e a l i k e i n t h e i r tendency o f g o i n g beyond the g i v e n ; a t the p r i c e o f u n c e r t a i n t y , they g i v e us r e a s o n t o b e l i e v e t h a t s o mething i s t r u e which we c o u l d n ot have deduced from what we a l r e a d y knew. I n d u c t i o n , o f c o u r s e , i s f a m i l i a r : i t i s making an i n f e r e n c e from a sample to a whole. A b d u c t i o n i s a type o f i n f e r e n c e o r i g i n a l t o P e i r c e ' s o b s e r v a t i o n , b u t d e s e r v i n g due h o n o r as the de f a c t o s o u r c e o f most s c i e n t i f i c h y p o t h e s i z i n g ; we w i l l pause m o m e n t a r i l y to e x p l o r e i t . I n e f f e c t , a b d u c t i o n i s d e d u c t i o n worked i n r e v e r s e . Suppose t h a t one p o s s e s s e d f a c t C. I f one then r e a s o n e d t h a t , i f A were t r u e , C would f o l l o w as a m a t t e r o f c o u r s e , one c o u l d a b d u c t i v e l y i n f e r t h a t A was the ca s e , i . e . one would have 4 r e a s o n t o b e l i e v e A. N o t i c e t h a t , a l t h o u g h i f g i v e n A, one can deduce C, A and C a r e n o t i n t e r d e d u c i b l e . An example f r o m m a t h e m a t i c s i l l u s t r a t e s a b d u c t i o n . From a g i v e n 3 x 3 m a t r i x , a d e t e r m i n a n t f o r t h a t m a t r i x may be o b t a i n e d d e d u c t i v e l y . However, i f g i v e n t h e number 360; w h i c h you a r e t o l d i s t h e d e t e r m i n a n t o f a 3 x 3 m a t r i x , and t o l d t o deduce t h e o r i g i n a l m a t r i x , y o u w o u l d n o t be a b l e t o do s o . I t w o u l d be p o s s i b l e t o p r o d u c e , a b d u c t i v e l y , a. m a t r i x w i t h d e t e r m i n a n t 360, and m o r e o v e r , one w o u l d have some r e a s o n to b e l i e v e t h a t t h i s m a t r i x was t h e o r i g i n a l one; b u t c e r t a i n t y w o u l d be l a c k i n g b e c a u s e t h e d e t e r m i n a n t 360 i s n o t u n i q u e t o any one m a t r i x . T h e r e w i l l p r o b a b l y be l i t t l e o b j e c t i o n t o t h e p r o p o s a l t h a t l o g i c a l i n f e r e n c e i n c l u d e s e x p l i c a t i v e i n f e r e n c e s and e x c l u d e s a m p l i a t i v e . L o g i c has l o n g been i d e n t i f i e d w i t h d e d u c t i o n and d i f f e r e n t i a t e d from i n d u c t i o n . The s t i p u l a t e d e x c l u s i o n o f a b d u c t i o n , however, i s done w i t h some m i s g i v i n g s , s i n c e a b d u c t i o n complements d e d u c t i o n . The l o g i c a l forms w i t h w h i c h d e d u c t i o n w orks a r e f r e q u e n t l y p r o d u c e d a b d u c t i v e l y , by w o r k i n g f r o m some d e s i r e d e n d g o a l o r c o n c l u s i o n t o some d e s i r e d c o n d i t i o n s o r p r e m i s e s . A b d u c t i o n c o u l d be c a l l e d the c r e a t i v e , s y n t h e t i c s i d e o f l o g i c a l i t y . U n f o r t u n a t e l y , the c r e a t i v i t y i n v o l v e d i n s u c c e s s f u l a b d u c t i o n makes i t somewhat d i f f i c u l t t o s t u d y — a s a l l forms o f c r e a t i v i t y a r e d i f f i c u l t t o 5 s t u d y . A form o f i n f e r e n c e which P e i r c e o v e r l o o k e d i s the outcome o f what i s known as a n a l o g i c a l r e a s o n i n g . A n a l o g i c a l r e a s o n i n g c l e a r l y b e l o n g s w i t h the a m p l i a t i v e forms o f i n f e r e n c e , as i t i s a means o f e x p a n d i n g o u r r e a l i z a t i o n from the w e l l known to the b a r e l y known. N e v e r t h e l e s s , t h e r e i s a r e g i o n o f o v e r l a p between l o g i c a l and a n a l o g i c a l r e a s o n i n g . When we say t h a t two t h i n g s , e.g. arguments, s h a r e a common l o g i c a l form, we a r e s t a t i n g t h a t t h e r e i s a s p e c i a l k i n d o f s t r i c t a n a l o g y h o l d i n g between them. T h i s m a tching o f e n t i t i e s on the b a s i s o f t h e i r l o g i c a l form i s r e f e r r e d to i n t h i s t h e s i s as l o g i c a l i n t u i t i o n , and i t w i l l be i n c l u d e d w i t h d e d u c t i o n i n the s p e c i f i c a t i o n o f what c o n s t i t u t e s l o g i c a l c o g n i t i o n . L e v e l s o f I n f e r e n t i a l P r o c e s s e s . As has j u s t been s t i p u l a t e d , some t y p e s o f i n f e r e n c e — i n d u c t i v e , a b d u c t i v e — w i l l be d e n i e d s t a t u s as l o g i c a l i n c h a r a c t e r . A f u r t h e r r e s t r i c t i o n w i l l now be p u t . I n f e r e n t i a l p r o c e s s e s amenable to d e d u c t i v e m o d e l i n g may o c c u r a t d i v e r s e l e v e l s o f a w a r e n e s s — o r e n t i r e l y b e n e a t h c o n s c i o u s awareness. I w i l l say the n t h a t by r e f e r e n c e t o l o g i c a l c o g n i t i o n I r e f e r t o a c e r t a i n k i n d o f r e a s o n i n g , t a k i n g i t t h a t r e a s o n i n g connotes a f a i r l y e x p l i c i t l e v e l o f c o g n i t i v e f u n c t i o n i n g , one r e q u i r i n g , among o t h e r t h i n g s , a t t e n t i o n . In t h i s c o n n e c t i o n i t i s u s e f u l to 6 d i s t i n g u i s h between e x p l i c i t and i m p l i c i t l e v e l s o f r e a l i z a t i o n . L o g i c a l c o g n i t i o n s h a l l be s a i d to be an e x p l i c i t a c t i v i t y , i n s o f a r as t h e s u b j e c t must be a t l e a s t aware t h a t he o r she i s w o r k i n g on a l o g i c a l p r o b l e m , o r p r o c e e d i n g i n a l o g i c a l o r n e a r l o g i c a l f a s h i o n . T h i s d i s t i n c t i o n between i m p l i c i t and e x p l i c i t i n f e r e n t i a l p r o c e s s w i l l be p u r s u e d f o r a moment. Some o f the p r o c e s s e s u n d e r l y i n g c o g n i t i o n can be d e s c r i b e d i n l o g i c a l terms. F o r example, t h e o r i s t s ( e . g . M c C u l l o u g h & P i t t s , 1943) have made r e c o u r s e to p a t e n t l y l o g i c a l models i n t r y i n g to d e p i c t n e u r o n a l w o r k i n g . But the " l o g i c " i n h e r e n t i n one's n e u r o l o g i c a l a c t i v i t y i s t o t a l l y i m p l i c i t , i . e . the n eurons don't " r e a s o n " . A t the o t h e r end o f the s p e c t r u m , t h e o r i s t s , i n w o r k i n g out t h e i r d e s c r i p t i v e l o g i c a l model, o p e r a t e a t a s u f f i c i e n t l y e x p l i c i t l e v e l to mark t h e i r work as p r o p e r l y l o g i c a l a c t i v i t y . We may a l s o d i s t i n g u i s h i m p l i c i t and e x p l i c i t i n f e r e n c e i n c o g n i t i o n . Take f o r example the f o l l o w i n g h y p o t h e t i c a l p r o t o c o l o f an i n d i v i d u a l r e c o l l e c t i n g some p a r t i c u l a r , d e f i n i t e f a c t : ...There i t was, t h e b l o c k o f c o n j o i n e d apartment u n i t s t h a t had been my home f o r n e a r l y a l l o f my s i x t h y e a r . But w hich o f the f o u r u n i t s o f the b l o c k had been mine? I was s u r e I ' d l i v e d i n one o f the two u n i t s on the r i g h t . I t r i e d assuming I'd l i v e d i n the end u n i t . D i d t h a t c o n f l i c t w i t h my deep and n o t q u i t e a c c e s s i b l e memories o f the p l a c e ? I wasn't s u r e . . . 7 Who e l s e had l i v e d on the b l o c k ? W e l l . . . the P o w e l l s l i v e d somewhere h e r e . To the l e f t o f o u r p l a c e , b u t not r i g h t next door. And not on the end. ...As t h e se r e a l i z a t i o n s a c cumulated a c o n c l u s i o n was f o r c e d on me as to which u n i t had t o have been mine. To the e x t e n t t h i s r e c o l l e c t i v e d e d u c t i o n was c a r r i e d out e x p l i c i t l y , i t was g e n u i n e l y l o g i c a l . But suppose t h a t a l l one " r e m e m b e r e d " — o r was c o n s c i o u s l y aware o f — w a s the " c o n c l u s i o n " to the e f f e c t t h a t one must have l i v e d on the end u n i t . I t ' s c e r t a i n l y p o s s i b l e t h a t one's r e c o l l e c t i o n a c t u a l l y was " d e d u c t i v e " i n the way t h a t has been v e r b a l i z e d , b u t a t a s u b c o n s c i o u s l e v e l . A c c o r d i n g to the d e f i n i t i o n a d o p t e d h e r e , though, t h i s l a t t e r i n f e r e n c e would n o t be deemed l o g i c a l i f the s u b j e c t was unaware t h a t t h e r e was s o m e t h i n g l i k e i n f e r e n c e b e h i n d i t . N e v e r t h e l e s s one may n a t u r a l l y wonder whether such s u b c o n s c i o u s d e d u c t i o n s ( i f t h e r e be such) a r e n o t p a r t o f one's l o g i c a l f u n c t i o n i n g . R i p s (1983) has s p e c u l a t e d i n p a s s i n g t h a t one g e n e r a l i n f e r e n c e mechanism might be b e h i n d i n f e r e n c e drawing a t e x p l i c i t and l e s s - t h a n - e x p l i c i t l e v e l s o f c o g n i t i v e f u n c t i o n i n g . I t i s w o r t h n o t i n g i n t h i s r e g a r d t h a t the tendency i n c o g n i t i v e p s y c h o l o g y has been to e x p l a i n l o g i c a l t h i n k i n g i n terms o f o t h e r c o g n i t i v e p r o c e s s e s s a i d to be more b a s i c ( s e e , e.g., S t e r n b e r g , 1982). R i p s , however, t u r n s t h i s i d e a on i t s head: i n f e r e n c e i s i n t e g r a l to o t h e r c o g n i t i v e p r o c e s s e s , such as 8 remembering; hence, an e x p l a n a t i o n o f i n f e r e n c e drawing a c c o u n t s f o r a b a s i c c o g n i t i v e p r o c e s s . I t seems p l a u s i b l e t h a t a model o f c o n s c i o u s i n f e r e n c e c o u l d be e x t e n d e d t o c o v e r some " n e a r the s u r f a c e " i n f e r e n t i a l a c t i v i t y . R e t u r n i n g to the i n s t a n c e o f remembering g i v e n above, i f s o m e thing v e r y much l i k e t h a t v e r b a l i z e d p r o t o c o l o c c u r r e d j u s t b e n e a t h t h e l e v e l o f c o n s c i o u s n e s s , might i t not be governed by some " f a c u l t y " a l s o r e s p o n s i b l e f o r c o n s c i o u s d e d u c t i o n ? P e r h a p s . But t h e r e may be so m e t h i n g v e r y s p e c i a l about an i n f e r e n t i a l p r o c e s s t h a t i s s u b j e c t e d t o the s p o t l i g h t o f a t t e n t i o n . And i n any c a s e , t h e p l a u s i b i l i t y o f t h e r e b e i n g a g e n e r a l i n f e r e n t i a l "mechanism" l e s s e n s r a p i d l y as one drops deeper i n t o t h e l e v e l s o f t h e mind. C o n s i d e r the u n c o n s c i o u s p r o c e s s t h a t H e l m h o l t z d e s c r i b e d ( i n the t h i r d volume o f the O p t i k , p u b l i s h e d i n 1866) as e q u i v a l e n t to an i n f e r e n c e which p e r m i t s us t o make a p e r c e p t u a l judgment as to the p r e s e n c e o f a c e r t a i n o b j e c t o f a c e r t a i n c h a r a c t e r . T h i s p r o c e s s i s n e v e r r e n d e r e d c o n s c i o u s and i t may i n d e e d be q u e s t i o n e d whether the same "mechanism" i s r e s p o n s i b l e f o r t h i s as i s r e s p o n s i b l e f o r t h e moves a l o g i c i a n makes i n p r o v i n g one o f the theorems o f P r i n c i p i a M a t h e m a t i c a . Or, t a k i n g t h i s even f u r t h e r , one can go a l l the way down to the l e v e l o f the n e u r o l o g i c a l f u n c t i o n s . The p o i n t i s : how c o u l d one " g e n e r a l i n f e r e n t i a l 9 t h e o r y " a p p l y a c r o s s a l l these d i s p a r a t e l e v e l s ? Throughout the p r e s e n t t h e s i s I w i l l be e x c l u s i v e l y c o n c e r n e d w i t h l o g i c a l a c t i v i t y w h i c h i s amenable i n some degree t o c o n s c i o u s r e f l e c t i o n and a t t e n t i o n . T h i s a c t i v i t y i s c l e a r l y a v a i l a b l e to some a d u l t s a n d — a s w i l l be seen s h o r t l y — t a k e s v a r i o u s forms. The V a r i a b l e s o f L o g i c a l i t y Is L o g i c a l i t y U n i t a r y ? L a y p e r s o n s and even p s y c h o l o g i s t s t e n d t o speak o f x ( i n d i v i d u a l o r group) as b e i n g "more l o g i c a l " than y ( i n d i v i d u a l o r g r o u p ) . T h ere i s i n t h i s perhaps a t a c i t a s s u m p t i o n t h a t l o g i c a l i t y i s a s i n g l e t r a i t w hich may be p o s s e s s e d to some degree. But i t might be w e l l to ask whether o r not x might n o t be "more l o g i c a l " than y i n r e s p e c t to o n l y one o r two o f s e v e r a l v a r i a b l e s i n t o w h i c h l o g i c a l i t y might be decomposed. A l s o , a l t h o u g h l o g i c a l i t y may be a u n i t a r y d e v e l o p a b l e , i t i s a t l e a s t c o n c e i v a b l e t h a t v a r i a b l e s making up l o g i c a l i t y d e v e l o p somewhat i n d e p e n d e n t l y o f one a n o t h e r . I t i s a l o n g t h e s e l i n e s t h a t we w i l l come to the main e m p i r i c a l q u e s t i o n r a i s e d i n t h e r e s e a r c h t o be r e p o r t e d i n t h i s t h e s i s : How i n d e p e n d e n t a r e the v a r i a b l e s o f l o g i c a l i t y ? Or, p u t the o t h e r way, how u n i t a r y i s l o g i c a l i t y ? 10 The t a s k a t hand, then, i s to a n a l y z e l o g i c a l i t y i n t o c o n c e p t u a l l y d i s t i n c t v a r i a b l e s . I n d o i n g t h i s r e f e r e n c e w i l l be made t o so m e t h i n g c a l l e d l o g i c a l form. T h e r e f o r e , t h i s s e c t i o n p r o c e e d s w i t h a d i s c u s s i o n o f the n a t u r e and o r i g i n o f l o g i c a l form. L o g i c a l Form. One approach to u n d e r s t a n d i n g l o g i c a l form i s t hrough a n a l o g y t o R u s s e l l & wh i t e h e a d ' s a c c o u n t o f the c a r d i n a l numbers ( s e e , e.g., D a n t z i g , 1933). What do t h r e e eggs, t h r e e words, and t h r e e days have i n common? T h r e e n e s s . So the number t h r e e can be d e f i n e d as t h a t t h i n g w h i c h a l l members o f a c e r t a i n c l a s s have i n common, the c l a s s t o which t h r e e eggs, t h r e e days, e t c . , b e l o n g . By the same to k e n , what the f o l l o w i n g two arguments have i n common w i t h one a n o t h e r (and w i t h some o t h e r arguments) i s t h e i r l o g i c a l form: (1) S t o i c P h i l o s o p h e r : I f I can r i g h t l y c o n c l u d e t h a t I n e v e r draw c o n c l u s i o n s , t h e n i t i s wrong to c o n c l u d e t h a t I can n e v e r draw c o n c l u s i o n s . T h e r e f o r e , i t i s wrong f o r me to c o n c l u d e t h a t I can n e v e r draw c o n c l u s i o n s . (2) P s y c h o t h e r a p i s t : I f y o u r e a l l y t r y to s t o p t r y i n g t h e n y o u r e a l l y d on't t r y t o s t o p t r y i n g . So you r e a l l y don't t r y to s t o p t r y i n g . We c o u l d say t h a t arguments (1) and (2) b e a r the Q form, i f we wanted to g i v e i t a name, and we can d e f i n e t h e Q form as b e i n g what a l l arguments b e l o n g i n g to some c e r t a i n c l a s s 11 have i n common. There a r e o t h e r argument forms than Q, o f c o u r s e , i n c l u d i n g some t h a t have names, such as the " d i s j u n c t i v e s y l l o g i s m " and the " c o n s t r u c t i v e dilemma" forms, and many, many more t h a t have no c o n v e n t i o n a l names. Each argument form s t a n d s a t the head o f a c l a s s , so to speak, and the c l a s s o f a l l t h e s e c l a s s e s i s " l o g i c a l form", j u s t as " t h e c a r d i n a l numbers" s e t i s made up o f i n d i v i d u a l s e t s t h a t have, r e s p e c t i v e l y , oneness, twoness, t h r e e n e s s , e t c . , i n common. The i n f l u e n t i a l modern p h i l o s o p h e r P.F. Strawson (1952) gave an a c c o u n t o f l o g i c a l form t h a t i s c o m p a t i b l e w i t h the one j u s t s k e t c h e d : The l o g i c i a n i s c o n c e r n e d w i t h a n a l o g i e s o f a c e r t a i n k i n d between i n f e r e n c e s on w i d e l y d i f f e r i n g t o p i c s ; a n a l o g i e s e i t h e r c l o s e enough to p e r m i t the f r a m i n g o f a g e n u i n e l y r e p r e s e n t a t i v e p a t t e r n s u i t a b l e f o r q u o t i n g i n a l o g i c i a n ' s r u l e f o r i n f e r e n c e s o f t h a t c l a s s , o r a t l e a s t c l o s e enough to admit o f a more o r l e s s p r e c i s e d e s c r i p t i o n o f t h e common f e a t u r e s o f such a c l a s s , ( p . 5 0 ) . I f o l l o w the l o g i c i a n s i n d e n o m i n a t i n g the o b j e c t o f l o g i c a l c o g n i t i o n to be l o g i c a l form. I t might be wondered now how the i n d i v i d u a l a c q u i r e s a c o g n i t i v e g r a s p o f l o g i c a l form i n h i s o r h e r p s y c h o l o g i c a l development, i . e . how l o g i c a l form comes t o be r e a l i z e d as su c h . P i a g e t has had the most to say on t h i s and an o u t l i n e o f h i s views i s p r e s e n t e d n e x t . 12 Pia g e t on the R e a l i z a t i o n of L o g i c a l Form. A springboard to P i a g e t ' s t h e o r i z i n g has been the idea that l o g i c can be r e a l i z e d not only v e r b a l l y , but i n a c t i o n , and t h a t , moreover, the l a t t e r s o r t of l o g i c i s source to the former. "There i s no b a s i c d i f f e r e n c e between v e r b a l l o g i c and the l o g i c i n h e r e n t i n the c o o r d i n a t i o n of a c t i o n s , but the l o g i c of a c t i o n s i s more profound and more p r i m i t i v e , " he t e l l s us i n one pla c e (1963, p.79). And i n another: "We have emphasized the f a c t t h a t the source of l o g i c a l o p e r a tions i s a c t i o n i t s e l f . " (1964, p. 127) . L i v i n g t h i n g s have a common s t o r e of l o g i c a l a c t i o n forms P i a g e t c a l l s schemata. The workings of the Venus F l y - T r a p , a carnivorous p l a n t , evidence the a u t o r e g u l a t i o n that arranges n e c e s s i t y i n t o a p a t t e r n and a f f o r d an example of a simple l i f e form's a c t i o n l o g i c . In hi g h e r animals, the schemata i n c l u d e r e f l e x e s and i n s t i n c t u a l p a t t e r n s . The human being begins w i t h sensori-motor a c t i o n schemata (displacement groups, permanent o b j e c t schemata, i n c l u s i o n s t r u c t u r e s , and order s t r u c t u r e s such as are found i n the c o o r d i n a t i o n of a s s i m i l a t i o n schemata, etc.) which develop i n the f i r s t two yea r s . The schemata develop as a product of P i a g e t ' s famous a s s i m i l a t i o n and accomodation o r d e r i n g p r i n c i p l e s . 13 Over subsequent y e a r s r e c o n s t r u c t i o n o f these same schemata o c c u r a t a h i g h e r p l a n e o f a c t i o n r e p r e s e n t a t i o n s . F i n a l l y , by the e a r l y t e e n s , the schemata have emerged onto the h i g h p l a n e o f l o g i c o - m a t h e m a t i c a l a b s t r a c t i o n . Thus: i n the b e g i n n i n g , the schemata a r e r e a l i z e d p h y s i c a l l y ; the p h y s i c a l forms o f the schemata a r e n e x t r e a l i z e d c o n s c i o u s l y ; and f i n a l l y , the forms a r e e x t r a c t e d o u t o f t h e i r p h y s i c a l embodiment e n t i r e l y and r e a l i z e d as pure a b s t r a c t i o n s . The f o r m e r l y i m p l i c i t l o g i c - i n - a c t i o n thus becomes the e x p l i c i t l o g i c o f thought. P i a g e t ' s a c c o u n t o f t h i s f a s c i n a t i n g p r o c e s s i s g i v e n h e r e ( i n t r a n s l a t i o n ) : I n the a s c e n t t o l o g i c o - m a t h e m a t i c a l a b s t r a c t i o n what i s g i v e n i s an a g g l o m e r a t i o n o f a c t i o n s o r o p e r a t i o n s p r e v i o u s l y made by the s u b j e c t h i m s e l f , w i t h t h e i r r e s u l t s . I n t h i s c a s e , a b s t r a c t i o n c o n s i s t s f i r s t o f t a k i n g c o g n i z a n c e o f the e x i s t e n c e o f one o f th e s e a c t i o n s o r o p e r a t i o n s , t h a t i s to s a y , n o t i n g i t s p o s s i b l e i n t e r e s t , h a v i n g n e g l e c t e d i t so f a r ; ... Second, the a c t i o n n o t e d has to be " r e f l e c t e d " ( i n the p h y s i c a l s ense o f the term) by b e i n g p r o j e c t e d o nto a n o t h e r p l a n e — f o r example, t h e p l a n e o f t h o u g h t as opposed to t h a t o f p r a c t i c a l a c t i o n , o r the p l a n e o f a b s t r a c t s y s t e m a t i z a t i o n as opposed to t h a t o f c o n c r e t e thought ( s a y , a l g e b r a , v e r s u s a r i t h m e t i c ) . T h i r d , i t has to be i n t e g r a t e d i n t o a new s t r u c t u r e , w h i c h means t h a t a new s t r u c t u r e has to be s e t up, b u t t h i s i s o n l y p o s s i b l e i f two c o n d i t i o n s a r e f u l f i l l e d : (a) the new s t r u c t u r e must f i r s t o f a l l 14 be a r e c o n s t r u c t i o n o f the p r e c e d i n g one i f i t i s no t to l a c k c o h e r e n c e and c o n g r u i t y ; i t w i l l thus be the p r o d u c t o f the p r e c e d i n g one on a p l a n e chosen by i t ; (b) i t must a l s o , however, widen the scope o f the p r e c e d i n g one, making i t g e n e r a l . . . T h e name I p r o p o s e t o g i v e t h i s p r o c e s s o f r e c o n s t r u c t i o n . . . i s " r e f l e c t i v e a b s t r a c t i o n " . ( P i a g e t , 1971, p.320). P i a g e t does n o t d i r e c t l y a d d r e s s the q u e s t i o n o f how the mind " r e f l e c t s " schemata o n t o h i g h e r p l a n e s ; h i s s t a t e m e n t t h a t the p r o c e s s i s one o f r e f l e c t i o n " i n the p h y s i c a l sense o f the term" i s n ' t v e r y h e l p f u l . But i n s p i t e o f i t s many a m b i g u i t i e s and u n r e s o l v e d q u e s t i o n s P i a g e t ' s unique s y n t h e s i s o f b i o l o g y and p s y c h o l o g y , t r a c k i n g as i t does the development o f e x p l i c i t l o g i c a l f u n c t i o n i n g o u t o f the most i m p l i c i t a c t i o n forms s t a n d s u n c h a l l e n g e d a t p r e s e n t as the d e f i n i t i v e a c c o u n t o f how l o g i c a l form i s r e a l i z e d i n and by the human b e i n g . L o g i c a l Form and the V a r i a b l e s o f L o g i c a l i t y . H a v i n g i n t r o d u c e d the c o n c e p t o f l o g i c a l form the c o n n e c t i o n t o be made now i s t h a t between c e r t a i n o f i t s a t t r i b u t e s and c o r r e s p o n d i n g v a r i a b l e s o f l o g i c a l i t y . The a t t r i b u t e s and c o r r e s p o n d e n c e s : (1) The form o f an argument ( o r e l e c t r i c a l c i r c u i t , o r p l a n ) may be v a l i d o r i n v a l i d . T h i s makes p o s s i b l e l o g i c a l judgment, which depends on the c l a s s i f i a b l l i t y o f forms a c c o r d i n g to a s i n g l e c r i t e r i o n , namely, t h a t o f v a l i d i t y . L o g i c a l forms may be e v a l u a t e d , i n s h o r t , and l o g i c a l judgment i s t h a t e v a l u a t i o n . (2) A p a r t i c u l a r v a l i d form may be common to v a r i o u s i n s t a n c e s (e.g. the Q form i n t r o d u c e d above was common to the sample arguments g i v e n t h e r e ) . T h i s makes p o s s i b l e l o g i c a l  i n t u i t i o n . L o g i c a l judgment, we j u s t saw, i s a k i n d o f dichotomous c l a s s i f i c a t i o n i n which forms ( i n our r e s e a r c h , argument forms) a r e s o r t e d a c c o r d i n g to the s i n g l e g e n e r a l c r i t e r i o n o f v a l i d i t y . In l o g i c a l i n t u i t i o n , by c o n t r a s t , v a l i d forms are s o r t e d i n t o c l a s s e s i n which e v e r y member o f a c l a s s b e a r s the e x a c t same l o g i c a l form. There a r e i n d e f i n i t e l y many d i s t i n g u i s h a b l y d i f f e r e n t v a l i d l o g i c a l forms. L o g i c a l i n t u i t i o n , u n l i k e l o g i c a l judgment, thus r e q u i r e s a grasp o f the form p e c u l i a r to a p a r t i c u l a r argument s e t . L o g i c a l i n t u i t i o n can be thought o f as a s p e c i a l k i n d o f a n a l o g i c a l r e a s o n i n g ( r e f e r back to the passage by Strawson quoted above a t page 11). And, i n d e e d , the term " l o g i c a l i n t u i t i o n " i t s e l f corues from the p h i ] o s o p h e r / l o g i c i a n S.K. La n g e r (1953) who d e f i n e d i t i n h e r s e c t i o n on l o g i c a l form as "the power o f r e c o g n i z i n g s i m i l a r £logicalj forms i n v a r i o u s e x e m p l i f i c a t i o n s , i . e . the power o f d i s c o v e r i n g 16 a n a l o g i e s . " ( p . 3 3 ) . One sometimes e n c o u n t e r s c l a i m s to the e f f e c t t h a t a n a l o g i c a l r e a s o n i n g i s d r a s t i c a l l y d i f f e r e n t from, i f n o t somehow opposed t o , l o g i c a l r e a s o n i n g . I t i s a l i t t l e b i t s u r p r i s i n g t h e n to f i n d some form o f i t d e e p l y i m p l i c a t e d w i t h l o g i c a l i t y . No doubt i t would be w o r t h w h i l e to d e t e r m i n e j u s t how l o g i c a l i n t u i t i o n c o r r e l a t e s w i t h more m e t a p h o r i c a l k i n d s o f a n a l o g i c a l r e a s o n i n g . In t h i s t h e s i s , however, t h e r e s e a r c h emphasis goes the o t h e r way: we s h a l l be s e e i n g how l o g i c a l i n t u i t i o n c o r r e l a t e s w i t h the o t h e r v a r i a b l e s o f l o g i c a l i t y , w hich i n c l u d e l o g i c a l judgment, and the t h i r d v a r i a b l e , d i s c u s s e d n e x t . (3) A l o g i c a l form may be e l a b o r a t e d i n v a r i o u s p e r m i s s i b l e ways. T h a t i s , an i n f e r e n c e can be drawn out o f a g i v e n l o g i c a l l y s t r u c t u r e d s e t o f p r e m i s e s o r c o n d i t i o n s . T h i s a l l o w s f o r answer f i n d i n g , o r d e d u c t i o n , as i n d e d u c t i v e p r o b l e m  s o l v i n g . The answer to a d e d u c t i v e p r o b l e m (I mean by " d e d u c t i v e p r o b l e m " what W i c k e l g r e n , 1974, d e f i n e s as a " f i n d problem") i s b e s t thought o f as b e i n g i m p l i c i t l y c o n t a i n e d i n the g i v e n s . Because the g i v e n s a r e l o g i c a l l y s t r u c t u r e d , they can be worked on by s t r i c t l y l o g i c a l o p e r a t i o n s , so as to y i e l d an a n s w e r — i f the p r o b l e m i s a n s w e r a b l e . Something i m p l i c i t 17 i n a l o g i c a l l y i n t e g r a t e d s e t o f g i v e n s i s r e n d e r e d e x p l i c i t , i n d e d u c t i v e p r o b l e m s o l v i n g . D e d u c t i o n can be thought o f as a v e r y s p e c i a l k i n d o f a c c e s s i n g , t o be c l a s s e d i n t h a t r e s p e c t w i t h remembering and some k i n d s o f m e t a c o g n i t i o n , f o r i t i s a mode o f r e a l i z a t i o n i n which t h e i m p l i c a t i o n s o f what i s " a l r e a d y known" a r e b r o u g h t o u t . To sum up t h i s s e c t i o n , i t can be s a i d t h a t one way to go about d e t e r m i n i n g whether l o g i c a l i t y i s u n i t a r y i s t o s e p a r a t e o u t i t s c o n s t i t u e n t v a r i a b l e s , o b t a i n measures on e a c h , and t h e n see i f p e r f o r m a n c e on t h e s e v a r i a b l e s i s s t r o n g l y c o r r e l a t e d . I n t h i s s e c t i o n the f i r s t p a r t o f t h a t program was c a r r i e d o u t : l o g i c a l i t y was a n a l y z e d i n t o a c t i v i t i e s r e l a t i n g t o l o g i c a l form. Three ways o f w o r k i n g w i t h l o g i c a l form were d e s c r i b e d : l o g i c a l judgment, l o g i c a l i n t u i t i o n , and d e d u c t i v e p r o b l e m s o l v i n g . As a b i l i t i e s t h e s e t h r e e v a r i a b l e s a r e presumed to be p o s s e s s e d by p e o p l e t o a d e g r e e ; t h a t i s , what i s easy f o r one p e r s o n t o j u d g e , match, o r work might be d i f f i c u l t f o r a n o t h e r . I n d i v i d u a l d i f f e r e n c e s , t h e n , a r e l i k e l y t o be e v i d e n c e d i n any assessment o f the l o g i c a l i t y o f p e r s o n s . However, can i t be i n f e r r e d t h a t where one i s s u p e r i o r i n one l o g i c a l a b i l i t y , t h a t one i s bound t o be s u p e r i o r i n the o t h e r ways as w e l l ? T h i s i s t h e q u e s t i o n o f the i n t e r r e l a t i o n o f the v a r i a b l e s o f l o g i c a l i t y t h a t i s t h e f o c u s o f t h i s t h e s i s . R a t h e r t h a n s e e i n g i f x c o u l d be d i f f e r e n t (.better o r worse) t h a n y, I am i n t e r e s t e d i n s e e i n g o f x's p e r f o r m a n c e on some l o g i c a l t a s k , s u c h as a d e d u c t i v e p r o b l e m s o l v i n g t a s k , c o u l d p o s s i b l y be d i f f e r e n t ( b e t t e r o r worse) t h a n x's pe r f o r m a n c e on a n o t h e r l o g i c a l t a s k , s uch as t h e f o r m m a t c h i n g t h a t c a l l s on one's l o g i c a l i n t u i t i o n . 19 I I : ISSUES AND PRECEDENTS IN THE PSYCHOLOGICAL LITERATURE PERTAINING TO LOGICALITY T h i s c h a p t e r b e g i n s w i t h c o n s i d e r a t i o n o f an e p i s t e m o l o g i c a l • c h a l l e n g e to the p r e s e n t o r any s i m i l a r v e n t u r e : the i d e a i s e n t e r t a i n e d and th e n r e j e c t e d t h a t any a t t e m p t to measure l o g i c a l i t y i s f u t i l e b e c ause c o g n i t i v e p s y c h o l o g y "must" a s c r i b e r a t i o n a l i t y to the i n d i v i d u a l a_ p r i o r i . The subsequent s e c t i o n p r e s e n t s a c r i t i c a l o v e r v i e w o f one major approach to the p s y c h o l o g i c a l u n d e r s t a n d i n g o f l o g i c a l i t y — t h a t o f P i a g e t . I n the end h i s s t r u c t u r a l i s t program i s d e c l a r e d u n f e a s i b l e , and h i s a n a l y s i s o f l o g i c a l i t y w a n t i n g . F i n a l l y , t hen, we t u r n t o modern c o g n i t i v e p s y c h o l o g i c a l t h e o r y and r e s e a r c h . I n the p r e v i o u s c h a p t e r t h r e e v a r i a b l e s o f l o g i c a l i t y were i n t r o d u c e d ; i n the l a t t e r p o r t i o n o f t h i s c h a p t e r the p s y c h o l o g i c a l l i t e r a t u r e most r e l e v a n t to each o f t h o s e t h r e e v a r i a b l e s i s r e v i e w e d , w i t h one s e c t i o n d e v o t e d t o each v a r i a b l e . U n d e r s t a n d i n g and L o g i c a l i t y Smedslund (19 70) has c a l l e d a t t e n t i o n to what he c a l l s the " p r o b l e m a t i c a l c i r c u l a r r e l a t i o n between u n d e r s t a n d i n g and 20 l o g i c . " From a s k e p t i c a l p o s i t i o n he argues t h a t p r o c e d u r e s f o r d e t e r m i n i n g l o g i c a l i t y always p r e s u p p o s e p e r f e c t u n d e r s t a n d i n g , w h i l e p r o c e d u r e s f o r d e t e r m i n i n g u n d e r s t a n d i n g always i n t u r n take f o r g r a n t e d human r a t i o n a l i t y . An i l l u s t r a t i o n h e l p s t o c l a r i f y h i s p o i n t . Suppose a s u b j e c t i n a r e a s o n i n g e x p e r i m e n t i n d i c a t e s t h a n an argument t h a t happens t o have a f a l s e c o n c l u s i o n i s n e c e s s a r i l y " i n v a l i d " , though the e x p e r i m e n t e r can demonstrate t h r o u g h , s a y , t r u t h t a b l e c o n s t r u c t i o n , t h a t the argument i n q u e s t i o n i s v a l i d i n the l o g i c i a n ' s s e n s e . I n a case l i k e t h i s the e x p e r i m e n t e r must be c e r t a i n t h a t h i s s u b j e c t i s n o t c o n f u s i n g soundness w i t h v a l i d i t y (because an argument w i t h a f a l s e c o n c l u s i o n cannot be sound, b u t may o r may n o t be i n v a l i d ) , o r the e x p e r i m e n t e r w i l l count as an i l l o g i c a l r e s p o n s e what was a c t u a l l y o n l y an i r r e l e v a n t ( f o r the e x p e r i m e n t e r ' s immediate p u r p o s e ) r e s p o n s e . T h a t the e x p e r i m e n t e r s h o u l d take e v e r y p r e c a u t i o n t o a v o i d i r r e l e v a n t m i s u n d e r s t a n d i n g by s u b j e c t s i s o b v i o u s . I n the Method c h a p t e r (IV) o f t h i s t h e s i s I s p e c i f y some measures t a k e n to re d u c e the p r o b a b i l i t y o f g e t t i n g u n i n t e r p r e t a b l e r e s u l t s t h r o u g h " n o i s y " m i s u n d e r s t a n d i n g . N e v e r t h e l e s s , one may wonder whether s t e p s such as t h e s e s u f f i c e t o e l i m i n a t e any p o s s i b l e m i s u n d e r s t a n d i n g on the p a r t o f s u b j e c t s . I n d e ed, one might wonder whether any s u b j e c t would e v e r " m i s s " a 21 l o g i c a l p r o b l e m i f t h a t s u b j e c t o n l y r e a l l y u n d e r s t o o d e x a c t l y what he/she c o u l d and s h o u l d do! To r e t u r n t o Smedslund, though, i t w i l l be found t h a t h i s p o s i t i o n goes w e l l beyond t h a t o f a d v i s i n g prudence i n the d e s i g n o f e x p e r i m e n t a l s i t u a t i o n s . I n view o f the c i r c u l a r r e l a t i o n between u n d e r s t a n d i n g and l o g i c a l i t y , he r e a s o n s , the d i a g n o s i s o f l o g i c a l i t y i s an u n t e n a b l e u n d e r t a k i n g . In coming to t h i s c o n c l u s i o n he has supposed t h a t the c i r c u l a r i t y can o n l y be b r o k e n o u t o f by d e c l a r i n g a_ p r i o r i one o f the f a c t o r s ( u n d e r s t a n d i n g o r l o g i c a l i t y ) as a c o n s t a n t ; and r a t i o n a l i t y s h o u l d be t h a t c o n s t a n t . To j u s t i f y t h i s l a s t he asks us t o d e f e r to "common s e n s e " : I n e v e r y d a y l i f e , he a s s e r t s , when an a p p a r e n t l y i r r a t i o n a l r e s p o n s e i s p e r c e i v e d i t i s n o r m a l l y t r e a t e d as b e i n g the p r o d u c t o f some l a t e n t m i s a p p r e h e n s i o n o r misc o m m u n i c a t i o n . From t h i s the c o g n i t i v e p s y c h o l o g i s t s h o u l d a p p r e c i a t e t h a t "when d a t a a r e i n t e r p r e t e d as r e f l e c t i n g i l l o g i c a l i t y , t hey do n o t make any sense i n t u i t i v e l y . . . " ( p . 2 1 8 ) . Smedslund's c o n c l u s i o n t h e n i s t h a t e v e r y o n e must be t r e a t e d as p r e s u m p t i v e l y l o g i c a l , s o t h a t a p p a r e n t f a i l u r e on a l o g i c a l t a s k c o u l d o n l y be a t t r i b u t e d to some f a i l u r e to comprehend what was g i v e n , o r r e q u i r e d , o r due to a 22 breakdown i n communication between s u b j e c t and e x p e r i m e n t e r (as where t h e s u b j e c t says " i n v a l i d " b u t means "unsound"). Smedslund's case seems r e a s o n a b l y s t r o n g a t f i r s t g l a n c e , and c e r t a i n r e s e a r c h f i n d i n g s can be a s s i m i l a t e d t o i t . Take f o r example C e r a s o and P r o v i t e r a (19 71), who compared p e r f o r m a n c e by s u b j e c t s on the same c a t e g o r i c a l s y l l o g i s m s which were p r e s e n t e d v e r b a l l y o r as Venn diagrams, and found s u b j e c t s d i d b e t t e r on t h e l a t t e r . S u r e l y t h e y were n o t more l o g i c a l when they d i d b e t t e r on diagrammed s y l l o g i s m s , n o r l e s s l o g i c a l when d e a l i n g w i t h t h e v e r b a l ones. A l l one can say i s t h a t t h e i r u n d e r s t a n d i n g o f the v i s u a l f i g u r e s was s u p e r i o r t o t h e i r u n d e r s t a n d i n g o f the s e t e x t e n t i o n a l terms. L o g i c a l i t y remains c o n s t a n t — u n d e r s t a n d i n g v a r i e s . T h e r e i s y e t a f u r t h e r r e a s o n , n o t e d by Smedslund, t h a t might make h i s c o n c l u s i o n a t t r a c t i v e . C o g n i t i v e p s y c h o l o g i s t s c e r t a i n l y hope t h a t t h e i r s u b - d i s c i p l i n e i s s c i e n t i f i c i n the s t r i c t s e n s e . T h i s w ould seem to mean, among o t h e r t h i n g s , t h a t i t be r a t i o n a l . But can t h a t c l a i m be m a i n t a i n e d i f c o g n i t i o n c a n n o t be r a t i o n a l l y modeled, as would be the c a s e i f t h e human mind were ( a t t i m e s , and on some p l a n e ) i r r a t i o n a l ? Smedslund g i v e s us to b e l i e v e t h a t , however c o n f u s e d p e o p l e can be, they a r e n e v e r i r r a t i o n a l — o n p r e s u m p t i o n . 23 So much the b e t t e r f o r c o g n i t i v e p s y c h o l o g y as a s c i e n c e — a n d so much the worse f o r those l i k e me who w i s h t o a s s e s s the degree o f l o g i c a l i t y e x h i b i t e d i n v a r i o u s d i f f e r e n t i a l t a s k s i t u a t i o n s . Some r e f u t a t i o n o f Smedslund's argument seems i n o r d e r , c l e a r l y . To go about t h i s l e t us view l o g i c a l i t y as a f a m i l y o f forms o f u n d e r s t a n d i n g : u n d e r s t a n d i n g how ( e . g . how to d e r i v e a c o n c l u s i o n ) , u n d e r s t a n d i n g what ( e . g . what a " n e c e s s a r y c o n n e c t i o n " i s ) , and u n d e r s t a n d i n g t h a t ( e . g . t h a t a c o n d i t i o n a l a s s u m p t i o n might be a l l o w a b l e and u s e f u l ) . Now c l e a r l y t h i s l i s t does n o t exh a u s t a l l the forms o f under-s t a n d i n g . A r g u a b l y , to u n d e r s t a n d what the s e n t e n c e " E i t h e r i t i s J u l y 10'or i t i s n o t J u l y 10" means i s n o t n e c e s s a r i l y to u n d e r s t a n d what p r o p e r t i e s the s e n t e n c e p o s s e s s e s as a t a u t o l o g y , and the e x p e r i m e n t a l p s y c h o l o g i s t ' s g o a l , i f i n t e r e s t e d i n a s s e s s i n g l o g i c a l i t y , i s t o c o n t r o l f o r the former k i n d o f u n d e r s t a n d i n g so t h a t the l a t t e r k i n d o f u n d e r s t a n d i n g may v a r y as i t w i l l . The "human u n d e r s t a n d i n g " i s r e a l l y a c o l l e c t i o n o f forms o f u n d e r s t a n d i n g t h a t can be " d i s t i n g u i s h e d i n many c a s e s w i t h o u t d i f f i c u l t y , and i t i s n o t n e a r l y so m o n o l i t h i c as to c r e a t e the a b s o l u t e c o n f o u n d Smedslund i s w o r r i e d about. 24 To b r i n g t h i s i s s u e to a c l o s e , I would s u g g e s t t h a t t h e r e i s no paradox i n s a y i n g t h a t someone comprehends what he/she has been t o l d to do, b u t y e t does n o t u n d e r s t a n d how he/she i s to do i t , b e c a u s e t h o s e a r e d i s t i n c t k i n d s o f u n d e r s t a n d i n g . The p s y c h o l o g i s t i n t e r e s t e d i n , s a y , d e d u c t i v e p r o b l e m s o l v i n g , w i l l d e s i g n a s i t u a t i o n where the t a s k demands a r e e a s i l y u n d e r s t o o d by a l l .(or p r a c t i c a l l y a l l ) s u b j e c t s even though s u b j e c t s w i l l have and r e v e a l d i f f e r e n t i a l u n d e r s t a n d i n g o f how the t a s k demands may be v a l i d l y met. P i a g e t ' s S t r u c t u r a l i s t Approach One i n d i v i d u a l u n d e t e r r e d by e p i s t e m o l o g i c a l b a r r i e r s to the d i a g n o s i s o f l o g i c a l i t y i s J e a n P i a g e t . P i a g e t ' s i n f l u e n c e i n the a r e a o f the p s y c h o l o g y o f r e a s o n i n g i s e n o r m o u s — p a r t l y b ecause o f h i s s t a t u s as p i o n e e r , and p a r t l y b e c a u s e o f h i s p r o l o n g e d and r e m a r k a b l y f r u i t f u l i n d u s t r y . H i s a c c o u n t o f the development o f the human b e i n g ' s r e a l i z a t i o n o f l o g i c a l form was a p p r o v i n g l y r e c o u n t e d i n the i n t r o d u c t o r y c h a p t e r . T h i s t h e s i s , however, does n o t r e a l l y f o l l o w i n the P i a g e t i a n t r a d i t i o n , and i t i s p r o b a b l y w e l l to e s t a b l i s h t h e where and why o f my d i f f e r e n c e s w i t h the Genevan. F o r t h a t p u r p o s e a s k e t c h o f h i s s t r u c t u r a l i s t a p p r o a c h t o l o g i c a l i t y w i l l be g i v e n . P i a g e t ' s views on l o g i c a l i t y a p pear i n numerous p u b l i s h e d works; I have drawn p r i n c i p a l l y on P i a g e t 1953, 1958, and 1968. The S t r u c t u r e . The c e n t e r p i e c e o f P i a g e t ' s t h e o r y i s the s t r u c t u r e w h i c h he p o s i t s as t h e s o u r c e and r e p o s i t o r y o f a l l l o g i c a l c o g n i t i o n i n human b e i n g s . T h i s m e n t a l s t r u c t u r e i s s a i d to p o s s e s s e q u i l i b r i u m ; i n d e e d , i t d e v e l o p s t h r o u g h e q u i l i b r a t i o n . P i a g e t b e l i e v e d t h a t h i s s t r u c t u r e had g r e a t e x p l a n a t o r y v a l u e , and one main t h i n g to be e x p l a i n e d was how h i s o l d e r s u b j e c t s ( a d o l e s c e n t s ) were a b l e t o r e a s o n s y s t e m a t i c a l l y even w h i l e p r o f e s s i n g no awareness o f any "system" o p e r a t i v e w i t h i n them. The i n d i v i d u a l who uses l o g i c a l o p e r a t i o n s u s u a l l y "does t h i s w i t h o u t e n u m e r a t i n g them, o r r e f l e c t i n g on them o r t h e i r r e l a t i o n s h i p s , and he o n l y f a i n t l y s u s p e c t s t h a t they form s u c h a system. He i s unaware o f t h i s , i n the same way t h a t i n s i n g i n g o r w h i s t l i n g he i s unaware o f the laws o f harmony." ( P i a g e t , 1953, p . 4 0 ) . But how c o u l d a p e r s o n i n s u ch a s t a t e o f i g n o r a n c e engage i n o b s e r v a b l y l o g i c a l b e h a v i o r ? I t seemed t o P i a g e t t h a t t h e r e must be some k i n d o f s e l f - r e g u l a t o r y h o l i s t i c p r o p e r t y t o t h e s t r u c t u r e i t s e l f s e r v i n g to safeguard i t s " e q u i l i b r i u m " a g a i n s t d i s t u r b i n g i n c o n s i s t e n c y . In t h i s way, we can e x p l a i n why the s u b j e c t i s a f f e c t e d by such s t r u c t u r e s , w i t h o u t being conscious of them. When s t a r t i n g from an a c t u a l l y performed p r o p o s i t i o n a l o p e r a t i o n , or endeavouring to express the c h a r a c t e r s of a given s i t u a t i o n by such an o p e r a t i o n , he cannot proceed i n any way he l i k e s . He f i n d s h i m s e l f , as i t were, i n a f i e l d of f o r c e governed by the laws of e q u i l i b r i u m , c a r r y i n g out t r a n s f o r m a t i o n s or operations determined not only by occurrences i n the immediate pa s t , but by the laws of the whole o p e r a t i o n a l f i e l d of which these past occurrences form a p a r t . ( P i a g e t , 1953, p.41) The mature l o g i c a l s t r u c t u r e then i s s a i d to possess a s e l f - r e g u l a t i n g e q u i l i b r i u m which somehow achieves compensation f o r change, r e c o n c i l i a t i o n of apparent opposites and accomodation of d i f f e r e n t p e r s p e c t i v e s . The INRC Group Model. The model P i a g e t promoted f o r t h i s s t r u c t u r e i s termed the INRC group. The l e t t e r s "INRC" stand f o r f o u r t r a n s f o r m a t i o n s that can be worked on b i n a r y , t r u t h - f u n c t i o n a l l y connected p r o p o s i t i o n s . For example, i n v e r s i o n (N) transforms the negated i m p l i c a t i o n - ( p — q ) i n t o the c o n j u n c t i o n p & -q. The other three t r a n s f o r m a t i o n s are the c o r r e l a t i v e (C), r e c i p r o c a l (R), and i d e n t i t y ( I ) . These f o u r t r a n s f o r m a t i o n s i n c o o r d i n a t i o n c o n s t i t u t e an a b s t r a c t group, and i n t h i s "group" P i a g e t saw the s o r t of s e l f - m a i n t a i n i n g l o g i c a l e q u i l i b r i u m he a t t r i b u t e d to the 27 s t r u c t u r e . A group has four p r o p e r t i e s : (1) a s s o c i a t i v i t y ; (2) r e c i p r o c a l elements f o r a l l group members; (3) an i d e n t i t y element good f o r the e n t i r e group; and (4) every t r a n s f o r m a t i o n of a group member produces a group member, so that no new or non-group members can be produced. In e m p i r i c a l work P i a g e t and h i s a s s o c i a t e s ( n o t a b l y , B a r b e l Inhelder) have conducted, the presence of t h i s INRC group has been s a i d to have been demonstrated i n the adolescent mind. At e a r l i e r ages, l o g i c a l i t y i s s p o r a d i c , incomplete, l a c k i n g i n s y s t e m a t i c i t y . However, i n d i v i d u a l s , by the e a r l y teens, " a f t e r having f a i l e d at the lower l e v e l s , are able to c o o r d i n a t e the four t r a n s f o r m a t i o n s INRC i n q u i t e d i f f e r e n t problems; such as those of r e l a t i v e motion, i . e . the p r e d i c t i o n of changes i n p o s i t i o n of a moving body w i t h i n a framework of re f e r e n c e i t s e l f i n motion w i t h r e f e r e n c e to a f i x e d system ( f o r example, the changes i n p o s i t i o n of a s n a i l on a moving board). A l l t h i s seems to occur as i f the a c q u i s i t i o n of the l o g i c of p r o p o s i t i o n s went together w i t h an understanding of the group INRC, not, of course, i n a b s t r a c t o , but as a p p l i e d to v a r i o u s problems." ( P i a g e t , 1953, p.43). 28 A C r i t i q u e o f the S t r u c t u r a l i s t Program. P i a g e t ' s INRC group model has a c e r t a i n a e s t h e t i c - a t t r a c t i o n . U n f o r t u n a t e l y , i t s a p p e a l does n o t r u n much deeper than t h a t . W h i l e P i a g e t ' s r e s e a r c h and t h e o r i z i n g on the whole has s t i m u l a t e d p s y c h o l o g y enormously, t h i s p a r t i c u l a r c o n t r i b u t i o n has f a i l e d t o i n s p i r e t h o s e o u t s i d e t h e Genevan s c h o o l . I t ' s t r u e t h a t few p s y c h o l o g i s t s have a f i r m g r a s p o t the l o g i c a l model P i a g e t i s a c t u a l l y p u s h i n g , b u t i t ' s e q u a l l y t r u e t h a t P i a g e t has n e v e r done a v e r y s a t i s f a c t o r y j o b o f o p e r a t i o n a l i z i n g h i s c o n s t r u c t i n an e d i f y i n g way. Moreover, those few p s y c h o l o g i s t s who have been b e s t q u a l i f i e d t o e v a l u a t e the INRC group model have r e j e c t e d i t . P e rhaps f o r e m o s t among t h e s e I n O s h e r s o n , (, 1975) , who c r i t i c i z e s t h e model on two main grounds: F i r s t , t h a t the INRC group i s i n a d e q u a t e as the model o f the l o g i c a l s t r u c t u r e b e c a u s e i t spans o n l y a fragment o f l o g i c ; and sec o n d , t h a t n o t h i n g i n the Genevan e m p i r i c a l work ( e . g . I n h e l d e r & P i a g e t , 1958) c o m p e l l s one to a c c e p t t h e INRC group o v e r some o t h e r s y s t e m c a p a b l e o f p r o d u c i n g t h e t r u t h s o f p r o p o s i t i o n a l l o g i c . The only t h i n g I have t o add to Osh e r s o n ' s c r i t i c i s m i s t h a t i t do e s n ' t go f a r enough; i t l e a v e s the would-be s t r u c t u r a l i s t w i t h hopes i n t a c t t h a t the s t r u c t u r e can be 29 i d e n t i f i e d . As w i l l be e x p l a i n e d , I do n o t s h a r e t h i s o ptimism, which s e t s me a p a r t c o m p l e t e l y from the Genevan s t r u c t u r a l i s t s . A n derson (19 76) has a r g u e d p e r s u a s i v e l y t h a t no unique i d e n t i f i c a t i o n o f c o g n i t i v e s t r u c t u r e s i s p o s s i b l e . H i s p o i n t r e s t s on the a n a l o g y between a u t o m a t i c f o r m a l systems (e. g . computers) and the human mind. V e r y d i f f e r e n t a u t o m a t i c f o r m a l systems can mimic one a n o t h e r ' s o u t p u t . By t h e same token then human minds w i t h v e r y d i f f e r e n t l o g i c a l s t r u c t u r e s c o u l d p r o d u c e i d e n t i c a l r e s p o n s e p a t t e r n s . C a r r i e d t o an extreme, no two i n d i v i d u a l s g e n e r a t i n g the same r e s p o n s e s need s h a r e the same s t r u c t u r e o r s e t o f schemata o r whate v e r i t i s one b e l i e v e s the l o g i c a l f a c u l t y c o n s i s t s o f . We can i n s p e c t a computer's a c t u a l hardware and s o f t w a r e t o see whether i t i s d i f f e r e n t l y b u i l t t h a n a computer whose o u t p u t i t mimics. But the n a t u r e o f t h e c o g n i t i v e p s y c h o l o g i s t s ' o b j e c t o f i n t e r e s t — t h e m i n d — i s such t h a t i t cannot be so i n s p e c t e d ( a t l e a s t , n o t by o b j e c t i v e o u t s i d e r s ) . An a n l o g y may make t h i s whole i d e a more c o m p r e h e n s i b l e . Suppose you a r e to deduce which e x a c t a i r c o n d i t i o n i n g s y s t e m i s i n use i n a g i v e n b u i l d i n g , b u t a r e u n a b l e t o s i m p l y go to t h e u n i t i n q u e s t i o n t o see what i t i s . You a r e thus l e f t w i t h i n d i r e c t means o f a s c e r t a i n m e n t . A l t e r i n g the t h e r m o s t a t s and n o t i n g the degree and r a p i d i t y o f change would e n a b l e y o u to r u l e o u t some models. But i n the end, t h e r e would p r o b a b l y be s e v e r a l models o f d i f f e r e n t b u i l d s , c a p a b l e o f m e e t i n g the s p e c i f i c a t i o n s demanded by y o u r o b s e r v a t i o n a l r e c o r d . Moreover, t h e r e might be i n d e f i n i t e l y many o t h e r , as y e t u n i n v e n t e d models c a p a b l e too o f m e e t i n g those s p e c i f i c a t i o n s . W i t h t h i s a n a l o g y one s e e s j u s t how l i t t l e advances i n b r a i n l o c a l i z a t i o n o f l o g i c a l f u n c t i o n i n g would h e l p i n r e s o l v i n g t h e dilemma. Though you knew what room the a i r c o n d i t i o n i n g u n i t was i n (suppose a l l b u i l d i n g s o f t h i s t y p e have a s p e c i a l p l a c e where the a i r c o n d i t i o n i n g u n i t g o e s ) , y o u s t i l l w o u l d n ' t know j u s t w h i c h e x a c t u n i t was t h e r e . A n derson's t h r u s t was aimed a t c o g n i t i v e p s y c h o l o g y i n g e n e r a l no c o g n i t i v e s t r u c t u r e c a p a b l e o f b e i n g e n t i r e l y modeled by l o g i c can be p o s i t i v e l y i d e n t i f i e d . However, the p o i n t i s p a r t i c u l a r l y i n e s c a p a b l e f o r the p s y c h o l o g i s t i n q u i r i n g a f t e r the n a t u r e o f the l o g i c a l f a c u l t y . O s h e r s o n (1975), one o f t h o s e i n q u i r e r s , d i s c u s e s t h e i s s u e v e r y c a n d i d l y a t the end o f h i s t h i r d volume ( 21.2 "The P r o b l e m o f E q u i v a l e n t D e d u c t i o n M o d e l s " ) : . . . d e d u c t i o n models l i k e o u r s a r e open t o a... p e r n i c i o u s k i n d o f u n d e r d e t e r m i n a t i o n . . . A l l o f the e m p i r i c a l c o n s t r a i n t on t h e o r y c o n s t r u c t i o n i s f o c u s e d on the model's d e r i v a t i o n s ; the o p e r a t i o n s and e x e c u t i v e a r e t e s t e d o n l y t h r o u g h t h e d e r i v a t i o n s they p r o d u c e . . . . C o n s e q u e n t l y , two d e d u c t i o n models t h a t p r o d u c e the same 31 d e r i v a t i o n s f o r the same arguments, no m a t t e r how d i s t i n c t o t h e r w i s e , a r e e m p i r i c a l l y i n d i s t i n g u i s h a b l e . . . p p . 2 5 0 - 2 5 1 . O s h e r s o n e x p r e s s e s h i s own p r e f e r e n c e i n f a v o r o f a d e d u c t i o n model which i s m o d e r a t e l y e f f i c i e n t , b u t concedes t h a t we a r e n o t c o m p e l l e d t o a c c e p t the more e l e g a n t s y s t e m — because t h e r e i s no b a s i s f o r assuming t h a t t h e human mind i s " e l e g a n t " . The Genevan C o n c e p t i o n o f L o g i c a l i t y . The Genevan c o n c e p t i o n o f l o g i c a l i t y i s the most f u l l y d e v e l o p e d y e t to appear i n p s y c h o l o g y . I t i s i n t e r e s t i n g t h a t P i a g e t ' s a n a l y s i s o f l o g i c a l i t y i n terms o f t h e employment o f the schemata l e d him to q u e s t i o n the u n i t a r i n e s s o f l o g i c a l i t y . As a t h e o r i s t he c l e a r l y l e a n e d towards t h e i d e a t h a t t h e l o g i c a l i t y a s s o c i a t e d w i t h an o p e r a t i o n a l " s t r u c t u r e d'assemble" would be p r e t t y u n i t a r y . As a r e s e a r c h e r he h a d t o accomodate h i s t h e o r y t o t h e f i n d i n g s t h a t s u g g e s t e d d i f f e r e n t i a l m a n i f e s t a t i o n o f l o g i c a l i t y ( " d e c a l a g e " ) . But i n any c a s e , h i s i n t e r e s t was i n the u n i f o r m i t y o f development o f l o g i c a l i t y , and n o t so much w i t h t h e i s s u e o f t h e u n i t a r i n e s s o f l o g i c a l i t y i n mature human b e i n g s p e r s e . I t i s my i n t e n t i o n , however, to s h e d some l i g h t on j u s t what s o r t o f q u e s t i o n s my i n t e r e s t s would l e a d t o w i t h i n t h e Genevan framework. 32 C o n s i d e r the famous c o n s e r v a t i o n problems ( c o n s e r v a t i o n o f number, mass, l e n g t h , volume, e t c . ) . These are problems s h a r i n g more o r l e s s the same form. But who can a c t u a l l y t e l l t h a t they have the same form? And i s the a b i l i t y to see t h a t two problems s h a r e the same form s t r o n g l y c o r r e l a t e d w i t h one's a b i l i t y to do the problems? I t can be a r g u e d t h a t r e c o g n i z i n g the form o f a p r o b l e m i s no l e s s a l o g i c a l a c t than i s th e d o i n g o f the problem. Moreover, i t seems p o s s i b l e t h a t one c o u l d r e c o g n i z e t h e form o f t h e p r o b l e m w i t h o u t b e i n g a b l e to do the p r o b l e m . These a r e the s o r t o f q u e s t i o n s and p o s s i b i l i t i e s t h a t i n s p i r e d t h i s t h e s i s . The V a r i a b l e s o f L o g i c a l i t y i n the  P s y c h o l o g i c a l L i t e r a t u r e A t l e a s t two o f t h e v a r i a b l e s o f l o g i c a l i t y i d e n t i f i e d i n the I n t r o d u c t i o n have r e c e i v e d , i n i s o l a t i o n , t h e a t t e n t i o n o f p s y c h o l o g i s t s . Some r e s e a r c h has a l s o been done on a s u b j e c t c l o s e l y c o n n e c t e d w i t h my t h i r d v a r i a b l e , l o g i c a l i n t u i t i o n . The r e m a i n d e r o f t h i s c h a p t e r s u r v e y s t h i s l i t e r a t u r e . L o g i c a l Judgment. L o g i c a l judgment i s s i m p l y one's u n s c h o o l e d a b i l i t y t o r e c o g n i z e t h a t a l o g i c a l form i s v a l i d . 33 I t should be p o i n t e d out that my usage agrees g e n e r a l l y w i t h Osherson's (1975), although, u n f o r t u n a t e l y , Osherson a l s o uses, as a synonym f o r the term " l o g i c a l judgment," the term " l o g i c a l i n t u i t i o n " — w h i c h l a t t e r term has a completely d i f f e r e n t meaning i n t h i s t h e s i s . P s y c h o l o g i s t s have been i n t e r e s t e d i n l o g i c a l judgment f o r many years. A p e r s i s t i n g f a s c i n a t i o n w i t h the r a t h e r a r c h a i c A r i s t o t e l i a n s y l l o g i s m has l e d to f o r m u l a t i o n of s e v e r a l explanatory models f o r t h i s h i g h l y r e s t r i c t e d e x e r c i s e of l o g i c a l judgment ( E r i c k s o n , 1974; Guyote & Sternberg, 1981). These models are what Osherson (19 75) would c a l l " r e d u c t i v e " , i n that they attempt to e x p l a i n l o g i c a l judgment i n terms of c o g n i t i v e r e p r e s e n t a t i o n and p r o c e s s i n g that i s g e n e r a l , i . e . not s p e c i f i c to l o g i c a l f u n c t i o n i n g . Guyote and Sternberg (1981) f o r example, t r y to e x p l a i n l o g i c a l judgment of s y l l o g i s m s ( A r i s t o t e l i a n and c o n d i t i o n a l ) i n terms of r e p r e s e n t a t i o n s of premise i n f o r m a t i o n and combination r u l e s f o r th a t i n f o r m a t i o n . One of the c h i e f goals of the makers of such models i s to o f f e r an account of what goes wrong when t y p i c a l e r r o r s i n l o g i c a l judgment occur. E r i c k s o n (19 74), f o r example, has a stage model i n which the i n i t i a l stage c o n s i s t s i n r e p r e s e n t a t i o n of the major premise of the c a t e g o r i c a l s y l l o g i s m . 34 He p o i n t s out t h a t a t t h i s s t a g e the e x t e n s i o n a l p r o p o s i t i o n " A l l S a r e M" can sometimes be m i s i n t e r p r e t e d to mean " A l l S a r e M and A l l M a r e S". T h i s r e f e r s us back to o u r e a r l i e r d i s c u s s i o n o f Smedslund (19 70), f o r t h i s i s a r g u a b l y a m a t t e r o f v e r b a l noncomprehension r a t h e r than a m a t t e r o f d e f i c i e n t l o g i c a l judgment. C e r t a i n l y i t i s n e c e s s a r y t o u n d e r s t a n d the meaning o f the c o p u l a ( t h e " a r e " i n " A l l S a r e M") i n a c a t e g o r i c a l s y l l o g i s m b e f o r e one can j u d g e i t c o r r e c t l y . S i m i l a r l y , one must be a b l e to e i t h e r g r a s p the e n t i r e argument i n one's immediate a p p r e h e n s i o n , o r one must be a b l e to remember t h o s e p a r t s w h i c h a r e not i n one's immediate a p p r e h e n s i o n , i n o r d e r to have i n mind the argument to be j u d g e d . A l l t h i s i l l u s t r a t e s i s the f a c t t h a t a g r e a t d e a l o f what one does i n p a s s i n g judgment on the v a l i d i t y o f a l o g i c a l form i n v o l v e s g e n e r a l h i g h e r c o g n i t i v e p r o c e s s e s . In t h i s way the p s y c h o l o g y o f r e a s o n i n g i s a s s i m i l a t e d i n t o c o g n i t i v e p s y c h o l o g y . There i s a n o t h e r a pproach to l o g i c a l judgment, however, r e d u c t i o n i s t i c i n i t s own way. The i d e a i s t h a t t h e r e i s some f i n i t e , d e f i n i t e s e t o f p r i m i t i v e p r o t o t y p i c a l l o g i c a l forms (sometimes c a l l e d i n f e r e n c e schemata) e v e r y o n e ( a t l e a s t , the n o r m a l a d u l t ) i s e q u i p p e d to r e c o g n i z e as v a l i d . And r e c o g n i t i o n 35 of a more complex l o g i c a l form i s e x p l a i n e d as c o n s i s t i n g of a process resembling the d e r i v a t i o n of the l o g i c i a n . I d e n t i f i c a t i o n of the p r i m i t i v e s of l o g i c a l judgment becomes important i n t h i s scheme, but e x p l a n a t i o n of those p r i m i t i v e s i s not attempted; thus the p s y c h o l o g i s t never leaves the realm of s t r i c t l y l o g i c a l c o g n i t i o n , i n t h i s approach. Braine (19 78) has proposed a s e t of such p r i m i t i v e or elementary schemata. Osherson (1975) has gone f u r t h e r . Not only has he t r i e d to i d e n t i f y a s e t of p r i m i t i v e argument schemata (he c a l l s them "operators") s a i d to c o n s t i t u t e the foundations of l o g i c a l judgment, he has developed f o r each o p e r a t o r a corresponding " h e l p i n g c o n d i t i o n " which s p e c i f i e s when an operator i s to be used i n a v i r t u a l d e r i v a t i o n performed i n s e r v i c e of l o g i c a l judgment passed on a more complex form. The h e l p i n g c o n d i t i o n s c o l l e c t i v e l y comprise the " e x e c u t i v e " of h i s system. Together the operators and e x e c u t i v e of Osherson's model are supposed to account f o r at l e a s t many in s t a n c e s of our l o g i c a l judgment. To t e s t h i s system's o v e r a l l t e n a b i l i t y he has imposed upon i t h i s a d d i t i v i t y and i n v e n t o r y requirements, which w i l l be e x p l a i n e d next. Osherson apparently b e l i e v e s t h a t a l o g i c a l form i n v a r i a b l y t r i g g e r s c e r t a i n o p e r a t i o n s i n the c o g n i z i n g s u b j e c t . 36 Suppose that a s i n g l e operator Qi enables a subj e c t to judge argument form A i , and, s i m i l a r l y , 02 f o r A2. Suppose f u r t h e r now that a s u b j e c t r a t e s A^ as bein g a "2" on a l - t o - 7 s c a l e o f d i f f i c u l t y ( d i f f i c u l t to j u d g e ) , and A2 as being a "3". Now i t i s p o s s i b l e to c o n s t r u c t a m u l t i o p e r a t i o n a l argument form out of A i and A2 by p u t t i n g them together. I f the deductive system which s e t s out to e x p l a i n the l o g i c a l judgment of t h i s m u l t i o p e r a t i o n a l composite argument form meets the a d d i t i v i t y requirement, then the s u b j e c t ' s d i f f i c u l t y r a t i n g o f t h i s A l + A2 composite form w i l l be p r e d i c t a b l e , up to l i n e a r i t y , as a f u n c t i o n of t h a t s u b j e c t ' s d i f f i c u l t y r a t i n g s of A i and A2- Therefore, i f the s u b j e c t r a t e d the d i f f i c u l t y o f the composite as b e i n g , say, l e s s than the d i f f i c u l t y of A2 taken by i t s e l f , the a d d i t i v i t y requirement would not be met. The i n v e n t o r y requirement r e s t s on the i d e a that arguments can be subsets of other arguments. The argument that i s d e r i v a b l e by s u c c e s s i v e o p e r a t i o n s Oi and 02 i s a subset of the argument that i s d e r i v a b l e by s u c c e s s i v e operations O i , O2, and O3, because every o p e r a t i o n i n v o l v e d i n the former's d e r i v a t i o n i s i n v o l v e d i n the l a t t e r ' s . The i n v e n t o r y requirement p r e d i c t s that a s u b j e c t who f a i l s to c o r r e c t l y judge the f i r s t argument w i l l n e c e s s a r i l y f a i l to c o r r e c t l y judge the second, encompassing argument. 37 A number of experiments have been c a r r i e d out by Osherson and appear i n h i s book (1975). His procedure i n some of h i s experiments i s to compare, on the b a s i s of i n v e n t o r y and a d d i t i v i t y a n a l y s e s , the p l a u s i b i l i t y of two a l t e r n a t i v e s e t s of elementary schemata, where the d i f f e r e n t s e t s produce d i f f e r e n t d e r i v a t i o n s f o r the same arguments w i t h respect to the o p e r a t i o n s appearing i n them. U n f o r t u n a t e l y , although Osherson's i n g e n u i t y must be applauded, the r e s u l t s of these comparisons are not t e r r i b l y i m p r e s s i v e . Very l i t t l e b a s i s f o r d i s c r i m i n a t i o n arose out of experiment #3. In experiment #4 the i n v e n t o r y r e s u l t s f a i l e d to d i s t i n g u i s h between the r i v a l systems, although the a d d i t i v i t y a n a l y s i s d i d seem to favor one over the o t h e r . Rips (1983) has r e c e n t l y o f f e r e d an account of l o g i c a l judgment which he claims to represent an improvement over that of Osherson. His computer simul-ation, c a l l e d ANDS (A N a t u r a l Deduction System), has an e x e c u t i v e which not only " l o o k s ahead" i n order to t r i g g e r h e l p i n g c o n d i t i o n s , but which i s capable of s e t t i n g sub-goals i n i t s v i r t u a l d e r i v a t i o n s . In g e n e r a l , p s y c h o l o g i s t s have s t u d i e d l o g i c a l judgment i n i s o l a t i o n from o t h e r forms of l o g i c a l i t y . Sternberg (1982) draws a t t e n t i o n to the need to i n q u i r e i n t o the r e l a t i o n of l o g i c a l judgment to other h i g h e r c o g n i t i v e processes. In 38 p a r t i c u l a r he has po s e d the q u e s t i o n , how does l o g i c a l judgment c o r r e l a t e w i t h g e n e r a l i n t e l l i g e n c e ? I n t h i s t h e s i s we s h a l l see how l o g i c a l judgment does r e l a t e t o o t h e r h i g h e r c o g n i t i v e p r o c e s s e s — n a m e l y to the o t h e r forms o f l o g i c a l i t y . D e d u c t i v e P r o b l e m S o l v i n g . The problems i n v o l v e d i n d e d u c t i v e p r o b l e m s o l v i n g as i t i s h e r e d i s c u s s e d a r e f o r m a l p r o b l e m s — i n the sense t h a t W i c k e l g r e n (19 74) speaks o f f o r m a l p r o b l e m s . I t s h o u l d be k e p t i n mind t h a t g r e a t numbers o f the problems t h a t we d e a l w i t h i n e v e r y d a y l i f e and i n s c h o o l and work a r e n o t d e d u c t i v e p r o b l e m s . (Most o f the " d e d u c t i o n " done i n p o p u l a r m y s t e r y t a l e s i s not d e d u c t i v e p r o b l e m s o l v i n g ) . More on t h e n a t u r e o f d e d u c t i v e problems w i l l be p r e s e n t e d i n the a n a l y s i s o f c h a p t e r I I I . F o r now the p o i n t to make i s t h a t a good d e a l o f the p s y c h o l o g i c a l l i t e r a t u r e d e v o t e d t o " p r o b l e m s o l v i n g " i s n o t e s p e c i a l l y r e l e v a n t t o s t r i c t l y l o g i c a l p r o b l e m s o l v i n g a c t i v i t y , and we s h a l l r e s t r i c t o u r s e l v e s to a t h e o r y t h a t does d e a l w i t h f o r m a l p r o b l e m s . U n d o u b t e d l y t h e most p r o m i n e n t p s y c h o l o g i c a l t h e o r y o f p r o b l e m s o l v i n g i n t h e d e d u c t i v e r e a l m i s t h a t o f N e w e l l and Simon (.1972; a l s o N e w e l l , Shaw, and Simon, 1958). N e w e l l and Simon i n v e n t e d the c o n c e p t o f the p r o b l e m space w h i c h i s to be spanned by a c h a i n o f moves an a l a g o u s t o a s y m b o l i c l o g i c d e r i v a t i o n . Two " s t a t e s " form the t e r m i n i o f t h i s c h a i n , 39 the i n i t i a l p r o b l e m s t a t e , d e f i n e d by the g i v e n s , and the g o a l s t a t e , w hich i s e i t h e r g i v e n o r to be found. P r o b l e m s o l v i n g i s a c c o m p l i s h e d by, f i r s t , d e t e c t i n g the d i f f e r e n c e s between t h e p r o b l e m a n d g o a l s t a t e s ; s e c o n d , by s e t t i n g up sub g o a l s w h i c h can be d e r i v e d by known o p e r a t i o n s p r o c e e d i n g from the p r o b l e m s t a t e ( t h e s u b g o a l s b e i n g more s i m i l a r f e a t u r e w i s e to the g o a l s t a t e than i s t h e p r o b l e m s t a t e ) ; and f i n a l l y , by i t e r a t i n g t h e above p r o c e s s u n t i l t h e g o a l s t a t e i s e q u i v a l e n t t o an a c h i e v a b l e s u b g o a l w h i c h i s t h e n a r r i v e d a t . N e w e l l and Simon s i m u l a t e d human p r o b l e m s o l v i n g v i a computer, b u t a l s o o b t a i n e d i n t r o s p e c t i v e p r o t o c o l s from human s u b j e c t s i n o r d e r to c o r r o b o r a t e , i n a l o o s e way, the r e l e v a n c e o f t h e i r s i m u l a t i o n model. An example o f a p r o b l e m w h i c h y i e l d s t o t h e i r G e n e r a l P r o b l e m S o l v e r (GPS) i s t h e famous c a n n i b a l s and m i s s i o n a r i e s problem. T h i s i s a p r o b l e m w i t h two w e l l d e f i n e d s t a t e s , and known o p e r a t i o n s which can be a p p l i e d to span t h e s t a t e s (see S o l s o , 19 79, f o r an i l l u s t r a t e d d e s c r i p t i o n o f t h i s p r o b l e m ) . S u b g o a l s a r e r e l a t i v e l y o b v i o u s and the p r o b l e m s t a t e r e a d i l y u n d e r s t o o d . One o f the main g o a l s o f N e w e l l and Simon has been to d e s c r i b e the c o n s i d e r a t i o n s e n t e r t a i n e d by a p r o b l e m s o l v e r a t any g i v e n s t a g e o f p r o g r e s s toward, the g o a l s t a t e . The f o l l o w i n g a r e " c o n s i d e r a t i o n s a t a p o s i t i o n i n p r o b l e m s p a c e " ( f r o m N e w e l l , 1968): E v a l u a t e the p o s i t i o n : I s i t the d e s i r e d s t a t e ? S h o u l d i t be remembered, so t h a t e i t h e r i t can be r e t u r n e d to l a t e r , o r i t can be r e c o g n i z e d i f e n c o u n t e r e d a g a i n ? I s t h e r e some new i n f o r m a t i o n t h a t s h o u l d be e x t r a c t e d and remembered i n d e p e n d e n t l y o f p o s i t i o n ? I s p r o g r e s s b e i n g made, so t h a t s e a r c h s h o u l d be c o n t i n u e d ; o r a r e t h e r e d i f f i c u l t i e s ? S e l e c t new o p e r a t o r : Has i t been used b e f o r e ? I s i t d e s i r a b l e ? W i l l i t l e a d t o p r o g r e s s ? I s i t f e a s i b l e ? W i l l i t work i n t h e p r e s e n t p o s i t i o n i f a p p l i e d ? A p p l y o p e r a t o r to p r e s e n t p o s i t i o n : I f i t works, then i t p r o d u c e s new p o s i t i o n . I f i t does n o t work, what i s the d i f f i c u l t y ? E v a l u a t e d i f f i c u l t y : S h o u l d a s u b g o a l be s e t up to overcome t h i s d i f f i c u l t y ? S h o u l d the p o s i t i o n be r e j e c t e d ? R e t u r n t o p r i o r p o s i t i o n ? R e t u r n to i n i t i a l p o s i t i o n ? R e t u r n to a remembered p o s i t i o n ; i f so, w h i c h one? E v a l u a t e o l d p o s i t i o n , j u s t r e t u r n e d t o : S h o u l d i t be used, o r r e j e c t e d ? The p i o n e e r i n g work o f N e w e l l and Simon has s e t the tone f o r t h i n k i n g about d e d u c t i v e p r o b l e m s o l v i n g i n t h e p r e s e n t p a p e r i n a t l e a s t one i m p o r t a n t r e s p e c t : t h e s e p s y c h o l o g i s t s have e n v i s a g e d d e r i v a t i o n - l i k e c o g n i t i v e a c t i v i t y as b e i n g r e s p o n s i b l e f o r o u r d e d u c t i v e p r o b l e m s o l v i n g . T h i s s h o u l d 41 remind uS o f the s i m i l a r a c c o u n t s g i v e n f o r l o g i c a l judgment ( e . g . , t h a t o f O s h e r s o n ) , w h i c h r a i s e s t h e q u e s t i o n : what jLs the d i f f e r e n c e between t h o s e two forms o f l o g i c a l c o g n i t i o n — i f t h e r e i s any d i f f e r e n c e ? Thus f a r t h r e e s o r t s o f l o g i c a l c o g n i t i o n have been d i s t i n g u i s h e d : t h e p r i m i t i v e , " u n e x p l a i n e d " r e c o g n i t i o n o f some b a s i c l o g i c a l forms ( t h e e l e m e n t a r y schemata o f B r a i n e o r O s h e r s o n ) ; the v i r t u a l d e r i v a t i o n s i n v o l v e d i n l o g i c a l judgment o f more complex forms; and the a n s w e r - p r o d u c i n g i n f e r e n t i a l s e a r c h o f d e d u c t i v e p r o b l e m s o l v i n g . How c l o s e l y do t h e s e s o r t s o f l o g i c a l t h i n k i n g hang t o g e t h e r ? T h i s i s the u n i t a r i n e s s q u e s t i o n o f l o g i c a l i t y . R i p s ' (1983) i n t u i t i o n s l e a d h i m t o an o p i n i o n on t h i s p o i n t : " i t w o u l d be odd to suppose t h a t humans have e v o l v e d t h r e e d i f f e r e n t l o g i c a l s y s t e m s , one f o r p r o d u c t i o n o f i n f e r e n c e s , a n o t h e r f o r e v a l u a t i o n o f s i n g l e arguments, and a t h i r d f o r more c o m p l i c a t e d o n e s . " There must be a " g e n e r a l p u r p o s e d e d u c t i v e program" b e h i n d them a l l ( R i p s , p . 5 3 ) . I hope t o s h ed some l i g h t on t h i s e x a c t q u e s t i o n i n the n e x t c h a p t e r by e x a m i n i n g i n some d e t a i l l o g i c a l judgment, d e d u c t i v e p r o b l e m s o l v i n g , and d e r i v a t i o n . A n a l o g i c a l R e a s o n i n g and F o r m a l Problems. Problems, l i k e arguments and d e v i c e s , can have i s o m o r p h i c forms. T h a t i s , 42 one problem can be mapped p r e c i s e l y onto another problem when they share the same l o g i c a l form. Now, suppose that a s u b j e c t works h i s way through to the s o l u t i o n to one problem, and then i s faced w i t h a second problem t h a t happens to be isomorphic to the f i r s t . W i l l t h i s s u b j e c t n o t i c e t h e i r equivalence and use t h i s f a c t i n reasoning by analogy to produce the e q u i v a l e n t s o l u t i o n to the second problem? This h y p o t h e t i c a l q u e s t i o n has been r a i s e d by p s y c h o l o g i s t s (Reed, E r n s t & B a n e r j i , 1974; Gick & Holyoak, 1980) and put to the e m p i r i c a l t e s t . R e s u l t s have been mixed. I n the Reed, E r n s t & B a n e r j i (1974) study, s u b j e c t s worked w i t h the c a n n i b a l s / m i s s i o n a r i e s problem and a n e a r l y isomorphic t w i n , " j e a l o u s husbands". Subjects q u i t e n a t u r a l l y worked a problem more r a p i d l y and s u r e l y when i t was given to them a second time i n i t s o r i g i n a l guise (e.g. s u b j e c t s were given j e a l o u s husbands two times r u n n i n g ) , but s u r p r i s i n g l y showed l i t t l e t r a n s f e r from one problem to i t s twin (e.g. from c a n n i b a l s / m i s s i o n a r i e s to j e a l o u s husbands). A check experiment had the experimenters i n f o r m i n g the s u b j e c t s t h a t the problems were the same, so t h e i r s o l u t i o n s must be the same. S p e c i f i c s of mapping were even p r o v i d e d . Even then the m a j o r i t y of s u b j e c t s claimed under q u e s t i o n i n g t h a t they 43 made p r a c t i c a l l y no use o f the i n f o r m a t i o n . There were m u l t i p l e p e r f o r m a n c e measures, and some showed t r a n s f e r e f f e c t s w h i l e o t h e r s d i d n o t , b u t the o v e r a l l i n d i c a t i o n seemed to be t h a t s u b j e c t s d i d n o t make much good use o f a n a l o g i c a l r e a s o n i n g i n d e a l i n g w i t h a n a l o g o u s d e d u c t i v e p r o b l e m s . I n a more e x t e n s i v e i n v e s t i g a t i o n G i c k and Ho l y o a k (1980) t e s t e d s u b j e c t s f o r t r a n s f e r e f f e c t s u s i n g homomorphic i n s i g h t p r o b l e m s . K i n d and degree o f e x p e r i m e n t e r i n t e r v e n t i o n ( p r o m p t i n g ; h i n t s ) was m a n i p u l a t e d , and i n some c o n d i t i o n s the s o l u t i o n to the f i r s t p r o b l e m was a r r i v e d a t by the s u b j e c t h i m / h e r s e l f w h i l e i n o t h e r s the e x p e r i m e n t e r s u p p l i e d the s o l u t i o n . T r a n s f e r e f f e c t s were o b t a i n e d i n some c o n d i t i o n s , as where s u b j e c t s were g i v e n s t r o n g h i n t s . A r e c e n t a d d i t i o n to t h e l i t e r a t u r e by the same a u t h o r s ( G i c k & H o l y o a k , 1983) a d d r e s s e d i t s e l f t o t h e q u e s t i o n o f when and why s u b j e c t s s p o n t a n e o u s l y n o t i c e and u t i l i z e a n a l o g i e s f o r the s o l u t i o n o f homomorphic prob l e m s . They found t h a t a " p r o b l e m schema" ( o r r e p r e s e n t a t i o n o f t h e s t r u c t u r e common t o two o r more problems) c o u l d be b e s t i n d u c e d i n s u b j e c t s by h a v i n g them d e s c r i b e the s i m i l a r i t i e s between (and thus i n c i d e n t a l l y match) two a n a l o g o u s p r o b l e m s . The p r o b l e m schema b e i n g so i n d u c e d f a c i l i t a t e d s t r o n g t r a n s f e r e f f e c t s . The p r o b l e m t r a n s f e r e x p e r i m e n t s a r e r e l e v a n t to the t h i r d v a r i a b l e o f l o g i c a l i t y i n t r o d u c e d h e r e , t h a t o f l o g i c a l i n t u i t i o n , b e c ause they a r e c o n c e r n e d w i t h r e c o g n i t i o n o f s i m i l a r i t y o r e q u i v a l e n c e o f form between p r o b l e m s . But the p r o b l e m t r a n s f e r r e s e a r c h t r i e s t o get a t something i n d i r e c t l y w h ich I have, as w i l l be se e n , a t t e m p t e d t o g e t a t d i r e c t l y . C o n c l u s i o n s I have t r i e d t o g i v e some i d e a o f t h e e x t e n t to w h i c h the forms o f l o g i c a l i t y I have i d e n t i f i e d have been s t u d i e d by p s y c h o l o g i s t s . In a good o v e r v i e w o f t h i s whole a r e a S t e r n b e r g (1982) c i t e s much o f the work t h a t has been done on a n a l o g i c a l r e a s o n i n g , d e d u c t i v e p r o b l e m s o l v i n g , and l o g i c a l judgment. What i s c o n s p i c u o u s l y m i s s i n g from the i n v e n t o r y o f r e s e a r c h done on t h e s e k i n d s o f r e a s o n i n g i s any r e c o r d e d e f f o r t to b r i n g t o g e t h e r i n one s t u d y the t h r e e v a r i a b l e s o f l o g i c a l judgment, d e d u c t i v e p r o b l e m s o l v i n g , and l o g i c a l i n t u i t i o n so as to see how they i n t e r r e l a t e . I t i s p r e c i s e l y t h a t which the r e s e a r c h r e p o r t e d i n t h i s t h e s i s a c c o m p l i s h e s . 45 I I I . LOGICAL ACTIVITIES The p u r p o s e o f t h i s c h a p t e r i s to examine the o p e r a t i o n a l i n dependence o f the v a r i a b l e s o f l o g i c a l i t y . O b s e r v a t i o n o f the i n t e r r e l a t i o n s h i p s o f the v a r i a b l e s f o l l o w s ; the i d e a f o r now i s to u n d e r s t a n d what we s h o u l d be l o o k i n g f o r . I n t h e f i r s t c h a p t e r i t was p r o p o s e d t h a t t h e r e a r e t h r e e t h i n g s t h a t can be done w i t h l o g i c a l i t e m s : they can be j u d g e d , worked, and matched. The q u e s t i o n s may be r a i s e d : what o v e r l a p i s t h e r e between t h e s e j u d g i n g , w o r k i n g , and m a t c h i n g a c t i v i t i e s ? I s one v a r i a b l e dependent upon a n o t h e r i n some way? Can the v a r i a b l e s — o r some p a i r o f t h e m — b e r e d u c e d to a s i n g l e v a r i a b l e ? I n g e n e r a l , I e x p e c t t h a t a b i l i t i e s t o p e r f o r m a c t i v i t i e s t h a t o v e r l a p one a n o t h e r a r e c o r r e l a t e d v a r i a b l e s , as b a s e b a l l p i t c h i n g and j a v e l i n t h r o w i n g a r e . The p r e s e n t e x a m i n a t i o n t h e r e f o r e c o n n e c t s somewhat w i t h t h e q u e s t i o n t o w h i c h we hope to r e t u r n an e m p i r i c a l answer, namely, how t i g h t l y c o r r e l a t e d a r e the l o g i c a l i t y measures we d e v e l o p f o r the r e s p e c t i v e v a r i a b l e s . Thus f a r l o g i c a l i t y has been l o o k e d a t from a d i s t a n c e . We w i l l i n t h i s c h a p t e r come c l o s e r t o the a c t u a l i t i e s o f l o g i c a l r e a s o n i n g . I n t r o d u c t i o n o f a sample l o g i c a l i t e m , 46 v i e w e d v a r i o u s l y as a d e d u c t i v e p r o b l e m and as an argument, s h o u l d a i d i n t h i s cause. You Be the Judge The p r o b l e m , "You Be the Judge" ("Judge"), p r e s e n t e d i n T a b l e 1, c o n s i s t s o f a s e t o f p r o p o s i t i o n s s t a n d i n g i n e x p l i c i t l o g i c a l r e l a t i o n s h i p to one a n o t h e r , i . e . i t has a l o g i c a l form. W i t h i t s q u e s t i o n s , i n c l u d e d a t the b o t t o m o f T a b l e 1, "Judge" i s a f i n d p r o b l e m : one i s to make a f i n d i n g as t o the g u i l t o f the c h a n g i n g c l e r k . A f i n d p roblem, i n c o n t r a s t w i t h a p r o v e problem, has an i n c o m p l e t e l y s p e c i f i e d g o a l e x p r e s s i o n (see W i c k e l g r e n , 1974, f o r t h i s d i v i s i o n o f f o r m a l p r o b l e m s ) . Y e t "Judge" i s e a s i l y c o n v e r t e d i n t o an argument which can be a s s e s s e d as t o i t s v a l i d i t y . T h i s c o n v e r s i o n would be e f f e c t e d by s i m p l y i n c l u d i n g among the g i v e n s a c o n c l u s i o n , e.g. t h a t the c l e r k i s g u i l t y . A p s y c h o l o g i c a l q u e s t i o n now i s : how i s h a n d l i n g an argument d i f f e r e n t from h a n d l i n g a d e d u c t i v e problem? F o r one t h e v a r i a b l e s , l o g i c a l i n t u i t i o n , the d i f f e r e n c e does n o t seem c r u c i a l . L o g i c a l i n t u i t i o n i n v o l v e s r e c o g n i t i o n o f the s i m i l a r i t y o f form o f arguments and problems, and a p r o b l e m can be matched t o a p r o b l e m j u s t as an argument can be matched to an argument. "You Be the Judge", f o r example, 47 "YOU BE THE JUDGE" PROBLEM You a r e a c a s i n o d i r e c t o r i n Las Vegas h a v i n g to d e a l w i t h a p r o b l e m . I t would appear t h a t the change-making t i l l i s l o w e r t h a n i t s h o u l d be. But has money a c t u a l l y been t a k e n o r i s the d i s c r e p a n c y o n l y i n a c c o u n t - k e e p i n g ? Y o u r house s e c u r i t y men, i n p a r t n e r s h i p w i t h the c a s i n o b u r s a r and an i n d e p e n d e n t s t a t e i n s p e c t o r , have come t o the f o l l o w i n g c o n c l u s i o n s , w h i c h t h e y p r e s e n t to you. Because the i n v e s t i g a t i o n has been t h o r o u g h and e x a c t i n g , c o n d u c t e d by h i g h l y r e l i a b l e p e o p l e , y o u a r e o b l i g e d to assume the r e s u l t s o f t h e i n v e s t i g a t i o n — a s g i v e n b e l o w — a r e t r u e . B a s i n g y o u r d e c i s i o n t h e n s o l e l y on t h e i n f o r m a t i o n p r o v i d e d below, draw the most l o g i c a l c o n c l u s i o n s y o u can i n a n s w e r i n g the q u e s t i o n s y o u a r e a s k e d below. I f t h i s i s a g e n u i n e c a s e o f embezzlement, then the C hanging C l e r k i s d e f i n i t e l y i m p l i c a t e d as the g u i l t y p a r t y . E i t h e r t h e r e was an i l l i c i t c o n v e r s i o n o f f u n d s — e m b e z z l e m e n t — o r the T r a n s a c t i o n s R e c o r d i s wrong, o r b o t h . I f the T r a n s a c t i o n s R e c o r d i s wrong, t h e n i t was i m p r o p e r l y e n t e r e d b e f o r e the t h e f t . I f t h e D a t e s / e n t r i e s s e c t i o n i s r i g h t , t h e n the T r a n s a c t i o n R e c o r d c o u l d n ' t have been e n t e r e d b e f o r e the a l l e g e d embezzlement. I f a mere c l e r i c a l e r r o r i s b e h i n d a l l t h i s , t h e n the D a t e s / e n t r i e s s e c t i o n i s O.K. b u t the b ookkeeper i s to be f a u l t e d . I f the C h a n g i n g C l e r k i s not g u i l t y , t h e n i t ' s a l l a c l e r i c a l m i s t a k e . Q u e s t i o n s . You can r e s p o n d t o the f o l l o w i n g q u e s t i o n s w i t h a " y e s " o r a "no" o n l y i f y o u have enough i n f o r m a t i o n to be c e r t a i n . I f y o u f e e l t h e r e i s n o t enough i n f o r m a t i o n to draw a f i r m c o n c l u s i o n , p u t "not enough i n f o r m a t i o n " . The q u e s t i o n s : 1. I s t h e Changing C l e r k g u i l t y ? 2. Is t h e T r a n s a c t i o n s R e c o r d wrong? T a b l e 1: A f o r m a l p r o b l e m , "You Be the Judge", w i t h q u e s t i o n s . 48 can be matched to a p r o b l e m i n c l u d e d i n the Appendix IV, e n t i t l e d " C a r 54". And, were we to c o n v e r t "You Be the Judge" i n t o an argument, a c o r r e s p o n d i n g m o d i f i c a t i o n to "Car 54" w ould p r e s e r v e the isomorphy between them. On the o t h e r hand, the v e r y e s s e n c e o f t h e d i s t i n c t i o n between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g may be t i e d up i n the d i f f e r e n c e s i n h e r e n t between d e d u c t i v e p r o b l e m s , w i t h t h e i r t o - b e - c o m p l e t e d forms, and arguments, w i t h t h e i r o s t e n s i b l y complete form. These two v a r i a b l e s w i l l c o n c e r n us e s p e c i a l l y i n t h i s c h a p t e r . L o g i c a l Judgment v s . D e d u c t i v e P r o b l e m S o l v i n g As an argument, "You Be the Judge" has a c o n c l u s i o n , and the judgment to be p a s s e d i s whether the c o n c l u s i o n f o l l o w s n e c e s s a r i l y from the g i v e n s . As a d e d u c t i v e problem, the g i v e n s must be e x t e n d e d to d i s c l o s e , i f p o s s i b l e , an answer to the q u e s t i o n g i v e n . I t i s i m p o r t a n t to r e a l i z e t h a t problems can be u n d e c i d a b l e w i t h r e s p e c t to some q u e s t i o n s . The s e c o n d q u e s t i o n p u t i n "You Be the Judge" i s u n d e c i d a b l e : t h e r e i s s i m p l y no way o f d e d u c i n g e i t h e r t h a t the t r a n s a c t i o n r e c o r d i s c o r r e c t o r t h a t i t i s i n e r r o r . I n g e n e r a l t h e r e a r e t h r e e p o s s i b i l i t i e s f o r a q u e s t i o n r e g a r d i n g a p r o p o s i t i o n P a d d r e s s e d t o a s e t o f c o n s i s t e n t , 49 l o g i c a l l y s t r u c t u r e d g i v e n s : P may f o l l o w ( e . g . the c l e r k i s g u i l t y ) ; P's n e g a t i o n may f o l l o w ( e . g . the c l e r k i s n o t g u i l t y ) ; o r the q u e s t i o n may be unanswerable f o r want o f f u r t h e r i n f o r m a t i o n ( e . g . the c l e r k ' s g u i l t c a n n o t be e s t a b l i s h e d o r r u l e d o u t ) . T h i s c o n t r a s t s w i t h t h e dichotomous e v a l u a t i o n — v a l i d o r n o t v a l i d — m a d e o f an argument's form i n l o g i c a l judgment. One d i f f e r e n c e between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g , then, i s t h a t the p r o b l e m s o l v e r has to make s u r e t h a t t h e r i g h t q u e s t i o n has been asked. F o r t u n a t e l y , some q u e s t i o n s a r e narrow enough t o d e l i m i t the scope o f the s u b j e c t ' s e f f o r t s to a manageable degree. In "You Be the Judge" the q u e s t i o n , " I s the c h a n g i n g c l e r k g u i l t y ? " i s much e a s i e r t o answer than t h e more open-ended q u e s t i o n "What a c c o u n t s f o r the d i s c r e p a n c y i n the c a s i n o ' s b o o k s ? " We a r e i n t e r e s t e d i n the r e l a t i o n s h i p between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g . I t i s a p p a r e n t t h a t they d i f f e r a t l e a s t i n p a r t b ecause they d e a l w i t h d i f f e r e n t l o g i c a l i t e m s : arguments and d e d u c t i v e p r o b l e m s . But i t was n o t e d t h a t a p r o b l e m l i k e "You Be the Judge" c o u l d be c o n v e r t e d i n t o an argument. I t f o l l o w s t h e n t h a t a d e d u c t i v e p r o b l e m s o l v i n g t a s k can be c o n v e r t e d i n t o a l o g i c a l judgment t a s k — t h e c a t c h b e i n g t h a t the c o n v e r s i o n may n o t be a l l t h a t 50 e a s y . C l e a r l y , the h a r d p a r t i n making the c o n v e r s i o n comes i n c h o o s i n g the a p p r o p r i a t e " c o n c l u s i o n " . The d e f i n i t e n e s s o f the q u e s t i o n a d d r e s s e d t o the p r o b l e m f i g u r e s h e r e . F o r example, the n a r r o w l y framed q u e s t i o n s o f "You Be the Judge" ease i t s c o n v e r s i o n i n t o an argument form: T e n t a t i v e l y c o n c l u d e t h a t t h e c l e r k i s i n n o c e n t — d o e s t h a t " c o n c l u s i o n " seem t o n e c e s s a r i l y f o l l o w from the g i v e n s ? "You Be the Judge" has been r e n d e r e d as a l o g i c a l judgment i t e m 0 There i s some danger o f making too much o f the f a c t o f t h i s " c o n v e r t i b i l i t y " . F o r one t h i n g , the c o n v e r s i o n i t s e l f may be so d i f f i c u l t as to be the c r u x o f the p r o b l e m i t s e l f . And, i n any c a s e , as p s y c h o l o g i s t s we cannot be c o n t e n t w i t h knowing t h a t d e d u c t i v e p r o b l e m s o l v i n g t a s k s may be c o n v e r t e d i n many o r even a l l c a s e s t o l o g i c a l judgment t a s k s — w e s h a l l want to know whether p e o p l e a c t u a l l y h a n d l e d e d u c t i v e problems and arguments i n t h e same way. I t t u r n s o u t t h a t one f a i r l y p e r s p i c u o u s method o f a t t a c k e x i s t s w h i c h s u f f i c e s t o work "You Be the Judge" as a p r o b l e m and t o p r o v e the v a l i d i t y o f "Judge" as an argument. T h i s l o g i c a l mode o f o p e r a t i o n , w h i c h was i n v e n t e d w i t h a view to f o r m a l i z i n g v a l i d human r e a s o n i n g , i s c a l l e d d e r i v a t i o n . I t w i l l be t r e a t e d below as an i d e a l i z a t i o n o f l o g i c a l r e a s o n i n g , 51 on the presumption t h a t an understanding of i t w i l l c o n t r i b u t e to our understanding of other reasoning. I t may be remembered that i n the preceding review of the p s y c h o l o g i c a l l i t e r a t u r e e x p l a n a t i o n s of l o g i c a l judgment (Osherson, 1975; B r a i n e , 1978) and of deductive problem s o l v i n g (Newell & Simon, 19 72) a l i k e made recourse to the hypothesis that something l i k e d e r i v a t i o n occurs i n the mind of n o n - l o g i c i a n s performing l o g i c a l t a s k s . This bears on the i s s u e of the u n i t a r i n e s s of l o g i c a l i t y , f o r i t sounds as i f two a b i l i t i e s ( l o g i c a l judgment, deductive problem s o l v i n g a b i l i t y ) might be r e d u c i b l e to o n e — d e r i v a t i o n a l a b i l i t y . The p l a u s i b i l i t y of t h i s r e d u c t i o n i s one of the t o p i c s to be covered below. D e r i v a t i o n D e r i v a t i o n , a l s o known as n a t u r a l deduction, i s a reasoning process, one which can be and i s taught i n formal l o g i c . Development of d e r i v a t i o n as a formal technique i s c r e d i t e d to Gentzen (1934), the l o g i c i a n , who h i m s e l f claimed to be s y s t e m a t i z i n g and rendering e x p l i c i t the s e m i - e x p l i c i t reasoning a c t u a l l y used i n s u c c e s s f u l attempts at mathematical p r o o f - f i n d i n g . The product of d e r i v a t i o n i s a. d e r i v a t i o n , such as the one given here i n Table 2 ( i t i s recorded i n The L o g i c a l Form of the Problem: 1. A - * G 2. A v B 3. -B v C 4. D-*- -C 5. E - * (D & F) 6. -E —* G G D e r i v a t i o n #1 (Move) 7. -E v (D & F) 8. (-E v D) & (-E v F) 9. -E v D 10. E —» D 11. -C 12. B - » C 13. -C-+-B 14. E - » - B 15. — A v B 16. -A—• B 17. -B-+A 18. E - » A 19. E - * G 20. - G - » - E 21. -G-*G 22. G v G 23. G ( Rule) 5, I m p l i c a t i o n 7, D i s t r i b u t i v e 8, S i m p l i f i c a t i o n 9, I m p l i c a t i o n 4, 10, T r a n s i t i v i t y 3, I m p l i c a t i o n 12, T r a n s p o s i t i o n 11, 13, T r a n s i t i v i t y 2, Double N e g a t i o n 15, I m p l i c a t i o n 16, T r a n s p o s i t i o n 14, 17, T r a n s i t i v i t y 1, 18, T r a n s i t i v i t y 19 T r a n s p o s i t i o n 6, 20, T r a n s i t i v i t y 21, I m p l i c a t i o n 22, T a u t o l o g y T a b l e 2. An example o f a d e r i v a t i o n , i n the n o t a t i o n s y m b o l i c l o g i c . 53 the n o t a t i o n o f s y m b o l i c l o g i c ) as D e r i v a t i o n #1. D e r i v a t i o n i n v o l v e s : (1) a b s t r a c t i n g t h e l o g i c a l form o f the g i v e n s ( u n l e s s someone has done t h a t f o r y o u i n advance, e.g. i n a t e x t b o o k e x e r c i s e ) ; and then (2) moving s t e p by s t e p ( r e c o r d e d as " l i n e by l i n e " ) — making s u r e each s t e p i s v a l i d l y t a k e n — (3) towards a g o a l . A d e r i v a t i o n i s s a i d to be c o n s t r u c t e d ; and a d e r i v a t i o n once c o n s t r u c t e d and made a v a i l a b l e to o t h e r s can be f o l l o w e d . C o n s t r u c t i o n — t h e a c t i v e , c r e a t i v e a s p e c t o f d e r i v a t i o n — i s what we w i l l be p r i m a r i l y i n t e r e s t e d i n . However, a good way to u n d e r s t a n d what c o n s t r u c t i o n i n v o l v e s i s t o c o n t r a s t i t w i t h t h e mere f o l l o w i n g o f a d e r i v a t i o n . P s y c h o l o g i c a l l y , p e r h aps the most s t r i k i n g f a c t about f o l l o w i n g a d e r i v a t i o n l i k e t h e one g i v e n h e r e f o r "You Be the Judge" ( D e r i v a t i o n #1) i s t h a t i t seems to be e n t i r e l y a m a t t e r o f l o g i c a l judgment. A l l the i n f e r e n c e s c o n s t i t u t i n g t h e s t e p s o f t h e d e r i v a t i o n a r e l a i d o u t i n o r d e r from g i v e n s to g o a l ; the o n l y t h i n g f o r the f o l l o w e r t o do i s t o take t h e s t e p s , i . e . a p p l y l o g i c a l judgment t o each o f t h e p r e s c r i b e d i n f e r e n c e s . Much o f the power and u t i l i t y o f modern }4 l o g i c stems from d i v i d e and conquer s t r a t e g y . The d i f f i c u l t "You Be t h e Judge" p r o b l e m i s r e n d e r e d as a sequence o f v e r y s i m p l e l o g i c a l judgments: " I s i t v a l i d to i n f e r l i n e 18 from l i n e s 1 and 17? I s i t v a l i d t o move from l i n e 9 t o l i n e 10?" e t c . F o l l o w i n g a d e r i v a t i o n r e q u i r e s l o g i c a l judgment; however, the l e v e l o f l o g i c a l judgment i n v o l v e d i s v e r y b a s i c . P r a c t i c a l l y anyone can l e a r n to f o l l o w a l o g i c a l d e r i v a t i o n l i k e t h e one shown, which means t h a t p r a c t i c a l l y anyone can gras p t h e v a l i d i t y o f the i n f e r e n c e s and t r a n s f o r m a t i o n s needed to be made a t each s t e p . P u t a n o t h e r way, t h e i n f e r e n c e s and t r a n s f o r m a t i o n s c o n s t i t u t i n g the s t e p s o f an e x t r e m e l y d i f f i c u l t l o g i c a l p r o o f a r e j u s t the same as would be used i n an e x c e p t i o n a l l y s i m p l e d e r i v a t i o n . I t i s n ' t c l e a r then t h a t good d e r i v e r s have to have b e t t e r l o g i c a l judgment than anybody e l s e . Thus f a r t h e f o l l o w i n g o f a d e r i v a t i o n has been d i s c u s s e d ; to c o n s t r u c t t h e d e r i v a t i o n i s q u i t e a n o t h e r m a t t e r . " W h i l e we might guess t h a t e a c h p e r s o n f o l l o w i n g a c e r t a i n d e r i v a t i o n goes t h r o u g h p r e t t y much the same c o g n i t i v e p r o c e s s e s , g r e a t d i v e r s i t y can be e x h i b i t e d among t h o s e c o n s t r u c t i n g d e r i v a t i o n s f o r the same l o g i c a l form. T h i s i s i n p a r t b e cause t h e r e a r e ' ^ C o n s t r u c t i o n o f a d e r i v a t i o n s h o u l d n o t be c o n f u s e d w i t h i n v e n t i o n o f the l o g i c a l form to be p r o v e d . 55 i n d e f i n i t e l y many d i s t i n c t d e r i v a t i o n s p o s s i b l e f o r a g i v e n l o g i c a l form (even i f most a r e i n e l e g a n t ) , and i n f i n i t e l y many wrong roads o f r e a s o n i n g t h a t do n o t l e a d to the d e s i r e d g o a l e x p r e s s i o n . This l e a d s us to c o n s i d e r s o mething o f v i t a l i m p o r t a n c e i n d e r i v a t i o n : l o g i c a l w a y f i n d i n g , the c h o o s i n g o f a sequence o f s m a l l s t e p s t h a t w i l l l e a d one to one's g o a l i n a c e r t a i n and e c o n o m i c a l manner. L o g i c a l W a y f i n d i n g i n D e r i v a t i o n The g o a l - s e e k i n g a s p e c t o f d e r i v a t i o n has o f t e n been l i k e n e d m e t a p h o r i c a l l y to more g e o g r a p h i c a l k i n d s o f b e h a v i o r . N e w e l l (1968) s a y s i n t h i s c o n n e c t i o n : P r o b l e m s o l v i n g i s always a m a t t e r o f s e a r c h — o f s t a r t i n g f r o m some i n i t i a l p o s i t i o n ( s t a t e o f knowledge) and e x p l o r i n g u n t i l a p o s i t i o n i s a t t a i n e d t h a t i n d i c a t e s t h e s o l u t i o n — t h e d e s i r e d s t a t e o f knowledge. . . . S e a r c h i n a p r o b l e m space i s c o n s t r u c t i v e . The e l e m e n t s o f the s p a c e , a l t h o u g h they e x i s t a b s t r a c t l y , do n o t e x i s t f o r the p r o b l e m s o l v e r u n l e s s he g e n e r a t e s them, o r remembers them f o r l a t e r r e t r i e v a l once g e n e r a t e d . T h i s g i v e s the s e a r c h a d i f f e r e n t c h a r a c t e r from t h a t t h r o u g h a w o r l d t h a t e x i s t s i n d e p e n d e n t l y o f the p r o b l e m . s o l v e r — e.g. a f o r e s t , ( p . 4 8 ) . N e w e l l ' s remark makes the i m p o r t a n t p o i n t t h a t the p r o b l e m s o l v e r — w h i c h f o r N e w e l l i s e s s e n t i a l l y a d e r i v e r e q u i p p e d w i t h a s e t o f h e u r i s t i c s — h a s to c o n s t r u c t the v e r y r o u t e 56 he p a s s e s o v e r . However, I sometimes become u n c o m f o r t a b l e w i t h the term " s e a r c h " , f o r i t a c c o r d s to the " s e a r c h e r " a d e l i b e r a t e n e s s o f movement t h a t i s sometimes r a t h e r l a c k i n g i n a c t u a l a t t e m p t s a t d e r i v a t i o n . I t i s p r o b a b l y worth l i s t i n g the p o s s i b l e s t a t e s — p s y c h o l o g i c a l s t a t e s — o n e can be i n w h i l e w a y f i n d i n g . (1) One can, o f c o u r s e , be s i m p l y w a n d e r i n g about i n the p r o b l e m s p a c e , h o p i n g p e rhaps t h a t an o p p o r t u n i t y w i l l open up. In t h i s s t a t e i t i s p o s s i b l e to f e e l t r u l y " l o s t " , b e i n g d e v o i d o f any s ense o f which d i r e c t i o n i s the r i g h t d i r e c t i o n . (2) One m i g h t have a p l a n o r s t r a t e g y t h a t one t h i n k s might l e a d to t h e g o a l , b u t u n c e r t a i n t y s u r r o u n d s the c o r r e c t n e s s o f t h i s b e l i e f and one must t r o d the p a t h t o see where i t a c t u a l l y l e ads. (3) One may j u s t see v e r y c l e a r l y the open way between g i v e n s and g o a l t h a t a s s u r e s one o f t h e v a l i d i t y o f the form. These t h r e e s t a t e s o f mind can s u c c e e d one a n o t h e r i n the c o u r s e o f one s u b j e c t ' s e f f o r t s a t w o r k i n g a d e r i v a t i o n , o f c o u r s e . One may wander f o r some ways, and then r e a c h a j u n c t u r e t h a t s u g g e s t s a p l a n . And a t some p o i n t i n the e x e c u t i o n o f the p l a n , i t may become c l e a r t h a t s u c c e s s i s a s s u r e d — t h e s u b j e c t e n t e r s t h e t h i r d , c e r t a i n s t a t e . 57 On the u n h a p p i e r s i d e , a s e e m i n g l y p l a u s i b l e p l a n e n t e r t a i n e d i n s t a t e two may n o t pan o u t — s o t h a t one i s r e d u c e d t o w a n d e r i n g . "Wandering" i n the pr o b l e m s t a t e no doubt a b s o r b s much o f o ur r e a l p r o b l e m s o l v i n g time, b u t t h e r e seems t o be l i t t l e to s a y about i t . I t u r n t h e n t o the s e c o n d and t h i r d s t a t e s o f the w a y f i n d e r , b e g i n n i n g w i t h t h e l a t t e r . I n s i g h t . Sometimes one can s i m p l y t e l l t h a t a form i s v a l i d , o r t h a t s o m e t h i n g f o l l o w s . I n such c a s e s s t e p - b y - s t e p d e r i v a t i o n may be d i s p e n s e d w i t h , p r o v i d e d no d e m o n s t r a t i o n o f the t h i n g i s r e q u i r e d . The a b i l i t y to gr a s p d i r e c t l y the v a l i d i t y o f a form o r sequence i s r e m i n i s c e n t o f the i n s i g h t o f G e s t a l t p s y c h o l o g y . I t a p p e a r s t h a t some k i n d o f whole i s s u b j e c t i v e l y r e a l i z e d i n t h e s e c a s e s , a whole p o s s e s s i n g a f o r m a l i n t e g r i t y t h a t can be r e c o g n i z e d . I n s i g h t o f t h i s s o r t i s o f t e n f a i r l y sudden. I t i s n o t a m a t t e r o f d e r i v a t i o n . As a m a t t e r o f f a c t , d e r i v a t i o n i t s e l f depends on our a b i l i t y to r e l i a b l y r e c o g n i z e w i t h o u t f u r t h e r to do some v a l i d f o r m s — namely t h o s e used as e l e m e n t a r y i n f e r e n c e and s u b s t i t u t i o n schemata. Such schemata a r e p r i m i t i v e t o n a t u r a l d e d u c t i o n s y s t e m s . They cannot be d e r i v e d i n such systems f o r the v e r y good r e a s o n t h a t t h i s w ould l e a d t o v i c i o u s r e g r e s s as one t r i e d t o j u s t i f y the s t e p s o f such d e r i v a t i o n s - o f - t h e - p r i m i t i v e s 58 by reference to "more elementary" schemata. In the e a r l i e r review of the p s y c h o l o g i c a l l i t e r a t u r e i t was seen that some psychologists have set for themselves the task of determining j u s t which l o g i c a l forms or inference patterns are b a s i c or u n i v e r s a l f o r human beings (e.g. Braine, 1978; Osherson, 19.75). For now the point relevant to t h i s i s that, even i f people do something l i k e d e r i v a t i o n when they evaluate forms f o r v a l i d i t y and draw inferences, i t i s necessary to assume that they must be able to recognize some forms and sequences as v a l i d without recourse to d e r i v a t i o n . This d i r e c t apperception may, of course, be l i m i t e d to the simpler forms. Assumption-based Strategy i n Wayfinding. Returning to the second state of mind of the l o g i c a l wayfinder, we f i n d the i n d i v i d u a l guided by a plan or strategy. In a n a t u r a l deduction system i n the t r a d i t i o n of Gentzen (1934) assumptions play an extremely important r o l e i n planning and s t r a t e g i c wayfinding. The k i n d of assumptions r e f e r r e d to here are " c o n d i t i o n a l assumptions" (also known as " p r o v i s i o n a l assumptions"). A c o n d i t i o n a l assumption i s something made by .a subject at the subject's e l e c t i o n . "I s h a l l p r o v i s i o n a l l y assume that the t r a n s a c t i o n record i s r i g h t " would be an assumption of t h i s type. The assumption can open up what would o t h e r w i s e appear to be an i m p e n e t r a b l e s h e l l ; i t s u p p l i e s a b a s i s from which i n f e r e n c e s can be drawn. To u n d e r s t a n d t h a t one can make c o n d i t i o n a l a s s u m p t i o n s , t h e use they would s e r v e , and the r e s t r i c t i o n s encumbering t h e i r c o n d i t i o n a l n a t u r e , i s t o have the h a l l m a r k s o f a good d e r i v e r . Assumption-making e n t e r s i n t o l o g i c a l w a y f i n d i n g a t b o t h ends. Not o n l y does an a s s u m p t i o n p r o v i d e a p o i n t o f d e p a r t u r e , i t a l s o i m p a r t s a d e f i n i t e d i r e c t i o n t o the d e r i v a t i o n by i m p o s i n g on the d e r i v e r the o b l i g a t i o n t o d i s c h a r g e (see a s t a n d a r d l o g i c t e x t , e.g. Blumberg, 19 76, on d i s c h a r g i n g a s s u m p t i o n s ) . One e s p e c i a l l y p o w e r f u l , c o n v e n i e n t , and g e n e r a l l y a p p l i c a b l e a s s u m p t i o n - b a s e d s t r a t e g y goes under t h e a n c i e n t name o f r e d u c t i o ad a b s u r d u m — r e f e r r e d to h e r e a f t e r as the RAD t e c h n i q u e . (RAD i s p a r t i a l l y c o v e r e d i n W i c k e l g r e n i n h i s c h a p t e r on C o n t r a d i c t i o n ; a l s o see Wason, 1977). I t t u r n s o u t t h a t i n many ca s e s the b e s t p o s s i b l e a s s u m p t i o n to make i s s i m p l y the n e g a t i o n o f the c o n c l u s i o n y o u might t e n t a t i v e l y be a i m i n g t o e s t a b l i s h . T h e r e i n l i e s the p o i n t o f d e p a r t u r e f o r RAD. To some, assuming t h e o p p o s i t e o f what one s e e k s to p r o v e i s c o u n t e r i n t u i t i v e (and one o f the f i n d i n g s t o be r e p o r t e d i n the e m p i r i c a l p a r t o f t h i s p aper i s an 60 i n d i c a t i o n o f what p r o p o r t i o n o f our sample a c c e p t e d the v a l i d i t y o f RAD). Y e t the p r o b l e m we have been c o n s i d e r i n g , "You Be the Judge," l i k e many o t h e r p r o blems, l e n d s i t s e l f p a r t i c u l a r l y t o t h i s s t r a t e g y . I t i s p r o b a b l y w o r t h e x p l a i n i n g how t h i s s o l u t i o n i s worked. The narrowness o f the f i r s t q u e s t i o n a d d r e s s e d i n "You. Be the Judge", " I s the c h a n g i n g c l e r k g u i l t y ? " h e l p s us i n our assumption-making. We might s t a r t by assuming t h a t the c l e r k i s g u i l t y , and t r y to p r o v e the o p p o s i t e , o r v i c e v e r s a ; t h e r e a r e o n l y two t h i n g s t o t r y . ( I f t h e q u e s t i o n were more open-ended, t h e r e m ight be many t h i n g s to t r y ) . L e t us a r b i t r a r i l y d e c i d e to assume f i r s t t h a t the c l e r k i s not g u i l t y . The s t r a t e g y then i n RAD i s to work w i t h i n the scope o f t h a t a s s u m p t i o n towards e i t h e r the g o a l p r o p e r ( i . e . t h a t the c l e r k i s g u i l t y ) , o r towards a member o f a c l a s s o f sub g o a l s , any member o f which adduces a c o n t r a d i c t i o n ( e . g . t h a t t h e t r a n s a c t i o n r e c o r d i s wrong b u t a l s o c o r r e c t ) . I f t h i s a s s u m p t i o n l e a d s nowhere, one would s t a r t o v e r and t h i s time make t h e o p p o s i t e a s s u m p t i o n ; b u t i t so happens t h a t i n t h i s p r o b l e m the a s s u m p t i o n t h a t the c l e r k i s n o t g u i l t y i s the c o r r e c t one f o r p r o v i n g t h a t the c l e r k i s g u i l t y . 61 T h e r e a r e two forms o f RAD, w h i c h c o r r e s p o n d to two ways o f s o l v i n g "You Be the Judge". Both ways f i g u r e i n the q u e s t i o n s p u t to s u b j e c t s i n the r e s e a r c h t o be r e p o r t e d l a t e r . E i t h e r form o f RAD a t t a i n s t h e d e s i r e d r e s u l t , and they s h a r e a common p o i n t o f d e p a r t u r e . The d i f f e r e n c e between them i s as f o l l o w s : I f one makes an a s s u m p t i o n l e a d i n g t o a c o n t r a d i c t i o n , t h e n one can c o n c l u d e t h a t t h e s t a r t i n g a s s u m p t i o n was wrong. I f t h a t a s s u m p t i o n happened t o be the n e g a t i o n o f what one s u s p e c t e d was t h e c a s e , t h e n w o u l d have p r o v e d wrong the o p p o s i t e o f what was s u s p e c t e d to be the c a s e — w h i c h i s the same as p r o v i n g the l a t t e r r i g h t i n t h e dichotomous w o r l d of l o g i c . I n the o t h e r form, one a g a i n chooses to assume the , o p p o s i t e o f something one s u s p e c t s t o be the c a s e . Assume t h a t t h e c l e r k i s n o t g u i l t y . T h a t opens up a c h a i n o f i n f e r e n c e s . I f G i t s e l f ( t h e p r o p o s i t i o n t h a t the c h a n g i n g c l e r k i s g u i l t y ) e v e r o c c u r s i n t h a t c h a i n (as i t would, i n f a c t ) t h e n one i s f i n i s h e d f o r a l l p r a c t i c a l p u r p o s e s , h a v i n g e s t a b l i s h e d G, t h e g u i l t o f the c l e r k . * RAD i s e f f e c t i v e f o r o b t a i n i n g some g o a l G, b u t i t has a f u r t h e r use, w h i c h w i l l be b r i e f l y m entioned. A " d o u b l e -u n f o r t u n a t e l y , W i c k e l g r e n (1974) o n l y c o v e r s the form o f RAD i n which a c o n t r a d i c t i o n i s p r o d u c e d . 62 b a r r e l e d " u t i l i z a t i o n o f RAD can a l s o i n d i c a t e t h a t n e i t h e r G n o r -G can be a t t a i n e d a t a l l — w h i c h means t h a t the p r o b l e m can be pronounced d e d u c t i v e l y u n s o l v a b l e as r e g a r d s G. T h i s a p p r o a c h r e q u i r e s one t o e s t a b l i s h t h a t , assuming G, -G cannot be a t t a i n e d , and moreover, t h a t assuming -G, G cannot be a t t a i n e d . I t i s i m p o r t a n t t h a t a would-be p r o b l e m s o l v e r u n d e r s t a n d t h e uses o f making c o n d i t i o n a l a s s u m p t i o n s . But i t i s a l s o i m p o r t a n t t h a t the i n d i v i d u a l r e a l i z e t h a t c o n d i t i o n a l a s s u m p t i o n s c o n d i t i o n e v e r y c o n c l u s i o n r e a c h e d w i t h i n t h e i r s c o p e . F a i l u r e t o honor the i n t e g r i t y o f an assu m p t i o n ' s s c o p e can l e a d t o d e d u c t i v e d i s a s t e r , i n the form o f c o n d i t i o n a l c o n c l u s i o n s b e i n g p a r a d e d as u n c o n d i t i o n a l c o n c l u s i o n s . D e r i v a t i o n , L o g i c a l Judgment, and D e d u c t i v e P r o b l e m S o l v i n g We have j u s t c o n c l u d e d a d i s c u s s i o n o f how one d e r i v a t i o n a l s t r a t e g y , t h e a s s u m p t i o n - b a s e d RAD, can f i n d o r p r o v e t h e "You Be the Judge" problem. However, RAD i s not t h e o n l y means o f s o l v i n g t h e pro b l e m . D e r i v a t i o n #1 ( T a b l e 2) de m o n s t r a t e d a n o t h e r d e r i v a t i o n f o r "You Be the Judge", one 63 which made no assumptions a t a l l . I t i s worth n o t i n g t h a t D e r i v a t i o n #1 d o e s n ' t even seem t o be a s t r a t e g i c s o l u t i o n ; a l l t h a t a p pears i s a s e r i e s o f l o g i c a l t r a n s f o r m a t i o n s t h a t l e a d t o t h e d e s i r e d g o a l e x p r e s s i o n . I t seems d o u b t f u l t h a t an u n t r a i n e d p e r s o n would c o n s c i o u s l y work a p r o b l e m i n sueh a manner, b u t the p o s s i b i l i t y cannot be r u l e d o ut t h a t answers and judgments a r e worked i n t h i s way a t a l e v e l somewhat b e n e a t h i n t r o s p e c t i v e a c c e s s . I n any c a s e , one must add to the p r o v i s o t h a t t h e r e a r e m u l t i p l e d e r i v a t i o n s p o s s i b l e f o r "You Be the Judge" the f u r t h e r p r o v i s o t h a t t h e r e a r e methods o t h e r than d e r i v a t i o n i t s e l f w h i c h s u f f i c e t o p r o v e "You Be the Judge". N a t u r a l d e d u c t i o n does n o t e x h a u s t the r e p e r t o i r e o f f o r m a l l o g i c . N a t u r a l d e d u c t i o n d e r i v a t i o n i s a l i n e a r and d i s c r e t e mode o f p r o c e d u r e . By l i n e a r I mean n o n - b r a n c h i n g , and s e q u e n t i a l r a t h e r t h a n p a r a l l e l . By d i s c r e t e I r e f e r t o . the d i s c r e t e s t e p s o f r e a s o n i n g t h a t a r e r e c o r d e d and j u s t i f i e d l i n e by l i n e i n w r i t t e n d e r i v a t i o n s . Now o f c o u r s e we know t h a t we a r e c a p a b l e o f t h i n k i n g i n t h i s l i n e a r , d i s c r e t e way. T h e r e i s no i n c o m p a t i b i l i t y between o u r " l o g i c a l f a c u l t y " and d e r i v a t i o n — e l s e t h e l o g i c i a n s would be u n a b l e to use o r t e a c h o t h e r s t o use n a t u r a l d e d u c t i o n . T h i s c o m p a t i b i l i t y no doubt t e l l s us something i m p o r t a n t ; b u t i 64 i t does n o t c o n s t i t u t e s t r o n g e v i d e n c e f o r the p r o p o s i t i o n t h a t we a r e c o n s t r a i n e d to r e a s o n i n a d e r i v a t i o n - l i k e way. Th e r e i s no i n c o m p a t i b i l i t y between d e r i v a t i o n and o t h e r p o s s i b l e k i n d s o f l o g i c a l c o g n i t i o n , so f a r as anyone knows. As a m a t t e r o f f a c t we have seen t h a t d e r i v a t i o n depends on some b a s i c l e v e l l o g i c a l judgment t h a t i s d i r e c t and a k i n t o G e s t a l t i n s i g h t . Some p s y c h o l o g i s t s have h y p o t h e s i z e d t h a t t h e r e i s some d e f i n i t e s e t o f e l e m e n t a r y judgments everyone i s e q u i p p e d to make. The e v i d e n c e s u p p o r t i n g t h i s h y p o t h e s i s i s as y e t r a t h e r weak. B r a i n e o f f e r s no e m p i r i c a l s u p p o r t f o r h i s p r o p o s e d s e t o f schemata. As f o r Os h e r s o n , none o f h i s schemata i s h o n o r e d by a l l h i s s u b j e c t s a l l t h e time (Modus Ponens comes c l o s e ) . I t i s i m p o r t a n t to c o n s i d e r a l t e r n a t i v e s to t h e n o t i o n o f a s e t o f u n i v e r s a l l y h e l d e l e m e n t a r y schemata. I t may be t h a t d i f f e r e n t p e o p l e have d i f f e r e n t e l e m e n t a r y schemata. I t may be t h a t no one has a s e t o f e l e m e n t a r y schemata. I t ' s t r u e t h a t the v a l i d i t y o f some forms a p p e a r s o b v i o u s t o most o f us most o f the time. But i t ' s a l s o t r u e t h a t we r i g h t l y j u d g e some s i m p l e i n v a l i d forms r a t h e r c o n s i s t e n t l y , and I have n e v e r h e a r d o f anyone p r o p o s i n g t h a t we p o s s e s s a s e t o f e l e m e n t a r y i n v a l i d schemata n e c e s s a r y f o r making t h e s e judgments. Moreover, I 65 am s t r u c k by the f a c t t h a t some i n s i g h t s an i n d i v i d u a l has a r e u n i q u e t o a g i v e n l o g i c a l c o n t e x t . I am t h i n k i n g o f the odd o c c a s i o n when one i s w o r k i n g a d e r i v a t i o n and s u d d e n l y j u d g e s t h a t the g o a l e x p r e s s i o n f o l l o w s from a g i v e n p o s i t i o n , w i t h o u t t h i n k i n g i n terms o f the s t e p s needed to span t h a t p o s i t i o n and g o a l e x p r e s s i o n gap. The d e r i v e r , we may assume, has n e v e r been i n t h i s e x a c t s i t u a t i o n b e f o r e , and so has n o t l e a r n e d t h a t t h i s e x t e n s i o n f o l l o w s . I t seems i m p l a u s i b l e t h a t some e l e m e n t a r y schema e x i s t e d i n the s u b j e c t ' s r e p e r t o i r e and swung i n t o p l a y f o r t h i s one-time a c t o f i n s i g h t . What I would s u g g e s t i s the f o l l o w i n g : t h a t we p o s s e s s some n o n - d e r i v a t i o n a l l o g i c a l judgment w h i c h we o f t e n use i n e c o l o g i c a l l y r e a l s i t u a t i o n s , e s p e c i a l l y where t h e r e i s no time to "work t h r o u g h " a l o g i c a l form. A l a w y e r , f o r example, a s s e s s i n g the argument o f a w i t n e s s , j u d g e , o r o t h e r l a w y e r , o f t e n has to make an immediate judgment as to the argument's v a l i d i t y . Moreover, i t i s t h i s a b i l i t y which a c c o u n t s f o r the i n s i g h t s sometimes e n c o u n t e r e d i n d e r i v a t i o n as d e s c r i b e d above. The c e i l i n g on t h i s l o g i c a l judgment i s p r o b a b l y low ( i . e . , o n l y s i m p l e r forms can be s u c c e s s f u l l y j u d g e d i n t h i s way), and may d i f f e r among p e o p l e . D e r i v a t i o n i s a method 66 w h ich e x t e n d s t h i s b a s i c l o g i c a l judgment d r a s t i c a l l y . We have seen how complex problems l i k e "You Be the Judge" can be d e r i v e d ; and, i n f a c t , f a r more d i f f i c u l t l o g i c a l forms y i e l d t o t h i s t e c h n i q u e . I t h i n k we do f e e l t h a t i n e v e r y d a y p r a c t i c e we have t o "work t h r o u g h " problems o f comparable d i f f i c u l t y . I t e n t a t i v e l y e q u a t e d e d u c t i v e p r o b l e m s o l v i n g w i t h d e r i v a t i o n - l i k e c o g n i t i o n , t h e n , i m p l i c i t l y p r e s u m i n g a l o n g w i t h t h i s t h a t d e d u c t i v e problems worthy o f the name a r e , on the whole, r a t h e r more complex t h a n t h e l o g i c a l forms we ( a r e a b l e t o ) s i m p l y j udge. Coming to the " u n i t a r i n e s s " q u e s t i o n , i t must be a s k e d how d e d u c t i v e p r o b l e m s o l v i n g (as d e r i v a t i o n - l i k e ) and l o g i c a l judgment (as G e s t a l t i n s i g h t - l i k e ) might be e x p e c t e d to c o r r e l a t e . R i p s (1983), as i n d i c a t e d i n t h e l a s t c h a p t e r , r e a s o n s t h a t t h e r e must be some one g e n e r a l i n f e r e n c e mechanism o r d e d u c t i v e program b e h i n d a l l m a n i f e s t a t i o n s o f l o g i c a l i t y , and one w ould n a t u r a l l y e x p e c t t h e r e to be a p o s i t i v e c o r r e l a t i o n between ou r v a r i a b l e s to the e x t e n t t h a t he i s c o r r e c t . On t h e o t h e r hand, t h e f o r e g o i n g a n a l y s i s opens up the p o s s i b i l i t y o f a low o r even n o n s i g n i f i c a n t c o r r e l a t i o n between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g . L o g i c a l judgment i s n e c e s s a r y f o r d e r i v a t i o n ; t h e r e f o r e i t w o u l d be n e c e s s a r y f o r d e r i v a t i o n - l i k e d e d u c t i v e 67 p r o b l e m s o l v i n g . But I have s u g g e s t e d t h a t l o g i c a l judgment may e x t e n d , a t l e a s t i n some i n d i v i d u a l s , t o more complex forms ( i . e . more complex than t h e " e l e m e n t a r y " s chemata), and t h o s e good a t e v a l u a t i n g t h e s e more complex forms a r e n o t n e c e s s a r y t h o s e who p o s s e s s the r e q u i s i t e w a y f i n d i n g a b i l i t y needed t o be good a t f i n d i n g answers i n d i f f i c u l t d e d u c t i v e p r o b l e m s . On the o t h e r s i d e o f the same c o i n , good d e r i v e r s need n o t be b l e s s e d w i t h more than v e r y m i n i m a l l o g i c a l judgment. No doubt much t u r n s on t h e p r i o r l o g i c a l e x p e r i e n c e o f s u b j e c t s . I n t h i s r e s p e c t I w o u l d h a z a r d the o b s e r v a t i o n t h a t some d i s c i p l i n e s and a c t i v i t i e s g i v e one p r a c t i c e i n d e d u c t i v e p r o b l e m s o l v i n g ( e . g . e n g i n e e r i n g , mathematics, computer s c i e n c e ) , w h i l e o t h e r s g i v e p r a c t i c e i n l o g i c a l judgment ( e . g . law, p h i l o s o p h y ) . Because o f t h i s , one a s p e c t o f l o g i c a l i t y may w e l l be g r e a t l y d e v e l o p e d i n i s o l a t i o n from o t h e r a s p e c t s . F o r example, one who has d e v e l o p e d some f a c i l i t y w i t h d e r i v a t i o n a l t e c h n i q u e may have remained a t a " n a i v e " l e v e l when i t comes to j u d g i n g m o d e r a t e l y c o m p l i c a t e d arguments "on the s p o t " ( s a y — a n argument i n c o r p o r a t e d i n a s p e e c h ) . To the e x t e n t t h a t s u c h o n e - s i d e d development o c c u r s , l o g i c a l i t y w i l l n o t appear to be v e r y u n i t a r y . 6 8 L o g i c a l I n t u i t i o n How does l o g i c a l i n t u i t i o n , o u r third,, v a r i a b l e , f i t i n w i t h l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g ? L o g i c a l i n t u i t i o n has been n e g l e c t e d i n the p r e c e d i n g d i s c u s s i o n p r e c i s e l y b e c a u s e i t has l i t t l e o r n o t h i n g to do w i t h d e r i v a t i o n . F o r m a l l o g i c has d e v e l o p e d methods f o r p r o v i n g and s o l v i n g , b u t has n o t d e v e l o p e d a n y t h i n g comparable aimed a t e x t e n d i n g the r e a c h o f our n a t i v e l o g i c a l i n t u i t i o n — a l t h o u g h s y m b o l i z i n g the forms o f , e.g., two arguments, a i d s l o g i c a l i n t u i t i o n g r e a t l y . A b s t r a c t i o n o f f o r m — o r , i n more p s y c h o l o g i c a l terms, r e p r e s e n t a t i o n o f f o r m — s e e m s to be the key t o l o g i c a l i n t u i t i o n . T h i s p o i n t s to a p o s s i b l e o v e r l a p w i t h l o g i c a l judgment, s i n c e the l a t t e r , i n i t s b a s i c l e v e l as e x p l a i n e d above, must i n v o l v e some c o g n i t i v e r e p r e s e n t a t i o n o f form ( t h i s on the a n a l o g y to G e s t a l t a p p e r c e p t i o n ) . The d i f f e r e n c e between the two i s i n what i s done w i t h th e form, once e x t r a c t e d : i n t h e c a s e o f l o g i c a l i n t u i t i o n , i t i s matched t o a n o t h e r a b s t r a c t e d form; i n the case o f l o g i c a l judgment i t i s somehow a s s e s s e d f o r v a l i d i t y . B o t h l o g i c a l judgment and l o g i c a l i n t u i t i o n would seem to be l i m i t e d t o r e p r e s e n t a b l e forms, and t h e s e w i l l p r o b a b l y n o t i n c l u d e e s p e c i a l l y complex forms, which a r e , 69 f o r most p e o p l e , too h a r d to g r a s p as a whole. "You Be the Judge", f o r example, has a form t h a t i s r a t h e r d i f f i c u l t t o h o l d i n one's mind as a whole. I t can be worked by drawing on i t s g i v e n s one p i e c e a t a time, so i t i s n ' t n e c e s s a r y to r e p r e s e n t i t as a whole. To the e x t e n t t h a t d e d u c t i v e p r o b l e m s o l v i n g i s l i k e d e r i v a t i o n , i t appears d i f f e r e n t i n t h i s r e s p e c t t o l o g i c a l i n t u i t i o n and l o g i c a l judgment. L o g i c a l i n t u i t i o n does, however, c o n n e c t w i t h d e d u c t i v e p r o b l e m s o l v i n g when i t comes t o p r o b l e m t r a n s f e r . R e c a l l t h a t "You Be t h e Judge" has a t w i n c a l l e d " C a r 54". And now suppose t h a t a s u b j e c t was p r e s e n t e d w i t h b o t h p r o b l e m s , w i t h i n a l i m i t e d time frame. There a r e two ways i n w h i c h the s u b j e c t might be a i d e d i n h i s / h e r p e r f o r m a n c e on the s e c o n d p r o b l e m by v i r t u e o f e x p o s u r e to the f i r s t . I n a v e r y g e n e r a l s e n s e , i t i s no doubt t r u e t h a t one's p r o b l e m s o l v i n g a b i l i t y i s enhanced from any p r i o r e x p o s u r e to d e d u c t i v e p r o b l e m s . T h a t i s , t h e more problems one has f a c e d i n the p a s t , t h e b e t t e r one can d e a l w i t h p r e s e n t p r o b l e m s . But t h i s s o r t o f b e n e f i t i s g o i n g t o be v e r y s l i g h t when o n l y one p r o b l e m ("You Be the Judge", the f i r s t p r e s e n t e d o f the t w i n s ) i s i n v o l v e d . E x p o s u r e to hundreds o f problems d u r i n g , say, a c o l l e g e c a r e e r , may enormously improve one's p r o b l e m 70 s o l v i n g a b i l i t y , b u t e x p o s u r e to a s i n g l e p r o b l e m can h a r d l y make much d i f f e r e n c e . By p r o b l e m t r a n s f e r however i s meant something more s p e c i f i c . The i d e a i s t h a t e x p o s u r e t o , say, "You Be the Judge" w i l l a i d i n subsequent p e r f o r m a n c e o f " C a r 54" b e c a u s e , a t an a b s t r a c t l e v e l , they a r e the same problem, and the s o l u t i o n t o one i s a s o l u t i o n f o r b o t h . P r o b l e m t r a n s f e r c o u l d c o n c e i v a b l y be r e f l e c t e d i n d e d u c t i v e p r o b l e m s o l v i n g , t h e n , i n the sense t h a t t h o s e who saw the s i m i l a r i t y between t h e p r e s e n t p r o b l e m - t o - b e - s o l v e d and a p r e v i o u s l y s o l v e d p r o b l e m might t e n d to do b e t t e r on the l a t t e r p r o b l e m t h a n t h o s e who t a c k l e each p r o b l e m i n d e p e n d e n t l y ( o b l i v i o u s t o any s i m i l a r i t y ) . However, i t must be a d m i t t e d t h a t i d e n t i c a l l y s t r u c t u r e d problems a r e o n l y r a r e l y e n c o u n t e r e d i n t h e r e a l w o r l d . So r a r e l y t h a t i t may w e l l be s u s p e c t e d t h a t p e o p l e a r e n o t even c u s t o m a r i l y on the l o o k - o u t f o r such d u p l i c a t i o n . I t t h e r e f o r e h a r d l y seems d e s i r a b l e t o a l l o w s u c h i d e n t i c a l problems t o p l a y a l a r g e r o l e i n the c o n s t r u c t i o n o f a d e d u c t i v e p r o b l e m s o l v i n g measure. 71 C o n c l u s i o n s on t h e U n i t a r i n e s s o f L o g i c a l i t y I s h a l l t r y now to b r i n g t o g e t h e r the many t h r e a d s o f t h i s c h a p t e r r e l a t i n g t o t h e u n i t a r i n e s s o f l o g i c a l i t y . As was seen i n the r e v i e w o f the p s y c h o l o g i c a l l i t e r a t u r e i n c h a p t e r I I , t h e o r i s t s have ten d e d to t r e a t l o g i c a l judgments, e x c e p t f o r the e l e m e n t a r y schemata l e v e l ones, as v i r t u a l d e r i v a t i o n s . T h i s has t h e e f f e c t o f e q u a t i n g l o g i c a l judgment w i t h p r o v e p r o b l e m s o l v i n g . I f what I have c a l l e d d e d u c t i v e p r o b l e m s o l v i n g i s e q u a t e d w i t h t h e d e r i v a t i o n o f f i n d p r o b l e m s — as I have p r o p o s e d to d o — t h e n the o n l y d i f f e r e n c e between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g i s t h a t d i f f e r e n c e w h i c h l i e s between f i n d p r o b l e m a n d . p r o v e i p f r o b l e m s o l v i n g . J u s t how g r e a t i s t h a t d i f f e r e n c e ? As was p o i n t e d o u t , t h e y d i f f e r i n the degree o f l o g i c a l w a y f i n d i n g r e q u i r e d , b e c a u s e the p r o v e p r o b l e m s p e c i f i e s n o t o n l y the p o i n t o f d e p a r t u r e b u t the g o a l to be r e a c h e d , whereas a f i n d p r o b l e m p r o v i d e s o n l y the former. A r e l a t i v e l y open-ended q u e s t i o n a d d r e s s e d to a f i n d d e d u c t i v e p r o b l e m c a l l s f o r a keen sense o f l o g i c a l d i r e c t i o n . On t h e o t h e r hand, a n a r r o w l y framed q u e s t i o n , e . g . " i s the c h a n g i n g c l e r k g u i l t y ? " , - i s r e a d i l y c o n v e r t e d i n t o a t most two p r o v e p r o b l e m s . On t h i s b a s i s , where the q u e s t i o n s a r e as f o c u s s e d as t h e y . a r e i n "You Be 72 the Judge" we s h o u l d p r o b a b l y e x p e c t t h e r e to be a ' s i g n i f i c a n t c o r r e l a t i o n between l o g i c a l judgment and d e d u c t i v e p r o b l e m s o l v i n g ; i t may even be so s t r o n g as to cause us t o d e c i d e to throw out t h e s e two v a r i a b l e s t o r e p l a c e them w i t h the one: d e r i v a t i o n a l a b i l i t y . On t h e o t h e r hand, i t was p o i n t e d out t h a t n o t a l l l o g i c a l judgments can be d e r i v a t i o n a l . They cannot be b ecause d e r i v a t i o n depends on an a b i l i t y to g r a s p a t l e a s t e l e m e n t a r y forms w i t h o u t r e c o u r s e to d e r i v a t i o n . I t was s u g g e s t e d t h a t t h i s a b i l i t y might (1) not be l i m i t e d t o e l e m e n t a r y forms; and (2) may be p r e s e n t i n d i f f e r e n t measure i n d i f f e r e n t p e o p l e owing t o such f a c t o r s as m a t u r i t y and p r i o r e x p e r i e n c e . On t h r e a d s s u c h as t h e s e hangs the n o t i o n o f a n o n - d e r i v a t i o n a l k i n d o f l o g i c a l judgment which can be w i e l d e d on a t l e a s t s i m p l e r l o g i c a l forms. T h e r e does not seem to be any c o m p e l l i n g r e a s o n to t h i n k t h a t t h i s l o g i c a l judgment i s c o r r e l a t e d w i t h d e r i v a t i o n a l a b i l i t y , a l t h o u g h the r e c o g n i t i o n o f a v a l i d sequence g o i n g i n the r i g h t d i r e c t i o n c o u l d be u s e f u l i n d e r i v a t i o n . E c o l o g i c a l c o n s i d e r a t i o n s s u g g e s t t h a t t h i s l o g i c a l judgment m i g h t be most m a n i f e s t i n s i t u a t i o n s where t h e r e i s l i t t l e time o r m o t i v a t i o n to "work the t h i n g t h r o u g h " i n d e r i v a t i o n - l i k e manner. 73 L o g i c a l judgment as i t has emerged from t h i s a n a l y s i s can be l i k e n e d to G e s t a l t f o r m a p p e r c e p t i o n . The o t h e r l o g i c a l v a r i a b l e , l o g i c a l i n t u i t i o n , which t e s t s the a b i l i t y o f a s u b j e c t t o match i d e n t i c a l forms, a l s o r e q u i r e s an a b i l i t y t o s ee t h e whole f o r m o f a t h i n g . These two v a r i a b l e s seem a l i k e i n t h a t way, and d i f f e r e n t from d e d u c t i v e p r o b l e m s o l v i n g , where one need n o t see the whole form a t once. P o s s i b l y t h e n l o g i c a l i n t u i t i o n and l o g i c a l judgment a r e c o r r e l a t e d a b i l i t i e s , w i t h d e d u c t i v e p r o b l e m s o l v i n g the odd man o u t . T h i s t h e s i s now t u r n s from a n a l y s i s t o e m p i r i c a l r e s e a r c h . H a v i n g e x p l o r e d the n a t u r e and p o s s i b l e i n t e r r e l a t i o n s o f our t h r e e v a r i a b l e s , i t becomes time to c o n s i d e r how the v a r i a b l e s and t h e i r i n t e r r e l a t i o n s h i p s may be r e d u c e d to measures. IV. METHOD I n t h e I n t r o d u c t i o n t h r e e v a r i a b l e s o f l o g i c a l i t y were d e f i n e d : l o g i c a l judgment, l o g i c a l i n t u i t i o n , and d e d u c t i v e p r o b l e m s o l v i n g a b i l i t y . O p e r a t i o n a l i z a t i o n o f t h e s e v a r i a b l e s i s p r o p o s e d below, and a p o p u l a t i o n i s d e s c r i b e d on wh i c h measurements o f the v a r i a b l e s o f l o g i c a l i t y was t a k e n . A l l the m a t e r i a l s — a r g u m e n t s , p r o b l e m s , and q u e s t i o n s h e e t s — r e f e r r e d t o below a r e o r i g i n a l t o t h i s t h e s i s , and c o p i e s o f same a r e c o n t a i n e d i n t h e a p p e n d i c e s . Tasks and M a t e r i a l s T h r e e t a s k s were used: judgment o f argument v a l i d i t y t o a s s e s s l o g i c a l judgment, m a t c h i n g o f argument forms t o a s s e s s l o g i c a l i n t u i t i o n , and t h e .working o f l o g i c a l s t o r y problems t o a s s e s s d e d u c t i v e p r o b l e m s o l v i n g a b i l i t y . The arguments used i n t h e l o g i c a l judgment and l o g i c a l i n t u i t i o n t a s k s were p r e s e n t e d as n a t u r a l i s t i c , c o n v e r s a t i o n a l p a s s a g e s a s c r i b e d t o c h a r a c t e r s who make r e f e r e n c e t o p l a u s i b l e s t a t e s o f a f f a i r s . I t was i n t e n d e d — a n d q u e s t i o n i n g o f p i l o t s u b j e c t s h a d p r e v i o u s l y i n d i c a t e d — t h a t few i f any p r o p o s i t i o n s c o n t a i n e d i n t h e s e arguments a p p e a r e d p a t e n t l y f a l s e t o s u b j e c t s . Arguments c o n s i s t i n g o f a r b i t r a r i l y 75 c o n c a t e n a t e d , u n a s s o c i a t e d p r o p o s i t i o n s were a l s o a v o i d e d . The g o a l was s i m p l y t o e l i m i n a t e o r reduce the danger t h a t s u b j e c t s w o u l d be c o n f u s e d by unsound b u t v a l i d arguments. S i n c e c o n c l u s i o n s i n t h e s e arguments c o u l d n o t be known to be f a c t u a l l y f a l s e , s u b j e c t judgments s h o u l d have r e f l e c t e d s o l e l y t h e i r e v a l u a t i o n o f argument forms. A l l o f the arguments employed i n t h e l o g i c a l judgment and l o g i c a l i n t u i t i o n t a s k s c o u l d be framed i n terms o f the p r o p o s i t i o n a l l o g i c , i . e . t h e r e were no p r e d i c a t e l o g i c arguments. No argument was common to b o t h t a s k s , a l t h o u g h some forms were. L o g i c a l Judgment. T h i s t a s k i n c l u d e d 20 arguments, 12 o f w h i c h were v a l i d , 8 o f which were i n v a l i d . I n s t r u c t i o n s g i v e n f o r t h i s t a s k i n c l u d e d a d e f i n i t i o n o f v a l i d i t y and examples o f v a l i d and i n v a l i d arguments. Arguments c o u l d be j u d g e d " v a l i d " , " i n v a l i d " o r " u n d e c i d a b l e " . T h i s l a s t r e s p o n s e o p t i o n was made a v a i l a b l e i n t h i s task, i n o r d e r to reduce the impact o f s h e e r g u e s s i n g . When s u b j e c t s s e l e c t e d t h i s o p t i o n , t h e i r r e s p o n s e was t r e a t e d as tantamount t o no r e s p o n s e , i . e . as a " m i s s " . T h i s was j u s t i f i e d on the s u p p o s i t i o n t h a t each o f the arguments s u b j e c t s were p r e s e n t e d w i t h were d e t e r m i n a b l e as b e i n g e i t h e r v a l i d o r i n v a l i d . Arguments, i n s t r u c t i o n s , and answer s h e e t f o r the l o g i c a l 76 judgment t a s k appear i n Appendix I I . L o g i c a l I n t u i t i o n . To o b t a i n a measure o f l o g i c a l i n t u i t i o n s u b j e c t s were as k e d to s p e c i f y w h i c h p a i r ( i f any) o r p a i r s o f arguments from a g i v e n s e t o f f o u r arguments were i d e n t i c a l as t o l o g i c a l form. There were f o u r s u c h s e t s o f arguments. I n one s e t no two arguments s h a r e d the same form. I n two of the s e t s , a s i n g l e i d e n t i c a l p a i r o c c u r r e d . I n t h e f o u r t h s e t t h e r e were two p a i r s o t m a t c h i n g arguments. A l l 16 arguments u s e d i n t h i s t a s k were v a l i d . The argument s e t s appear i n Appendix I I I , a l o n g w i t h the answer s h e e t s t a t i n g a l l c o r r e c t matches. D e d u c t i v e P r o b l e m S o l v i n g . To o b t a i n a c o m p o s i t e s c o r e r e p r e s e n t i n g a . s u b j e c t ' s a b i l i t y i n d e d u c t i v e p r o b l e m s o l v i n g r e s p o n s e s to t h r e e k i n d s o f q u e s t i o n s were t a k e n : (1) q u e s t i o n s r e q u e s t i n g answers where answers i n f a c t were d e d u c i b l e ; (2) q u e s t i o n s r e q u e s t i n g answers w h i c h were n o t i n f a c t d e r i v a b l e ; and (.3) q u e s t i o n s which a s k e d the s u b j e c t to j u d g e the r e a s o n e d s o l u t i o n s o f f i c t i o n a l t h i r d p a r t i e s . T h r e e problems were used: "Young Lawyer's Dilemma", "You Be the Judge", and "Car 54". The d e d u c t i v e problems and t h e i r q u e s t i o n s a p p e a r i n Appendix IV, w i t h e x p l a n a t i o n as t o w h i c h q u e s t i o n s f i t i n t h e t h r e e c a t e g o r i e s l i s t e d above. 77 S u b j e c t s The 31 s u b j e c t s used i n t h i s s t u d y were summer s t u d e n t s a t the U n i v e r s i t y o f B r i t i s h C olumbia, r a n g i n g from u n d e r c l a s s m e n t o g r a d u a t e s t u d e n t s . M a j o r s r e p r e s e n t e d among the s u b j e c t s i n c l u d e d Commerce, Computer S c i e n c e , M u s i c , Botany, M a t h e m a t i c s , P s y c h o l o g y , P h y s i c a l T h erapy, and F i n e A r t . T h e r e was an a p p r o x i m a t e b a l a n c e o f the s e x e s , and n e a r l y e q u a l numbers o f E u r o p e a n - d e s c e n t and A s i a n - d e s c e n t s u b j e c t s . A l l s u b j e c t s r e s p o n d e d t o s o l i c i t a t i o n s e i t h e r made t o lo w e r l e v e l p s y c h o l o g y c l a s s e s o r v i a p o s t e r s p u t up around the U.B.C. campus, r e q u e s t i n g v o l u n t e e r s f o r a p s y c h o l o g y e x p e r i m e n t i n v o l v i n g l o g i c a l p r o b l e m s . S u b j e c t s were p r o m i s e d and r e c e i v e d f e edback on t h e i r p e r f o r m a n c e , and i n s t r u c t i o n i n one l o g i c a l p r o b l e m s o l v i n g t e c h n i q u e (RAD), f o l l o w i n g p a r t i c i p a t i o n . S u b j e c t s were not p a i d and r e c e i v e d no c l a s s c r e d i t o f any k i n d f o r p a r t i c i p a t i o n . P r o c e d u r e S u b j e c t s were t e s t e d i n d i v i d u a l l y . A f t e r r e a d i n g and s i g n i n g a c o n s e n t t o p a r t i c i p a t e form (Appendix I) they were g i v e n , i n o r d e r , t h e l o g i c a l judgment, l o g i c a l i n t u i t i o n , and d e d u c t i v e p r o b l e m s o l v i n g t a s k s . The p a r t i c u l a r o r d e r o f 78 p r e s e n t a t i o n r e f l e c t e d t h e f o l l o w i n g c o n s i d e r a t i o n s . The d e d u c t i v e p r o b l e m s o l v i n g t a s k was g i v e n t o s u b j e c t s o n l y a f t e r they h a d been i n s t r u c t e d i n and h a d p r a c t i c e d i d e n t i f y i n g l o g i c a l forms i n t h e o t h e r two t a s k s . T h e r e a r e k i n d s o f p r o b l e m s o l v i n g — i r r e l e v a n t t o o u r p r e s e n t p u r p o s e s — o t h e r t h a n t h e d e d u c t i v e v a r i e t y . What s e t s a d e d u c t i v e p r o b l e m a p a r t from o t h e r t y p e s o f problems i s t h e f a c t t h a t i t p o s s e s s e s a l o g i c a l form. The hope t h e n was t h a t s u b j e c t s , h a v i n g f i r s t done t h e o t h e r two t a s k s , would be s e n s i t i z e d t o t h e i d e a o f l o g i c a l form and w o u l d thus be more l i k e l y t o r e c o g n i z e t h e l o g i c a l f orm o f t h e d e d u c t i v e s t o r y problems and a t t a c k them a c c o r d i n g l y . The l o g i c a l i n t u i t i o n t a s k f o l l o w e d the l o g i c a l judgment t a s k i n the o r d e r o f p r e s e n t a t i o n b e c a u s e i t r e q u i r e d s u b j e c t s to make a f i n e r d i s c r i m i n a t i o n o f form. Whereas i n l o g i c a l judgment, arguments were s i m p l y grouped as v a l i d o r i n v a l i d , i n l o g i c a l i n t u i t i o n v a l i d l o g i c a l forms were p l a c e d i n more s e l e c t i v e s u b c l a s s e s (see p.15 a b o v e ) . S u b j e c t s t h u s began by d i f f e r e n t i a t i n g arguments a c c o r d i n g to one v i t a l p r o p e r t y o f l o g i c a l f orm ( t h e v a l i d i t y c r i t e r i o n ) , and t h e n p r o g r e s s e d t o making the d i s t i n c t i o n o f j u s t what e x a c t form an argument d i d o r d i d n ' t have i n common w i t h o t h e r arguments. The term l o g i c a l f o r m was o n l y i n t r o d u c e d i n the i n s t r u c t i o n s t o t h e s e c o n d t a s k ( t h e l o g i c a l i n t u i t i o n t a s k ) . The i t e m s making up the l o g i c a l judgment measure were p r e s e n t e d i n a f i x e d random o r d e r , as were t h o s e making up the l o g i c a l i n t u i t i o n measure. The d e d u c t i v e s t o r y p roblems were p r e s e n t e d i n i n c r e a s i n g o r d e r o f d i f f i c u l t y , w i t h t h e e a s i e s t p r o b l e m ("Young Lawyer's Dilemma") f i r s t , f o l l o w e d by "You Be t h e Judge" and "Car 54", the t w i n p r o b l e m s . S u b j e c t s had 25 minutes t o r e a d t h e i n s t r u c t i o n s f o r t h e l o g i c a l judgment t a s k and to e v a l u a t e a l l 20 i t e m s . Most found t h i s t o be a f a i r l y q u i c k p a c e , b u t a l l managed t o complete t h e e n t i r e t a s k . The l o g i c a l i n t u i t i o n t a s k a l s o had 25 m i n u t e s a l o t t e d t o i t . S u b j e c t s had a t o t a l o f 40 minutes to work on the t h r e e d e d u c t i v e p r o b l e m s , 10 m i n u t e s f o r the f i r s t p r e s e n t e d p r o b l e m and 15 minutes each on the o t h e r p r o b l e m s . Most s u b j e c t s r e q u i r e d t h e f u l l 90 minutes t o p e r f o r m t h e t h r e e t a s k s . 80 V. RESULTS AND DISCUSSION How Subjects Performed L o g i c a l Judgment. Mean performance on the 20 argument set was 14.7 (74% c o r r e c t ) , w i t h s= 2.0. Scores ranged from 11 (55%) to 19 (95%). The 20 l o g i c a l judgment items f a l l i n t o three c l a s s e s : (1) those which were c o r r e c t l y judged at a r a t e above chance (by b i n o m i a l p r o b a b i l i t y assessment, w i t h a l p h a s e t at .05); (2) those which were appa r e n t l y guessed a t ; and (3) those which were i n c o r r e c t l y judged at a r a t e exceeding chance. 14 arguments f e l l i n t o the f i r s t c ategory, 4 i n the second, and 2 i n the t h i r d . Those i n the second category, arguments ##11,13,15, and 20 (see Appendix I I ) , tended to be the most complex and/or s u b t l e ; i t can be supposed that they were beyond the reach of most s u b j e c t s ' l o g i c a l judgment. But how could there be any arguments i n the t h i r d category? This r e q u i r e s e x p l a n a t i o n . The arguments i n q u e s t i o n were #3 and #14. Each was missed by the same number of s u b j e c t s : 26 (84% of the sample). The f i r s t t h i n g to note about these arguments i s t h a t they have the same form. The r e s u l t can thus compactly put: there was one form which c o n s i s t e n t l y f o o l e d s u b j e c t s . Both arguments b e g i n by making a p r o p o s i t i o n a l a c c o u n t w h i c h i s t h e n d e c l a r e d t o be f a l s e . A p u t a t i v e c o n c l u s i o n i m m e d i a t e l y f o l l o w s . The l o g i c a l way t o h a n d l e t h i s i s t o n e g a t e t h e l o g i c a l e x p r e s s i o n c o r r e s p o n d i n g t o t h e f a l s e " a c c o u n t " and t o work w i t h t h i s n e g a t e d p r o p o s i t i o n as the argument's p r e m i s e . I n f a c t , t h e c o n c l u s i o n can be v a l i d l y f o u n d i n t h i s way. S u b j e c t s , however, must n o t have done t h i s , and so t h e q u e s t i o n i s , what d i d t h e y do? We c a n draw on two s o u r c e s e x t e r n a l t o the p r e s e n t r e s e a r c h t o a r r i v e a t an e x p l a n a t i o n . The f i r s t s o u r c e b e a r s d i r e c t l y on t h e s e arguments: i t i s i n f o r m a t i o n g l e a n e d f r o m i n t e r r o g a t i o n o f p i l o t s u b j e c t s who e v a l u a t e d t h e s e m a t e r i a l s . As t h e t e n d e n c y o f s u b j e c t s co w r o n g l y e v a l u a t e t h i s f o r m had a l r e a d y s u r f a c e d d u r i n g p i l o t i n g , t h e e x p e r i m e n t e r s i m p l y a s k e d : why are y o u c a l l i n g t h i s argument f o r m i n v a l i d ? The answer w h i c h a number o f p i l o t s u b j e c t s c o n c u r r e d w i t h was w e l l a r t i c u l a t e d by one o f t h e i r members, who s t a t e d t h a t the n e g a t i o n o f what a t f i r s t was p r e s e n t e d as i n f o r m a t i o n amounted t o h i m t o an e l i m i n a t i o n o f t h e i n f o r m a t i o n . S i n c e no o t h e r i n f o r m a t i o n was f o r t h c o m i n g , n o t h i n g r e m a i n e d f r o m w h i c h any c o n c l u s i o n c o u l d be drawn. I n s h o r t , i t seems t h a t s u b j e c t s have a s e r i o u s m i s u n d e r s t a n d i n g o f what n e g a t i o n a c c o m p l i s h e s , and f a i l t o r e a l i z e the v a l u e o f 82 negated logical statements. This of Donaldson (1959), who found that i n problem-solving^ negative information was distrusted as "good currency." As in the present research, her subjects were reluctant to derive positive information from that which had shown to be false. Logical Intuition. Subjects had to make a total of 24 pairwise comparisons in this matching task, hence scores from 0 to 24 were theoretically possible. Mean performance of this sample was 20.1 (84Z correct), with s» 1.4. Scores ranged from a high of 24 (100% correct, achieved by only one subject) to a low of 17 (71Z). Arguments on this task were comparable, though not identical with, the arguments used on the logical judgment task; one can therefore hazard a comparative judgment based on the mean percentage correct for each measure (74% for logical judgment; 84Z for logical i n t u i t i o n ) , that matching valid arguments according to their form i s a b i t easier than judging arguments as to their v a l i d i t y . This i s interesting i f for no other reason than that l o g i c a l intuition i s presumably the less practiced s k i l l . Perhaps too the fact that subjects must have been f a i r l y equal in their Inexperience with logical 83 intuition type tasks accounts for the relatively slight dispersion of scores (s=1.4, vs. 2.0 for logical judgment). It is informative to categorize the errors made by subjects on this task as being either false positive or false negative in nature. A false positive error would occur when a subject made a match that should not have been made; a false negative when a subject failed to make a match that should have been made. The former sort of error outnumbered the latter by nearly a 2 to 1 proportion. The total on errors: false positives =78, and false negatives =44. From this i t appears that subjects were not as strict as they should have been in applying their matching criterion. Deductive Problem Solving. The sample mean, out of a maximum of 10, was 5.90, with s=1.8. Scores ranged from 2 (20% correct) to 9 (90%). Both from these percentages, and from remarks made by subjects during debriefing, the deductive problem solving was the hardest task of the three. This measure can be decomposed into three parts, allowing for close analysis of our sample's performance. Problems and questions, i t will be remembered, are available in Appendix IV. (1) Each problem had one question addressed to i t which got at what would normally be considered the "answer" to the problem. However, only 3 of the 31 subjects actually got 84 c o r r e c t answers f o r a l l t h ree prob lems. C l e a r l y these problems were a b i t too tough f o r these s u b j e c t s . However, i tem by i tem examinat ion o f t h e i r performance i s s t i l l i n s t r u c t i v e . 25 s u b j e c t s (81%) c o r r e c t l y determined tha t the Wexler l i n e o f cases " a p p l i e s " i n the "Young L a w y e r ' s Di lemma" prob lem. Rate o f s o l u t i o n f o r t h i s , the most r e a l i s t i c o f the th ree p rob lems, was s i g n i f i c a n t l y b e t t e r than would be expected by chance, as i n d i c a t e d by a p p l i c a t i o n o f the b i n o m i a l p r o b a b i l i t y t e s t (p<.01) . On the s t r u c t u r a l l y i d e n t i c a l tw in p rob lems, "You Be the Judge " and " C a r 5 4 " , s u b j e c t s had g rea t d i f f i c u l t y . Only 11 s u b j e c t s (36%) c o r r e c t l y a s c e r t a i n e d the g u i l t o f the changing c l e r k . G r a n t i n g a .25 p r o b a b i l i t y o f guess i ng the c o r r e c t response to t h i s q u e s t i o n , the samp le ' s c o l l e c t i v e per formance d i d not dev i a te s i g n i f i c a n t l y from chance (p>.05) . 13 s u b j e c t s (42%) c o r r e c t l y p l a c e d Car 54 on Grand, and t h i s s o l u t i o n r a t e d i d exceed chance e x p e c t a t i o n s (p<.05) , a g a i n g i v e n a .25 p r o b a b i l i t y o f guess i ng the r i g h t answer h e r e . There i s reason though f o r wonder ing why the re wasn ' t a g r e a t e r d i f f e r e n c e between per formance on ; t he i somorph ic " J u d g e " and " C a r 54" q u e s t i o n s , because s u b j e c t s were exposed to one c o r r e c t reasoned s o l u t i o n to " C a r 54" ( J o e ' s ) be fo re they e n t e r e d t h e i r own answer on the p rob lem. There were a total of 8 subjects who missed the corresponding question on "You Be the Judge", but approved Joe's correct solution and entered the correct answer for themselves on "Car 54". It would seem that number of subjects getting "Car 54" right would be as much as 8 larger than the number of subjects getting "Judge" right, then. However, the 11 subjects who had gotten "Judge" right apparently f e l l victim to regression to the mean, with only 3 of them repeating their success on "Car 54". Obviously, many of those who got "Judge" right did so by guessing, and they did not even remain consistent in their guessing when faced with the isomorphic "Car 54". (2) For two of the questions, the correct answer was "undecidable for want of further information". These were the "transaction record" question of "You Be the Judge" and the "Bypass" question of "Car 54". 17 subjects (55%) got the former correct, and 19 (61%) the latter. However, i t is impossible to say how many subjects really understood that these problems were undecidable in principle with respect to the propositions put, and how many simply put "undecidable" as an admission of their defeat in their attempts at solution. The group's performance does not depart from chance levels, statistically (p>.05), and i t should be noted that "undecidable was a frequent choice of response for the subjects on the answerable questions of "Judge" and "Car 54". (3) In the "Young Lawyer's Dilemma" problem s u b j e c t s had to judge the soundness of the reasoned s o l u t i o n s of the f i c t i t i o u s c h a r a c t e r s Roger R i v a l and Mr. Bigg. Subjects d i d w e l l on both q u e s t i o n s , r e c o g n i z i n g the soundness of R i v a l ' s s o l u t i o n and the unsoundness of Mr. Bigg's to the exact same degree: 23 (74%) got each q u e s t i o n r i g h t . Again, t h i s i s b e t t e r than chance performance (p<.01). The f i c t i o n a l t h i r d p a r t i e s of "Car 54" a l s o proposed reasoned s o l u t i o n s , but these were assumption-based s t r a t e g i e s , and the items were intended to d i s c o v e r s u b j e c t understanding of the a p p r o p r i a t e n e s s / i n a p p r o p r i a t e n e s s of such s o l u t i o n s . The m a j o r i t y of s u b j e c t s c o r r e c t l y r e j e c t e d the f a l l a c i o u s c i r c u l a r reasoning of "Mary", w i t h 22 of 31 (71%) g e t t i n g i t r i g h t . T his was s u p e r i o r to chance e x p e c t a t i o n s (p<.01). On the other hand, s u b j e c t s f a i l e d to honor Joe's c o r r e c t usage of RAD technique, and s i m i l a r l y f a i l e d to r e j e c t Sam's wrong RAD c o n c l u s i o n . Only 13 s u b j e c t s (42%) approved Joe, 18 s u b j e c t s (58%) r e j e c t i n g Sam. N e i t h e r of these represents departure from chance performance, and, indeed, when they are c o l l a p s e d to form a "RAD understanding" subscore, one sees that s u b j e c t s got RAD questions r i g h t e x a c t l y 50% of the t i m e — j u s t what one would expect of guessing. This numerical a n a l y s i s was reconfirmed by i n f o r m a l means when the experimenter demonstrated the RAD s o l u t i o n to the problems i n post- e x p e r i m e n t a l s e s s i o n s . Subjects were almost e n t i r e l y and u n i v e r s a l l y i g n o r a n t of RAD approaches, although they 87 caught on t o t h e g i s t o f i t q u i c k l y . I t i s u n f o r t u n a t e t h a t a p r o b l e m s o l v i n g t e c h n i q u e so f u n d a m e n t a l and w i d e l y a p p l i c a b l e has been i g n o r e d i n the c u r r i c u l u m o f h i g h e r e d u c a t i o n . (4) To sum up on d e d u c t i v e p r o b l e m s o l v i n g : S u b j e c t s p e r f o r m e d as a whole a t a l e v e l s i g n i f i c a n t l y b e t t e r t h a n chance ( p ^ . O l ) on a l l t h r e e q u e s t i o n s i n v o l v e d i n t h e "Young Lawyer's Dilemma" problem, b u t were r e d u c e d to g u e s s i n g on the answer to "You Be t h e Judge", t h e " u n d e c i d a b l e " q u e s t i o n s , and t h e RAD q u e s t i o n s . The V a r i a b l e I n t e r r e l a t i o n s h i p s P e a r s o n r c o r r e l a t i o n c o e f f i c i e n t s were computed f o r a l l p a i r w i s e comparisons o f t h e t h r e e v a r i a b l e s . These v a l u e s a r e p r e s e n t e d i n T a b l e 3. The C o n f i d e n c e I n t e r v a l s (C.I.s) f o r t h e c o r r e l a t i o n s a p p e a r as F i g u r e 1, p l a c e d on a s i n g l e number l i n e f o r p u r p o s e s o f c o m p a r i s o n . S p a n n i n g t h e p o i n t s from r=+.03 to r=+.65 i s the C o n f i d e n c e I n t e r v a l f o r the L o g i c a l I n t u i t i o n : L o g i c a l Judgment c o r r e l a t i o n . T h e r e i s a .95 p r o b a b i l i t y t h a t the t r u e p a r a m e t e r o f t h i s p o p u l a t i o n l i e s between t h e s e p o i n t s . A s i g n i f i c a n t , p o s i t i v e r e l a t i o n s h i p e x i s t s f o r t h e s e v a r i a b l e s . 88 Logical Logical Intuit ion Judgment Deductive Problem Solving Logical Intuit ion Logical Judgment Deductive Problem Solving 1.00 + .38 + .13 1.00 + .13 1.00 Table 3: The correlation matrix variables . for the three log ica l H # - . 3 - . 2 - . 1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 .1.00 ft * C . I . f o r l o g i c a l judgment: d e d u c t i v e p r o b l e m s o l v i n g c o r r e l a t i o n . H r C.I. f o r l o g i c a l i n t u i t i o n : d e d u c t i v e p r o b l e m s o l v i n g c o r r e l a t i o n . # ff C . I . f o r l o g i c a l judgment: l o g i c a l i n t u i t i o n c o r r e l a t i o n . F i g u r e 1. C o n f i d e n c e I n t e r v a l s f o r the P e a r s o n _r c o r r e l a t i o n s between v a r i a b l e s o f l o g i c a l i t y . <* =.05 90 The Confidence I n t e r v a l f o r the L o g i c a l I n t u i t i o n : Deductive Problem So l v i n g c o r r e l a t i o n l i e s between r=-.10 and r=+.56. Again, the parameter i s l i k e l y (to .95 p r o b a b i l i t y ) to l i e w i t h i n these l i m i t s . However, because the parameter's value could be p o s i t i v e , negative, or zero, the c o r r e l a t i o n i s deemed s t a t i s t i c a l l y n o n s i g n i f i c a n t . The Confidence I n t e r v a l f o r the L o g i c a l Judgment: Deductive Problem Solving c o r r e l a t i o n l i e s between r=-.23 and r=+.46. This c o r r e l a t i o n too, then, i s n o n s i g n i f i c a n t s t a t i s t i c a l l y . The Kendall's Tau s t a t i s t i c confirms these r e s u l t s at a rank l e v e l of measurement, and contributes an i n t e r e s t i n g d e s c r i p t i v e i n t e r p r e t a t i o n which complements the Pearson _r. The reader i s urged to see Appendix V f o r t h i s . Comparing the C o r r e l a t i o n s Inspection of Figure 1 shows enough overlap of the C.I.s of our three c o r r e l a t i o n s to r a i s e the question, i s there any r e a l d i f f e r e n c e between the strength of one c o r r e l a t i o n and that of another? I t has been noted that one c o r r e l a t i o n ( L o g i c a l Judgment: L o g i c a l I n t u i t i o n ) a t t a i n e d s t a t i s t i c a l s i g n i f i c a n c e , while the other two c o r r e l a t i o n s 91 were nonsignificant. The meaning of this i s quite limited, however. It may be inferred that the population i n question is characterized by a positive correlation between logical judgment and logical intuition, and no such correlation may be imputed to the population for the other variables. This does not mean that the significant correlation i s significantly stronger than the nonsignificant ones, nor that the nonsignificant correlations are the same vis a vis one another. Some parameter values that are included i n the Logical Judgment: Deductive Problem Solving C.I. are excluded from the l o g i c a l Intuition: Deductive Problem Solving C.I., so that these correlations cannot simply be equated even though they are alike "nonsignificant". Moreover, i f the parameters of a l l three correlations happened to have the same value, namely +.30, our present findings would not stand contradicted, because +.30 l i e s within the C.I.s established for a l l three correlations. In fact, elements of our correlation matrix (Table 3 ) can be compared for relative strength by a technique developed by Williams (1959), the T 2 s t a t i s t i c , recommended as the "best all-round choice" for this purpose by Steiger (1980). 92 The c r i t i c a l value of for df=28 and p<.05 i s 2.05, and 1.31 where p<. 10. Evaluating the most discrepant pair of correlations f i r s t , the Logical Judgment: Logical Intuition correlation with the Logical Judgment: Deductive Problem Solving correlation, we find that T 2-I . I 8 , df-28. Obviously these correlations are not significantly differing in strength, not even at the .10 alpha lev e l , and further computations of T2 would be entirely superfluous to our main conclusion which is that no correlation is significantly stronger than any other correlation i n this matrix. General Discussion On the Unitariness of Logicality. In view of the present findings, l o g i c a l i t y does not appear as particularly unitary. None of the three correlations obtained for our three variables was especially strong, and two of them were s t a t i s t i c a l l y nonsignificant. The one s t a t i s t i c a l l y significant correlation(between l o g i c a l judgment and lo g i c a l intuition) was no stronger than the nonsignificant correlations. The lack of a strong association between the lo g i c a l judgment and deductive problem solving measures i s not very surprising. However, the lack of association between the lo g i c a l judgment and deductive problem solving measures i s . Nothing could be more l o g i c a l than e v a l u a t i n g argument forms as to t h e i r v a l i d i t y . And n o t h i n g could be more l o g i c a l than working a deductive s t o r y problem. Yet i t appears th a t these are not only d i f f e r e n t k i n d s of l o g i c a l a c t i v i t y , the a b i l i t i e s behind the performance of the a c t i v i t i e s are u n c o r r e l a t e d . A b e t t e r f e e l f o r t h i s f i n d i n g may be gotten by n o t i n g one o r two i n d i v i d u a l s u b j e c t s from our sample. Subject #17 was second ranked on l o g i c a l judgment ( s c o r i n g 9 0 % j , but t i e d f o r dead l a s t on deductive problem s o l v i n g ( s c o r i n g 20%)! Of course, the v a r i a b l e s were not n e g a t i v e l y c o r r e l a t e d , and cannot be taken t o be i n c o m p a t i b l e w i t h one another. Subject #19, s c o r i n g 90% on deductive problem s o l v i n g and 85% on l o g i c a l judgment ranked i n the top 4 on both measures. However, no s u b j e c t ranked i n the top 4 on a l l 3 measures. 1 attempted i n the t h i r d chapter of t h i s t h e s i s to i n d i c a t e how l o g i c a l judgment and deductive problem s o l v i n g might be thought of as i n v o l v i n g r a t h e r d i f f e r e n t k i n d s of c o g n i t i o n . And to some degree the present m a t e r i a l s and procedure were designed to a l l o w f o r the independence, i f any, of the v a r i a b l e s to be d i s c l o s e d . The deductive problem s o l v i n g composite measure i n c l u d e d s p e c i f i c measures not only of answers o b t a i n e d , but of s u b j e c t understanding of sound answer-getting techniques as used i n n a t u r a l deduction. And i t might be s a i d that the very s t r u c t u r e of the problems u s e d — a t l e a s t of "You Be the Judge" and "Car 54"—was such as to i n v i t e i f not mandate a "working through" type of s o l u t i o n . On the whole, then, i t was a d e r i v a t i o n - l i k e deductive problem s o l v i n g that was probably measured. On the other hand, c o n d i t i o n s were f a v o r a b l e f o r the measurement of a n o n - d e r i v a t i o n a l type of l o g i c a l judgment: the arguments, f a i r l y simple i n form, were to be judged without any requirement of proo f , and s u b j e c t s were given l i t t l e time to "work them through". Our f i n d i n g s may be i n t e r p r e t a b l e i n t h i s way: D e r i v a t i o n - l i k e problem s o l v i n g does not c o r r e l a t e w i t h n o n - d e r i v a t i o n - l i k e l o g i c a l judgment. Put i n t h i s way, the r e s u l t s seem l e s s s u r p r i s i n g . I t i s p o s s i b l e t h a t things would t u r n out d i f f e r e n t l y i f changes were made i n the m a t e r i a l s and procedure used. I n c r e a s i n g the complexity l e v e l o f the arguments used i n the l o g i c a l judgment task might move the v a r i a b l e s c l o s e r together by f o r c i n g s u b j e c t s to "work through" them. Reducing the s p e c i f i c i t y of the questions asked i n the deductive problems might keep the v a r i a b l e s apart by p l a c i n g a premium on l o g i c a l w a y f i n d i n g a b i l i t y . These and other f a c t o r s l e n d themselves to 95 experimental m a n i p u l a t i o n which could prove e n l i g h t e n i n g . As f o r the L o g i c a l I n t u i t i o n : L o g i c a l Judgment c o r r e l a t i o n , which was s t a t i s t i c a l l y s i g n i f i c a n t i n a p o s i t i v e d i r e c t i o n , the degree of i t s s t r e n g t h i s roughly what would be expected. Both l o g i c a l i n t u i t i o n and l o g i c a l judgment tasks depend on r e p r e s e n t a t i o n of l o g i c a l form, but diverge on the subsequent assessment o r use made of the r e p r e s e n t a t i o n . There i s a p a r t i a l o v e r l a p between the t a s k s , i n other words, and t h i s corresponds to the o v e r l a p i n performance r e g i s t e r e d by the c o r r e l a t i o n . I b e l i e v e t h a t the res e a r c h f i n d i n g s here have uncovered a b a s i c f a c t about l o g i c a l i t y , which i s that i t c o n s i s t s of r a t h e r independent components. A good theory w i l l need to e x p l a i n t h i s independence. My own e x p l a n a t i o n i s very general and was covered i n chapter I I I . On a n a l y s i s , the a b i l i t i e s c omprising l o g i c a l i t y amount to c o n c e p t u a l l y d i s t i n g u i s h a b l e ways of working w i t h l o g i c a l form. The e m p i r i c a l s i d e of t h i s t h e s i s has p r o v i d e d evidence f o r the i d e a that these ways of working w i t h l o g i c a l form may be m a n i f e s t l y  independent as regards performance. In t h i s l a s t s e c t i o n I i n t e n d to b r i e f l y remark an those i m p l i c a t i o n s I see as f o l l o w i n g from t h i s f i n d i n g . y6 Some Research I m p l i c a t i o n s . I t was suggested at an e a r l i e r p o i n t i n t h i s t h e s i s t h a t the c o r r e l a t i o n of l o g i c a l i n t u i t i o n w i t h more m e t a p h o r i c a l k i n d s of a n a l o g i c a l reasoning might be worth determining. Now that l o g i c a l i n t u i t i o n has been shown to be p o s i t i v e l y c o r r e l a t e d to a s i g n i f i c a n t degree w i t h l o g i c a l judgment the p o s s i b i l i t y e x i s t s of a l i n k a g e between a n a l o g i c a l reasoning and one type of l o g i c a l reasoning. Of course, i t must be kept i n mind that i t i s p o s s i b l e f o r l o g i c a l i n t u i t i o n to c o r r e l a t e p o s i t i v e l y w i t h more metaphorical a n a l o g i c a l reasoning on the one hand, and w i t h l o g i c a l judgment on the o t h e r , and yet f o r the l a t t e r to be n o n c o r r e l a t e d . Moving to the more b a s i c f i n d i n g r e p o r t e d above, namely that of the v i r t u a l n o n u n i t a r i n e s s of l o g i c a l i t y , we f i n d many research questions cast i n a new l i g h t o r opened up f o r the f i r s t time. For one t h i n g , i t now seems q u i t e p o s s i b l e that some x (person or group) c o u l d be b e t t e r than y (person or group) i n one type o f l o g i c a l t h i n k i n g (say, l o g i c a l judgment), but equal to or i n f e r i o r to y i n another way (say, deductive problem s o l v i n g ) . T h i s has great relevance to any research undertaking comparison of p o p u l a t i o n s as to t h e i r l o g i c a l i t y , e.g. r e s p e c t i n g sex d i f f e r e n c e s , age group d i f f e r e n c e s , 97 o c c u p a t i o n / v o c a t i o n group d i f f e r e n c e s , e t c . For that matter, a w h o l l y new k i n d of comparison between po p u l a t i o n s becomes p o s s i b l e now. Given the present f i n d i n g of n o n - u n i t a r i n e s s of l o g i c a l i t y i n a p a r t i c u l a r p o p u l a t i o n the q u e s t i o n n a t u r a l l y a r i s e s , i s l o g i c a l i t y more or l e s s u n i t a r y i n other p o p u l a t i o n s ? For example, i f d i f f e r e n t i a l p r a c t i c e i s r e s p o n s i b l e f o r the l a c k of c o r r e l a t i o n between l o g i c a l judgment and deductive problem s o l v i n g , the p o s s i b i l i t y e x i s t s t h a t w i t h somewhat l e s s experienced s u b j e c t s , e.g. h i g h s c h o o l s t u d e n t s , a g r e a t e r c o r r e l a t i o n w i l l o b t a i n between these v a r i a b l e s . More g e n e r a l l y , the u n i t a r i n e s s of l o g i c a l i t y may a l t e r over time, w i t h experience or simply w i t h m a t u r a t i o n . F i n a l l y , by combining the v a r i a b l e s of l o g i c a l i t y i n t o a s i n g l e g l o b a l measure, i t becomes p o s s i b l e to c o r r e l a t e t h i s bundle of c o r r e l a t i o n s w i t h other a t t r i b u t e s such -as gen e r a l i n t e l l i g e n c e , academic performance, v o c a t i o n a l p r e f e r e n c e , e t c . The c o r r e l a t i o n that l o g i c a l i t y as a whole enjoys w i t h other a t t r i b u t e s c o u l d be q u i t e d i f f e r e n t than the c o r r e l a t i o n any one component of l o g i c a l i t y enjoys w i t h t h a t o t h e r a t t r i b u t e . REFERENCES Anderson, J.R. Language, Memory, and Thought. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1976. Blumberg, A. Logic. New York: Alfred A. Knopf, 1976. Braine, M.S. On the relation between the natural logic of reasoning and standard logic. Psychological Review, 1978, 85, 1-21. Ceraso, J., Provitera, A . Sources of error in s y l l o g i s t i c reasoning. Cognitive Psychology, 1971 , 2, 400-410. Dantzig, T. Number, the Language of Science. New York: The MacMillan Co., 1930. Donaldson, M. Positive and negative information in matching problems. Bri t i s h Journal of Psychology, 1959, 50, 235-262. Erickson, J.R. A set analysis theory of behavior in formal s y l l o g i s t i c reasoning casks. In R.L. Solso (Ed.), Theories in cognitive psychology: The Loyola Symposium. Pocomic, Md.: Erlbaum Associates, 1974. Fann, K.T. Peirce's Theory of Abduction. The Hague: Martinus Nijhoff, 1970. 99 Gentzen, G. Investigations into Logical Deduction. In M.E. Szabo (Ed.), The Collected Papers of Gerhard Gentzen. London: North Holland Publishing Co., 1969. Gick, M.L. & Holyoak, K. Analogical problem solving. Cognitive  Psychology, 1980, 12_, 306-355. Gick, M.L. & Holyoak, K. Schema induction and analogical transfer. Cognitive Psychology, 1983, 15, 1-38. Glass, G.V. & Stanley, J.C. S t a t i s t i c a l Methods in Education  and Psychology. Englewood C l i f f s , N.J.: Prentice-Hall, 1970. Guyote, S. & Sternberg, R.J. A transitive-chain theory of s y l l o g i s t i c reasoning. Cognitive Psychology, 1981, 13 461-525. Inhelder, B. & Piaget, J. The Growth of Logical Thinking from  Childhood to Adolescence. New York: Basic Books, 1958. Langer, S.K. An Introduction to Symbolic Logic. New York: Dover, 1953. McCulloch, W.S. & P i t t s , W. A lo g i c a l calculus of the ideas imminent in nervous act i v i t y . Bulletin of Mathematical Biophysics. 1943, 5, 115-133. Newell, A. On the analysis of human problem solving protocols. In Johnson-Laird, P. . & Wason, P.C. (Ed.s), Thinking. New York: Cambridge Press, 1977. 100 Newell, A., Shaw, J.C. & Simon, H.A. Elements of a theory of human problem solving. Psychological Review, 1958, 65 151-166. Newell, A. & Simon, H.A. Human Problem Solving. Englewood C l i f f s , N.J.: Prentice-Hall, 1972. Osherson, D.C. Reasoning i n Adolescence: Deductive Inference. (Volume III of Logical A b i l i t i e s in Children). Hillsdale, N.J.: Erlbaum Associates, 1975. Piaget, J. Logic and Psychology. Manchester, England: Manchester University Press, 1953. Piaget, J . Problems of genetic psychology. In D. Elkind (Ed.), Six Psychological Studies. New York: Random House, 1967. (Originally published i n Voprossi Psychkhologuii, 1956). Piaget, J . The thought of the young child. In D. Elkind (Ed.), Six Psychological Studies. New York: Random House, 1967. (Lecture given orig i n a l l y in 1963). Piaget, J . Biology and Knowledge. Chicago: University of Chicago Press, 1971. Reed, S.K., Ernst, C.W., & Banerji, R. The role of analogy i n transfer between similar problem states. Cognitive Psychology. 1974, 6_, 436-450. R i p s , L . J . C o g n i t i v e processes i n p r o p o s i t i o n s ! reasoning. P s y c h o l o g i c a l Review, 1983, 90 , 38 -71 . S t e i g e r , J . Tests f o r comparing elements of a c o r r e l a t i o n m a t r i x . P s y c h o l o g i c a l B u l l e t i n , 1980, J37, 245-251 Sternberg, R.J. Reasoning, p r o b l e m - s o l v i n g , and i n t e l l i g e n c e In Sternberg, R.J. (Ed.), Handbook of Human I n t e l l i g e n c e New York: Cambridge U n i v e r s i t y P r e s s , 1982. Strawson, P.F. I n t r o d u c t i o n to L o g i c a l Theory. ..London: Methuen & Co. , 1952. Wason, P.C. S e l f - c o n t r a d i c t i o n s . In J o h n s o n - l a i r d , P.N. & Wason, P.C. ( E d . s ) , T h i n k i n g . New York: Cambridge U n i v e r s i t y P r e s s , 19 77. Wickelgren, W. How to Solve Problems—Elements of a Theory of Problems and Problem S o l v i n g . San F r a n c i s c o : W.H. Freeman & Co., 1974. W i l l i a m s , E.J. The comparison of r e g r e s s i o n v a r i a b l e s . J o u r n a l of the Royal S t a t i s t i c a l S o c i e t y , S e r i e s B, 1959, 2J., 396-399. 102 APPENDIX I: THE SUBJECT CONSENT FORM In t h i s session you w i l l be given various problems which you w i l l be asked to answer using your powers of reasoning. You may not exceed 90 minutes t o t a l working time i n answering these questions. Before s e t t i n g to work on these problems, however, you must be made aware that we need your consent i n order f o r you to p a r t i c i p a t e i n t h i s psychology experiment. In order f o r you to give informed consent you must, of course, know something about the nature and o b j e c t i v e s of the pr o j e c t involved here. Please read the fo l l o w i n g c a r e f u l l y . I f you decide to p a r t i c i p a t e i n t h i s experiment sign at the bottom of the page. ( I f your answer sheets are completed i t w i l l be assumed that consent has been given). What i s t h i s p r o j e c t about? L o g i c a l reasoning i s one (only one) important aspect of adult t h i n k i n g . This research p r o j e c t concerns c e r t a i n a b i l i t i e s which we b e l i e v e make up what i s commonly c a l l e d l o g i c a l t h i n k ing. Those component mental a b i l i t i e s are s p e c i f i c a l l y tested i n t h i s experiment by s p e c i a l l y designed problems. The problems in v o l v e comparing and ev a l u a t i n g b r i e f v e r b a l arguments. (Your answers take the form of simple d e c i s i o n s ) . We expect that, f o r the normal a d u l t , some of the judgments you w i l l make w i l l be f a i r l y e f f o r t l e s s and obvious, w h i l e some other judgments w i l l be very hard to make. Is t h i s an i n t e l l i g e n c e t e s t ? In a word, "no"! No measurement comparable to an i n t e l l i g e n c e q u o t i e n t i s bein g taken i n t h i s experiment. Our concern i s not w i t h "how l o g i c a l " you a r e , but w i t h how your s e v e r a l ways of working w i t h l o g i c a l form hang together across d i f f e r e n t kinds of l o g i c a l t a s k s . Am I bein g p e r s o n a l l y evaluated? No. F o l l o w i n g c o l l e c t i o n of data, your name w i l l cease to be a s s o c i a t e d w i t h your t e s t measures, which w i l l be t h e r e a f t e r r e f e r r e d to only by an a r b i t r a r y number. N e i t h e r your performance i n t h i s experiment, nor your r e f u s a l to p a r t i c i p a t e i n t h i s experiment, can i n f l u e n c e your c l a s s s t a n d i n g a t UBC i n any way. Your r i g h t as a s u b j e c t . You are f r e e to withdraw a t any time o r to re f u s e to answer any questions without p e n a l t y . -Who i s conducting t h i s research? Merry B u l l o c k and Harol d C. M o r r i s , both of the HBC psychology department. Having read and understood the above, I hereby consent to p a r t i c i p a t e as a s u b j e c t i n t h i s experiment: (Signature) P r i n t name below l i n e APPENDIX I I : LOGICAL JUDGMENT MATERIALS I n s t r u c t i o n s . In t h i s p a r t o f y o u r s e s s i o n you w i l l be p r e s e n t e d w i t h 20 numbered i t e m s . Each i t e m c o n s i s t s o f a s h o r t s e r i e s o f s t a t e m e n t s . The s t a t e m e n t s a r e a t t r i b u t e d t o v a r i o u s f i c t i o n a l c h a r a c t e r s . F o r a g i v e n i t e m the s t a t e m e n t ' s ) a p p e a r i n g above t h e row o f s t a r s make up the p r e m i s e s . The s t a t e m e n t below t h e row o f s t a r s i s c a l l e d the c o n c l u s i o n . A complete i t e m , w h i c h i n c l u d e s s t a t e m e n t s above and below the s t a r s i s c a l l e d an argument. F o r each one o f t h e s e 20 arguments y o u r t a s k w i l l be t o j u d g e whether o r n o t the l i n e below the row o f s t a r s ( t h e c o n c l u s i o n ) n e c e s s a r i l y f o l l o w s from t h e s t a t e m e n t s above the row o f s t a r s ( t h e p r e m i s e s ) . F o r the p u r p o s e s o f y o u r t a s k , y o u must assume t h a t t h e c h a r a c t e r s a r e t e l l i n g the t r u t h when they make the v a r i o u s c l a i m s and a s s e r t i o n s a p p e a r i n g as p r e m i s e s i n t h e argument. The q u e s t i o n t o ask y o u r s e l f t h e n i s , do t h e s t a t e m e n t s above the row o f s t a r s w a r r a n t ( o r e n t a i l ) t h e i n f e r e n c e , d e c l a r a t i o n o r d e c i s i o n s t a t e d below t h e row o f s t a r s ? I f s o , you s h o u l d j u d g e t h e argument t o be v a l i d . H ere i s an example o f a v a l i d argument: F r e d : I knew t h a t i f the L i o n s won t h i s game t h e y ' d make the p l a y o f f s t h i s y e a r . The L i o n s won t h i s game. * * * * A ft ft So I know t h e y ' v e made the p l a y o f f s t h i s y e a r . I n p a s s i n g judgment on t h i s argument y o u would have to assume t h a t F r e d i s c o r r e c t i n making the a s s e r t i o n s he makes above the row o f s t a r s . Then y o u would ask y o u r s e l f , i f the s t a t e m e n t s above a r e t r u e , t h e n does F r e d ' s c o n c l u s i o n f o l l o w , l o g i c a l l y ? 105 Here i s an example of an i n v a l i d argument: Chip: I know that i f the L i o n s win t h i s game, t h e y ' l l make the p l a y o f f s t h i s year. The L i o n s made the p l a y o f f s l a s t y e a r . * * * * * * * So I know the Li o n s w i l l make the p l a y o f f s t h i s year. In the case of an i n v a l i d argument l i k e the one made by Chip above, the c o n c l u s i o n cannot be s a i d to f o l l o w n e c e s s a r i l y from the premises, and f o r that reason, - the argument i s not v a l i d . N o t i c e i t i s not enough t h a t the c o n c l u s i o n be p l a u s i b l e , or probable. For an argument to be v a l i d , the c o n c l u s i o n must i n e v i t a b l y , i n v a r i a b l y f o l l o w from the given premises. I t might help to pretend that you are a computer, t r y i n g to decide whether the c o n c l u s i o n f o l l o w s from the premises i n each argument as a u t o m a t i c a l l y as 4 i s produced by adding 2 and 2. As a " l o g i c machine" you know no t h i n g about the world except what you're given i n the premises. That way you w i l l not be tempted to c a l l an argument v a l i d simply because i t s c o n c l u s i o n i s p l a u s i b l e o r " f e e l s " r i g h t i n and of i t s e l f . For each of the 20 arguments you are g i v e n , then, make a judgment: i s i t v a l i d ? Enter your answer on the answer s h e e t that i s pr o v i d e d . I f at any time you wish to c o n s u l t t h e s e i n s t r u c t i o n s i n order to r e f r e s h your memory as to the meaning of v a l i d i t y , you may f e e l f r e e to do so. However, keep i n mind that your time f o r working on t h i s task i s l i m i t e d , so you w i l l want to avo i d spending any lon g amount of time on a p a r t i c u l a r argument. (.You have, on average, o n l y one minute per argument). Good l u c k ' 106 Arguments Used i n the L o g i c a l Judgment Task. (1) Journeyman e l e c t r i c i a n : E i t h e r the problem's w i t h the swi t c h o r i t ' s w i t h the w i r i n g — t h o u g h o f course both could be out. App r e n t i c e : I've examined the s w i t c h , and i t ' s O.K. * * * * * * Journeyman: So the problem's w i t h the w i r e . (VALID) (2) Husband: E i t h e r t h a t p l a n t ' s g e t t i n g too much water or i t ' s not g e t t i n g enough s u n l i g h t , or both. Wife: Look at the dark corner i t ' s i n : i t ' s o b v i o u s l y n< been g e t t i n g enough l i g h t . * * * * * * Husband: Hmmm. Then I guess t h a t means i t ' s g e t t i n g too much water. (INVALID) (3) D e t e c t i v e : Joe's s t o r y used t o be th a t i f the v i c t i m drowned, then e i t h e r i t wasn't an a c c i d e n t o r the f i n k t o l d the t r u t h , o r both. But Joe has j u s t admitted t h a t h i s s t o r y i s f a l s e . * * * * * * Perry Mason: So i f the v i c t i m drowned then i t was an a c c i d e n t , and i f i t was an a c c i d e n t , then the v i c t i m drowned: two s i d e s of one c o i n . (VALID) (4) Nancy: I f you knew what I've been through, I know you wouldn't blame me. So you must know what I've been through. (INVALID) 107 (5) G i g i : I'm t h i n k i n g of a number which i s e i t h e r l e s s than 4 or l e s s than n. I f i t ' s l e s s than n and a p e r f e c t square, i t ' s not even. * * * * * * P h i l : So i f i t ' s e i t h e r even or a p e r f e c t square, then i t ' s got to be l e s s than 4. (INVALID) (6) A l i c e : I f i t i s not r a i n i n g today, I s h a l l c e r t a i n l y have tea w i t h the White Rabbit i n the garden. Vixen: W e l l , my dear, s u r e l y you see that i t i s r a i n i n g today! * * * * * * A l i c e : Hooray! For th a t means I s h a l l c e r t a i n l y have t ea w i t h the White Rabbit today! (INVALID) (7) Steve: I f e i t h e r the Comets o r the T i g e r s won then i t ' s i m p o s s i b l e f o r the Beagles and Darts to meet i n the t i t l e game. Chuck: I f the T i g e r s don't win, the Beagles won't advance to the t i t l e game. * * * * * * B i l l : Gee. That means th a t i f the Comets won, the Darts won't advance to the t i t l e game. (INVALID) (8) Jan: Why, i f she's h i s mother, then that means she i s Mrs. Farnhouse'. Rob: True, but she i s n ' t Mrs. Farnhouse. That lady there i s Mrs. B o r i n g . * * * * * * Jan: Oh, then she can't be h i s mother. (VALID) 108 (9) Meg: I f the box i s small and f a i r l y heavy, i t ' s the agate paperweight I wrapped for Marjie. Ted: Well, l e t ' s see. I t ' s small. * * * * * * Meg: So i f i t ' s f a i r l y heavy i t ' s the agate paperweight I wrapped f o r Ma r j i e . (VALID) ( 1 0 ) Analyst: In making the world safe f o r democracy by accumulating a huge store of nuclear weapons, we've wound up not making the world safe f o r democracy. * * * * * * So we f i n d ourselves i n a world which has most c e r t a i n l y not been rendered safe f o r democracy by v i r t u e of our s t o c k p i l i n g of nuclear weapons. (VALID) ( 1 1 ) Professor Johnson: The f a c t that the s i g n a l bounced and the axis didn't spike implies that the device wasn't functioning. Professor Stevens: I f the device was functioning r i g h t and the s i g n a l hadn't bounced, then the axis would've spiked. * * * * * * Fred: So obviously, i f the device was functioning the axis should have spiked. (VALID) ( 1 2 ) Nosy Neighbor: I f she gives him the check and cl e a r s out her s t u f f , h e ' l l give her back her key. She cleared out her s t u f f . * * * * * * Now i t follows that i f he gives her back her key, she won't give him the check! (INVALID) 109 (13) Stu: E i t h e r heaven e x i s t s , or h e l l doesn't e x i s t — t h o u g h i t ' s p o s s i b l e there i s a heaven but no h e l l . Heaven doesn't e x i s t . * * * * * * So h e l l doesn't e i t h e r . (VALID) (.14) P r o f e s s o r : Now you might suppose t h a t " i f the quantum theory i s r i g h t , then i t f o l l o w s t h a t e i t h e r Young i s wrong or Newton i s r i g h t . " But th a t i s a c t u a l l y an i n c o r r e c t a p p r a i s a l of the matter. * * * * * * Student: So you're now i m p l y i n g t h a t i f Young's r i g h t , then the theory i s r i g h t , and v i c e v e r s a — i f the theory's r i g h t that means Young's r i g h t . (VALID) (15) Parmenides: The very f a c t that I am t h i n k i n g of not h i n g i m p l i e s t h a t I'm not t h i n k i n g of j u s t n o t h i n g . * * * * * * Of course i t f o l l o w s then that I cannot be t h i n k i n g of nothing. (VALID) (16) Joe: I f I connect the speaker and s w i t c h the amp to phono mode, we can hear the r e c o r d . Jim: I connected the speaker w h i l e you were on the phone. * * * * * * Joe: So i f I s w i t c h to phono mode, we can hear the r e c o r d now. (VALID) (.17) T o u r i s t on comprehensive 5-day European t o u r : I f t h i s i s Tuesday, t h i s must be Belgium, according to my schedule. Tour guide: This i s n ' t B e l g i u m — t h i s i s France. * * * * * * T o u r i s t : Oh, I see. Then t h i s i s n ' t Tuesday. (VALID) (18) Economist: I f we seek to reduce our n a t i o n a l debt, w e ' l l be f o r c e d to reduce the amount of money i n c i r c u l a t i o n . Y e t, whether we reduce the amount of money i n c i r c u l a t i o n , or e s t a b l i s h a f a v o r a b l e trade balance, or both, i n f l a t i o n i s going to continue unabated. I f we launch an ambitious jobs program, of course, w e ' l l i n c r e a s e our n a t i o n a l debt. * * * * * * Finance M i n i s t e r : So i f we go about reducing our n a t i o n a l debt we can b r i n g a h a l t to i n f l a t i o n . (INVALID) (19) Ben: E i t h e r t h i s t y p e w r i t e r column s e t t e r i s broken or the r e t u r n mechanism i s broken, or both are m a l f u n c t i o n i n g . Examining the r e t u r n mechanism, I see that i t i s broken. * * * * * * So the t y p e w r i t e r column s e t t e r must be m a l f u n c t i o n i n g too. (INVALID) (20) P r o f e s s o r Jones: I f these p a r t i c l e s b i n d together and don't a n n i h i l a t e one another, then we can i n f e r t h a t they aren' of o p p o s i t e charges. I f they are of opposite charges, and don't b i n d t o g e t h e r , then t h e y ' l l a n n i h i l a t e one another. * * * * * * P r o f e s s o r Smith: So i f they have opposite charges t h e y ' l l a n n i h i l a t e each o t h e r . (VALID) I l l L o g i c a l Judgment Answer Sheet. For each of the 20 arguments you must decide whether there i s adequate b a s i s f o r j u d g i n g whether or not an argument i s v a l i d o r i n v a l i d . I f there i s i n s u f f i c i e n t b a s i s f o r making a judgment of v a l i d i t y / i n v a l i d i t y c i r c e l UNDEC ( f o r u n d e c i d a b l e ) . Otherwise c i r c l e e i t h e r VALID or INVALID a c c o r d i n g to your best judgment. ARGUMENT // 1. VALID INVALID UNDEC 2. VALID INVALID UNDEC 3. VALID INVALID UNDEC 4, VALID INVALID UNDEC 5. VALID INVALID UNDEC 6. VALID INVALID UNDEC 7. VALID INVALID UNDEC 8. VALID INVALID UNDEC 9. VALID INVALID UNDEC 10. VALID INVALID UNDEC 11. VALID INVALID UNDEC 12. VALID INVALID UNDEC 13. VALID INVALID UNDEC 14. VALID INVALID UNDEC 15. VALID INVALID UNDEC 16. VALID INVALID UNDEC 17. VALID INVALID UNDEC 18. VALID INVALID UNDEC 19. VALID INVALID UNDEC 20. VALID INVALID UNDEC 112 APPENDIX I I I : LOGICAL INTUITION MATERIALS I n s t r u c t i o n s . In t h i s task you w i l l be comparing arguments i n order to see which have i d e n t i c a l forms. Arguments are presented to you i n groups of f o u r . You may wonder what i t means f o r arguments to have i d e n t i c a l form. There are many ways that arguments could be p a i r e d , of course, because they can be s i m i l a r i n many d i f f e r e n t ways. We are i n t e r e s t e d i n only one k i n d of s i m i l a r i t y between arguments: the s i m i l a r i t y of t h e i r l o g i c a l form. We w i l l e x p l a i n t h i s n o t i o n of l o g i c a l form below. Consider the f o l l o w i n g arguments: 1. A l l rodents are animals. Mice are rodents. Therefore, a mouse i s an animal. 2. A l l c l o c k s have hands. Watches are c l o c k s . So a l l watches have hands. 3. A l l clowns wear makeup. My mother wears makeup. Therefore my mother i s a clown. 4. Some men are s o l d i e r s . A l l s o l d i e r s wear uniforms. Thus, some men wear uniforms. These arguments are about d i f f e r e n t t h i n g s . But some share the same l o g i c a l form, j u s t as a s i n g l e joke format can be used as a mold to cr e a t e d i f f e r e n t jokes t h a t have the same b a s i c form. Can you see that arguments 1 and 2 above have the same l o g i c a l form? Argument 3, which i s i n v a l i d , has a d i f f e r e n t form than 1 or 2. Argument 4, which i s v a l i d , a l s o has a d i f f e r e n t form than 1 or 2. Do arguments 3 and 4 have the same form? (No.') As s t a t e d above, your task now w i l l be to t r y to i d e n t i f y any p a i r o f arguments from among the four you are presented which have i d e n t i c a l l o g i c a l form. A s e t of arguments may have no p a i r s that match. 113 L o g i c a l I n t u i t i o n Task Arguments. SET I CI) Attorney: I f your tenant i s v a c a t i n g and t h i s machine mount q u a l i f i e s as a f i x t u r e i n the l e g a l sense, then you own than f i x t u r e . L andlord: W e l l , they're d e f i n i t e l y v a c a t i n g . A t t o r n e y : So i f the machine mount q u a l i f i e s as a f i x t u r e then i t ' s yours. (2) High P r i e s t : I f , but only i f , one of the p a r t i e s was mentally incompetent can t h i s church t r i b u n a l annul t h e i r marriage. The f i n d i n g of our s p e c i a l master i s that the groom was mentally incompetent. By v i r t u e of the s a i d incompetence we may annul t h i s marriage. (3) Dan: A c c o r d i n g to t h i s medical reference book, i f you have y e l l o w s k i n under your n a i l s , and red b l o t c h e s on your e y e l i d s , then you e i t h e r have Forbes' disease or a v i t a m i n G d e f i c i e n c y . Pam: You've got both the symptoms: y e l l o w under your n a i l s , b l o t c h e s on your e y e l i d s . Dan: So i f I don't have Forbes' disease then I must have a v i t a m i n G d e f i c i e n c y . (4) Photog: I f he used h i g h speed f i l m and an o r d i n a r y t e l e p h o t o l e n s , he wouldn't have gotten such good c o n t r a s t s h o o t i n g those snowy mountain peaks. But o b v i o u s l y he d i d get good c o n t r a s t . So i f he used h i g h speed f i l m then he didn' t use an o r d i n a r y telephoto l e n s . SET II (1) Troubleshooter: If the relayer belt had jammed, then this hopper would be empty. But the hopper isn't empty. So the relayer belt didn't jam. (2) Stoic Philosopher: If I can rightly conclude that I never draw conclusions, then i t is wrong to conclude that I never draw conclusions. Therefore, i t is wrong for me to conclude that I never draw conclusions. (3) Psychotherapist: If you really try to stop trying, then you really don't try to stop trying. So you really don't try to stop trying. (4) Anthropologist: When these people like a visitor, they give him a farewell gift. Explorer: Well, they didn't give me a thing when I visited them Anthropologist: Then I think we can figure that they didn't exactly like you. SET III (1) Gloria: If UFOs are psychic projections, as opposed to actual physical entities, then they aren't violating the laws of inertia and motion. But i f they aren't psychic projections, then they must be actual physical devices that nevertheless do not violate the laws of inertia and motion. So i f UFOs defy the laws of inertia and motion, then they have to be actual physical entities. (2) Engineer / / i : E i t h e r the turbulance was bad and the f l a p s d i d n ' t compensate o r we can i n f e r t h a t our aerodynamics are wrong. But i f e i t h e r the f l a p s compensated or the aerodynamics were wrong then the turbulance . must not "have been bad. Engineer #2: I t f o l l o w s that i f the f l a p s d i d compensate th a t means our aerodynamics were wrong! 13) F i r s t Alderman: E i t h e r we put up the e x h i b i t i o n booths at the marina and f o r g e t about s e t t i n g up the c a r n i v a l r i d e s on the courthouse lawn or w e ' l l have to move the f i r e w o r k s d i s p l a y . Second Alderman: J u s t as I was sa y i n g : I f we put the booths up a t the marina but go ahead and s e t up the r i d e s on the lawn, then we don't have to move the fi r e w o r k s d i s p l a y . S e n i o r Alderman: I t ' s s e t t l e d then. S e t t i n g up the r i d e s on the courthouse lawn means we have to move the f i r e w o r k s d i s p l a y . (4) P u z z l e r : I f , I say i f f , t h i s c o i n i n my hand i s l e s s than a q u a r t e r i n value then you may conclude t h a t i t i s not a n i c k l e . But i f i t ' s not l e s s than a q u a r t e r , then i t ' s a U.S. c o i n b esides b e i n g something other than a n i c k l e . B a r r y : So i f - i t ' s a n i c k l e then i t ' s a U.S. c o i n . SET IV (1) George: C o n s t r u c t i o n of that new b r i d g e c e r t a i n l y exceeded i n cost the estimate given by the c o n t r a c t o r s . I f anyone had read the bureau i n s p e c t o r ' s r e p o r t the t h i n g might s t i l l have cost as much as i t d i d , but we might at l e a s t have been spared the long d e l a y s . C h a r l e s : Yes, i f they'd have p a i d a t t e n t i o n to that r e p o r t , the delay might have been avoided. (2) Sherry: I j u s t heard that Artworx has gone broke. Tammy: W e l l , you know i f t h e i r a u c t i o n had n e t t e d more or they'd thought to make a v a i l a b l e t h e i r f u l l i n v e n t o r y before i t was too l a t e , they could've avoided t h a t . Sherry: Hmmm. I gather i f they'd made a v a i l a b l e t h e i r f u l l i n v e n t o r y then they'd have n e t t e d more at t h e i r a u c t i o n . (3) S p o r t s f a n : You s e e — t h e y ' r e s c o r i n g up the middle a g a i n s t us every time! When A l ' s p r e s s u r i n g and Carousky's checking you j u s t wouldn't see t h a t . S p o r t s t y r o : I guess then i f A l ' s p r e s s u r i n g , Carousky must not be checking. (4) D e t e c t i v e : The b u t l e r has confessed: he p u l l e d the t r i g g e r But i f Anson and Carsdale were both t e l l i n g the t r u t h then the b u t l e r couldn't have done i t . S i d e k i c k : So, s i n c e Anson's t e l l i n g the t r u t h , Carsdale couldn't be! Answer Sheet.* You are to judge which p a i r s , i f any, of arguments w i t h i n a set of f o u r arguments share the same l o g i c a l form. Beside the roman numeral corresponding to the s e t of arguments you're working w i t h , w r i t e the numbers o f the arguments you b e l i e v e have the same form. For example, i f you b e l i e v e t h a t arguments 1 and 2 of Set I share the same l o g i c a l form, put "1:2" b e s i d e the roman numeral I below. Put n o t h i n g f o r a p a i r that does not match. Set I : (No match) Set I I I : (1:4) Set I I : ( 1 : 4 and 2:3) Set IV: (3:4) *Correct matches are i n parentheses. 117 APPENDIX IV: DEDUCTIVE PROBLEM SOLVING MATERIALS Three deductive problems and ten questions comprise the deductive problem solving measures. The problems, l i s t e d i n order of their presentation to subjects, are "Young Lawyer's Dilemma", "You Be the Judge", and "Car 54". "You Be the Judge" appeared earl i e r as Table 1 (page 47) and w i l l not be duplicated here, although the questions attached to i t w i l l be discussed. The questions subjects were asked in connection with the deductive problems f a l l into three categories: (1) Answer question; (2) Unanswerable questions that should be recognized as such; and (3) Questions that put the subject i n the position of having to judge the reasoned solutions of third parties. The j u s t i f i c a t i o n for the f i r s t class of questions i s only too obvious. As for those of the second category, the rationale is straightforward. Creatures with limited resources would do well to identify wrong questions i n order to avoid waste of time and effort. In short, a good problem solver discriminates. Finally, with regard to the third class of questions, i t seems quite legitimate to say that a good problem solver should be a good judge of the problem solving of others. Real world problem solving i s very often collaborative; proposals 118 are bandied about and must be judged. And in any case, a good problem solver learns from others, following their example i f not their advice. It i s submitted that the three kinds of questions described above together yield a measure of deductive problem solving that is superior to a measure which simply counts right answers. This being said, i t remains to present the two new problems, and to classify a l l 10 questions according to the scheme just given. The two problems, "Young Lawyer's Dilemma" and "Car 54" follow, then, and the complete l i s t of 10 questions related to the three problems w i l l be presented. YOUNG LAWYER'S DILEMMA You are a r t i c l i n g for a law firm, assisting a senior member, Mr. Bigg, in his representation of an important firm c l i e n t , Robinson. Mr. Bigg has delegated to you a particular task: to find out whether the Wexler line of cases apply to Robinson's situation. As usual, Bigg's given you a hard question and l i t t l e time to get the answer. In fact, you've only just finishing doing the library research when your intercom buzzes. Mr. Bigg wants the answer—now. On the way to his office the various things you've learned float before your mind as you try to come to a conclusion: does the Wexler line apply? From your research i t appears that: Either of two cases—Evans, or LockwoodT-should govern here. If the Lockwood case applies then the Wexler line of cases would seem to govern this point of law. But i f Evans applies then the Weatherby case on which i t relies would have to be considered good law, which forces you to consider the fact that Weatherby directly contradicts Conrad. You know very well that the Supreme Court recently cited Conrad with approval, indicating in no uncertain terms that i t (Conrad) i s 8 t i l l good law. 119 When you get to the office your boss has an unpleasant surprise for you. He has brought in the other legal intern, Roger Rival, i n order to see i f he draws the same conclusion-from your library research as you do. Accordingly, you f i r s t present your research findings, as given above, so that everyone knows what they're dealing with. But before you can of£er an opinion as to whether the Wexler line of cases apply, Roger Rival, always quicker on the draw than you, throws out his opinion "Well, of course my knowledge on this area is limited to what our junior colleague here has supplied us with, but I daresay the answer is clear enough. "Since they c o n f l i c t , we must reject Conrad or Weatherby. The Supreme Court, having done our work for us here, has seen f i t to affirm Conrad, thus implicitly rejecting Weatherby. Weatherby being no good Evans must not apply—since i t has been said that i f Evans applies Weatherby would have to be considered good law. At the outset we were told that the alternatives were Evans and Lockwood. Having ruled out Evans, that leaves Lockwood. Which brings us to our conclusion, for i f Lockwood applies, the Wexler line governs this point of law." Before you can open your mouth, Mr. Bigg opens his: "I don't follow you, Roger. It seems to me that ' i f Lockwood then Wexler' means ' i f not Wexler then not Lockwood'. Now, i f not Lockwood, then that leaves Evans. Evans, then, not the Wexler-Lockwood l i n e , must apply. What do you think?" Mr. Bigg's pointing at you, and you realize that he has again forgotten your name. You feel your face f l u s h i n g — you're on the spot! 120 "CAR 54: WHERE ARE WE?" PROBLEM You are the night d i s p a t c h e r f o r the p o l i c e mobile u n i t s . The men of Car 54 are l o s t , and have radioed you f o r help i n o r i e n t i n g themselves. A l l the r e l e v a n t i n f o r m a t i o n you possess regarding t h e i r c u r r e n t l o c a t i o n i s s t a t e d below. Making use only of t h i s i n f o r m a t i o n — a l l of which you can assume to be t r u e — t r y to determine where Car 54 must be. 1. I f and only i f they took. Arbor Road are they on Grand. 2 . They e i t h e r took Arbor Road or they took the Bypass—though i t ' s p o s s i b l e they took both. 3. They e i t h e r missed the Bypass or they went through the tunnel under the r i v e r , though of course they could have missed the Bypass and gone through the t u n n e l . 4. I f they took the Detour, then they couldn't have gone through the tunnel under the r i v e r . 5. I f they took the Express, then i t f o l l o w s that they took the Detour and passed under the b r i d g e . 6. I f they're not on Grand then they must have taken the Express. 121 The Q u e s t i o n s Young L a w y e r ' 8 Dilemma• (1) Does t h e W e x l e r l i n e o f c a s e s a p p l y ? YES NO The c o r r e c t answer t o t h i s q u e s t i o n i s y e s . C l e a r l y t h i s i s an example o f what I r e f e r t o as an "answer q u e s t i o n " . (2) I s Roger R i v a l ' s r e a s o n i n g sound? YES NO (3) I s Mr. B i g g ' s r e a s o n i n g sound? YES NO Q u e s t i o n s (2) and (3) f a l l i n t h e c a t e g o r y o f a s s e s s i n g t h e s u b j e c t ' s a b i l i t y t o j u d g e t h e s o l u t i o n s o f o t h e r s . I n t h i s c a s e ( 2 ) ' s answer i s y e s , and ( 3 ) ' s i s no. Car 54. (1) J o e t a c k l e d t h e C a r 54 p r o b l e m i n t h i s way: " J u s t s u p p o s e , " he t h o u g h t , " I assume t h e y ' r e n o t on G r a n d . " Of c o u r s e J o e d i d n ' t know w h e t h e r o r n o t t h e y were'on G r a n d , b u t he j u s t d e c i d e d t o assume t h e y were n o t on G r a n d , t o see how t h a t a s s u m p t i o n f i t t h e i n f o r m a t i o n he'd been g i v e n i n t h e p r o b l e m . So J o e assumed t h e y were n o t on G r a n d , and on t h a t b a s i s c a r e f u l l y w o r k e d t h r o u g h t o t h e i d e a t h a t t h e y must be...on G r a n d ! He was p u z z l e d , when he t h o u g h t a bout where he'd s t a r t e d h i s l i n e o f r e a s o n i n g , and where he'd ended up, b u t he f i g u r e d t h a t i t . m u s t mean t h e y r e a l l y were on G r a n d , and he gave t h a t 122 as his answer. QUESTION: Is Joe RIGHT or WRONG ? The answer to this question is "right", of course, for the description of Joe's solution is a clear description of one of the forms of RAD discussed at page 61 in the text. This question gets at the subject's a b i l i t y to understand and appreciate this important problem solving technique. (2) Mary had a somewhat different approach to Car 54. She started off by supposing that the men must be on Grand. "Well," she thought, "started off assuming, just to get the b a l l r o l l i n g , that they were on Grand, and that never led me to infer that they're not on Grand, so I^ust've proved that they are on Grand—that's the answer." QUESTION: Is Mary's conclusion JUSTIFIED pr UNJUSTIFIED ? Mary's conclusion is unjustified, for i t is possible that the question i s undecidable. To return to one's starting assumption i s to commit the fallacy of circular reasoning, a fallacy to be recognized and shunned by the good problem solver. (3) Sam's point of departure was identical to Joe's: he started off by assuming "maybe they're not on Grand," and then tried to see where that assumption would take him. And where did i t lead him? Well, he was rather surprised to find that, on the one hand, assuming they're not on Grand leads one to 123 i n f e r t h a t t h e y d i d n ' t t a k e t h e D e t o u r , w h i l e , on the o t h e r hand, t h a t same a s s u m p t i o n l e a d s one t o i n f e r t h a t t h e y d i d t a k e the D e t o u r ! He wasn't s u r e what t o make o f the f a c t t h a t he'd p r o d u c e d a c o n t r a d i c t i o n by ass u m i n g t h e men w e r e n ' t on G r a n d , and i t made h i m c o n c l u d e t h a t t h e p r o b l e m was n o t l o g i c a l l y s o l v a b l e a t a l l . QUESTION: I s Sam's c o n c l u s i o n J U S T I F I E D o r UNJUSTIFIED ? A g a i n , t h i s i s a q u e s t i o n g e t t i n g a t a s u b j e c t ' s u n d e r s t a n d i n g o f RAD. But i t a l s o t e s t s t h e s u b j e c t ' s awareness o f when and why a q u e s t i o n c a n be r e j e c t e d as u n a n s w e r a b l e . T h i s i s , o f c o u r s e , an a n s w e r a b l e p r o b l e m , and Sam has drawn t h e wrong c o n c l u s i o n f r o m a s u c c e s s f u l w o r k i n g o f RAD. T h i s q u e s t i o n f a l l i n b o t h c a t e g o r i e s (2) and (3) s k e t c h e d above. ( 4 ) A r e t h e y on Grand? YES NO UNDECIDABLE Q u e s t i o n (4) i s t h e "answer" q u e s t i o n o f " C a r 54" and c o r r e s p o n d s e x a c t l y t o t h e answer q u e s t i o n o f "You Be t h e J u d g e " . The answer i s y e s . (5) D i d t h e y t a k e t h e B y p a s s ? YES NO UNDECIDABLE T h i s i s an u n a n s w e r a b l e q u e s t i o n , c o r r e s p o n d i n g e x a c t l y t o t h e q u e s t i o n a b o u t t h e t r a n s a c t i o n r e c o r d i n "You Be the J u d g e " . 124 APPENDIX V: KENDALL'S TAU--AN ALTERNATIVE CORRELATIONAL STATISTIC The P e a r s o n _r c o r r e l a t i o n c o e f f i c i e n t i s a s t a t i s t i c i n t e n d e d f o r use on i n t e r v a l l e v e l d a t a . In p s y c h o l o g i c a l r e s e a r c h d a t a i s o f t e n o b t a i n e d which f a l l s somewhere between i n t e r v a l and o r d i n a l l e v e l s o f measurement. I n such c a s e s the P e a r s o n r_ i s t y p i c a l l y used. An example o f a p s y c h o l o g i c a l measure w h i c h i s n o t q u i t e i n t e r v a l i n c h a r a c t e r i s the f a m i l i a r I.Q. However, a l t h o u g h the I.Q. may not meet s t r i c t s t a n d a r d s o f i n t e r v a l l e v e l measurement, t h e r e a r e numerous s t u d i e s i n the l i t e r a t u r e r e p o r t i n g P e a r s o n r_ c o r r e l a t i o n s i n v o l v i n g I.Q. I t seems t h a t the measures taken o f the v a r i a b l e s o f l o g i c a l i t y i n t h i s t h e s i s f a l l w i t h i n t h i s g r a y a r e a between o r d i n a l and i n t e r v a l d a t a . These measures a r e p r o b a b l y q u i t e c l o s e to the I.Q. i n t h i s r e s p e c t , and, f o l l o w i n g p r e c e d e n t , I have gone ahead and used the P e a r s o n _r as my c h i e f d e s c r i p t i v e s t a t i s t i c . .However, I have a l s o computed c o r r e l a t i o n s f o r our v a r i a b l e s u s i n g a s t a t i s t i c i n t e n d e d f o r use on o r d i n a l l e v e l d a t a . T h i s s t a t i s t i c , the K e n d a l l Tau, i s not an o r d i n a l l e v e l v e r s i o n o f a P e a r s o n _r, as G l a s s & S t a n l e y (19 70; e mphasize. I t i s , i n f a c t , "one o f the few b a s i c a l l y new 125 approaches to s t a t i s t i c a l d e s c r i p t i o n i n modern t i m e s " ( G l a s s & S t a n l e y , p.176). Those who have qualms about u s i n g an i n t e r v a l l e v e l s t a t i s t i c l i k e the P e a r s o n _r on d a t a t h a t i s p r o b a b l y not q u i t e i n t e r v a l l e v e l may be more c o m f o r t a b l e w i t h the K e n d a l l T a u — a l t h o u g h i t t u r n s out to y i e l d a c o r r e l a t i o n m a t r i x p r a c t i c a l l y i d e n t i c a l to t h a t o f the P e a r s o n _r. But 'there i s an i n t e r e s t i n g i n t e r p r e t a t i o n f o r K e n d a l l ' s Tau f o r which t h e r e i s n o t h i n g comparable i n the c a s e o f P e a r s o n _r o r i t s r e l a t i v e s , as w i l l be s e e n below. F i r s t , the c o r r e l a t i o n m a t r i x i t s e l f , which i s b a s e d on o b s e r v e d r a n k s o f s u b j e c t s on the s e v e r a l v a r i a b l e s : L o g i c a l L o g i c a l P r o b l e m I n t u i t i o n Judgment S o l v i n g TL ° g i c a l 1.00 I n t u i t i o n L o g i c a l Judgment ^ r f l e m +.15 +.11 1.00 S o l v i n g **p<.02 Of the t h r e e c o r r e l a t i o n s , o n l y the L o g i c a l I n t u i t i o n : L o g i c a l Judgment c o r r e l a t i o n i s s t a t i s t i c a l l y s i g n i f i c a n t (z=2.13). We thus may impute to the p o p u l a t i o n c o r r e s p o n d i n g to our sample a s i g n i f i c a n t a s s o c i a t i o n ( p o s i t i v e i n d i r e c t i o n ) between the l o g i c a l i n t u i t i o n and l o g i c a l judgment a b i l i t i e s . 126 K e n d a l l ' s Tau p e r m i t s o f a f u r t h e r i n t e r p r e t a t i o n , however. " I f two p e r s o n s a r e drawn a t random (by chance) from the group o f n, the d i f f e r e n c e between the p r o b a b i l i t y t h a t they w i l l have the same o r d e r on b o t h X and Y and the p r o b a b i l i t y t h a t they w i l l have d i f f e r e n t o r d e r s on X and Y i s e q u a l to the v a l u e o f Tau. M a t h e m a t i c a l s t a t i s t i c i a n s f i n d t h i s a p a r t i c u l a r l y p l e a s i n g p r o p e r t y f o r such a c o e f f i c i e n t to have..." ( G l a s s & S t a n l e y , 19 70, p.178). F o r any p a i r o f s u b j e c t s , they c o u l d have the same o r d e r i n the se n s e t h a t one i s h i g h e r r a n k e d than the o t h e r on b o t h measures i n v o l v e d , o r they c o u l d complement one a n o t h e r such t h a t each has a h i g h e r rank th an the o t h e r on one measure. The l a t t e r c ase i s termed one o f d i f f e r e n t o r d e r . Drawing on o u r a c t u a l sample, I f i n d t h a t s u b j e c t s #17 and #4 a r e same o r d e r e d : s u b j e c t #17 ranks 2nd i n l o g i c a l judgment and e q u a l 9 t h on l o g i c a l i n t u i t i o n , w h i l e //4 ranks e q u a l 9 t h on l o g i c a l judgment and e q u a l 18th on l o g i c a l i n t u i t i o n . S u b j e c t #17 thus i s h i g h e r r a n k e d on b o t h measures. On the o t h e r hand, s u b j e c t s #3 and #16 a r e d i f f e r e n t o r d e r e d : #3 ranks e q u a l 9 t h on l o g i c a l judgment and e q u a l 9 t h on l o g i c a l i n t u i t i o n . S u b j e c t #16, however, i s l o w e r r a n k e d on l o g i c a l judgment ( e q u a l 2 1 s t ) w h i l e h i g h e r r a n k e d on l o g i c a l i n t u i t i o n ( 1 s t ) . 127 K e n d a l l ' s Tau takes i n t o account a l l the p a i r w i s e combinations, c o n c i s e l y summarizing i n one f i g u r e the d i f f e r e n c e between the p r o b a b i l i t i e s o f there being d i f f e r e n t ordered o r same ordered p a i r s . D i c h o t o m i z i n g , we can say any p a i r of s u b j e c t s must be same or d i f f e r e n t ordered. So the p r o b a b i l i t y i s 1.00 that A and B are e i t h e r same or d i f f e r e n t ; that i s , i f S denotes the p r o b a b i l i t y they are the same, and D the p r o b a b i l i t y they are d i f f e r e n t , then S + D = 1.00. Now K e n d a l l ' s Tau happens to equal the d i f f e r e n c e between S and D. Th i s enables us to s o l v e f o r S or D, given the ap p r o p r i a t e Tau. K e n d a l l ' s Tau f o r the L o g i c a l I n t u i t i o n : L o g i c a l Judgment c o r r e l a t i o n i s +.32. S o l v i n g f o r S we f i n d i t s value to be .66. Th e r e f o r e , the chance that any randomly chosen p a i r of s u b j e c t s from our sample w i l l be same ordered i s .66. Given 100 p a i r s of s u b j e c t s , w i t h each s u b j e c t r a n k i n g h i g h e r on l o g i c a l judgment w i t h i n h i s p a i r being nominally i d e n t i f i e d as A, about 66 of the 100 As would have h i g h e r l o g i c a l i n t u i t i o n rank than t h e i r r e s p e c t i v e p a r t n e r s . This i s a reasonably s u c c i n c t and p r e c i s e way of c h a r a c t e r i z i n g j u s t how c l o s e l y these v a r i a b l e s hang toget h e r . 

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