Behaviorism to Cognition: A System-Theoretic Inquiry into Brains, Minds and Mechanism

NOT FOR QUOTATION WITHOUT THE PERMISSION OF THE AUTHOR

BEHAVlORISM TO COGNITION:

A

SYSt'EM-THEORITIC INQUIRY INTO BRAINS. _HINDS

AND

MEcHANBM

J o h n

L.

C a s t i

J u l y 1 9 8 5 VJP-85-49

P a p e r p r e p a r e d f o r presentation at t h e workshop on Brain R e s e a r c h , Cognition and Artificial Intelligence, t o be held in Abisko, Sweden, Yay 1986.

W o r k i n g P a p e r s a r e interim r e p o r t s on work of t h e International Institute f o r Applied Systems Analysis and have received only limited review. Views o r opinions e x p r e s s e d h e r e i n d o not necessarily r e p r e s e n t t h o s e of t h e Institute o r of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

ABSTRACT

Arguments f r o m mathematical system t h e o r y are used t o show t h a t t h e behaviorist-cognitivist d e b a t e in psychology i s a c t u a l l y a non-issue: abstractly, t h e two a r e e q u i v a l e n t ; b u t f r o m t h e s t a n d p o i n t of a p r e d i c t i v e , s c i e n t i f i c t h e o r y of b r a i n s a n d b e h a v i o r only t h e cognitivist p r o g r a m holds a n y promise.

A f t e r a b r i e f summary of t h e a l g e b r a i c t h e o r y of s y s t e m s , t h e p a p e r employs t h e s e a l g e b r a i c tools t o p r o p o s e a functional means b y which a b r a i n (human o r a r t i f i c i a l ) may compactly s t o r e a n d r e t r i e v e information. This scheme is t h e n e x t e n d e d to p r o v i d e a means f o r t h e g e n e r a t i o n of t h o u g h t s a n d emotions, as well.

Finally, t h e p a p e r concludes with a discussion of t h e i n t e r c o n n e c t i o n s between t h e b r a i n model s u g g e s t e d h e r e a n d a number of o t h e r models p r o p o s e d in t h e l i t e r a t u r e .

1. Introduction

In t h e e a r l y 19'70s, t h e r e w a s a brief f l u r r y of a c t i v i t y d i r e c t e d toward t h e t r a n s c r i p t i o n of c l a s s i c a l system t h e o r y into t h e terminology of c a t e g o r y t h e o r y . One of t h e c o n s e q u e n c e s of t h e s e e f f o r t s w a s a p a r t i c u l a r l y c l e a r and e x p l i c i t cla- r i f i c a t i o n of t h e r e l a t i o n s h i p between a n input/output a n d a s t a t e - v a r i a b l e d e s c r i p t i o n of a dynamical p r o c e s s . In c a t e g o r y - t h e o r e t i c t e r m s , t h e y are adjoints. Thus, with e a c h input/output d e s c r i p t i o n t h e r e i s automatically associ- a t e d a natural s t a t e - v a r i a b l e d e s c r i p t i o n , a n d c o n v e r s e l y . In t h i s s e n s e , t h e two d e s c r i p t i o n s a r e a b s t r a c t l y equivalent.

Having b e e n sensitized by a c e r t a i n amount of r e a d i n g a n d a s t r o n g p e r s o n a l i n t e r e s t in problems of mind a n d human psychology, when I f i r s t e n c o u n t e r e d t h e duality between e x t e r n a l and i n t e r n a l system d e s c r i p t i o n s , my immediate t h o u g h t w a s t h a t s u c h a r e s u l t w a s a systems version of t h e behaviorist-cognitivist s p l i t in psychology, a n d t h a t p e r h a p s t h e system c o n c e p t s would p r o v i d e a framework f o r c o n s i d e r a t i o n of t h i s dichotomy in more formal a n d p r e c i s e t e r m s . During t h e p a s t d e c a d e I h a v e had o c c a s i o n to periodically r e - c o n s i d e r t h i s duality, e a c h time a r m e d with somewhat more powerful s y s t e m - t h e o r e t i c tools provided by t h e sub- s t a n t i a l a d v a n c e s in mathematicz! syslerr. c;'er t h i s period. The e c c a s i o n of t h i s meeting at t h e systems i n t e r f a c e between b r a i n r e s e a r c h , cognitive psychol- ogy a n d a r t i f i c i a l intelligence p r o v i d e s t h e o p p o r t u n i t y t o p u t f o r w a r d what amounts t o a model f o r abstract thought p r o c e s s e s . The d e t a i l s of t h e f r a m e w o r k p r e s e n t e d h e r e are almost s u r e t o b e wrong; n o n e t h e l e s s , I would be g r e a t l y ( b u t not unhappily) s u r p r i s e d if when t h e final word i s written o n t h e s t r u c t u r e of t h e b r a i n , t h e g e n e r a l c o n c e p t s p r e s e n t e d h e r e d o not p r o v e to b e t h e foundation upon which a working t h e o r y of any b r a i n , real o r a r t i f i c i a l , i s c o n s t r u c t e d .

The b a s i c questions t h a t t h e p a p e r a d d r e s s e s a r e :

1) d o i n t e r n a l cognitive s t a t e s e x i s t ;

ii) if t h e y do, in what way d o t h e y s t o r e e x p e r i e n c e s as memory;

iii) how d o s u c h cognitive s t a t e s i n t e r a c t to p r o d u c e t h o u g h t s ;

iv) i s i t p o s s i b l e f o r a r t i f i c i a l d e v i c e s l i k e c o m p u t e r s a n d non-neuronal i n t e l l i g e n c e s to h a v e mental s t a t e s , or are s u c h s t a t e s uniquely c h a r a c - t e r i s t i c of human b r a i n s ?

The mathematical s t r u c t u r e p r e s e n t e d h e r e p r o v i d e s a framework f o r t h e a b s t r a c t c o n s i d e r a t i o n of t h e s e m a t t e r s . T h e i r i n t e r p r e t a t i o n f o r real p h y s i c a l b r a i n s r e m a i n s a t o p i c f o r f u t u r e r e s e a r c h .

B e f o r e moving o n , I want to emphasize t h a t t h i s p a p e r i s n o t a n a t t a c k o n behaviorism; o n t h e o n e hand. i t ' s f r u i t l e s s to b e a t a d e a d ( o r , at l e a s t , dying) h o r s e , while o n t h e o t h e r hand t h e s y s t e m - t h e o r e t i c a r g u m e n t s given h e r e s t r e n g t h e n t h e b e h a v i o r i s t school, a t least to t h e d e g r e e t h a t t h e y show t h a t a b s t r a c t l y behaviorism a n d a b s t r a c t cognition a r e t w o s i d e s of t h e same coin. One s i d e c o n t a i n s mental s t a t e s ; t h e o t h e r doesn't. But t h e coin c a n n o t b e s p l i t a p a r t a n d t h e t w o h a l v e s s e p a r a t e d . The b e s t we c a n d o i s to view i t o n e s i d e at a time.

Our p r i n c i p a l a r g u m e n t i s t h a t o n e view i s m o r e u s q f u l t h a n t h e o t h e r , n o t m o r e

" c o r r e c t " .

2. B e h a v i o r i s m . Structuralism and S y s t e m M o d e l s

Stimulated by t h e g e n e r a l philosophical i d e a of logical positivism which w a s in vogue at t h e time, in t h e early-1920s John Watson made t h e r a d i c a l s u g g e s t i o n t h a t b e h a v i o r d o e s n o t h a v e mental c a u s e s . This t h e s i s , f u r t h e r d e v e l o p e d a n d modified by Hull, S k i n n e r a n d o t h e r s , h a s come to b e t e r m e d p s y c h o l o g i c d b e h a v i o r i s m . A p r i n c i p a l motivation f o r adoption of t h e b e h a v i o r i s t view was to r i d psychology of t h e d u a l i s t a t t i t u d e t h a t mind i s a non-physical e n t i t y , somehow disjoint f r o m t h e p h y s i c a l b r a i n . The b e h a v i o r i s t solution i s t o eliminate all notions of mind, mental

s t a t e s a n d mental r e p r e s e n t a t i o n f r o m psychological i n v e s t i g a t i o n , c o n c e n t r a t i n g solely upon e x t e r n a l l y o b s e r v a b l e s t i m u l u s - r e s p o n s e b e h a v i o r p a t t e r n s .

By t h e early-1960s, i t was r e c o g n i z e d t h a t both t h e d u a l i s t a n d t h e b e h a v i o r i s t a p p r o a c h to human b e h a v i o r w e r e u n a t t r a c t i v e , a n d effort was f o c u s e d upon developing a m a t e r i a l i s t t h e o r y of mind t h a t allowed f o r mental c a u s e s . One s u c h t h e o r y , t e r m e d logical b e h a v i o r i s m , was q u i t e s i m i l a r to c l a s s i c a l behaviorism a n d i s r e a l l y just c l a s s i c a l b e h a v i o r i s m in a s e m a n t i c form. Another t h e o r y , c e n t r d - s t a t e i d e n t i t y , p o s t u l a t e s t h a t mental e v e n t s , states a n d p r o c e s s e s a r e identical with n e u r o p h y s i o l o g i c a l e v e n t s in t h e b r a i n . Thus, u n d e r t h e c e n t r a l - state identity t h e o r y , a b e h a v i o r a l e f f e c t i s t h e r e s u l t of a c a u s a l p a t t e r n of physi- cal e v e n t s in t h e b r a i n . The p r o b l e m with t h e c e n t r a l - s t a t e identity notion i s t h a t in e i t h e r i t s weak o r i t s s t r o n g f o r m , t o k e n a n d t y p e p h y s i c d i s m , r e s p . , i t asserts t h a t a l l mental p a r t i c u l a r s t h a t e x i s t o r could e v e r e x i s t are neurophysiological.

Thus. t h e logical possibility of machines a n d o t h e r disembodied s p i r i t s having men- tal p r o p e r t i e s i s r u l e d o u t b e c a u s e t h e y are n o t composed of n e u r o n s .

During t h e last d e c a d e o r s o , a way o u t of t h e s e dilemmas h a s b e e n p r o v i d e d by t h e t h e o r y of f u n c t i o n a l i s m , a n o u t g r o w t h of t h a t amalgam of p h y s i c s , neuro- physiology, c o m p u t e r s c i e n c e a n d psychology loosely l a b e l e d , "cognitive science."

Functionalism is b a s e d upon t h e i d e a t h a t a mental s t a t e c a n b e defined by i t s c a u s a l r e l a t i o n s to o t h e r mental states a n d t h a t s u c h mental states c a n , b o t h in p r i n c i p l e a n d in d e e d , b e r e a l i z e d b y many systems. In e s s e n c e , b e h a v i o r i s d r i v e n b y s o f t w a r e , n o t h a r d w a r e . A v e r y r e a d a b l e a c c o u n t of t h e s e v a r i o u s notions i s given in t h e p o p u l a r a r t i c l e b y Fodor [I] o r t h e b o o k s [2,3,22]. S i n c e i t will not b e n e c e s s a r y f o r u s to distinguish between t h e c e n t r a l - s t a t e i d e n t i t y t h e o r y a n d func- tionalism, we a d o p t t h e g e n e r i c t e r m s t r u c t u r a l i s m to r e p r e s e n t a n y t h e o r y of t h e mind t h a t involves p h y s i c a l mental s t a t e s , b e t h e y manifested in a human b r a i n , a disembodied cloud f r o m s p a c e o r a collection of silicon w a f e r s in a machine.

The p r i n c i p a l aim of t h i s p a p e r is Lo p r o v i d e a p r e c i s e , s y s t e m - t h e o r e t i c argument f o r a s s e r t i n g t h e a b s t r a c t equivalence of behaviorism a n d s t r u c t u r a l i s m , while at t h e same time showing t h a t o p e r a t i o n a l l y only t h e s t r u c t u r a l i s t view o f f e r s t h e basis f o r a p r e d i c t i v e , c a u s a l view of human b e h a v i o r . Such a conclu- sion i s a n a t u r a l c o n s e q u e n c e of t h e so-called Realization Theorem of mathematical system t h e o r y . Following t h e p a t h laid out by t h e s t r u c t u r a l i s t f r a m e w o r k , w e t h e n p r o v i d e a f a i r l y d e t a i l e d mathematical d e s c r i p t i o n of t h e way i n which a ' b r a i n "

would p r o c e s s a n d s t o r e e x t e r n a l stimuli in o r d e r t o g e n e r a t e o b s e r v e d b e h a v i o r a l r e s p o n s e s . The p a p e r t h e n c o n c l u d e s with some s p e c u l a t i o n s b a s e d upon t h e t h e o r y of system i n v a r i a n t s f o r how thoughts are g e n e r a t e d as c o n s e q u e n c e s of i n t e r n a l system dynamics.

3. Stimulus-Response Patterns and External System Modeb

Let us imagine o u r information-processing o b j e c t 0 (human being, machine.

cloud, ...) as consisting of t h e p r o v e r b i a l "black-box" c o n n e c t e d t o i t s environment by c e r t a i n input a n d o u t p u t c h a n n e l s (Fig. 1). Assume t h a t at a n y given moment t , t h e stimulus u ( t ) i s s e l e c t e d f r o m some set of symbols U , while t h e o b s e r v e d r e s p o n s e at t h a t moment, y ( t ) , belongs

to

a n o t h e r set of symbols Y. To simplify t h e exposition, assume t h a t

t

t a k e s on only t h e d i s c r e t e v a l u e s t

=

0,1,2. ^o

.

Figure 1. Information p r o c e s s i n g o b j e c t .

Then a given stimulus-response p a t t e r n of 0 ,

Bo,

i s r e p r e s e n t e d by t h e sequence

Bo =

^{( U} ( t ) , y ( t ) ) , t

=

0 , 1 , 2 ,

. . .

If we let

II

d e n o t e t h e set of all possible stimuli sequences, with

l?

r e p r e s e n t i n g t h e s e t of all r e s p o n s e sequences, t h e n t h e overall e z t e r n a l b e h a v i o r of t h e o b j e c t 0 c a n b e denoted by a stimulus-response map

where

while

7

= tu

( 0 1 , ~ ( l ) , ~

. . . 1

, Y E ~ y ( . ) r Y . ,

According t o t h e behaviorists, all t h a t c a n e v e r b e known a b o u t 0 are t h e s e t s

n

^and

^l?,

t o g e t h e r with t h e map

I.

The e n t i r e c o n t e n t of t h e behaviorist p r o g r a m is t o determine

I,

given

R

and

r,

without postulating any i n t e r n a l mechanisms inside t h e box. Or, p u t a n o t h e r way, a behaviorist would claim t h a t t o b e given

I

would b e t o b e given e v e r y t h i n g t h a t could b e known about t h e disposition of t h e o b j e c t t o behave in a c e r t a i n way, and t h a t i t would b e nonscientific t o a s s e r t t h e existence of any unobservable internal mechanism g e n e r a t i n g

I.

Mathematical system t h e o r y provides a n honest, t r u e , c l e a r and d i r e c t r e f u t a t i o n of this claim.

4. Cognitive States and Internal Models

An i n t e r n a l model

C

of t h e behavioral p a t t e r n involves postulating t h e existence of a set X of i n t e r n a l s t a t e v a r i a b l e s , a n d a dynamic relationship g link- ing t h e stimuli u a n d t h e s t a t e s , a s w e l l a s a r u l e h specifying how i n t e r n a l s t a t e s combine to g e n e r a t e t h e r e s p o n s e y . More compactly, w e h a v e

z ( t ) E X , u ( t ) E U , y ( t ) E Y . W e would then s a y t h a t

C

Is a n Internal model of t h e observed b e h a v i o r

I

if t h e stimulus-response p a t t e r n

B E = Bo,

I.e., If t h e

observed input-output b e h a v i o r of

C

a g r e e s with t h a t of 0. Note t h a t in o r d e r f o r

B E = Bo,

i t is n e c e s s a r y to c o n s t r u c t an a p p r o p r i a t e set X , t o g e t h e r with a p p r o p r i a t e maps

From a n a b s t r a c t point of view, t h e f i r s t s t e p in t h e s t r u c t u r a l i s t program is t o e n s u r e t h a t f o r any given e x t e r n a l model 0

= ( R , r J ) ,

a c o r r e s p o n d i n g internal model

C =

(X,g , A ) exists. If t h i s is t h e c a s e , t h e n i t would b e n a t u r a l to associate t h e a b s t r a c t states X with t h e postulated physical states of t h e b r a i n in some fashion, while at t h e same time i n t e r p r e t i n g t h e maps g and h as means for encod- ing and decoding e x t e r n a l stimuli and mental states, respectively. I t is one of t h e g r e a t triumphs of mathematical system t h e o r y to h a v e been a b l e t o provide a r a t h e r definitive resolution of t h i s question, happily in t h e affirmative. The remainder of t h e p a p e r i s devoted t o a n account of t h i s solution in t h e above con- t e x t , t o g e t h e r with a detailed exposition of how t h e encoding/decoding o p e r a t i o n s are explicitly c a r r i e d out, followed by some semi-speculative discussion of t h e p r o c e s s of cognition from a systems p e r s p e c t i v e .

5. Realizations and Canonical Models

Loosely speaking, w e c a n p h r a s e t h e b e h a v i o r i s t - s t r u c t u r a l i s t problem as fol- lows:

G i v e n a s t i m u l u s - r e s p o n s e p a t t e r n

Bo,

f i n d a "good" i n t e r n a l model

C

s u c h t h a t

Bo = BE.

The c a t c h in t h e a b o v e statement is t h e qualifying condition t h a t t h e model

C

b e

"good." I t t u r n s out t h a t without imposition of t h i s condition t h e solution to t h e problem is trivially easy: t h e r e a r e a n infinite number of models

C =

CY,g , h ) such