A

Computational

Foundation

for

the

Study

of

Cognition

David

J.

Chalmers

Department

of

Philosophy

Washington

University

St.

Louis

Missouri

dave@twinearth.wustl.edu

May

Short

abstract

Computation

is

central

to

the

foundations

of

modern

cognitive

science

but

its

role

is

controversial

Questions

about

computation

abound

What

is

it

for

a

physical

system

to

implement

a

computation

Is

computation

sufficient

for

thought

What

is

the

role

of

computation

in

a

theory

of

cognition

What

is

the

relation

between

different

sorts

of

computational

theory

such

as

connectionism

and

symbolic

computation

This

article

develops

a

systematic

framework

that

addresses

all

of

these

questions

A

careful

analysis

of

computation

and

its

relation

to

cognition

suggests

that

the

ambitions

of

artificial

intelligence

and

the

centrality

of

computation

in

cognitive

science

are

justified

Long

abstract

Computation

is

central

to

the

foundations

of

modern

cognitive

science

but

its

role

is

controversial

Questions

about

computation

abound

What

is

it

for

a

physical

system

to

implement

a

computation

Is

computation

sufficient

for

thought

What

is

the

role

of

computation

in

a

theory

of

cognition

What

is

the

relation

between

different

sorts

of

computational

theory

such

as

connectionism

and

symbolic

computation

In

this

paper

I

develop

a

systematic

framework

that

addresses

all

of

these

questions

Justifying

the

role

of

computation

requires

analysis

of

implementation

the

nexus

between

abstract

computations

and

concrete

physical

systems

I

give

such

an

analysis

based

on

the

idea

that

a

system

implements

a

computation

if

the

causal

structure

of

the

system

mirrors

the

formal

structure

of

the

computation

This

account

can

be

used

to

justify

the

central

commitments

of

artificial

intelligence

and

computational

cognitive

science

the

thesis

of

computational

sufficiency

which

holds

that

the

right

kind

of

computational

structure

suffices

for

the

possession

of

a

mind

and

the

thesis

of

computational

explanation

which

holds

that

computation

provides

a

general

framework

for

the

explanation

of

cognitive

processes

The

theses

are

consequences

of

the

facts

that

-LRB-

a

-RRB-

computation

can

specify

general

patterns

of

causal

organization

and

-LRB-

b

-RRB-

mentality

is

an

organizational

invariant

rooted

in

such

patterns

Along

the

way

I

answer

various

challenges

to

the

computationalist

position

such

as

those

put

forward

by

Searle

I

close

by

advocating

a

kind

of

minimal

computationalism

compatible

with

a

very

wide

variety

of

empirical

approaches

to

the

mind

This

allows

computation

to

serve

as

a

true

foundation

for

cognitive

science

Introduction

Perhaps

no

concept

is

more

central

to

the

foundations

of

modern

cognitive

science

than

that

of

computation

The

ambitions

of

artificial

intelligence

rest

on

a

computational

framework

and

in

other

areas

of

cognitive

science

models

of

cognitive

processes

are

most

frequently

cast

in

computational

terms

The

foundational

role

of

computation

can

be

expressed

in

two

basic

theses

First

underlying

the

belief

in

the

possibility

of

artificial

intelligence

there

is

a

thesis

of

computational

sufficiency

stating

that

the

right

kind

of

computational

structure

suffices

for

the

possession

of

a

mind

and

for

the

possession

of

a

wide

variety

of

mental

properties

Second

facilitating

the

progress

of

cognitive

science

more

generally

there

is

a

thesis

of

computational

explanation

stating

that

computation

provides

a

general

framework

for

the

explanation

of

cognitive

processes

and

of

behavior

These

theses

are

widely

held

within

cognitive

science

but

they

are

quite

controversial

Some

have

questioned

the

thesis

of

computational

sufficiency

arguing

that

certain

human

abilities

could

never

be

duplicated

computationally

-LRB-

Dreyfus

Penrose

-RRB-

or

that

even

if

a

computation

could

duplicate

human

abilities

instantiating

the

relevant

computation

would

not

suffice

for

the

possession

of

a

mind

-LRB-

Searle

-RRB-

Others

have

questioned

the

thesis

of

computational

explanation

arguing

that

computation

provides

an

inappropriate

framework

for

the

explanation

of

cognitive

processes

-LRB-

Edelman

Gibson

-RRB-

or

even

that

computational

descriptions

of

a

system

are

vacuous

-LRB-

Searle

-RRB-

Advocates

of

computational

cognitive

science

have

done

their

best

to

repel

these

negative

critiques

but

the

positive

justification

for

the

foundational

theses

remains

murky

at

best

Why

should

computation

rather

than

some

other

technical

notion

play

this

foundational

role

And

why

should

there

be

the

intimate

link

between

computation

and

cognition

that

the

theses

suppose

In

this

paper

I

will

develop

a

framework

that

can

answer

these

questions

and

justify

the

two

foundational

theses

In

order

for

the

foundation

to

be

stable

the

notion

of

computation

itself

has

to

be

clarified

The

mathematical

theory

of

computation

in

the

abstract

is

well-understood

but

cognitive

science

and

artificial

intelligence

ultimately

deal

with

physical

systems

A

bridge

between

these

systems

and

the

abstract

theory

of

computation

is

required

Specifically

we

need

a

theory

of

implementation

the

relation

that

holds

between

an

abstract

computational

object

-LRB-

a

computation

for

short

-RRB-

and

a

physical

system

such

that

we

can

say

that

in

some

sense

the

system

realizes

the

computation

and

that

the

computation

describes

the

system

We

can

not

justify

the

foundational

role

of

computation

without

first

answering

the

question

What

are

the

conditions

under

which

a

physical

system

implements

a

given

computation

Searle

-LRB-

-RRB-

has

argued

that

there

is

no

objective

answer

to

this

question

and

that

any

given

system

can

be

seen

to

implement

any

computation

if

interpreted

appropriately

He

argues

for

instance

that

his

wall

can

be

seen

to

implement

the

Wordstar

program

I

will

argue

that

there

is

no

reason

for

such

pessimism

and

that

objective

conditions

can

be

straightforwardly

spelled

out

Once

a

theory

of

implementation

has

been

provided

we

can

use

it

to

answer

the

second

key

question

What

is

the

relationship

between

computation

and

cognition

The

answer

to

this

question

lies

in

the

fact

that

the

properties

of

a

physical

cognitive

system

that

are

relevant

to

its

implementing

certain

computations

as

given

in

the

answer

to

the

first

question

are

precisely

those

properties

in

virtue

of

which

-LRB-

a

-RRB-

the

system

possesses

mental

properties

and

-LRB-

b

-RRB-

the

system

's

cognitive

processes

can

be

explained

The

computational

framework

developed

to

answer

the

first

question

can

therefore

be

used

to

justify

the

theses

of

computational

sufficiency

and

computational

explanation

In

addition

I

will

use

this

framework

to

answer

various

challenges

to

the

centrality

of

computation

and

to

clarify

some

difficult

questions

about

computation

and

its

role

in

cognitive

science

In

this

way

we

can

see

that

the

foundations

of

artificial

intelligence

and

computational

cognitive

science

are

solid

A

theory

of

implementation

The

short

answer

to

question

-LRB-

-RRB-

is

straightforward

It

goes

as

follows

A

physical

system

implements

a

given

computation

when

the

causal

structure

of

the

physical

system

mirrors

the

formal

structure

of

the

computation

In

a

little

more

detail

this

comes

to

A

physical

system

implements

a

given

computation

when

there

exists

a

grouping

of

physical

states

of

the

system

into

state-types

and

a

one-to-one

mapping

from

formal

states

of

the

computation

to

physical

state-types

such

that

formal

states

related

by

an

abstract

state-transition

relation

are

mapped

onto

physical

state-types

related

by

a

corresponding

causal

state-transition

relation

This

is

still

a

little

vague

To

spell

it

out

fully

we

must

specify

the

class

of

computations

in

question

Computations

are

generally

specified

relative

to

some

formalism

and

there

is

a

wide

variety

of

formalisms

these

include

Turing

machines

Pascal

programs

cellular

automata

and

neural

networks

among

others

The

story

about

implementation

is

similar

for

each

of

these

only

the

details

differ

All

of

these

can

be

subsumed

under

the

class

of

combinatorial-state

automata

-LRB-

CSAs

-RRB-

which

I

will

outline

shortly

but

for

the

purposes

of

illustration

I

will

first

deal

with

the

special

case

of

simple

finite-state

automata

-LRB-

FSAs

-RRB-

An

FSA

is

specified

by

giving

a

set

of

input

states

Ik

a

set

of

internal

states

Sm

and

a

set

of

output

states

On

along

with

a

set

of

state-transition

relations

of

the

form

-LRB-

S

I

-RRB-

-LRB-

-RRB-

for

each

pair

-LRB-

S

I

-RRB-

of

internal

states

and

input

states

where

and

are

an

internal

state

and

an

output

state

respectively

S

and

I

can

be

thought

of

as

the

old

internal

state

and

the

input

at

a

given

time

is

the

new

internal

state

and

is

the

output

produced

at

that

time

-LRB-

There

are

some

variations

in

the

ways

this

can

be

spelled

out?e.g

one

need

not

include

outputs

at

each

time

step

and

it

is

common

to

designate

some

internal

state

as

a

final

state?but

these

variations

are

unimportant

for

our

purposes

-RRB-

The

conditions

for

the

implementation

of

an

FSA

are

the

following

A

physical

system

P

implements

an

FSA

M

if

there

is

a

mapping

f

that

maps

internal

states

of

P

to

internal

states

of

M

inputs

to

P

to

input

states

of

M

and

outputs

of

P

to

output

states

of

M

such

that

for

every

state-transition

relation

-LRB-

S

I

-RRB-

-LRB-

-RRB-

of

M

the

following

conditional

holds

if

P

is

in

internal

state

s

and

receiving

input

i

where

f

-LRB-

s

-RRB-

S

and

f

-LRB-

i

-RRB-

I

this

reliably

causes

it

to

enter

internal

state

and

produce

output

such

that

f

-LRB-

-RRB-

and

f

-LRB-

-RRB-

This

definition

uses

maximally

specific

physical

states

s

rather

than

the

grouped

state-types

referred

to

above

The

state-types

can

be

recovered

however

each

corresponds

to

a

set

fsjf

-LRB-

s

-RRB-

Sig

for

each

Si

M

From

here

we

can

see

that

the

definitions

are

equivalent

The

causal

relations

between

physical

state-types

will

precisely

mirror

the

abstract

relations

between

formal

states

There

is

a

lot

of

room

to

play

with

the

details

of

this

definition

For

instance

it

is

generally

useful

to

put

restrictions

on

the

way

that

inputs

and

outputs

to

the

system

map

onto

inputs

and

outputs

of

the

FSA

We

also

need

not

map

all

possible

internal

states

of

P

if

some

are

not

reachable

from

certain

initial

states

These

matters

are

unimportant

here

however

What

is

important

is

the

overall

form

of

the

definition

in

particular

the

way

it

ensures

that

the

formal

state-transitional

structure

of

the

computation

mirrors

the

causal

state-transitional

structure

of

the

physical

system

This

is

what

all

definitions

of

implementation

in

any

computational

formalism

will

have

in

common

Combinatorial-state

automata

Simple

finite-state

automata

are

unsatisfactory

for

many

purposes

due

to

the

monadic

nature

of

their

states

The

states

in

most

computational

formalisms

have

a

combinatorial

structure

a

cell

pattern

in

a

cellular

automaton

a

combination

of

tape-state

and

head-state

in

a

Turing

machine

variables

and

registers

in

a

Pascal

program

and

so

on

All

this

can

be

accommodated

within

the

framework

of

combinatorial-state

automata

-LRB-

CSAs

-RRB-

which

differ

from

FSAs

only

in

that

an

internal

state

is

specified

not

by

a

monadic

label

S

but

by

a

vector

-LSB-

The

elements

of

this

vector

can

be

thought

of

as

the

components

of

the

overall

state

such

as

the

cells

in

a

cellular

automaton

or

the

tape-squares

in

a

Turing

machine

There

are

a

finite

number

of

possible

values

Sij

for

each

element

Si

where

Sij

is

the

jth

possible

value

for

the

ith

element

These

values

can

be

thought

of

as

substates

Inputs

and

outputs

can

have

a

similar

sort

of

complex

structure

an

input

vector

is

-LSB-

Ik

-RSB-

and

so

on

State-transition

rules

are

determined

by

specifying

for

each

element

of

the

state-vector

a

function

by

which

its

new

state

depends

on

the

old

overall

state-vector

and

input-vector

and

the

same

for

each

element

of

the

output-vector

Input

and

output

vectors

are

always

finite

but

the

internal

state

vectors

can

be

either

finite

or

infinite

The

finite

case

is

simpler

and

is

all

that

is

required

for

any

practical

purposes

Even

if

we

are

dealing

with

Turing

machines

a

Turing

machine

with

a

tape

limited

to

squares

will

certainly

be

all

that

is

required

for

simulation

or

emulation

within

cognitive

science

and

AI

The

infinite

case

can

be

spelled

out

in

an

analogous

fashion

however

The

main

complication

is

that

restrictions

have

to

be

placed

on

the

vectors

and

dependency

rules

so

that

these

do

not

encode

an

infinite

amount

of

information

This

is

not

too

difficult

but

I

will

not

go

into

details

here

The

conditions

under

which

a

physical

system

implements

a

CSA

are

analogous

to

those

for

an

FSA

The

main

difference

is

that

internal

states

of

the

system

need

to

be

specified

as

vectors

where

each

element

of

the

vector

corresponds

to

an

independent

element

of

the

physical

system

A

natural

requirement

for

such

a

vectorization

is

that

each

element

correspond

to

a

distinct

physical

region

within

the

system

although

there

may

be

other

alternatives

The

same

goes

for

the

complex

structure

of

inputs

and

outputs

The

system

implements

a

given

CSA

if

there

exists

such

a

vectorization

of

states

of

the

system

and

a

mapping

from

elements

of

those

vectors

onto

corresponding

elements

of

the

vectors

of

the

CSA

such

that

the

state-transition

relations

are

isomorphic

in

the

obvious

way

The

details

can

be

filled

in

straightforwardly

as

follows

A

physical

system

P

implements

a

CSA

M

if

there

is

a

vectorization

of

internal

states

of

P

into

components

-LSB-

and

a

mapping

f

from

the

substates

sj

into

corresponding

substates

Sj

of

M

along

with

similar

vectorizations

and

mappings

for

inputs

and

outputs

such

that

for

every

state-transition

rule

-LRB-

-LSB-

Ik

-RSB-

-LSB-

-RRB-

-LRB-

-LSB-

-LSB-

Ol

-RSB-

-RRB-

of

M

if

P

is

in

internal

state

-LSB-

and

receiving

input

-LSB-

in

-RSB-

which

map

to

formal

state

and

input

-LSB-

and

-LSB-

Ik

-RSB-

respectively

this

reliably

causes

it

to

enter

an

internal

state

and

produce

an

output

that

map

to

-LSB-

and

-LSB-

Ol

-RSB-

respectively

Once

again

further

constraints

might

be

added

to

this

definition

for

various

purposes

and

there

is

much

that

can

be

said

to

flesh

out

the

definition

's

various

parts

a

detailed

discussion

of

these

technicalities

must

await

another

forum

-LRB-

see

Chalmers

-LRB-

forthcoming

b

-RRB-

for

a

start

-RRB-

This

definition

is

not

the

last

word

in

a

theory

of

implementation

but

it

captures

the

theory

's

basic

form

One

might

think

that

CSAs

are

not

much

of

an

advance

on

FSAs

Finite

CSAs

at

least

are

no

more

computationally

powerful

than

FSAs

there

is

a

natural

correspondence

that

associates

every

finite

CSA

with

an

FSA

with

the

same

input/output

behavior

Of

course

infinite

CSAs

-LRB-

such

as

Turing

machines

-RRB-

are

more

powerful

but

even

leaving

that

reason

aside

there

are

a

number

of

reasons

why

CSAs

are

a

more

suitable

formalism

for

our

purposes

than

FSAs

First

the

implementation

conditions

on

a

CSA

are

much

more

constrained

than

those

of

the

corresponding

FSA

An

implementation

of

a

CSA

is

required

to

consist

in

a

complex

causal

interaction

among

a

number

of

separate

parts

a

CSA

description

can

therefore

capture

the

causal

organization

of

a

system

to

a

much

finer

grain

Second

the

structure

in

CSA

states

can

be

of

great

explanatory

utility

A

description

of

a

physical

system

as

a

CSA

will

often

be

much

more

illuminating

than

a

description

as

the

corresponding

FSA

Third

CSAs

reflect

in

a

much

more

direct

way

the

formal

organization

of

such

familiar

computational

objects

as

Turing

machines

cellular

automata

and

the

like

Finally

the

CSA

framework

allows

a

unified

account

of

the

implementation

conditions

for

both

finite

and

infinite

machines

This

definition

can

straightforwardly

be

applied

to

yield

implementation

conditions

for

more

specific

computational

formalisms

To

develop

an

account

of

the

implementation-conditions

for

a

Turing

machine

say

we

need

only

redescribe

the

Turing

machine

as

a

CSA

The

overall

state

of

a

Turing

machine

can

be

seen

as

a

giant

vector

consisting

of

-LRB-

a

-RRB-

the

internal

state

of

the

head

and

-LRB-

b

-RRB-

the

state

of

each

square

of

the

tape

where

this

state

in

turn

is

an

ordered

pair

of

a

symbol

and

a

flag

indicating

whether

the

square

is

occupied

by

the

head

-LRB-

of

course

only

one

square

can

be

so

occupied

this

will

be

ensured

by

restrictions

on

initial

state

and

on

state-transition

rules

-RRB-

The

state-transition

rules

between

vectors

can

be

derived

naturally

from

the

quintuples

specifying

the

behavior

of

the

machine-head

As

usually

understood

Turing

machines

only

take

inputs

at

a

single

time-step

-LRB-

the

start

-RRB-

and

do

not

produce

any

output

separate

from

the

contents

of

the

tape

These

restrictions

can

be

overridden

in

natural

ways

for

example

by

adding

separate

input

and

output

tapes

but

even

with

inputs

and

outputs

limited

in

this

way

there

is

a

natural

description

as

a

CSA

Given

this

translation

from

the

Turing

machine

formalism

to

the

CSA

formalism

we

can

say

that

a

given

Turing

machine

is

implemented

whenever

the

corresponding

CSA

is

implemented

A

similar

story

holds

for

computations

in

other

formalisms

Some

formalisms

such

as

cellular

automata

are

even

more

straightforward

Others

such

as

Pascal

programs

are

more

complex

but

the

overall

principles

are

the

same

In

each

case

there

is

some

room

for

maneuver

and

perhaps

some

arbitrary

decisions

to

make

-LRB-

does

writing

a

symbol

and

moving

the

head

count

as

two

state-transitions

or

one

-RRB-

but

little

rests

on

the

decisions

we

make

We

can

also

give

accounts

of

implementation

for

nondeterministic

and

probabilistic

automata

by

making

simple

changes

in

the

definition

of

a

CSA

and

the

corresponding

account

of

implementation

The

theory

of

implementation

for

combinatorial-state

automata

provides

a

basis

for

the

theory

of

implementation

in

general

Questions

answered

The

above

account

may

look

complex

but

the

essential

idea

is

very

simple

the

relation

between

an

implemented

computation

and

an

implementing

system

is

one

of

isomorphism

between

the

formal

structure

of

the

former

and

the

causal

structure

of

the

latter

In

this

way

we

can

see

that

as

far

as

the

theory

of

implementation

is

concerned

a

computation

is

simply

an

abstract

specification

of

causal

organization

This

is

important

for

later

purposes

In

the

meantime

we

can

now

answer

various

questions

and

objections

Does

every

system

implement

some

computation

Yes

For

example

every

physical

system

will

implement

the

simple

FSA

with

a

single

internal

state

most

physical

systems

will

implement

the

cyclic

FSA

and

so

on

This

is

no

problem

and

certainly

does

not

render

the

account

vacuous

That

would

only

be

the

case

if

every

system

implemented

every

computation

and

that

is

not

the

case

Does

every

system

implement

any

given

computation

No

The

conditions

for

implementing

a

given

complex

computation?say

a

CSA

whose

state-vectors

have

elements

with

possibilities

for

each

element

and

complex

state-transition

relations?will

generally

be

sufficiently

rigorous

that

extremely

few

physical

systems

will

meet

them

What

is

required

is

not

just

a

mapping

from

states

of

the

system

onto

states

of

the

CSA

as

Searle

-LRB-

-RRB-

effectively

suggests

The

added

requirement

that

the

mapped

states

must

satisfy

reliable

state-transition

rules

is

what

does

all

the

work

In

this

case

there

will

effectively

be

at

least

constraints

on

state-transitions

-LRB-

one

for

each

possible

state-vector

and

more

if

there

are

multiple

possible

inputs

-RRB-

Each

constraint

will

specify

one

out

of

at

least

possible

consequents

-LRB-

one

for

each

possible

resultant

state-vector

and

more

if

there

are

outputs

-RRB-

The

chance

that

an

arbitrary

set

of

states

will

satisfy

these

constraints

is

something

less

than

one

in

-LRB-

-RRB-

-LRB-

actually

significantly

less

because

of

the

requirement

that

transitions

be

reliable

-RRB-

There

is

no

reason

to

suppose

that

the

causal

structure

of

an

arbitrary

system

-LRB-

such

as

Searle

's

wall

-RRB-

will

satisfy

these

constraints

It

is

true

that

while

we

lack

knowledge

of

the

fundamental

constituents

of

matter

it

is

impossible

to

prove

that

arbitrary

objects

do

not

implement

every

computation

-LRB-

perhaps

every

proton

has

an

infinitely

rich

internal

structure

-RRB-

but

anybody

who

denies

this

conclusion

will

need

to

come

up

with

a

remarkably

strong

argument

Can

a

given

system

implement

more

than

one

computation

Yes

Any

system

implementing

some

complex

computation

will

simultaneously

be

implementing

many

simpler

computations?not

just

and

FSAs

but

computations

of

some

complexity

This

is

no

flaw

in

the

current

account

it

is

precisely

what

we

should

expect

The

system

on

my

desk

is

currently

implementing

all

kinds

of

computations

from

EMACS

to

a

clock

program

and

various

sub-computations

of

these

In

general

there

is

no

canonical

mapping

from

a

physical

object

to

the

computation

it

is

performing

We

might

say

that

within

every

physical

system

there

are

numerous

computational

systems

To

this

very

limited

extent

the

notion

of

implementation

is

interest-relative

Once

again

however

there

is

no

threat

of

vacuity

The

question

of

whether

a

given

system

implements

a

given

computation

is

still

entirely

objective

What

counts

is

that

a

given

system

does

not

implement

every

computation

or

to

put

the

point

differently

that

most

given

computations

are

only

implemented

by

a

very

limited

class

of

physical

systems

This

is

what

is

required

for

a

substantial

foundation

for

AI

and

cognitive

science

and

it

is

what

the

account

I

have

given

provides

If

even

digestion

is

a

computation

is

n't

this

vacuous

This

objection

expresses

the

feeling

that

if

every

process

including

such

things

as

digestion

and

oxidation

implements

some

computation

then

there

seems

to

be

nothing

special

about

cognition

any

more

as

computation

is

so

pervasive

This

objection

rests

on

a

misunderstanding

It

is

true

that

any

given

instance

of

digestion

will

implement

some

computation

as

any

physical

system

does

but

the

system

's

implementing

this

computation

is

in

general

irrelevant

to

its

being

an

instance

of

digestion

To

see

this

we

can

note

that

the

same

computation

could

have

been

implemented

by

various

other

physical

systems

-LRB-

such

as

my

SPARC

-RRB-

without

it

's

being

an

instance

of

digestion

Therefore

the

fact

that

the

system

implements

the

computation

is

not

responsible

for

the

existence

of

digestion

in

the

system

With

cognition

by

contrast

the

claim

is

that

it

is

in

virtue

of

implementing

some

computation

that

a

system

is

cognitive

That

is

there

is

a

certain

class

of

computations

such

that

any

system

implementing

that

computation

is

cognitive

We

might

go

further

and

argue

that

every

cognitive

system

implements

some

computation

such

that

any

implementation

of

the

computation

would

also

be

cognitive

and

would

share

numerous

specific

mental

properties

with

the

original

system

These

claims

are

controversial

of

course

and

I

will

be

arguing

for

them

in

the

next

section

But

note

that

it

is

precisely

this

relation

between

computation

and

cognition

that

gives

bite

to

the

computational

analysis

of

cognition

If

this

relation

or

something

like

it

did

not

hold

the

computational

status

of

cognition

would

be

analogous

to

that

of

digestion

What

about

Putnam

's

argument

Putnam

-LRB-

-RRB-

has

suggested

that

on

a

definition

like

this

almost

any

physical

system

can

be

seen

to

implement

every

finite-state

automaton

He

argues

for

this

conclusion

by

demonstrating

that

there

will

almost

always

be

a

mapping

from

physical

states

of

a

system

to

internal

states

of

an

FSA

such

that

over

a

given

time-period

-LRB-

from

to

today

say

-RRB-

the

transitions

between

states

are

just

as

the

machine

table

say

they

should

be

If

the

machine

table

requires

that

state

A

be

followed

by

state

B

then

every

instance

of

state

A

is

followed

by

state

B

in

this

time

period

Such

a

mapping

will

be

possible

for

an

inputless

FSA

under

the

assumption

that

physical

states

do

not

repeat

We

simply

map

the

initial

physical

state

of

the

system

onto

an

initial

formal

state

of

the

computation

and

map

successive

states

of

the

system

onto

successive

states

of

the

computation

However

to

suppose

that

this

system

implements

the

FSA

in

question

is

to

misconstrue

the

state-transition

conditionals

in

the

definition

of

implementation

What

is

required

is

not

simply

that

state

A

be

followed

by

state

B

on

all

instances

in

which

it

happens

to

come

up

in

a

given

time-period

There

must

be

a

reliable

counterfactual-supporting

connection

between

the

states

Given

a

formal

state-transition

A

B

it

must

be

the

case

that

if

the

system

were

to

be

in

state

A

it

would

transit

to

state

B.

Further

such

a

conditional

must

be

satisfied

for

every

transition

in

the

machine

table

not

just

for

those

whose

antecedent

states

happen

to

come

up

in

a

given

time

period

It

is

easy

to

see

that

Putnam

's

system

does

not

satisfy

this

much

stronger

requirement

In

effect

Putnam

has

required

only

that

certain

weak

material

conditionals

be

satisfied

rather

than

conditionals

with

modal

force

For

this

reason

his

purported

implementations

are

not

implementations

at

all

-LRB-

Two

notes

First

Putnam

responds

briefly

to

the

charge

that

his

system

fails

to

support

counterfactuals

but

considers

a

different

class

of

counterfactuals?those

of

the

form

if

the

system

had

not

been

in

state

A

it

would

not

have

transited

to

state

B

It

is

not

these

counterfactuals

that

are

relevant

here

Second

it

turns

out

that

Putnam

's

argument

for

the

widespread

realization

of

inputless

FSAs

can

be

patched

up

in

a

certain

way

this

just

goes

to

show

that

inputless

FSAs

are

an

inappropriate

formalism

for

cognitive

science

due

to

their

complete

lack

of

combinatorial

structure

Putnam

gives

a

related

argument

for

the

widespread

realization

of

FSAs

with

input

and

output

but

this

argument

is

strongly

vulnerable

to

an

objection

like

the

one

above

and

can

not

be

patched

up

in

an

analogous

way

CSAs

are

even

less

vulnerable

to

this

sort

of

argument

I

discuss

all

this

at

much

greater

length

in

Chalmers

-LRB-

forthcoming

b

-RRB-

-RRB-

What

about

semantics

It

will

be

noted

that

nothing

in

my

account

of

computation

and

implementation

invokes

any

semantic

considerations

such

as

the

representational

content

of

internal

states

This

is

precisely

as

it

should

be

computations

are

specified

syntactically

not

semantically

Although

it

may

very

well

be

the

case

that

any

implementations

of

a

given

computation

share

some

kind

of

semantic

content

this

should

be

a

consequence

of

an

account

of

computation

and

implementation

rather

than

built

into

the

definition

If

we

build

semantic

considerations

into

the

conditions

for

implementation

any

role

that

computation

can

play

in

providing

a

foundation

for

AI

and

cognitive

science

will

be

endangered

as

the

notion

of

semantic

content

is

so

ill-understood

that

it

desperately

needs

a

foundation

itself

The

original

account

of

Turing

machines

by

Turing

-LRB-

-RRB-

certainly

had

no

semantic

constraints

built

in

A

Turing

machine

is

defined

purely

in

terms

of

the

mechanisms

involved

that

is

in

terms

of

syntactic

patterns

and

the

way

they

are

transformed

To

implement

a

Turing

machine

we

need

only

ensure

that

this

formal

structure

is

reflected

in

the

causal

structure

of

the

implementation

Some

Turing

machines

will

certainly

support

a

systematic

semantic

interpretation

in

which

case

their

implementations

will

also

but

this

plays

no

part

in

the

definition

of

what

it

is

to

be

or

to

implement

a

Turing

machine

This

is

made

particularly

clear

if

we

note

that

there

are

some

Turing

machines

such

as

machines

defined

by

random

sets

of

state-transition

quintuples

that

support

no

non-trivial

semantic

interpretation

We

need

an

account

of

what

it

is

to

implement

these

machines

and

such

an

account

will

then

generalize

to

machines

that

support

a

semantic

interpretation

Certainly

when

computer

designers

ensure

that

their

machines

implement

the

programs

that

they

are

supposed

to

they

do

this

by

ensuring

that

the

mechanisms

have

the

right

causal

organization

they

are

not

concerned

with

semantic

content

In

the

words

of

Haugeland

-LRB-

-RRB-

if

you

take

care

of

the

syntax

the

semantics

will

take

care

of

itself

I

have

said

that

the

notion

of

computation

should

not

be

dependent

on

that

of

semantic

content

neither

do

I

think

that

the

latter

notion

should

be

dependent

on

the

former

Rather

both

computation

and

content

should

be

dependent

on

the

common

notion

of

causation

We

have

seen

the

first

dependence

in

the

account

of

computation

above

The

notion

of

content

has

also

been

frequently

analyzed

in

terms

of

causation

-LRB-

see

e.g.

Dretske

and

Fodor

-RRB-

This

common

pillar

in

the

analyses

of

both

computation

and

content

allows

that

the

two

notions

will

not

sway

independently

while

at

the

same

time

ensuring

that

neither

is

dependent

on

the

other

for

its

analysis

What

about

computers

Although

Searle

-LRB-

-RRB-

talks

about

what

it

takes

for

something

to

be

a

digital

computer

I

have

talked

only

about

computations

and

eschewed

reference

to

computers

This

is

deliberate

as

it

seems

to

me

that

computation

is

the

more

fundamental

notion

and

certainly

the

one

that

is

important

for

AI

and

cognitive

science

AI

and

cognitive

science

certainly

do

not

require

that

cognitive

systems

be

computers

unless

we

stipulate

that

all

it

takes

to

be

a

computer

is

to

implement

some

computation

in

which

case

the

definition

is

vacuous

What

does

it

take

for

something

to

be

a

computer

Presumably

a

computer

can

not

merely

implement

a

single

computation

It

must

be

capable

of

implementing

many

computations?that

is

it

must

be

programmable

In

the

extreme

case

a

computer

will

be

universal

capable

of

being

programmed

to

compute

any

recursively

enumerable

function

Perhaps

universality

is

not

required

of

a

computer

but

programmability

certainly

is

To

bring

computers

within

the

scope

of

the

theory

of

implementation

above

we

could

require

that

a

computer

be

a

CSA

with

certain

parameters

such

that

depending

on

how

these

parameters

are

set

a

number

of

different

CSAs

can

be

implemented

A

universal

Turing

machine

could

be

seen

in

this

light

for

instance

where

the

parameters

correspond

to

the

program

symbols

on

the

tape

In

any

case

such

a

theory

of

computers

is

not

required

for

the

study

of

cognition

Is

the

brain

a

computer

in

this

sense

Arguably

For

a

start

the

brain

can

be

programmed

to

implement

various

computations

by

the

laborious

means

of

conscious

serial

rule-following

but

this

is

a

fairly

incidental

ability

On

a

different

level

it

might

be

argued

that

learning

provides

a

certain

kind

of

programmability

and

parameter-setting

but

this

is

a

sufficiently

indirect

kind

of

parameter-setting

that

it

might

be

argued

that

it

does

not

qualify

In

any

case

the

question

is

quite

unimportant

for

our

purposes

What

counts

is

that

the

brain

implements

various

complex

computations

not

that

it

is

a

computer

Computation

and

cognition

The

above

is

only

half

the

story

We

now

need

to

exploit

the

above

account

of

computation

and

implementation

to

outline

the

relation

between

computation

and

cognition

and

to

justify

the

foundational

role

of

computation

in

AI

and

cognitive

science

Justification

of

the

thesis

of

computational

sufficiency

has

usually

been

tenuous

Perhaps

the

most

common

move

has

been

an

appeal

to

the

Turing

test

noting

that

every

implementation

of

a

given

computation

will

have

a

certain

kind

of

behavior

and

claiming

that

the

right

kind

of

behavior

is

sufficient

for

mentality

The

Turing

test

is

a

weak

foundation

however

and

one

to

which

AI

need

not

appeal

It

may

be

that

any

behavioral

description

can

be

implemented

by

systems

lacking

mentality

altogether

-LRB-

such

as

the

giant

lookup

tables

of

Block

-RRB-

Even

if

behavior

suffices

for

mind

the

demise

of

logical

behaviorism

has

made

it

very

implausible

that

it

suffices

for

specific

mental

properties

two

mentally

distinct

systems

can

have

the

same

behavioral

dispositions

A

computational

basis

for

cognition

will

require

a

tighter

link

than

this

then

Instead

the

central

property

of

computation

on

which

I

will

focus

is

one

that

we

have

already

noted

the

fact

that

a

computation

provides

an

abstract

specification

of

the

causal

organization

of

a

system

Causal

organization

is

the

nexus

between

computation

and

cognition

If

cognitive

systems

have

their

mental

properties

in

virtue

of

their

causal

organization

and

if

that

causal

organization

can

be

specified

computationally

then

the

thesis

of

computational

sufficiency

is

established

Similarly

if

it

is

the

causal

organization

of

a

system

that

is

primarily

relevant

in

the

explanation

of

behavior

then

the

thesis

of

computational

explanation

will

be

established

By

the

account

above

we

will

always

be

able

to

provide

a

computational

specification

of

the

relevant

causal

organization

and

therefore

of

the

properties

on

which

cognition

rests

Organizational

invariance

To

spell

out

this

story

in

more

detail

I

will

introduce

the

notion

of

the

causal

topology

of

a

system

The

causal

topology

represents

the

abstract

causal

organization

of

the

system

that

is

the

pattern

of

interaction

among

parts

of

the

system

abstracted

away

from

the

make-up

of

individual

parts

and

from

the

way

the

causal

connections

are

implemented

Causal

topology

can

be

thought

of

as

a

dynamic

topology

analogous

to

the

static

topology

of

a

graph

or

a

network

Any

system

will

have

causal

topology

at

a

number

of

different

levels

For

the

cognitive

systems

with

which

we

will

be

concerned

the

relevant

level

of

causal

topology

will

be

a

level

fine

enough

to

determine

the

causation

of

behavior

For

the

brain

this

is

probably

the

neural

level

or

higher

depending

on

just

how

the

brain

's

cognitive

mechanisms

function

-LRB-

The

notion

of

causal

topology

is

necessarily

informal

for

now

I

will

discuss

its

formalization

below

-RRB-

Call

a

property

P

an

organizational

invariant

if

it

is

invariant

with

respect

to

causal

topology

that

is

if

any

change

to

the

system

that

preserves

the

causal

topology

preserves

P

The

sort

of

changes

in

question

include

-LRB-

a

-RRB-

moving

the

system

in

space

-LRB-

b

-RRB-

stretching

distorting

expanding

and

contracting

the

system

-LRB-

c

-RRB-

replacing

sufficiently

small

parts

of

the

system

with

parts

that

perform

the

same

local

function

-LRB-

e.g.

replacing

a

neuron

with

a

silicon

chip

with

the

same

I/O

properties

-RRB-

-LRB-

d

-RRB-

replacing

the

causal

links

between

parts

of

a

system

with

other

links

that

preserve

the

same

pattern

of

dependencies

-LRB-

e.g.

we

might

replace

a

mechanical

link

in

a

telephone

exchange

with

an

electrical

link

-RRB-

and

-LRB-

e

-RRB-

any

other

changes

that

do

not

alter

the

pattern

of

causal

interaction

among

parts

of

the

system

Most

properties

are

not

organizational

invariants

The

property

of

flying

is

not

for

instance

we

can

move

an

airplane

to

the

ground

while

preserving

its

causal

topology

and

it

will

no

longer

be

flying

Digestion

is

not

if

we

gradually

replace

the

parts

involved

in

digestion

with

pieces

of

metal

while

preserving

causal

patterns

after

a

while

it

will

no

longer

be

an

instance

of

digestion

no

food

groups

will

be

broken

down

no

energy

will

be

extracted

and

so

on

The

property

of

being

tube

of

toothpaste

is

not

an

organizational

invariant

if

we

deform

the

tube

into

a

sphere

or

replace

the

toothpaste

by

peanut

butter

while

preserving

causal

topology

we

no

longer

have

a

tube

of

toothpaste

In

general

most

properties

depend

essentially

on

certain

features

that

are

not

features

of

causal

topology

Flying

depends

on

height

digestion

depends

on

a

particular

physiochemical

makeup

tubes

of

toothpaste

depend

on

shape

and

physiochemical

makeup

and

so

on

Change

the

features

in

question

enough

and

the

property

in

question

will

change

even

though

causal

topology

might

be

preserved

throughout

The

organizational

invariance

of

mental

properties

The

central

claim

of

this

section

is

that

most

mental

properties

are

organizational

invariants

It

does

not

matter

how

we

stretch

move

about

or

replace

small

parts

of

a

cognitive

system

as

long

as

we

preserve

its

causal

topology

we

will

preserve

its

mental

properties

An

exception

has

to

be

made

for

properties

that

are

partly

supervenient

on

states

of

the

environment

Such

properties

include

knowledge

-LRB-

if

we

move

a

system

that

knows

that

P

into

an

environment

where

P

is

not

true

then

it

will

no

longer

know

that

P

-RRB-

and

belief

on

some

construals

where

the

content

of

a

belief

depends

on

environmental

context

However

mental

properties

that

depend

only

on

internal

-LRB-

brain

-RRB-

state

will

be

organizational

invariants

This

is

not

to

say

that

causal

topology

is

irrelevant

to

knowledge

and

belief

It

will

still

capture

the

internal

contribution

to

those

properties?that

is

causal

topology

will

contribute

as

much

as

the

brain

contributes

It

is

just

that

the

environment

will

also

play

a

role

The

central

claim

can

be

justified

by

dividing

mental

properties

into

two

varieties

psychological

properties?those

that

are

characterized

by

their

causal

role

such

as

belief

learning

and

perception?and

phenomenal

properties

or

those

that

are

characterized

by

way

in

which

they

are

consciously

experienced

Psychological

properties

are

concerned

with

the

sort

of

thing

the

mind

does

and

phenomenal

properties

are

concerned

with

the

way

it

feels

-LRB-

Some

will

hold

that

properties

such

as

belief

should

be

assimilated

to

the

second

rather

than

the

first

class

I

do

not

think

that

this

is

correct

but

nothing

will

depend

on

that

here

-RRB-

Psychological

properties

as

has

been

argued

by

Armstrong

-LRB-

-RRB-

and

Lewis

-LRB-

-RRB-

among

others

are

effectively

defined

by

their

role

within

an

overall

causal

system

it

is

the

pattern

of

interaction

between

different

states

that

is

definitive

of

a

system

's

psychological

properties

Systems

with

the

same

causal

topology

will

share

these

patterns

of

causal

interactions

among

states

and

therefore

by

the

analysis

of

Lewis

-LRB-

-RRB-

will

share

their

psychological

properties

-LRB-

as

long

as

their

relation

to

the

environment

is

appropriate

-RRB-

Phenomenal

properties

are

more

problematic

It

seems

unlikely

that

these

can

be

defined

by

their

causal

roles

-LRB-

although

many

including

Lewis

and

Armstrong

think

they

might

be

-RRB-

To

be

a

conscious

experience

is

not

to

perform

some

role

but

to

have

a

particular

feel

These

properties

are

characterized

by

what

it

is

like

to

have

them

in

Nagel

's

-LRB-

-RRB-

phrase

Phenomenal

properties

are

still

quite

mysterious

and

ill-understood

Nevertheless

I

believe

that

they

can

be

seen

to

be

organizational

invariants

as

I

have

argued

elsewhere

The

argument

for

this

very

briefly

is

a

reductio

Assume

conscious

experience

is

not

organizationally

invariant

Then

there

exist

systems

with

the

same

causal

topology

but

different

conscious

experiences

Let

us

say

this

is

because

the

systems

are

made

of

different

materials

such

as

neurons

and

silicon

a

similar

argument

can

be

given

for

other

sorts

of

differences

As

the

two

systems

have

the

same

causal

topology

we

can

-LRB-

in

principle

-RRB-

transform

the

first

system

into

the

second

by

making

only

gradual

changes

such

as

by

replacing

neurons

one

at

a

time

with

I/O

equivalent

silicon

chips

where

the

overall

pattern

of

interaction

remains

the

same

throughout

Along

the

spectrum

of

intermediate

systems

there

must

be

two

systems

between

which

we

replace

less

than

ten

percent

of

the

system

but

whose

conscious

experiences

differ

Consider

these

two

systems

N

and

S

which

are

identical

except

in

that

some

circuit

in

one

is

neural

and

in

the

other

is

silicon

The

key

step

in

the

thought-experiment

is

to

take

the

relevant

neural

circuit

in

N

and

to

install

alongside

it

a

causally

isomorphic

silicon

back-up

circuit

with

a

switch

between

the

two

circuits

What

happens

when

we

flip

the

switch

By

hypothesis

the

system

's

conscious

experiences

will

change

say

for

purposes

of

illustration

from

a

bright

red

experience

to

a

bright

blue

experience

-LRB-

or

to

a

faded

red

experience

or

whatever

-RRB-

This

follows

from

the

fact

that

the

system

after

the

change

is

a

version

of

S

whereas

before

the

change

it

is

just

N

But

given

the

assumptions

there

is

no

way

for

the

system

to

notice

these

changes

Its

causal

topology

stays

constant

so

that

all

of

its

functional

states

and

behavioral

dispositions

stay

fixed

If

noticing

is

defined

functionally

-LRB-

as

it

should

be

-RRB-

then

there

is

no

room

for

any

noticing

to

take

place

and

if

it

is

not

any

noticing

here

would

seem

to

be

a

thin

event

indeed

There

is

certainly

no

room

for

a

thought

Hmm

Something

strange

just

happened

unless

it

is

floating

free

in

some

Cartesian

realm

Even

if

there

were

such

a

thought

it

would

be

utterly

impotent

it

could

lead

to

no

change

of

processing

within

the

system

which

could

not

even

mention

it

-LRB-

If

the

substitution

were

to

yield

some

change

in

processing

then

the

systems

would

not

have

the

same

causal

topology

after

all

Recall

that

the

argument

has

the

form

of

a

reductio

-RRB-

We

might

even

flip

the

switch

a

number

of

times

so

that

red

and

blue

experiences

dance

before

the

system

's

inner

eye

it

will

never

notice

This

I

take

it

is

a

reductio

ad

absurdum

of

the

original

hypothesis

if

one

's

experiences

change

one

can

potentially

notice

in

a

way

that

makes

some

causal

difference

Therefore

the

original

assumption

is

false

and

phenomenal

properties

are

organizational

invariants

This

needs

to

be

worked

out

in

more

detail

of

course

I

give

the

details

of

this

Dancing

Qualia

argument

along

with

a

related

Fading

Qualia

argument

in

-LRB-

Chalmers

forthcoming

a

-RRB-

If

all

this

works

it

establishes

that

most

mental

properties

are

organizational

invariants

any

two

systems

that

share

their

fine-grained

causal

topology

will

share

their

mental

properties

modulo

the

contribution

of

the

environment

Justifying

the

theses

To

establish

the

thesis

of

computational

sufficiency

all

we

need

to

do

now

is

establish

that

organizational

invariants

are

fixed

by

some

computational

structure

This

is

quite

straightforward

An

organizationally

invariant

property

depends

only

on

some

pattern

of

causal

interaction

between

parts

of

the

system

Given

such

a

pattern

we

can

straightforwardly

abstract

it

into

a

CSA

description

the

parts

of

the

system

will

correspond

to

elements

of

the

CSA

state-vector

and

the

patterns

of

interaction

will

be

expressed

in

the

state-transition

rules

This

will

work

straightforwardly

as

long

as

each

part

has

only

a

finite

number

of

states

that

are

relevant

to

the

causal

dependencies

between

parts

which

is

likely

to

be

the

case

in

any

biological

system

whose

functions

can

not

realistically

depend

on

infinite

precision

-LRB-

I

discuss

the

issue

of

analog

quantities

in

more

detail

below

-RRB-

Any

system

that

implements

this

CSA

will

share

the

causal

topology

of

the

original

system

In

fact

it

turns

out

that

the

CSA

formalism

provides

a

perfect

formalization

of

the

notion

of

causal

topology

A

CSA

description

specifies

a

division

of

a

system

into

parts

a

space

of

states

for

each

part

and

a

pattern

of

interaction

between

these

states

This

is

precisely

what

is

constitutive

of

causal

topology

If

what

has

gone

before

is

correct

this

establishes

the

thesis

of

computational

sufficiency

and

therefore

the

the

view

that

Searle

has

called

strong

artificial

intelligence

that

there

exists

some

computation

such

that

any

implementation

of

the

computation

possesses

mentality

The

fine-grained

causal

topology

of

a

brain

can

be

specified

as

a

CSA

Any

implementation

of

that

CSA

will

share

that

causal

topology

and

therefore

will

share

organizationally

invariant

mental

properties

that

arise

from

the

brain

The

thesis

of

computational

explanation

can

be

justified

in

a

similar

way

As

mental

properties

are

organizational

invariants

the

physical

properties

on

which

they

depend

are

properties

of

causal

organization

Insofar

as

mental

properties

are

to

be

explained

in

terms

of

the

physical

at

all

they

can

be

explained

in

terms

of

the

causal

organization

of

the

system

We

can

invoke

further

properties

-LRB-

implementational

details

-RRB-

if

we

like

but

there

is

a

clear

sense

in

which

they

are

not

vital

to

the

explanation

The

neural

or

electronic

composition

of

an

element

is

irrelevant

for

many

purposes

to

be

more

precise

composition

is

relevant

only

insofar

as

it

determines

the

element

's

causal

role

within

the

system

An

element

with

different

physical

composition

but

the

same

causal

role

would

do

just

as

well

This

is

not

to

make

the

implausible

claim

that

neural

properties

say

are

entirely

irrelevant

to

explanation

Often

the

best

way

to

investigate

a

system

's

causal

organization

is

to

investigate

its

neural

properties

The

claim

is

simply

that

insofar

as

neural

properties

are

explanatorily

relevant

it

is

in

virtue

of

the

role

they

play

in

determining

a

systems

causal

organization

In

the

explanation

of

behavior

too

causal

organization

takes

center

stage

A

system

's

behavior

is

determined

by

its

underlying

causal

organization

and

we

have

seen

that

the

computational

framework

provides

an

ideal

language

in

which

this

organization

can

be

specified

Given

a

pattern

of

causal

interaction

between

substates

of

a

system

for

instance

there

will

be

a

CSA

description

that

captures

that

pattern

Computational

descriptions

of

this

kind

provide

a

general

framework

for

the

explanation

of

behavior

For

some

explanatory

purposes

we

will

invoke

properties

that

are

not

organizational

invariants

If

we

are

interested

in

the

biological

basis

of

cognition

we

will

invoke

neural

properties

To

explain

situated

cognition

we

may

invoke

properties

of

the

environment

This

is

fine

the

thesis

of

computational

explanation

is

not

an

exclusive

thesis

Still

usually

we

are

interested

in

neural

properties

insofar

as

they

determine

causal

organization

we

are

interested

in

properties

of

the

environment

insofar

as

they

affect

the

pattern

of

processing

in

a

system

and

so

on

Computation

provides

a

general

explanatory

framework

that

these

other

considerations

can

supplement

Some

objections

A

computational

basis

for

cognition

can

be

challenged

in

two

ways

The

first

sort

of

challenge

argues

that

computation

can

not

do

what

cognition

does

that

a

computational

simulation

might

not

even

reproduce

human

behavioral

capacities

for

instance

perhaps

because

the

causal

structure

in

human

cognition

goes

beyond

what

a

computational

description

can

provide

The

second

concedes

that

computation

might

capture

the

capacities

but

argues

that

more

is

required

for

true

mentality

I

will

consider

four

objections

of

the

second

variety

and

then

three

of

the

first

Answers

to

most

of

these

objections

fall

directly

out

of

the

framework

developed

above

But

a

computational

model

is

just

a

simulation

According

to

this

objection

due

to

Searle

-LRB-

-RRB-

Harnad

-LRB-

-RRB-

and

many

others

we

do

not

expect

a

computer

model

of

a

hurricane

to

be

a

real

hurricane

so

why

should

a

computer

model

of

mind

be

a

real

mind

But

this

is

to

miss

the

important

point

about

organizational

invariance

A

computational

simulation

is

not

a

mere

formal

abstraction

but

has

rich

internal

dynamics

of

its

own

If

appropriately

designed

it

will

share

the

causal

topology

of

the

system

that

is

being

modeled

so

that

the

system

's

organizationally

invariant

properties

will

be

not

merely

simulated

but

replicated

The

question

about

whether

a

computational

model

simulates

or

replicates

a

given

property

comes

down

to

the

question

of

whether

or

not

the

property

is

an

organizational

invariant

The

property

of

being

a

hurricane

is

obviously

not

an

organizational

invariant

for

instance

as

it

is

essential

to

the

very

notion

of

hurricanehood

that

wind

and

air

be

involved

The

same

goes

for

properties

such

as

digestion

and

temperature

for

which

specific

physical

elements

play

a

defining

role

There

is

no

such

obvious

objection

to

the

organizational

invariance

of

cognition

so

the

cases

are

disanalogous

and

indeed

I

have

argued

above

that

for

mental

properties

organizational

invariance

actually

holds

It

follows

that

a

model

that

is

computationally

equivalent

to

a

mind

will

itself

be

a

mind

Syntax

and

semantics

Searle

-LRB-

-RRB-

has

argued

along

the

following

lines

-LRB-

-RRB-

A

computer

program

is

syntactic

-LRB-

-RRB-

Syntax

is

not

sufficient

for

semantics

-LRB-

-RRB-

Minds

have

semantics

therefore

-LRB-

-RRB-

Implementing

a

computer

program

is

insufficient

for

a

mind

Leaving

aside

worries

about

the

second

premise

we

can

note

that

this

argument

equivocates

between

programs

and

implementations

of

those

programs

While

programs

themselves

are

syntactic

objects

implementations

are

not

they

are

real

physical

systems

with

complex

causal

organization

with

real

physical

causation

going

on

inside

In

an

electronic

computer

for

instance

circuits

and

voltages

push

each

other

around

in

a

manner

analogous

to

that

in

which

neurons

and

activations

push

each

other

around

It

is

precisely

in

virtue

of

this

causation

that

implementations

may

have

cognitive

and

therefore

semantic

properties

It

is

the

notion

of

implementation

that

does

all

the

work

here

A

program

and

its

physical

implementation

should

not

be

regarded

as

equivalent

they

lie

on

entirely

different

levels

and

have

entirely

different

properties

It

is

the

program

that

is

syntactic

it

is

the

implementation

that

has

semantic

content

Of

course

there

is

still

a

substantial

question

about

how

an

implementation

comes

to

possess

semantic

content

just

as

there

is

a

substantial

question

about

how

a

brain

comes

to

possess

semantic

content

But

once

we

focus

on

the

implementation

rather

than

the

program

we

are

at

least

in

the

right

ball-park

We

are

talking

about

a

physical

system

with

causal

heft

rather

than

a

shadowy

syntactic

object

If

we

accept

as

is

extremely

plausible

that

brains

have

semantic

properties

in

virtue

of

their

causal

organization

and

causal

relations

then

the

same

will

go

for

implementations

Syntax

may

not

be

sufficient

for

semantics

but

the

right

kind

of

causation

is

The

Chinese

room

There

is

not

room

here

to

deal

with

Searle

's

famous

Chinese

room

argument

in

detail

I

note

however

that

the

account

I

have

given

supports

the

Systems

reply

according

to

which

the

entire

system

understands

Chinese

even

if

the

homunculus

doing

the

simulating

does

not

Say

the

overall

system

is

simulating

a

brain

neuron-by-neuron

Then

like

any

implementation

it

will

share

important

causal

organization

with

the

brain

In

particular

if

there

is

a

symbol

for

every

neuron

then

the

patterns

of

interaction

between

slips

of

paper

bearing

those

symbols

will

mirror

patterns

of

interaction

between

neurons

in

the

brain

and

so

on

This

organization

is

implemented

in

a

baroque

way

but

we

should

not

let

the

baroqueness

blind

us

to

the

fact

that

the

causal

organization

real

physical

causal

organization?is

there

-LRB-

The

same

goes

for

a

simulation

of

cognition

at

level

above

the

neural

in

which

the

shared

causal

organization

will

lie

at

a

coarser

level

-RRB-

It

is

precisely

in

virtue

of

this

causal

organization

that

the

system

possesses

its

mental

properties

We

can

rerun

a

version

of

the

dancing

qualia

argument

to

see

this

In

principle

we

can

move

from

the

brain

to

the

Chinese

room

simulation

in

small

steps

replacing

neurons

at

each

step

by

little

demons

doing

the

same

causal

work

and

then

gradually

cutting

down

labor

by

replacing

two

neighboring

demons

by

one

who

does

the

same

work

Eventually

we

arrive

at

a

system

where

a

single

demon

is

responsible

for

maintaining

the

causal

organization

without

requiring

any

real

neurons

at

all

This

organization

might

be

maintained

between

marks

on

paper

or

it

might

even

be

present

inside

the

demon

's

own

head

if

the

calculations

are

memorized

The

arguments

about

organizational

invariance

all

hold

here

for

the

same

reasons

as

before

it

is

implausible

to

suppose

that

the

system

's

experiences

will

change

or

disappear

Performing

the

thought-experiment

this

way

makes

it

clear

that

we

should

not

expect

the

experiences

to

be

had

by

the

demon

The

demon

is

simply

a

kind

of

causal

facilitator

ensuring

that

states

bear

the

appropriate

causal

relations

to

each

other

The

conscious

experiences

will

be

had

by

the

system

as

a

whole

Even

if

that

system

is

implemented

inside

the

demon

by

virtue

of

the

demon

's

memorization

the

system

should

not

be

confused

with

demon

itself

We

should

not

suppose

that

the

demon

will

share

the

implemented

system

's

experiences

any

more

than

it

will

share

the

experiences

of

an

ant

that

crawls

inside

its

skull

both

are

cases

of

two

computational

systems

being

implemented

within

a

single

physical

space

Mental

properties

arising

from

distinct

computational

systems

will

be

quite

distinct

and

there

is

no

reason

to

suppose

that

they

overlap

Whatabout

the

environment

Some

mental

properties

such

as

knowledge

and

even

belief

depend

on

the

environment

being

a

certain

way

Computational

organization

as

I

have

outlined

it

can

not

determine

the

environmental

contribution

and

therefore

can

not

fully

guarantee

this

sort

of

mental

property

But

this

is

no

problem

All

we

need

computational

organization

to

give

us

is

the

internal

contribution

to

mental

properties

that

is

the

same

contribution

that

the

brain

makes

-LRB-

for

instance

computational

organization

will

determine

the

so-called

narrow

content

of

a

belief

if

this

exists

see

Fodor

-RRB-

The

full

panoply

of

mental

properties

might

only

be

determined

by

computation-plus-environment

just

as

it

is

determined

by

brain-plusenvironment

These

considerations

do

not

count

against

the

prospects

of

artificial

intelligence

and

they

affect

the

aspirations

of

computational

cognitive

science

no

more

than

they

affect

the

aspirations

of

neuroscience

Is

cognition

computable

In

the

preceding

discussion

I

have

taken

for

granted

that

computation

can

at

least

simulate

human

cognitive

capacity

and

have

been

concerned

to

argue

that

this

counts

as

honest-to-goodness

mentality

The

former

point

has

often

been

granted

by

opponents

of

AI

-LRB-

e.g.

Searle

-RRB-

who

have

directed

the

fire

at

the

latter

but

it

is

not

uncontroversial

This

is

to

some

extent

an

empirical

issue

but

the

relevant

evidence

is

solidly

on

the

side

of

computability

We

have

every

reason

to

believe

that

the

low-level

laws

of

physics

are

computable

If

so

then

low-level

neurophysiological

processes

can

be

computationally

simulated

it

follows

that

the

function

of

the

whole

brain

is

computable

too

as

the

brain

consists

in

a

network

of

neurophysiological

parts

Some

have

disputed

the

premise

for

example

Penrose

-LRB-

-RRB-

has

speculated

that

the

effects

of

quantum

gravity

are

noncomputable

and

that

these

effects

may

play

a

role

in

cognitive

functioning

He

offers

no

arguments

to

back

up

this

speculation

however

and

there

is

no

evidence

of

such

noncomputability

in

current

physical

theory

-LRB-

see

Pour-El

and

Richards

-LRB-

-RRB-

for

a

discussion

-RRB-

Failing

such

a

radical

development

as

the

discovery

that

the

fundamental

laws

of

nature

are

uncomputable

we

have

every

reason

to

believe

that

human

cognition

can

be

computationally

modeled

What

about

G?odel

's

Theorem

G?odel

's

theorem

states

that

for

any

consistent

formal

system

there

are

statements

of

arithmetic

that

are

unprovable

within

the

system

This

has

led

some

-LRB-

Lucas

Penrose

-RRB-

to

conclude

that

humans

have

abilities

that

can

not

be

duplicated

by

any

computational

system

For

example

our

ability

to

see

the

truth

of

the

G?odel

sentence

of

a

formal

system

is

argued

to

be

non-algorithmic

I

will

not

deal

with

this

objection

in

detail

here

as

the

answer

to

it

is

not

a

direct

application

of

the

current

framework

I

will

simply

note

that

the

assumption

that

we

can

see

the

truth

of

a

G?odel

sentence

requires

that

we

have

the

ability

to

determine

the

consistency

or

inconsistency

of

the

relevant

formal

system

and

there

is

no

reason

to

believe

that

we

have

this

ability

in

general

-LRB-

For

more

on

this

point

see

Putnam

Bowie

and

the

commentaries

on

Penrose

-RRB-

Discreteness

and

continuity

An

important

objection

notes

that

the

CSA

formalism

only

captures

discrete

causal

organization

and

argues

that

some

cognitive

properties

may

depend

on

continuous

aspects

of

that

organization

such

as

analog

values

or

chaotic

dependencies

A

number

of

responses

to

this

are

possible

The

first

is

to

note

that

the

current

framework

can

fairly

easily

be

extended

to

deal

with

computation

over

continuous

quantities

such

as

real

numbers

All

that

is

required

is

that

the

various

substates

of

a

CSA

be

represented

by

a

real

parameter

rather

than

a

discrete

parameter

where

appropriate

restrictions

are

placed

on

allowable

state-transitions

-LRB-

for

instance

we

can

require

that

parameters

are

transformed

polynomially

where

the

requisite

transformation

can

be

conditional

on

sign

-RRB-

See

Blum

Shub

and

Smale

-LRB-

-RRB-

for

a

careful

working-out

of

some

of

the

relevant

theory

of

computability

A

theory

of

implementation

can

be

given

along

in

a

fashion

similar

to

the

account

I

have

given

above

where

continuous

quantities

in

the

formalism

are

required

to

correspond

to

continuous

physical

parameters

with

an

appropriate

correspondence

in

state-transitions

This

formalism

is

still

discrete

in

time

evolution

of

the

continuous

states

proceeds

in

discrete

temporal

steps

It

might

be

argued

that

cognitive

organization

is

in

fact

continuous

in

time

and

that

a

relevant

formalism

should

capture

this

In

this

case

the

specification

of

discrete

statetransitions

between

states

can

be

replaced

by

differential

equations

specifying

how

continuous

quantities

change

in

continuous

time

giving

a

thoroughly

continuous

computational

framework

MacLennan

-LRB-

-RRB-

describes

a

framework

along

these

lines

Whether

such

a

framework

truly

qualifies

as

computational

is

largely

a

terminological

matter

but

there

it

is

arguable

that

the

framework

is

significantly

similar

in

kind

to

the

traditional

approach

all

that

has

changed

is

that

discrete

states

and

steps

have

been

smoothed

out

We

need

not

go

this

far

however

There

are

good

reasons

to

suppose

that

whether

or

not

cognition

in

the

brain

is

continuous

a

discrete

framework

can

capture

everything

important

that

is

going

on

To

see

this

we

can

note

that

a

discrete

abstraction

can

describe

and

simulate

a

continuous

process

to

any

required

degree

of

accuracy

It

might

be

objected

that

chaotic

processes

can

amplify

microscopic

differences

to

significant

levels

Even

so

it

is

implausible

that

the

correct

functioning

of

mental

processes

depends

on

the

precise

value

of

the

tenth

decimal

place

of

analog

quantities

The

presence

of

background

noise

and

randomness

in

biological

systems

implies

that

such

precision

would

inevitably

be

washed

out

in

practice

It

follows

that

although

a

discrete

simulation

may

not

yield

precisely

the

behavior

that

a

given

cognitive

system

produces

on

a

given

occasion

it

will

yield

plausible

behavior

that

the

system

might

have

produced

had

background

noise

been

a

little

different

This

is

all

that

a

proponent

of

artificial

intelligence

need

claim

Indeed

the

presence

of

noise

in

physical

systems

suggests

that

any

given

continuous

computation

of

the

above

kinds

can

never

be

reliably

implemented

in

practice

but

only

approximately

implemented

For

the

purposes

of

artificial

intelligence

we

will

do

just

as

well

with

discrete

systems

which

can

also

give

us

approximate

implementations

of

continuous

computations

It

follows

that

these

considerations

do

not

count

against

the

theses

of

computational

sufficiency

or

of

computational

explanation

To

see

the

first

note

that

a

discrete

simulation

can

replicate

everything

essential

to

cognitive

functioning

for

the

reasons

above

even

though

it

may

not

duplicate

every

last

detail

of

a

given

episode

of

cognition

To

see

the

second

note

that

for

similar

reasons

the

precise

values

of

analog

quantities

can

not

be

relevant

to

the

explanation

of

our

cognitive

capacities

and

that

a

discrete

description

can

do

the

job

This

is

not

to

exclude

continuous

formalisms

from

cognitive

explanation

The

thesis

of

computational

explanation

is

not

an

exclusive

thesis

It

may

be

that

continuous

formalisms

will

provide

a

simpler

and

more

natural

framework

for

the

explanation

of

many

dynamic

processes

as

we

find

in

the

theory

of

neural

networks

Perhaps

the

most

reasonable

version

of

the

computationalist

view

accepts

the

thesis

of

-LRB-

discrete

-RRB-

computational

sufficiency

but

supplements

the

thesis

of

computational

explanation

with

the

proviso

that

continuous

computation

may

sometimes

provide

a

more

natural

explanatory

framework

-LRB-

a

discrete

explanation

could

do

the

same

job

but

more

clumsily

-RRB-

In

any

case

continuous

computation

does

not

give

us

anything

fundamentally

new

Other

kinds

of

computationalism

Artificial

intelligence

and

computational

cognitive

science

are

committed

to

a

kind

of

computationalism

about

the

mind

a

computationalism

defined

by

the

theses

of

computational

sufficiency

and

computational

explanation

In

this

paper

I

have

tried

to

justify

this

computationalism

by

spelling

out

the

role

of

computation

as

a

tool

for

describing

and

duplicating

causal

organization

I

think

that

this

kind

of

computationalism

is

all

that

artificial

intelligence

and

computational

cognitive

science

are

committed

to

and

indeed

is

all

that

they

need

This

sort

of

computationalism

provides

a

general

framework

precisely

because

it

makes

so

few

claims

about

the

kind

of

computation

that

is

central

to

the

explanation

and

replication

of

cognition

No

matter

what

the

causal

organization

of

cognitive

processes

turns

out

to

be

there

is

good

reason

to

believe

that

it

can

be

captured

within

a

computational

framework

The

fields

have

often

been

taken

to

be

committed

to

stronger

claims

sometimes

by

proponents

and

more

often

by

opponents

For

example

Edelman

-LRB-

-RRB-

criticizes

the

computational

approach

to

the

study

of

the

mind

on

the

grounds

that

An

analysis

of

the

evolution

development

and

structure

of

brains

makes

it

highly

unlikely

that

they

could

be

Turing

machines

This

is

so

because

of

the

enormous

individual

variation

in

structure

that

brains

possess

at

a

variety

of

organizational

levels

-LSB-

-RSB-

-LSB-

Also

-RSB-

an

analysis

of

both

ecological

and

environmental

variation

and

of

the

categorization

procedures

of

animals

and

humans

makes

it

highly

unlikely

that

the

world

-LRB-

physical

and

social

-RRB-

can

function

as

a

tape

for

a

Turing

machine

-LRB-

Edelman

p.

-RRB-

But

artificial

intelligence

and

computational

cognitive

science

are

not

committed

to

the

claim

that

the

brain

is

literally

a

Turing

machine

with

a

moving

head

and

a

tape

and

even

less

to

the

claim

that

that

tape

is

the

environment

The

claim

is

simply

that

some

computational

framework

can

explain

and

replicate

human

cognitive

processes

It

may

turn

out

that

the

relevant

computational

description

of

these

processes

is

very

fine-grained

reflecting

extremely

complex

causal

dynamics

among

neurons

and

it

may

well

turn

out

that

there

is

significant

variation

in

causal

organization

between

individuals

There

is

nothing

here

that

is

incompatible

with

a

computational

approach

to

cognitive

science

In

a

similar

way

a

computationalist

need

not

claim

that

the

brain

is

a

von

Neumann

machine

or

has

some

other

specific

architecture

Like

Turing

machines

von

Neumann

machines

are

just

one

kind

of

architecture

particularly

well-suited

to

programmability

but

the

claim

that

the

brain

implements

such

an

architecture

is

far

ahead

of

any

empirical

evidence

and

is

most

likely

false

The

commitments

of

computationalism

are

more

general

Computationalism

is

occasionally

associated

with

the

view

that

cognition

is

rule-following

but

again

this

is

a

strong

empirical

hypothesis

that

is

inessential

to

the

foundations

of

the

fields

It

is

entirely

possible

that

the

only

rules

found

in

a

computational

description

of

thought

will

be

at

a

very

low

level

specifying

the

causal

dynamics

of

neurons

for

instance

or

perhaps

the

dynamics

of

some

level

between

the

neural

and

the

cognitive

Even

if

there

are

no

rules

to

be

found

at

the

cognitive

level

a

computational

approach

to

the

mind

can

still

succeed

Another

claim

to

which

a

computationalist

need

not

be

committed

are

the

brain

is

a

computer

as

we

have

seen

it

is

not

computers

that

are

central

but

computations

-RRB-

The

most

ubiquitous

strong

form

of

computationalism

has

been

what

we

may

call

symbolic

computationalism

the

view

that

cognition

is

computation

over

representation

-LRB-

Newell

and

Simon

Fodor

and

Pylyshyn

-RRB-

To

a

first

approximation

we

can

cash

out

this

view

as

the

claim

that

the

computational

primitives

in

a

computational

description

of

cognition

are

also

representational

primitives

That

is

to

say

the

basic

syntactic

entities

between

which

statetransitions

are

defined

are

themselves

bearers

of

semantic

content

and

are

therefore

symbols

Symbolic

computationalism

has

been

a

popular

and

fruitful

approach

to

the

mind

but

it

does

not

exhaust

the

resources

of

computation

Not

all

computations

are

symbolic

computations

We

have

seen

that

there

are

some

Turing

machines

that

lack

semantic

content

altogether

for

instance

Perhaps

systems

that

carry

semantic

content

are

more

plausible

models

of

cognition

but

even

in

these

systems

there

is

no

reason

why

the

content

must

be

carried

by

the

systems

computational

primitives

In

connectionist

systems

for

example

the

basic

bearers

of

semantic

content

are

distributed

representations

patterns

of

activity

over

many

units

whereas

the

computational

primitives

are

simple

units

that

may

themselves

lack

semantic

content

To

use

Smolensky

's

term

-LRB-

Smolensky

-RRB-

these

systems

perform

subsymbolic

computation

the

level

of

computation

falls

below

the

level

of

representation

But

the

systems

are

computational

nevertheless

Note

that

the

distinction

between

symbolic

and

subsymbolic

computation

does

not

coincide

with

the

distinction

between

different

computational

formalisms

such

as

Turing

machines

and

neural

networks

Rather

the

distinction

divides

the

class

of

computations

within

each

of

these

formalisms

Some

Turing

machines

perform

symbolic

computation

and

some

perform

subsymbolic

computation

the

same

goes

for

neural

networks

-LRB-

Of

course

it

is

sometimes

said

that

all

Turing

machines

perform

symbol

manipulation

but

this

holds

only

if

the

ambiguous

term

symbol

is

used

in

a

purely

syntactic

sense

rather

than

in

the

semantic

sense

I

am

using

here

-RRB-

Both

proponents

and

opponents

of

a

computational

approach

have

often

implicitly

identified

computation

with

symbolic

computation

A

critique

called

What

Computers

Ca

n't

Do

-LRB-

Dreyfus

-RRB-

for

instance

turns

out

to

be

largely

directed

at

systems

that

perform

computation

over

explicit

representation

Other

sorts

of

computation

are

left

untouched

and

indeed

systems

performing

subsymbolic

computation

seem

well-suited

for

some

of

Dreyfus

's

problem

areas

The

broader

ambitions

of

artificial

intelligence

are

therefore

left

intact

On

the

other

side

of

the

fence

Fodor

-LRB-

-RRB-

uses

the

name

Computational

Theory

of

Mind

for

a

version

of

symbolic

computationalism

and

suggests

that

Turing

's

main

contribution

to

cognitive

science

is

the

idea

that

syntactic

state-transitions

between

symbols

can

be

made

to

respect

their

semantic

content

This

strikes

me

as

false

Turing

was

concerned

very

little

with

the

semantic

content

of

internal

states

and

the

concentration

on

symbolic

computation

came

later

Rather

Turing

's

key

contribution

was

the

formalization

of

the

notion

of

mechanism

along

with

the

associated

universality

of

the

formalization

It

is

this

universality

that

gives

us

good

reason

to

suppose

that

computation

can

do

almost

anything

that

any

mechanism

can

do

thus

accounting

for

the

centrality

of

computation

in

the

study

of

cognition

Indeed

a

focus

on

symbolic

computation

sacrifices

the

universality

that

is

at

the

heart

of

Turing

's

contribution

Universality

applies

to

entire

classes

of

automata

such

as

Turing

machines

where

these

classes

are

defined

syntactically

The

requirement

that

an

automaton

performs

computation

over

representation

is

a

strong

further

constraint

a

semantic

constraint

that

plays

no

part

in

the

basic

theory

of

computation

There

is

no

reason

to

suppose

that

the

much

narrower

class

of

Turing

machines

that

perform

symbolic

computation

is

universal

If

we

wish

to

appeal

to

universality

in

a

defense

of

computationalism

we

must

cast

the

net

more

widely

than

this

The

various

strong

forms

of

computationalism

outlined

here

are

bold

empirical

hypotheses

with

varying

degrees

of

plausibility

I

suspect

that

they

are

all

false

but

in

any

case

their

truth

and

falsity

is

not

the

issue

here

Because

they

are

such

strong

empirical

hypotheses

they

are

in

no

position

to

serve

as

a

foundation

for

artificial

intelligence

and

computational

cognitive

science

If

the

fields

were

committed

to

these

hypotheses

their

status

would

be

much

more

questionable

than

it

currently

is

Artificial

intelligence

and

computational

cognitive

science

can

survive

the

discovery

that

the

brain

is

not

a

von

Neumann

machine

or

that

cognition

is

not

rule-following

or

that

the

brain

does

not

engage

in

computation

over

representation

precisely

because

these

are

not

among

the

fields

foundational

commitments

Computation

is

much

more

general

than

this

and

consequently

much

more

robust

Conclusion

Toward

a

minimal

computationalism

The

view

that

I

have

advocated

can

be

called

minimal

computationalism

It

is

defined

by

the

twin

theses

of

computational

sufficiency

and

computational

explanation

where

computation

is

taken

in

the

broad

sense

that

dates

back

to

Turing

I

have

argued

that

these

theses

are

compelling

precisely

because

computation

provides

a

general

framework

for

describing

and

determining

patterns

of

causal

organization

and

because

mentality

is

rooted

in

such

patterns

The

thesis

of

computational

explanation

holds

because

computation

provides

a

perfect

language

in

which

to

specify

the

causal

organization

of

cognitive

processes

and

the

thesis

of

computational

sufficiency

holds

because

in

all

implementations

of

the

appropriate

computations

the

causal

structure

of

mentality

is

replicated

Unlike

the

stronger

forms

of

computationalism

minimal

computationalism

is

not

a

bold

empirical

hypothesis

To

be

sure

there

are

some

ways

that

empirical

science

might

prove

it

to

be

false

if

it

turns

out

that

the

fundamental

laws

of

physics

are

noncomputable

and

if

this

noncomputability

reflects

itself

in

cognitive

functioning

for

instance

or

if

it

turns

out

that

our

cognitive

capacities

depend

essentially

on

infinite

precision

in

certain

analog

quantities

or

indeed

if

it

turns

out

that

cognition

is

mediated

by

some

non-physical

substance

whose

workings

are

not

computable

But

these

developments

seem

unlikely

and

failing

developments

like

these

computation

provides

a

general

framework

in

which

we

can

express

the

causal

organization

of

cognition

whatever

that

organization

turns

out

to

be

Minimal

computationalism

is

compatible

with

such

diverse

programs

as

connectionism

logicism

and

approaches

focusing

on

dynamic

systems

evolution

and

artificial

life

It

is

occasionally

said

that

programs

such

as

connectionism

are

noncomputational

but

it

seems

more

reasonable

to

say

that

the

success

of

such

programs

would

vindicate

Turing

's

dream

of

a

computational

intelligence

rather

than

destroying

it

Computation

is

such

a

valuable

tool

precisely

because

almost

any

theory

of

cognitive

mechanisms

can

be

expressed

in

computational

terms

even

though

the

relevant

computational

formalisms

may

vary

All

such

theories

are

theories

of

causal

organization

and

computation

is

sufficiently

flexible

that

it

can

capture

almost

any

kind

of

organization

whether

the

causal

relations

hold

between

high-level

representations

or

among

low-level

neural

processes

Even

such

programs

as

the

Gibsonian

theory

of

perception

are

ultimately

compatible

with

minimal

computationalism

If

perception

turns

out

to

work

as

the

Gibsonians

imagine

it

will

still

be

mediated

by

causal

mechanisms

and

the

mechanisms

will

be

expressible

in

an

appropriate

computational

form

That

expression

may

look

very

unlike

a

traditional

computational

theory

of

perception

but

it

will

be

computational

nevertheless

In

this

light

we

see

that

artificial

intelligence

and

computational

cognitive

science

do

not

rest

on

shaky

empirical

hypotheses

Instead

they

are

consequences

of

some

very

plausible

principles

about

the

causal

basis

of

cognition

and

they

are

compatible

with

an

extremely

wide

range

of

empirical

discoveries

about

the

functioning

of

the

mind

It

is

precisely

because

of

this

flexibility

that

computation

serves

as

a

foundation

for

the

fields

in

question

by

providing

a

common

framework

within

which

many

different

theories

can

be

expressed

and

by

providing

a

tool

with

which

the

theories

causal

mechanisms

can

be

instantiated

No

matter

how

cognitive

science

progresses

in

the

coming

years

there

is

good

reason

to

believe

that

computation

will

be

at

center

stage

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take

it

that

something

like

this

is

the

standard

definition

of

implementation

of

a

finitestate

automaton

see

for

example

the

definition

of

the

description

of

a

system

by

a

probabilistic

automaton

in

Putnam

-LRB-

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It

is

surprising

however

how

little

space

has

been

devoted

to

accounts

of

implementation

in

the

literature

in

theoretical

computer

science

philosophy

of

psychology

and

cognitive

science

considering

how

central

the

notion

of

computation

is

to

these

fields

It

is

remarkable

that

there

could

be

a

controversy

about

what

it

takes

for

a

physical

system

to

implement

a

computation

-LRB-

e.g.

Searle

-RRB-

at

this

late

date

Pylyshyn

p.

for

a

related

point

analyzing

a

related

thought-experiment

Searle

-LRB-

-RRB-

suggests

that

a

subject

who

has

undergone

silicon

replacement

might

react

as

follows

You

want

to

cry

out

I

ca

n't

see

anything

I

'm

going

totally

blind

But

you

hear

your

voice

saying

in

a

way

that

is

completely

out

of

your

control

I

see

a

red

object

in

front

of

me

-LRB-

pp.

-RRB-

But

given

that

the

system

's

causal

topology

remains

constant

it

is

very

unclear

where

there

is

room

for

such

wanting

to

take

place

if

it

is

not

in

some

Cartesian

realm

Searle

suggests

some

other

things

that

might

happen

such

as

a

reduction

to

total

paralysis

but

these

suggestions

require

a

change

in

causal

topology

and

are

therefore

not

relevant

to

the

issue

of

organizational

invariance

am

skeptical

about

whether

phenomenal

properties

can

be

explained

in

wholly

physical

terms

As

I

argue

in

Chalmers

-LRB-

forthcoming

c

-RRB-

given

any

account

of

the

physical

or

computational

processes

underlying

mentality

the

question

of

why

these

processes

should

give

rise

to

conscious

experience

does

not

seem

to

be

explainable

within

physical

or

computational

theory

alone

Nevertheless

it

remains

the

case

that

phenomenal

properties

depend

on

physical

properties

and

if

what

I

have

said

earlier

is

correct

the

physical

properties

that

they

depend

on

are

organizational

properties

Further

the

explanatory

gap

with

respect

to

conscious

experience

is

compatible

with

the

computational

explanation

of

cognitive

processes

and

of

behavior

which

is

what

the

thesis

of

computational

explanation

requires

course

there

is

a

sense

in

which

it

can

be

said

that

connectionist

models

perform

computation

over

representation

in

that

connectionist

processing

involves

the

transformation

of

representations

but

this

sense

is

to

weak

to

cut

the

distinction

between

symbolic

and

subsymbolic

computation

at

its

joints

Perhaps

the

most

interesting

foundational

distinction

between

symbolic

and

connectionist

systems

is

that

in

the

former

but

not

in

the

latter

the

computational

-LRB-

syntactic

-RRB-

primitives

are

also

the

representational

-LRB-

semantic

-RRB-

primitives

is

common

for

proponents

of

symbolic

computationalism

to

hold

usually

as

an

unargued

premise

that

what

makes

a

computation

a

computation

is

the

fact

that

it

involves

representations

with

semantic

content

The

books

by

Fodor

-LRB-

-RRB-

and

Pylyshyn

-LRB-

-RRB-

for

instance

are

both

premised

on

the

assumption

that

there

is

no

computation

without

representation

Of

course

this

is

to

some

extent

a

terminological

issue

but

as

I

have

stressed

in

and

here

this

assumption

has

no

basis

in

computational

theory

and

unduly

restricts

the

role

that

computation

plays

in

the

foundations

of

cognitive

science

other

claims

with

which

computationalism

is

sometimes

associated

include

the

brain

is

a

computer

the

mind

is

to

the

brain

as

software

is

to

hardware

and

cognition

is

computation

The

first

of

these

is

not

required

for

the

reasons

given

in

it

is

not

computers

that

are

central

to

cognitive

theory

but

computations

The

second

claim

is

an

imperfect

expression

of

the

computationalist

position

for

similar

reasons

certainly

the

mind

does

not

seem

to

be

something

separable

that

the

brain

can

load

and

run

as

a

computer

's

hardware

can

load

and

run

software

Even

the

third

does

not

seem

to

me

to

be

central

to

computationalism

perhaps

there

is

a

sense

in

which

it

is

true

but

what

is

more

important

is

that

computation

suffices

for

and

explains

cognition

See

Dietrich

-LRB-

-RRB-

for

some

related

distinctions

between

computationalism

computerism

and

cognitivism

artificial intelligence
cognition
computation
computationalism
connectionism
explanation
implementation
representation