S. Korner - The Impossibility of Transcendental Deductions

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1/16

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THE IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONSAuthor(s): S. KörnerSource: The Monist, Vol. 51, No. 3, Kant Today: Part I (JULY, 1967), pp. 317-331Published by: Oxford University PressStable URL: http://www.jstor.org/stable/27902036

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2/16

THE

IMPOSSIBILITY

OF

TRANSCENDENTAL

DEDUCTIONS

The

purpose

of this

paper

is

first

to

explain

a

general

notion

ot

transcendental

deductions,

of

which

the

Kantian

are

special

cases;

next to

show,

and

to

illustrate

by

examples

from Kant's

work,

that

no

transcendental

deduction

can

be

successful;

and

thirdly

to

put

one

of Kant's

achievements

in its

proper

light by substituting

for

his

spurious

distinction between

metaphysical

exposition

and

transcendental

deduction,

a

revised notion

of

metaphysical

expo

sition

and

of

the

philosophical

tasks

arising

out

of

it.

L

The General

Notion

oj

a

Transcendental

Deduction

Making

statements

about

the

external

world

presupposes

not

only

a

prior

distinction

between

oneself

and that

world,

but

also

a

method for

differentiating,

within

one's

experience

of

it,

external

objects

and

attributes-properties

and relations

of which external

objects

are

the

bearers.

I

shall

say

that

such

a

method of external

differentiation is associated

with,

or

belongs

to,

a

categorial

schema

or,

briefly,

a

schema

of

external differentiation

if,

and

only

if,

the attributes employed comprise what may be called respectively,

in

accordance

with

philosophical

tradition,

constitutive and

in

dividuating

attributes.

An

attribute

is

constitutive

(of

external

objects)

if,

and

only

if,

it

is

applicable

to external

objects

and

if,

in

addition,

its

applicability

to an

object

logically

implies,

and

is

logically

implied

by,

the

object's being

an

external

object.

I

shall

say,

more

briefly,

that

a

constitutive

attribute

is

comprehensively

applicable

to

external

objects.

An

attribute

is

individuating

(for

external

objects)

if,

and

only

if,

it is

applicable

to

every

external

object

and

if,

in

addition,

its

applicability

to

an

external

object

logically implies, and is logically implied by, the external object's

being

distinct from

all other external

objects.

I

shall

say,

more

briefly,

that

an

individuating

attribute

exhaustively

individuates

external

objects.


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3/16

318

THE MONIST

Some

comments

on

these definitions

may

be

helpful.

Although

not

yet

fully

general, they

fit,

for

example,

Kant's

view of

the

attribute

'x

is

a

substance*

as

constitutive

of,

and

his view

of

the

attribute

6x

wholly

occupies

a

region

of absolute

space

during

a

period

of

absolute time*

as

individuating

for,

external

objects.

The

term

logically

implies

is used

to

express

the

converse

of the

relation

of

logical

deducibility

with

respect

to

some

underlying

logic,

which

at

this

stage

need

not

be

made

explicit.

An

individuat

ing

attribute the

possession

of which

by

an external

object

logi

cally

implies

its

being

distinct from

all

others,

must not

be

confused

with

any

merely

identifying

attribute

the

possession

of

which

by

an

external

object

happens

as a

matter

of fact

to

distinguish

it from

all others.

Lastly

it

should be

emphasised

that

a

method of

prior

external

differentiation

does

not

necessarily

belong

to

a

categorial

schema.

Statements

about the external world

are

not

the

only

ones

which

presuppose

a

prior

differentiation of

experience

into

objects

and attributes,

and

thus, possibly,

a

categorial schema consisting

of constitutive

and

individuating

attributes.

We

also

make,

at

least

prima

facie,

statemer

of other

kinds,

presupposing

prior

dif

ferentiations

of other

gions

of

experience,

e.g. sensory,

moral

and

aesthetic

experience,

which

may

or

may

not

belong

to

categorial

schemata. A

schema

of

sensory

differentiation

would

con

tain constitutive

attributes

of,

and

individuating

attributes

for,

sen

sory

objects.

The*

same

would

hold

analogously

for schemata

of

moral

and aesthetic

differentiation,

if

any.

Such

considerations

per

mit

us to

generalize

the

definition of

a

categorial

schema

as

follows:

A method of prior differentiation of a region of experience is as

sociated

with,

or

belongs

to,

a

categorial

schema

if,

and

only

if,

the

attributes

employed

comprise

attributes

which

are

constitutive of

the

region's objects,

and attributes which

are

individuating

for

them.

For

my

purpose

here

it

is

not

necessary

to

raise,

much

less

to

answer,

the

question

why

anybody

uses

the

methods

of

prior

differentiation

which he

does

in

fact

use,

or

why

for him

experience

should

fall

into

more

or

less

clearly distinguishable

regions

and should

fall

into

them

in

one

way

rather than

in

any

other.

A

transcendental

deduction

can

now

be

defined

quite

generally

as a

logically

sound demonstration of the reasons

why

a

particular

categorial

schema

is

not

only

in

fact,

but also

necessarily

employed,




4/16

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 319

in

differentiating

a

region

of

experience.

This

definition is

very

wide

indeed

and will

presently

be

shown

to cover

Kant's

conception

of

a

transcendental

deduction.

Because

of

its

generality

it

must

be

protected

against

such

charges

of

vagueness

as

would rob

the

subsequent

discussion

of

all

cogency.

Such

protection

can

be

achieved

by

the

following

characterization

of

the

key-phrases

which

occur

in the

definition.

Although

a

logically

sound

demonstration

need

not

be

a

deductive

argument,

it

may

contain

deductive

argu

ments

in

which case thesemust not be fallacious.

Again,

whatever

else

may

be

meant

by

the

statement that

a

schema

is

necessarily

employed

in

differentiating

a

region

of

experience

it

logically

implies

that

any

method

actually

or

possibly

employed

in

differ

entiating

the

region

belongs

to

the

schema.

Apart

from

these

pro

visos

no

further restrictions

are

imposed

on

interpreting

the

definition.

Among

the

most

important

and

interesting

examples

of

at

tempted

transcendental

deductions

are,

of

course,

those

found

in

Kant's philosophy,

on

which

I

shall be drawing

for

illustrations

of

the

general

thesis

that

transcendental

deductions

are

impossible.

This choice

will limit

me

to

an

examination

of schemata

of

ex

ternal and

practical

differentiation.

Kant's

transcendental

deduc

tions contain

only

such.

He held

that of all

the

methods

of

prior

differentiation of

experience

which

he

investigated, only

those

of

external

and

practical

differentiation-and

not,

for

example,

any

method

of aesthetic

differentiation-belong

to

categorial

schemata.

It would

not

be

difficult

to

find,

in these

or

other

fields,

many

simpler

or more

simple-minded

philosophical

arguments

easily

rec

ognizable as attempts at transcendental deductions in the sense of

our

definition.

II.

The

Impossibility

of

Transcendental

Deductions

I

shall

now

examine

the

preconditions

of

the

possibility

of

any

transcendental

deduction,

and

show

that

at

least

one

of

them is

such

that

it

cannot

be

satisfied;

from

which

result,

of

course,

the

impossibility

of

transcendental

deductions

follows

immediately.

Be

fore

a

transcendental

deduction

can

be

attempted

for

any

region

of

experience,

a method of

prior

differentiation of the

region

must

first

be

exhibited

and

shown

to

belong

to

a

schema.

This,

as

was




5/16

320

THE MONIST

pointed

out

by

and

was

perfectly

clear

to

Kant,

need

not

be the

case.

But

if

the

method of

prior

differentiation does

belong

to

a

schema

the task

of

exhibiting

the schema

is

feasible. It consists

(a)

in

searching

for

nonempty

attributes,

e.g.

an

attribute

P

such

that

?x

is

an

object

of the

region*

logically

implies

and

is

implied

by,

'x

is

a

P\ Sometimes

one

may

succeed

in

the

more

ambitious

task

of

giving

a

complete,

finite

enumeration

of the

simplest

consti

tutive

attributes,

i.e. such

as are

not

logically

equivalent

to

a

con

junction

of other constitutive attributes. We

might,

following

Kant,

call

such

simple

and

finitely

enumerable

attributes

the

cate

gories

of the

region

and

say

that

they

are

ultimately

constitutive

of the

region's

objects.

But

this

pleasant

possibility

may

be

ignored.

The task further

consists

(b)

in

searching

for

at

least

one

non

empty

attribute,

say

such

that

Q

is

applicable

to

every

object

of

the

region,

and

is

such that

'x

is

an

object

of

the

region

and

a

Qf

logically

implies,

and

is

logically

implied

by,

*x

is

a

distinct

object

of

the

region*.

If

another

attribute

say

R,

should also

turn out

to

be

an

individuating attribute for the objects of the region then lx

is

an

object

of the

region

and

an

RJ

logically

implies,

and

is

logical

ly

implied

by,

'x

is

an

object

of

the

region

and

a

Q*.

We

may

again

ignore

this

possibility.

The

fulfilment

of the

first

precondition

of

the

possibility

of

a

transcendental

deduction,

i.e. of

the above

tasks

(a)

and

(b)

may

be called

the

establishment of

a

schema -on

the

basis

of

investigating

a

particular

method

of

prior

differentiation

of

a

region

of

experience

into

objects

and

attributes.

With

the

establishment

of

a

schema the

preconditions

for

its

transcendental deduction

are,

however,

not

yet

satisfied. For

to

establish a schema is to establish that a particular method for dif

ferentiating

a

region

of

experience belongs

to

the

schema,

and

not

that

any

method which

might

actually

or

possibly

be

thus

em

ployed,

also

belongs

to

it.

Before

one can

show

why

any

and

every

possible

method

belongs

to

the

schema

one

has

to

show

that

any

and

every

possible

method

belongs

to

it.

One

must,

as

I

shall

say,

demonstrate

the

schema's

uniqueness.

How could

this

be

done? Prima

facie

three

possibilities

are

open.

First,

to

demonstrate the

schema's

uniqueness

by

comparing

it with

experience

undifferentiated

by

any

method

of

prior

differ

entiation. But this cannot be done since the statements

by

which

the

comparison

would

have

to

be

made,

cannot

be

formulated

with




6/16


out

employing

some

prior

differentiation of

experience;

and

even

if

there

were

undifferentiated

experience,

one

could

at

best

show

that

a

certain

schema reflects

it,

and

not

that

some

other

schema

could

not

also

reflect

it.

Second,

to

demonstrate

the

schema's

uniqueness

by

comparing

it

with

its

possible competitors.

But

this

presupposes

that

they

all

can

be

exhibited,

and

is

self-contradictory

in

attempting

a

demonstration

of

the

schema's

uniqueness,

by

con

ceding

that

the

schema

was

not

unique. Thirdly,

one

might propose

to examine the schema and its

application

entirely

from

within

the

schema

itself,

i.e.

by

means

of

statements

belonging

to

it.

Such

an

examination,

at

best,

could

only

show

how the

schema

functions

in

the differentiation

of

a

region

of

experience,

not

that

it

is

the

only

possible

schema

to

which

every

differentiation of

the

region

must

belong.

The

three

methods

include

the

possible grounds

for

a

con

cordance between

reality

and

its

apprehension,

mentioned

in

the

preface

to

the

second

edition

of

The

Critique

of

Pure

Reason.

In

order

to

avoid vague appeals

to

demonstrations of

a

categorial

schema's

uniqueness

by

other

methods,

e.g.

some

mystical

insight

or some

special

Logic,

I

am

prepared

to

reduce

my

claim

to

the

thesis that

uniqueness

demonstrations

of

a

schema

by

comparing

it

with

undifferentiated

experience,

by

comparing

it

with

other

sche

mata,

or

by

examining

it

from

within,

are

impossible.

It

should

be

noted that

I am

speaking

not

of isolated

concepts,

such

as

'per

manence*

or

'change*,

which

may

or

may

not

be

indispensable

to

our

thinking,

but which

by

themselves

are

not

constitutive

of,

or

individuating

for,

the

objects

of

a

region

of

experience-even

though a demonstration of their uniqueness is, as I should be pre

pared

to

argue,

equally

impossible.

It is the

impossibility

of

demonstrating

a

schema's

uniqueness

that renders

transcendental

deductions

impossible.

The

general

argument

just

sketched

rests

mainly

on

two

distinctions:

the

dis

tinction

between

a

method

of

prior

differentiation

and

its

cate

gorial

schema,

if

any;

and

the distinction

between

(a)

establish

ing

that

a

method of

prior

differentiation

belongs

to

a

schema

and

(b)

demonstrating

the

uniqueness

of the

schema. In

order

to

illus

trate

my

conclusion

with

examples

from

Kant's

work,

I

shall

try

to choose such as will not

only

serve to draw attention to

errors,

but

will

also

suggest

reasons

why

these

errors

are

liable

to

escape




7/16

322

THE MONIST

undetected.

I

begin

with what

I

consider

to

be

a

mistake

which

all

the

Kantian

attempts

at

transcendental

deductions

have in

common.

Assume that

we

have

investigated

a

method of

prior

differentia

tion

of

a

region

of

experience

and

found that it

belongs

to

a

schema.

The

result,

as

we

have

seen,

is

formulated

(a)

by

state

ments

to

the

effect

that

some

of

the

attributes

employed

by

the

method

are

constitutive

of the

objects

of the

region,

e.g.

that

among

the attributes is

one,

say

P,

such that P

is

applicable

to

objects

of

the

region

and

such

that

*x

is

an

object

of

the

region* logically

implies,

and is

implied

by,

(x

is

a

P\

(b)

by

statements

to

the effect

that

one

(or

more)

of

the

attributes

employed

are

individuating

for

the

objects

of the

region,

e.g.

that

among

the attributes is

an

at

tribute,

say

Q,

such

that

Q

applies

to

every

object

of

the

region

and

such that

*x

is

an

object

of

the

region

and

a

Q*

logically

implies,

and

is

implied

by,

'x

is

a

distinct

object

of

the

region*.

Let

us

now,

as

Kant

did,

examine

the

logical

status

of

(a)

statements

of

compre

hensive applicability and (b) statements of exhaustive individuation.

Each

of

them

is

a

conjunction

of

two

statements. The

first

ex

presses

that the extension

of

an

attribute

is,

as

a

matter

of

fact,

not

empty,

that

something

exists,

the existence of

which

could

not

be

guaranteed

by logic

or

definitions alone.

It

is

therefore

a

synthetic

statement.

The second

is

clearly logically

necessary.

Since

a con

junction

of

a

synthetic

and

a

logically

necessary

statement

is

syn

thetic,

the

statements

of

comprehensive

applicability

and

exhaus

tive individuation

are

all

synthetic.

Moreover,

each of these

two

kinds

of statements

in

question,

namely that of comprehensive applicability and that of exhaustive

individuation,

is

compatible

with

any

statement

about

objects,

i.e.

with

any

statement

expressing

the

applicability

or

inapplicability

of attributes

to

objects-provided

that

such

a

statement

is

made

by

a

method of

prior

differentiation which

belongs

to

the

schema.

The

reason

for

this

is

that

in

that

case no

attribute

can

be

applied

or

refused

to

any

objects

except

such

as

are

constituted and

indi

viduated

by

the

schema's

constitutive

and

individuating

attributes.

Thus

no

incompatibility

can

arise

between

the

statements

of

com

prehensive applicability

and

exhaustive

individuation of

a

cate

gorial

schema on the one

hand,

and

any

statement

expressed

by

a

method of

prior

differentiation

belonging

to

the

schema

on

the




8/16


other. The

statements

of

comprehensive

applicability

and

exhaus

tive

individuation

are

thus

a

priori

with

respect

to

a

particular

rschema,

namely

the

schema which

comprises

them.

It

does

not

fol

low that

they

are

also

a

priori

with

respect

to

any

schema

which

can

be

claimed

to

be

the

only

one

possible,

i.e. that

they

are

uniquely

a

priori.

Thus

in

establishing

that

a

method of

prior

differentiation

belongs

to

a

schema

one

shows

eo

ipso

that

the

statements

of

comprehensive applicability

and

of

exhaustive

indi

viduation

are

synthetic

and

nonuniquely

a

priori.

To

show that

they

are

uniquely

a

priori

would

require

a

demonstration

of

the

schema's

uniqueness,

which

I

have

just

argued

to

be

impossible.

Kant

did

not see

this,

and he

conflates

uniquely

a

priori

with

nonuniquely

a

priori

statements.

This

conflation

not

only

per

vades

his

whole

philosophy,

but

even

determines

its

structure,

espe

cially

the division

of

all his

principal

arguments

into

metaphysical

expositions

and transcendental

deductions.1 A

metaphysical exposi

tion

which exhibits

a

concept

as,

or

exhibits

it insofar

as

it

is,

a

priori is always the result of inquiry into one actually employed

method of

differentiation.

It

can

thus

at

best establish the

schema,

if

any,

to

which the

method

belongs.

A

transcendental

deduction,

aimed

at

showing

that

and how

a

priori

concepts

are

applicable

or

possible,

examines

only

the

schema

which

has

been

established

by

the

metaphysical

exposition

of

this

particular

schema.

It

thus

does

not

examine

a

schema the

uniqueness

of

which

has been

dem

onstrated. Kant's

failure

even

to

consider the

need for

interpolating

a

uniqueness-demonstration

between

any

metaphysical

exposition

and

a

corresponding


and

his

conflation

of

nonuniquely and uniquely a priori statements are so intimately

related

that

they

deserve

to

be

regarded

as

two

aspects

of

the

same

error.

The

reasons

why

these

points,

which

in

our own

day

are

not

too

difficult

to

see,

have

escaped

Kant,

are

partly

historical and

partly

logical.

The historical

ones,

are,

of

course,

that

like

most

of

his

contemporaries,

Kant

considered the

mathematics

and

physics

of

his

day

and

the

moral code

by

which he

found

himself

bound,

to

be

true

beyond

doubt;

he felt in

no

way

compelled

to

consider,

therefore,

the

question

of schemata

other

than

those

to

which be

l

See

Critique

of

Pure

Reason,

B.

38,

80 etc.




9/16

324

THE MONIST

long

the

methods

of differentiation

employed

by

him

in his mathe

matical,

physical

and

moral

thinking.

The

logical

reasons

are

that

his

various

attempts

at

transcendental

deductions

contain

sub

sidiary

assumptions

which tend

to

reinforce

the

common

error

underlying

all of them.

The

Transcendental

Aesthetic

which

exhibits

the individuat

ing

attributes

of

the Kantian

schema

is

based

on

the

assumption

that the

propositions

of

Euclidean

geometry

describe

the

spatial

relations

between

external

objects;

also

the

more

general assump

tion that

ii-per

impossibile-two

different

geometries

were

con

ceivable,

then

at most

one

of them

would

describe,

and

at

least

one

would

misdescribe,

these

relations.

However,

neither

Euclidean

geometry,

nor

any

other,

describes

the

spatial

structure

of external

objects

or

the

spatial

relations

between

them.

A

physical

triangle,

for

example,

is

not

an

instance of the

concept

'Euclidean

triangle*,

or

for

that

matter

'non-Euclidean

triangle',

just

as

neither

a

Euclid

ean

triangle

nor

a

non-Euclidean

one

is

an

instance

of

the

con

cept 'physical triangle*.To apply geometry to the external world

is

not to

assert

geometrical

attributes

of

external

objects,

but

to

identify

external

objects

with

instances of

geometrical

attributes

in

certain

contexts

and

for certain

purposes,

i.e.

to

treat

them

as

if

they

were

identical. The

applicability,

in

this

sense

of

one

geometry

does

not

exclude the

applicability

of another.

Kant

assumes

the

unique

applicability

to

external

objects

of

Euclidean

geometry,

without

even

attempting

to

establish

the

assumption.

Yet the

assumption

of

the

unique applicability

of

Euclidean

geometry

to

external

objects

is

a

key

premiss

in

the

very

argument

by

which he

tries to establish that spatio-temporal location in Euclidean space

and

Newtonian

time

is

the

principle

of

individuation

for

all

ex

ternal

objects-a

principle

which

he

shows

to

be

synthetic,

and

non

uniquely

(not,

as

he

thinks,

uniquely)

a

priori.

Again,

the

Transcendental

Analytic,

which

exhibits

the

consti

tutive attributes

of

the

Kantian

schema,

assumes

as

a

principle

that

the

categories

must

be

recognized

as

conditions

a

priori

of

the

pos

sibility

of

experience2

conceived

as

differentiated

into

distinct

exter

nal

objects

and

attributes

of

such.

Sufficient

conditions

are

not

distinguished

from

sufficient

and

necessary

conditions.

The

former,

2

See

e.g.

B

126.




10/16


which

Kant

tries

to

establish,

are

satisfied

by

the

establishment

of

a

schema.

The latter

would

be satisfied

only

if the schema's

unique

ness were

also

demonstrated. Failure

to

distinguish

between

the

two

lands

of

conditions

thus

supports

the conflation of

statements

synthetic

and

nonuniquely

a

priori,

with

synthetic

and

uniquely

a

priori

statements

of

comprehensive

applicability.

The

most

convincing

way

to

expose

Kant's

failure

to

give

a

transcendental

deduction of

the

schema

of

external

differentiation

established in

the

Critique

of

Pure

Reason,

is

simply

to

provide

an

example

of

a

different

schema

of

external

differentiation. Since

I

have

gone

into this

point

in

detail

elsewhere,3

I

may

put

it

here

quite

briefly.

Grant

that

determinate

spatio-temporal

location,

as

conceived

by

Newton

and

Kant,

exhaustively

individuates

exter

nal

objects

of

which

the Kantian

categories

of

substance,

causality

and

the

rest,

are

the

constitutive

attributes;

and

grant

also

that

the

statements

to

this

effect

are

synthetic

a

priori.

The

existence

of

relativistic

quantum-mechanics

compels

us

to

grant

equally

that

determinate spatio-temporal location in a spatio-temporal con

tinuum

of

an

altogether

different kind

exhaustively

individuates

ex

ternal

objects

of

which the

constitutive

attributes

are

quite

other

than

the

Kantian

categories;

and

to

grant

equally

that

the

state

ments to

this

effect

are

synthetic

a

priori.

But

neither

schema

of

external

differentiation is

unique;

and the

synthetic

a

priori

state

ments

about the

comprehensive

applicability

of,

and the

exhaustive

individuation

for,

external

objects

with

respect

to

either

schema

are

non-uniquely

a

priori.

In

Kant's

practical

philosophy

he

investigates

a

method

for

dif

ferentiating objects and attributes within the experience of the

practicable.

The

objects

might

be

called

morally

relevant

objects

since their

attributes

include

moral

attributes.

By

exhibiting

the

constitutive

and

individuating

attributes

employed

by

the

method,

the

method

is

shown

to

belong

to

a

schema.

Again

no

attempt

is

made

to

demonstrate

the

uniqueness

of

the

schema.

Such

an

at

tempt

could

not,

as

I

have

argued,

in

any

case

have been

successful,

from

which

circumstance

the

impossibility

of

any

transcendental

deduction of

the schema

immediately

follows.

3'Zur

Kantischen

Begr

ndung

der

Mathematik und der

Naturwissenschaften*

Kant

Studien,

56,

No.

s/4

1966).




11/16

326

THE MONIST

At

this

point,

however,

Kant

varies

his usual

procedure.

Hav

ing

established the

schema,

he

does

not

immediately

attempt

its

transcendental deduction.

Instead

he

tries

to

derive

a new

principle

from

it,

namely

the

categorical

imperative,

the

applicability

of

which

does

not

only

characterize

the

merely

morally

relevant

ob

jects,

which

are

constituted and

individuated

by

the

schema,

but

also those

among

the

morally

relevant

objects

which

are

the

bearers

of

moral

value.

Only

after

the

alleged

derivation

of

the

cate

gorical

imperative

is

completed,

does he

attempt

a transcendental

deduction

of

it

and

the

schema.

Kant's belief

that

an

examination of

his schema

of

practical

differentiation

yields

the

categorical

imperative,

which

he

regarded

as

a

necessary

and

sufficient criterion

of

the

morality

of

any

action,

was one

of

the

main

reasons

why,

in his

practical

philosophy,

he

overlooked

the

circumstance

that

to

establish

a

schema

is

not to

demonstrate

its

uniqueness;

and

why

consequently

there

too

he

conflated

synthetic

statements

which

are

nonuniquely

a

priori

with

uniquely

a

priori ones. I shall not consider Kant's derivation of the

categorical

imperative

from

the

allegedly

unique

schema

of

practi

cal

differentiation. Instead

I

shall

compare

that

schema

with

a

dif

ferent

one,

thus

providing

the

strongest

possible

kind of

argu

ment

against

the

assumption

of

its

uniqueness,

and,

therefore,

against

the soundness of

the

attempted

transcendental

deduction

of it.

Since

what

is

practicable

is

practicable

in

the external

world,

any

method

of

practical

differentiation will

depend

on,

and

vary

with,

the

adopted

method of

external

differentiation

and

even

with substantive

assumptions

about the external world, formulated

by

means

of this method.

Let

us

ignore

such

variations,

however

important

they

may

be.

Kant's

metaphysical

exposition

as

a

search

for the

constitutive

and

individuating

attributes

employed

in

his

method

of

practical

differentiation

leads him

to

the

following

con

clusions:

(a)

the

attribute

'x

is

a

morally

relevant

object*

is

not

empty;

and it

logically

implies,

and

is

logically

implied

by,

lx

is

a

type

of

act

and

x

is

performed

in

accordance

with

a

maxim,

chosen

by

an

agent*,

(b)

The

latter attribute

is

not

only

constitutive

of

morally

relevant

objects,

but also individuates them

exhaustively.

The

key-terms

of the bilateral

implication require

comment.




12/16


An

act

is

the

intentional initiation

(prevention

or

nonpreven

tion)

by

a

person

of

a

change

in the situation which confronts

him.

A

maxim

is

a

rule

of the

general

form:

'If in

a

situation

of

type

S,

perform

an

act

of

type

A\

S

and

A

are

not

the

unmanage

ably

long,

and

possibly

unlimited,

conjunctions

of

attributes

which

are

respectively

characteristic of

concrete

situations

and

particular

acts.

They

are

manageable

conjunctions

of

relevant

attributes

their

relevance

or

irrelevance

being

determined

by

the

person

who

chooses themaxim before

acting,

who formulates it

retrospectively

or

who is

at

least assumed

to

be

capable

of

doing

so.

S

may,

and

usually

does,

comprise

some

reference

to

the

person's

desires

and

intentions

other

than

the

intention

involved

in

performing

the

act.

A

need

not,

usually

does

not,

and-on

some

interpretations

of

Kant's

theory-must

not,

comprise

such

a

reference.

Examples

of

maxims where

A

does

not

comprise

it

are:

If in

. . .

help

(or

don't

help)

your

neighbour,

commit

(or

don't

commit)

suicide

etc.

According

to

Kant

an

act

by

itself is

not

a

morally

relevant ob

ject.What constitutes and individuates the bearers of moral at

tributes,

i.e.

of

moral

value,

disvalue and

indifference,

is the

type

A

under

which

a

person

subsumes his

act,

and

the maxim

to

which

he conforms in

acting.

At this

point

a

glance

at

the

history

of moral

philosophy

is

sufficient

to

provide

examples

of

schemata

of

practical

differentiation,

which

are

internally

consistent,

have

been

actually

employed

and

are

quite

different from

the

Kantian.

According

to

a

whole class

of

such

schemata

a

morally

relevant

object

is

a

com

plicated

relation

between

an

act,

the

agent's

beliefs,

the truth

or

falsehood of his beliefs and his

desires. Such

a

relation

need

not

depend on the person's chosen maxims; and is quite compatible

with

the reasonable

assumption

that

not

every

act

is

governed

by

a

maxim.

The

Kantian

schema of

practical

differentiation

is

non

unique

and

its


therefore

impossible.

III.

A

Revised Notion

of

Metaphysical

Exposition

Before

arguing

that

the

spurious

distinction

between

meta

physical

exposition

and

transcendental

deduction

should

be

re

placed by

a

revised

notion of

metaphysical

exposition

and

showing

how much in

harmony

such

replacement

is with some of Kant's

insights,

another

attempt

must be

briefly

examined

at

reconstruct




13/16

328

THE MONIST

ing

the

strategy

of the transcendental

philosophy.

It

sees

the

fundamental

error not

in

neglecting

the

problem

of

demonstrating

the

(undemonstrable)

uniqueness

of

any

schema of

differentiation,

but

merely

in

a

narrowness

of

the

methods

investigated

by

Kant

of

prior

differentiation

and

a

corresponding

narrowness

of

the

schemata

established

by

him.

On this

view

the

post-Kantian

development

of

physics

and

mathematics,

for

example,

would

merely

show the

Kantian

schema

of external differentiation as

having

to be

widened

before a

transcendental

deduction

is

attempted;

one

need

not

regard

a

transcendental

deduction

as

in

principle

impossible.

Thus

the

indi

viduating

attribute

for

external

objects

'x

wholly

occupies

a

region

of

space

and

an

interval

of

time

as

conceived

by

Newton*

is

to

be

replaced

by

*x

wholly

occupies

a

region

of

space

and

an

interval

of

time

as

conceived

by

Newton

or a

spatio-temporal

region

as

conceived

by

Einstein*.

In

a

similar

manner

the

Kantian

con

stitutive attributes

are

to

be

replaced

by

unions of

them

with

other

corresponding constitutive attributes. But, then, how could one

show that the

available

constitutive

and

individuating

attributes

exhaust

all

the conceivable

ones,

or

that

all

those

conceivable

have

been

conceived?

To

show

this,

one

would

have

to

produce

a

dem

onstration

of

the

widened

schema's

uniqueness

and,

as

has been

argued

quite

generally,

such

a

demonstration is

impossible.

In

his

metaphysical

expositions

of

a

particular

method

of

prior

external

and

a

particular

method of

prior

practical

differentiation,

Kant

has established that

they

belong

to

schemata,

i.e.

that

they

employ

constitutive

and

individuating

attributes.

The

statements

to

the effect that the constitutive attributes are comprehensively ap

plicable

to

the

objects

of the

differentiated

region

of

experience

and

that the

individuating

are

exhaustively

individuating

for

them,

are

synthetic

and

nonuniquely

a

priori-not

as

Kant

thought

uniquely

a

priori.

These

statements

do

not

demarcate the

structure

of

any

method

of

external

or

of

practical

differentiation,

as

neces

sarily

unchangeable;

they

are

compatible

with the

assumption-and

the historical

truth-that

schemata of external

and

practical

dif

ferentiation

can

change

and

become obsolete.

The constitutive

and

individuating

attributes

of

a

schema

which is no

longer

employed,

may

even turn out, or be

judged,

to

be

empty.

Having

e.g.

abandoned

the

Kantian schema of

external




14/16


differentiation

in favour of

another,

it

becomes

possible-looking

as

it

were

from

the

outside-to

assert

that the

Kantian attribute

of

substance is

empty,

i.e.

that

the

synthetic,

nonuniquely

a

priori

statement

asserting

its

comprehensive

applicability

to

external

ob

jects

is

false.

A

social

anthropologist

may

in

a

similar

manner

judge

that

the

constitutive

and

individuating

attributes

of

a

de

monology,

which he has

investigated,

are

empty,

even

though

a

cer

tain

way

of life

might

be

inseparably

bound

up

with

it.

In order

to

do

justice

to

such

possibilities

I now

define

a

revised

notion

of

metaphysical

exposition,

which

relativizes

the Kantian

absolute

notion in

a

number

of

ways.

It

is the

analysis

of

methods

for

the

differentiation of

more-or-less-well-demarcated

domains into

objects

and

attributes

which aims

at

the

exhibition

of

synthetic

and

nonuniquely

a

priori

statements,

by

exhibiting

the

schemata

in

respect

of which

the

statements

are a

priori.

The

differentiated

domain,

as

became clear

in

discussing

geometrical

statements,

need

not

be

a

region

of

experience.

It

may

be

a

domain of

ideal

ob

jects. A method of differentiation belongs, we remember, to a

schema

if,

and

only

if,

it

employs

attributes

which

are

constitutive

of all

objects

of

the

domain

and

attributes

which

individuate

all

of

them.

The constitutive

and

individuating

attributes

are

the

schema.

A

statement

is

synthetic

if,

and

only

if,

it

is

not

logically

valid

with

respect

to

the

logic

underlying

the

methods

of

dif

ferentiation

being

considered.

Thus

we

must,

distinguish

e.g.

statements

synthetic

with

respect

to

classical

from

those

synthetic

with

respect

to

intuitionist

logic.

A

statement

is

a

priori

with

re

spect

to

a

schema

if,

and

only

if,

it

is

compatible

with

any

statement

in which an attribute is applied to one or more distinct objects

by

means

of

any

method

which

belongs

to

the schema.

Among

the

kinds

of

schemata

which

a

metaphysical

exposition

(in

the revised

sense)

of various

methods

of

differentiation

may

establish for

them

are

the

following:

Schemata

(a)

of

external

differentiation,

including

the schema

established in

the

Critique

of

Pure

Reason

for

the

method

of external

differentiation

investigated

by

it. But

there

are

other,

methods of

external

differentiation

be

longing

to

the

same or

other

schemata.

Schemata

(b)

of

practical

differentiation,

including

the

schema

established in

the

Critique

of

Practical Reason for the method of

practical

differentiation in

vestigated

by

it. But

there

are

other

methods

of

practical

differentia




15/16

330

THE MONIST

tion

belonging

to

the

same or

other

schemata.

Schemata

(c)

of

idealized external

or,

briefly,

mathematical

differentiation of

a

do

main

which is

an

idealization

of

some

aspects

of

external

experience.

The

methods

of

differentiating

such

a

domain

and

the

statements

which

are

true

about

it,

are

sometimes

expressed

in

axiomatic

mathematical

theories,

even

though

a

large

class

of

such

theories

cannot,

as

G

del has

shown,

comprise

all

the statements

which

are

true

about

the

domain.

Kant,

as

was

pointed

out

earlier,

failed

to

recognize

the

multiplicity

of

possible

mathematical

schemata

and

confused

mathematical

with

external

differentiation.

Schemata

(d)

of

idealized

practical

differentiation,

which

are

of

interest

in the

study

of certain

normative,

e.g.

legal,

systems.

Schemata

(e)

of

logical

differentiation.

Their

establishment

results

in

synthetic

non

uniquely

a

priori

statements

of

comprehensive

applicability.

Such

a

statement

is

a

conjunction

consisting

of

two

statements,

an

ana

lytic

statement

asserting

that

certain

statement-forms

are

true

of

all

objects

constituted

and

individuated

by

any

of

the available

meth

ods of differentiation, and

a

synthetic statement asserting that the

domain of

these

objects

is

not

empty.

Kant,

who

was

not

faced with

the

problem

of

alternative

logics,

naturally

did

not

consider this

possibility.

Every

synthetic,

nonuniquely

a

priori

statement

is

a

priori

with

respect

to

at

least

one

schema.

Thus

statements

of

comprehensive

applicability

and

exhaustive

individuation

are

a

priori

with

respect

to

the schema

to

whose

constitutive and

individuating

attributes

they

refer.

Next,

all

synthetic,

ideal

statements

are a

priori

with

respect

to

any

schema

of

external

differentiation,

because

no

state

ment solely about ideal objects can be incompatible with any state

ments

solely

about

external

objects,

however

these

may

be

consti

tuted

or

individuated.

Again

the

question

how

far

statements

which

belong

to

a

schema

of

practical

differentiation are

a

priori

with

re

spect

to

a

schema of

external

differentiation

cannot

be answered

in

general,

since

methods of

external

differentiation and

methods

of

practical

differentiation

(and

their

schemata,

if

any)

may

stand

in

a

variety

of

relations

to

each other.

The

important

Kantian

distinction

between

synthetic

a

priori

statements

and

regulative

principles

remains

valid.

We

might

de

fine a

regulative

principle

as

being

synthetic

if,

and

only

if,

the

statement

describing

the

type

of

action

prescribed

by

the

principle




16/16


is

synthetic;

and

as

a

priori

with

respect

to

a

schema of

differentia

tion

if,

and

only

if,

the

descriptive

statement

is

compatible

with

any

statement

in

which

attributes

are

applied

to

objects

by

a

method

of

differentiation

which

belongs

to

the

schema.

Regulative

prin

ciples

which

are

in this

sense

synthetic

and

nonuniquely

a

priori

dif

fer,

of

course,

from

synthetic

and

nonuniquely

a

priori

statements

by

having

no

truth-value.

In the

course

of

a

metaphysical exposition

such

principles

will

often be

uncovered,

whether

or

not

we

decide

to

include

their

exhibition

among

its

explicit

aims.

Epistemologi

cally

of

greatest

interest

are

those

regulative

principles

which

regu

late

the

construction

of theories

and those

which

express

preferences

for

some

schemata

over

others.

Transcendental

deductions of

schemata and

of

synthetic

a

priori

statements

are,

as

I

have

argued,

impossible

because

their

unique

ness

cannot

be

demonstrated.

The

Kantian

question

as

to

how

synthetic

and

uniquely

a

priori

judgements

are

possible

does

not

arise.

In

its

place,

however,

there

arises

another

question:

How

are

synthetic and nonuniquely a priori statements possible? To answer

this

question

is,

as we

have learned

from

Kant,

to

examine the

function

of

such

statements,

that

is

to

say

their

relations

to

each

other,

to

analytic

and

to

empirical

statements.

The

task is

by

no

means

simple

or

trivial

as can

be

seen,

for

example,

by

considering

the relation

in

scientific

thinking

between various

schemata

of

ex

ternal,

ideal

and

logical

differentiation.

Moreover,

since

contrary

to

Kant's

convictions,

not

only

methods of

differentiation

but

also

the

schemata

to

which

they

belong

can

and

do

change,

the task

cannot

be

completed

once

and for

all,

but

must

be

undertaken

over and over again.

S.

K

RNER

THE

UNIVERSITY,

BRISTOL

S. Korner - The Impossibility of Transcendental Deductions

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Transcript of S. Korner - The Impossibility of Transcendental Deductions