Categories, Logical Functions and Schemata in Kant

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2/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

N

KANT

ARTHURMELNICK

In

the first

edition

Transcendental

Deduction

of

the

categories

Kant

does not

mention

the

logical

functions

of

judgment.

In

the

sec

ond edition

(the

B

edition)

the

Deduction

can

be

said

to

be dominated

by

the

logical

functions

of

judgment.

A

transcendental

deduction

sup

plies a method for showing that pure concepts can have applicability.

My

contention

is

that

the

two

deductions

constitute

exactly

the

same

method,

and

so

are

the

exact

same

deduction.

The

difference be

tween

them, rather,

is

in the

characterization

of

the

pure

concepts

that

the method is

supposed

to

be

a

method

for.

The

undifferentiated

cate

gories

of the

A edition become the

logical

functions

together

with

their schemata

in the B

edition.

This does

not

mean

that Kant has

split

the A edition

notion

of

categories

since the

A

edition

categories

are

equivalent

to

just

the schemata

themselves.

The

B

edition

simply

adds

the

logical

functions

to

the

character

ization

of

the

pure

concepts.

The

rationale

for

this

addition

is

that

Kant's

radically

new

theory

of

cognition

had

so

changed

the

notion of

judgment

or

thought

that the issue

of

the

relation of

judgment,

thus

newly

understood,

to

logical

reasoning

was

called into

question.

I

be

lieve the

picture

I shall

present

clarifies

not

only

the

structure of the

B

edition

Deduction,

but

the

nature

of

the

Metaphysical

Deduction and

the

Schematism

as

well.

I

We

begin

with

a

characterization

of

the

A

edition Deduction.

In

the first

of

what

he

calls

the

preparatory

sections

of the

Deduction,1

Correspondence

to:

Department

of

Philosophy,

University

of

Illinois,

105 Gregory Hall, 810 S.Wright Street, Urbana, IL 61801-3611.

1Immanuel

Kant, Critique

of

Pure

Reason

(hereafter,

CP? ),

ed. Nor

man

Kemp

Smith

(New

York: St.

Martin's

Press,

1965),

131-8;

A98-110.

The

Review

of

Metaphysics

54

(March

2001):

615-639.

Copyright

?

2001

by

The

Review

of

Metaphysics

http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/26

616 ARTHUR

MELNICK

Kant

characterizes

objective cognition

or

objective

representation

as

cognition that involves a constraint which prevents our modes of

knowledge

from

being

haphazard

or

arbitrary. 2

Kant

holds

that

this

constraint

cannot be

from

an

object

outside

our

sensible

representa

tions.

I

believe

that such

objects

for

Kant

would

have

to

be

repre

sented

purely

conceptually

or

discursively,

a

kind

of

representation

Kant had

allowed

in the

Inaugural

Dissertation but

soon

after

came

to

reject.

In

any

case,

Kant

locates

the

constraint, rather,

in

rules

for

sensible

representation.3

My

actual

sensible

representations

or

reac

tions may

be

constrained by

a

rule of

how

it is

proper

or

legitimate

to

react.

This

unity

of

reactions

under

a

rule is

equally

a

necessary

unity

since

a

rule

unifies

according

to

how

it

is

necessary

or

required

to

pro

ceed.

Objective

unity,

in

thus

being

identified

with

rule

unity,

is said

by

Kant

to

be

nothing

other than

the formal

unity

of

consciousness 4

or

nothing

but the

necessary

unity

of

consciousness. 5

The

unity

of

a

rule,

I

suggest,

is the

unity

of

apperception.6

In the

second

of

the

preparatory

sections

of

the

Deduction,7

Kant

introduces

the

idea

of

one

single

experience

(one

and the

same

gen

eral

experience8)

to which

all

possible perception

belongs.

Rules

en

able

us

not

only

to constrain

our

actual

reactions

but

to

extend

cogni

tion

beyond

actual

experience

altogether.

Thus,

it

may

have

been

proper

to react so-and-so

a

long

time

ago

(before

my

birth)

even

though

such

reaction

is

beyond

my

actual

experience.

Kant

is

saying

here

that

not

only

do

we

cognize

objectively,

but

that

we

cognize

a

world

extending

way

beyond

the

course

of actual

experience.

All

2

CPR,

134;

A104.

3

See

CPR,

135;

A105.

4

GRB,

135;

A105.

5

CKR, 137;

A109.

6

Kant

identifies

the

unity

of

apperception

with the

understanding

(see

CPR,

143;

A119)

and

identifies

the

understanding

(the

power

of

thought)

as

the

faculty

of rules

(see

CPR,

147; A126).

Kant's

repeated

contention

that

the

unity

of

apperception

is

a

necessary

unity

can

thus be understood

as

the

con

tention

that

the form

of

thought

is rule-form

(how

it

is

necessary

or

required

to

react).

That

is,

our

cognitions

or

thoughts

are

rules,

so

that

the

unity

of

our intellectual or cognitive consciousness in regard to the sensible is in

terms of rules

for

proper

sensible

reactions.

Thus,

without

going

outside

sensible

representations

(appearances),

Kant

has

imported

intellectual

or

objective

representation

into the

sensible

realm

by

equating

itwith

rules

for

reacting.

7CPR,

138-40;

Alll-14.

8

CPR, 138;A110.



4/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA 617

possible

appearances,

Kant

says,

must

stand

in

relation

to

appercep

tion.9 That is, my present cognitive ability10 must encompass a set or

repertoire

of rules

that

together

cover

the

full

scope

of

all

proper

reac

tions

(ranging

over

our

entire

sensibility, 11

or over

the

full

reach of

space

and

time).

This

is

an

utterly

central

characterization of

our

cog

nitive

power

for Kant.

I shall be

suggesting

that

there

is

no

under

standing

of

Kant's

proofs

of

substance

and

causation

if

one

thinks

that

the functions of

synthesis,

as

Kant

puts

it,12

pertain

basically

to

other

possible aspects

of

one's

actual

experience

(such

as

the back side of

a

perceived object)

as

opposed

to

possible experience completely be

yond

actual

experience.

For

Kant,

we

always

cognize

even our

actual

experience

as

situated

in

a

world

that

extends

way

beyond

it.

It

is

in

the A Deduction

proper13

that

Kant

introduces the

produc

tive

synthesis

of

imagination.14

If

the

unity

of

apperception

(rule

unity)

is to

encompass

all

possible

(all proper)

reaction,

itmust

relate

to the

pure

synthesis

of

imagination.

Indeed,

it must

combine

or

unify

that

synthesis.

Now

the

synthesis

of

imagination produces

or

con

structs the

pure

manifold of

space

and time.

Already

in

the Aesthetic

Kant had

argued

that

space

and time

are

constructions. Just

as

for

a

constructivist

in

mathematics

numbers

exist

only

in

constructions

(say,

as

termini

of

proper

counting

procedures),

so

too

for

Kant

space

and

time exist

only

in

flowing

constructions. His

argument,

I

believe,

is

that

continuity

is that

kind

of

utter

seamlessness

of

a

whole

(such

as

a

spatial

region)

which

precludes

the

whole

being

made

up

of

ele

ments. In

a

flowing

construction,

such

as

the

producing

of

a

line

seg

ment,

the

construction

of

the whole

is

prior

to

the construction

of

the

parts

that are

properly

understood as cuts made

subsequently

to the

flow.

Indeed,

I believe that what

Kant

means

by

space

and time

being

given

in

pure

intuition

is that

they

are,

or

exist

in,

flowing

9

CPR, 139;

All?.

10

Since

apperception

stands

in

relation

to

proper

reactions

beyond

what

can

possibly

belong

to

my

personal

history,

apperception

does

not

refer

to

the idea

of

a

unified

subject

through

various actual

experiences.

Appercep

tion,

I

suggest,

is

more

closely

to be

understood

as

the

present

cognitive

ca

pacity that I am (that identifies me as an intellect).

11

CPR,

139;

Alll.

12

CPR, 139;

Al 12.

13

CPR, 141-3;

Al

16-19.

This is the

deduction

from

above

(starting

with

apperception).

I shall

not

directly

consider

the

deduction

from

below

that follows since

I

believe

it is

essentially

the

same

deduction.

14

CPR,

142;

Al

18.



5/26

618

ARTHUR

MELNICK

constructions.15

An

example

of

a

temporal

construction

would

be

the

downbeat gestures (flowing constructions) of an orchestra conduc

tor,

which

temper

or

mark

time

for

the

orchestra's

playing.

I

suggest

now

that

the

synthesis

of

the

productive

imagination

is

exactly

such

flowing

construction. That

is,

the

synthesis

is

not

putting

an

extent

of

space

together

out

of basic

elements,

but

rather

generating

a

spatial

extent in

a

flow.16

This

is

made

clear in

the

B

edition

Deduction,

where Kant

characterizes

the

transcendental

act

of

imagination

as

a

motion

...

of

the

subject 17

(a

flowing

construction

of

the

subject).

The

relation of

the unity

of

apperception to the transcendental synthe

sis of

imagination,

now,

is

that

apperception

brings

construction

un

der

rules for

proper

constructing. Finally,

the

way

apperception

has

rules

encompassing

all

possible

appearances

(the

full

scope

of

proper

reactions)

is

by

having

rules

for

all

possible

spatio-temporal

construc

tions since all

proper

reactions

take

place

within the

compass

of

space

and time

constituted

by

proper

constructions.18

We

now

have

all

the

elements

of

Kant's

account

of

what

cogni

tion

is.

Cognition

is the

capacity

to

form

rules

for

the full

propriety

of

spatio-temporal

construction and

thereby

for

the

full

propriety

of

em

pirical

reaction.

If

now

there

are

concepts

which

contain

the

neces

sary

unity

of

the

synthesis

of

imagination

in

respect

of all

possible

ap

pearances 19

(that

is,

concepts

which

are

required

for

bringing

the full

scope

of

spatio-temporal

construction to

rules),

then

these

concepts

apply

to

all

possible

appearances

(all

proper

reactions). This,

then,

is

the

method

for

deducing categories

or

for

showing

that

categories

have

applicability.

15

Thus,

in

producing

a

line

I

am

in

immediate

singular

relation

to

the

very

object (the production),

and

so

I

intuit

or

exhibit it.

Further,

I

do

so

in

dependently

of sensation

(affection by

an

object),

and

hence the

producing

is

in

pure

intuition.

16

In

the Aesthetic

Kant

says

that

space

and

time

are

given

in

pure

intu

ition.

However

(see

the

preceding

footnote),

he

means

by

this

that

expanses

of

space

and time

are

given by

flowing

constructions.

This

understanding

of

their

being

given

in

pure

intuition, then,

is

by

no

means

inconsistent

with

their being produced by a synthesis (a flowing generation of an expanse) of

the

imagination.

17

CPR,

167;B155.

18

Spatio-temporal

construction is

not

only given

in

pure

intuition

but

is

the

form of all

empirical

intuition

as

well.

Proper

reactions

have their

place

and

time

by

being

proper

at

certain

stages

of

spatio-temporal

construction.

19

CPR,

143;A119.



6/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

619

n

The

Transcendental Deduction

basically

sets

out

Kant's

theory

of

what

cognition

is.

Any

concepts

that

are

required

to

effect

or

to

real

ize

cognition,

so

understood,

are

concepts

that

apply

to

any

cogniza

ble

reality.

It

is

in the

Principles

that

Kant

applies

this method.

In

or

der

to

see

how

this method

works,

and in

order

to

have

examples

to

refer

to

in

our

later

discussion

of

logical functions,

I

shall

consider

in

this section how

Kant establishes

the

applicability

of

substance

and

causation.20

Rules for

temporally constructing

or

marking

time have

to

en

compass

past

time.

Indeed,

the

propriety

of

now

going

ahead

to

mark

time,

as

with

a

series of downbeat

gestures,

does

not

begin

a new

time

but

must

be

a

continuation

of

ongoing

time.

Thus

Kant

says

that

time

is the

permanent

form of

intuition. 21

Note that it is

constructive time

(time

as a

form of

intuition)

that

must

be

permanent

(that

must not

be

gin

anew

with

present construction).

It

must

then

somehow

be

proper

to

be

presently

in the

course

of

temporizing

procedures,

which

one's

present

constructions then continue.

If,

for

example,

the

procedure

is

to

mark

time

by

a

series

of

downbeat

gestures

accompanied

by

a

reci

tation of

numerals

in

order,

then

there

must be

rules

for

being

in

the

middle

of such

a

procedure,

or

rules

for

being

up

to

a

stage

k of such

a

procedure.

But

now

it

cannot

just

be

proper

to

be

in

the

middle

of

a

procedure

without

having

carried

out

earlier

steps,

since

a

procedure

is

exactly

a

construction

to

be carried out in

order.

Since

I

have

not

been

performing

earlier

stages,

the

question

arises

as

to

how it

can

be

proper for me to be in the course of the procedure. Suppose there is a

procedure

for

baking

a

cake

according

to

which

one

first

puts

in

cer

tain

ingredients,

mixes

them,

puts

in

a

further

ingredient,

and

so

forth.

Suppose

that I

have

this

procedure

and

that

I

walk into

a room

and

find

the cake

already partially

prepared

in

the

mixing

bowl,

so

that it

only

needs brown

sugar

added

to

be

ready

for

the

oven.

Then

it is

proper

for

me

to be

up

to,

or

as

far

along

as,

the brown

sugar

stage

of

the

procedure.

Equivalently,

it

is

proper

for

me

to

be

past

putting

in

oil

or

eggs despite the fact that Inever put them in. Something inmy

present

circumstances

to

which

my

procedure

is

geared

makes

it

20

What

follows

are

sketches

of Kant's

arguments

in

the first

two

Analo

gies.

21

CPR,

213;

B224.



7/26

620

ARTHUR

MELNICK

proper

to

be

in

the

course

of

the

procedure

without

my

having

per

formed the earlier stages. Likewise, now, if I am to be in the course of

a

temporizing

procedure,

then

something

in

my

present

circum

stances

to

which

it is

geared

must

set

me

ahead

or

put

me

at

that

non

beginning stage.22

This

something

will

not

be

objective

time

itself23

but

will

have

to

be

something

in

the

objects

of

perception. 24

That

is,

it must

be the

case

that

something

presently

real

(something

that

presently

affects

me25)

is

so

far

along

in

its

continuing

existence

or re

ality

that

to

keep

up

with

it,

as

it

were,

it

is

proper

to be

so

far

along

in

a temporizing procedure geared to its existence

or

reality (just

as

the

present mixing

bowl

of

ingredients

is

so

far

along

in

its

cake-baking

existence

that

in

order

to

keep

up

with

it,

it is

proper

to

be

so

far

along

in

the

cake

baking

procedure).

What

gears

a

temporizing

proce

dure

to continued

existence

is

tracking,

or

keeping

track

of,

what

ex

ists.

If

existence

pertains

to

that which affects

us,

then

continued

ex

istence

pertains

to

continued affection

in

keeping

track

of what

affects.

It is

not then

the

temporizing procedure

itself

(the

time

marking

procedure

of

a

series of

downbeats

accompanied

by

recita

tion

of

numerals)

but

that

procedure geared

to

or

imposed

on

keeping

track,

which

keeps

up

with the existence

of what is

presently

real

(or

keeps

up

with

how

far

along

what

is

present

is in its

continued

exist

ence).

We

can

summarize

this

in

the

following

representation:

With

respect

to

what

presently

affects

(the

real),

it

is

proper

to

be

so

far

along

(say,

up

to

stage k)

in

a

temporizing

cum

tracking procedure.

This

represents

what

presently

affects

as

that

which is

proper

to

have

been tracking and so what is now so far along in its existence. Equiv

alently,

it

represents

the

permanence

of

the

real

(at

least

through

k

stages

of

temporizing).

Thus

permanence

of the

real,

or

substance,

is

22

Whatever

this

something

is functions

as

the

substratum

which

repre

sents

time

in

general

(CPR,

213;

B225)

or

the

basis

of

representing

the

per

manence

(ongoingness)

of

time

as

a

form

of intuition

(constructive

time).

23

CPR, 213;

B225.

That

is,

it

cannot

be that

it

is in order

to

keep

up

with

how

far

objective

time has

progressed

that

I have

to

be

so

far

along

in

my

temporizing. The reason is that there is no objective time. Recall that the

continuity

or

expansiveness

of time is

incompatible

with

any

existence

of it

other

than

in

a

flowing

construction.

24

CPR,

213;

B225.

25

Kant

says

the

real

is

an

object

of

sensation,

where

(the

matter

of)

sensation

contains

the

consciousness

that

the

subject

is

affected ;

CPR,

201;

B207.

The

real,

then,

is

that

which

affects.



8/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

621

the

substratum

of

the

permanence

of

time

as a

form of

intuition.

That

is, the lasting existence of what presently exists is the basis of rules

for

temporal

construction that

pertain

to

the

past.

Note

that

in

accord

with

the

method

set

out

in

the

Transcendental

Deduction,

the

concept

of substance

is

shown

to

be

required

to

bring

the

pure

synthesis

of

imagination

(time

construction

pertaining

to

the

past)

to

the

unity

of

apperception

(to

a

present

rule

of

propriety

re

garding

such

construction).

Without the

concept

of

substance there

are

simply

no

rules for

being

the

course

of

temporizing

constructions.

Further, and still in accord with themethod of the Deduction, proper

reactions

or

appearances

in

past

time

are

also

thereby

brought

to

present

apperception.

Thus,

if

the

procedure

is

augmented

to

one

in

which

reacting

red

accompanies

the

initial

stage

of

temporizing,

we

get

the

following

representation:

(1)

With

respect

to

what

presently

affects,

it

is

proper

to

be

up

to

stage

k

in

temporizing

cum

tracking

from

first

reacting

red.

In

(1)

the

reaction

is

proper

with

respect

to

what

presently

affects

me,

only

not now, but at an initial

stage

of

keeping

track of it. Because the

reaction is

thus

proper

with

respect

to

the

permanence

of

the

real

(trackable

existence

through

a

temporizing

construction),

it

is

in

that

sense

simply

a

determination

or

mode

of

substance

(of

what is

perma

nent). Thus,

in

sum,

past

proper

reactions

can

be

brought

to

present

rule

(present

apperception),

or can

be

part

of

one

single

experience

in

which

all

reactions

or

perceptions

have their

place, only

by

the

appli

cability

of

the

concept

of

a

substance of

which

they

are

determina

tions (in regard to which they are proper).

Although

the

purported

scope

of

cognition

is

just

the full

propri

ety

of

reactions,

it is

only

by

those

proper

reactions

being

determina

tions

of

(proper

with

respect

to)

substances

that

they

can

be

cognized.

This

applicability

of the

category

of

substance

to

appearances

(proper

reactions)

is

a

refutation

of

phenomenalism

since

without substance

the

proper

reactions

of the

phenomenalist

cannot

be

represented

or

cognized.26

26

Note further that the basis

or

authority

of

the

rule in

(1)

that

includes

reacting

is

the real that is

permanent

(substance).

This

entails that the rules

for

reacting

are

not

arbitrary

or

invented

but

are

due

to

phenomenal

affec

tion,

which

ensures

that these rules

express

real

objectivity.



9/26

622

ARTHUR

MELNICK

In the

Second

Analogy

it is

not

time

itself

as a

magnitude

or

ex

panse that is at issue but rather the nature of the time series. This na

ture

is that

each

time

in

the

series

advances

necessarily

to,

or

forces,

the

later time.

It does not

just

happen

to

be that

the

succeeding

time

comes

after

the

preceding;

rather,

it

emerges

from it

or

is

determined

by

it to

arise.27

It

is this character

of

necessary

advance

that

must

be

brought

to

present

rule.

Neither time

construction

itself28

nor

an

ob

jective (extraconstructive)

temporal

series29

can

represent

the

neces

sary

advance. Hence

it is

only

the

appearances

themselves

(proper

reactions) that

can

represent the necessary advance. That is, it must

be that the

appearances

of

past

time

determine

all

existences

in

the

succeeding

time. 30

The

necessary

advance of

appearances

repre

sents

the

necessary

advance

of the

time

series

as

follows:

(2)

With

respect

to

what

presently

affects,

it is

proper

to be in

the

course

of

a

series

of

reactions,

each of

which

necessarily

advances

to

or

determines

the

succeeding

reaction.31

But

now

to

say

that the

propriety

of

reacting

a

certain

way

determines

(or necessarily advances to, or forces) the propriety of subsequently

reacting

another

way

is

to

express

a

causal

relation

between the

proper

reactions.

Thus,

in

order

to

bring

the

character

of the time

se

ries

(as

one

in

which the

preceding

necessarily

determines

the

suc

ceeding)

to

apperception,

the

concept

of causation is

required,

where

the

concept

of causation

consists

in

the

succession of the manifold

in

so

far

as

that succession

is

subject

to

a

rule 32

(namely,

a

rule that

27

See CPR, 222; A194/B239. See also 225; A199/B244, where Kant says

that

it

is

a

law of

our

sensibility

that the

preceding

time

necessarily

deter

mines the

succeeding.

28

Nothing

determines

the

propriety

of

now

going

ahead

to

temporize

or

produce

a

series of

downbeats.

It

just is,

all

on

its

own,

proper.

This

propri

ety

may

continue

the

propriety

of

being

in

the

course

of

temporizing,

but it

does

not

necessarily

advance

from

that

propriety.

29

All

temporality

is

in

relation

to

the

continuous

expanse

that

time

is,

and,

as

per

the

Aesthetic,

only

within construction

is there

continuity.

There

simply

is

no

objective

temporal

series

(whether

understood

relationally

or

absolutely).

30CP?,225;A199/B244.

31

In

(2)

the

series

is

with

respect

to

the real

(what

presently

affects).

Once

again,

because

what affects makes

it

proper

to

be

in

the

course

of

a se

ries

of

reactions,

it is

not

only

the real but the

permanence

of the

real.

I

am

thus

following

Kant

here

in

relativizing

the

necessary

series

(and

so causa

tion)

to

determinations

of

a

single

substance.

32

See

CPR,

185;

A144/B183.



10/26

CATEGORIES,

OGICAL

UNCTIONS,

ND

SCHEMATA

623

each

necessarily

advances

to

the

next).

It is

only by representing

any

proper reaction as emerging within a series of proper reactions where

each

determines

the

next that

I

can

represent

the

reaction

within the

(necessary

advance

of

the)

time

series

and

so

represent

it

as

deter

mined with

respect

to

the

unity

of time

under

present

rule.33

HI

We

turn

now

to

the

logical

functions

of

judgment.

Neither

the

categorical

nor

the

hypothetical

function

of

judgment

played

any

role

in

our

account

of

the

A

edition deduction of substance

(permanence

of

the

real)

or

causation

(necessary

determination of the

succeeding

by

the

preceding

appearance).

It

is

not

until

the

B

edition

that Kant

in

corporates

logical

functions

of

judgment

into

the

Deduction.

The

logi

cal

functions

are

introduced

in the

A

edition

in section

9

(A70/B95

A76/B101). They

are

forms

of

judgment

so

far

as

judgment

is

involved

in

reasoning

(general

logic),

and

perhaps

in

abstract

thinking

gener

ally.

Kant

goes

on in the next section

(the Metaphysical

Deduction)

to

derive the list

of

categories.

The

significance

of

this

deduction,

I

be

lieve,

is that

Kant

has

set

out

an

entirely

new

theory

and

account of

in

tellectual

cognition

or

thought

in

the Transcendental

Deduction,

ac

cording

to which

cognitions

are

rules for

the

propriety

of

reacting.

The

two

preparatory

sections

of

the

A

edition

Deduction

make

clear

that

it

is

indeed

a

theory

of intellectual

cognition,

since

the rules

ac

count both for

objective

cognition

and for

cognition

beyond

actual

ex

perience to the full scope of proper or possible reaction. Further,

these rules

pertain

to what is outside the

understanding

(namely,

proper

sensible

reacting),

and these

rules

may

be

true

or

false

(in

that

a

rule

that

imputes

the

propriety

of

reacting

so-and-so

may

be

an

in

correct

rule

since

it

may

not

be

proper

to react

so-and-so).

In

sum,

these

rules

are

complete thoughts (cognitions

capable

of

truth

and

fal

sity).

Not

only

then

is

Kant's

account

an

account of

intellectual

cogni

tion

but

it is also

an

account of

judgment

since

a

judgment

is

exactly

33

An

objective

succession

(such

as

ship

upstream, ship

downstream)

is

only objective

because

it

has

a

place

in

the

necessary

advance of the

time

se

ries

as

represented

in

(2).

Irreversibility

may

be

the rule

distinguishing

suc

cession

from

coexistence,

but

necessary

determination

in

the

time

series

(causation)

is

what

makes the succession

objective

in time.



11/26

624

ARTHURMELNICK

what

pertains

to

reality

outside the

understanding

in

such

a

way

as

to

be capable of truth or falsity. Thus Kant has a whole new conception

of

judgments

as

rules

for

proper

reacting.

Now

we

also

reason

and

think

abstractly

in

judgments.

If

the

notion

of

judgment

is

to

be

a

uni

tary

notion

(namely,

if

there

is

to

be

a

single

phenomenon

of

judgment

involved

both

in

reasoning

and in

cognizing

sensible

reality),

then

it

is

incumbent

upon

Kant

to

show

how

judgments

in

reasoning

are

related

to

judgments

in

real

cognition.

After

all,

so

far

on

his

new

theory

of

judgment

as

cognition,

there is

nothing

that

looks like

categorical

or

hypothetical form. In this sense, it is the very unity

or

integrity of the

understanding

as

the

faculty

of

judgment

that is

at

stake

in

the

Meta

physical

Deduction.

What

I

am

suggesting,

then,

is

that the

issue

Kant

characterizes

as

the

issue of

the

origin

of

the

categories

is

just

the

is

sue

of

the

understanding

being

a

unitary

capacity

of

judgment,

opera

tive

in

both

reasoning

and

in

cognizing

the

sensible?an

issue made

severe

by

Kant's

radically

new

account of

judgment

as

cognition

of

the sensible.34

Besides

the issue

of the

origin

of the

categories,

Kant

sees

the

derivation

from

logical

functions

as

providing

systematicity

and

completeness

to the

categories.

I

shall consider

these

issues

briefly,

but the

main

issue

is the issue

of

judgment

as

a

unitary

capac

ity.

The

list of

logical

functions

themselves

can

perhaps

be

faulted

over

their

systematicity

and

completeness

which,

of

course,

would

call

into

question

how

the

categories

could

then

inherit

these features

from

them.

First,

there

can

be

alternative

lists,

each

providing

suffi

cient

forms for

reasoning

(as

in

modern

quantificational logic).35

This

is no

problem

as far as the issue of there

being

a

unitary

judgmental

capacity

is

concerned,

so

long

as

at

least

one

complete

list of

logical

functions

can

be

paired

with

the

categories.

Second,

one

may

wonder

over

the

completeness

of the

logical

functions,

but

from

a

modern

point

of

view,

model

theoretic

completeness

provides

a

standard

for

a

complete proof

theory

and hence

a

standard

for

adequate

logical

34

The

origins

issue, then,

seems

to

me

to

be

a

real

one.

Theoretically,

Kant had two options, namely, to give a new theory of reasoning directly in

terms

of rules for

proper

reacting

(hence

abandoning

the

traditional

logical

forms),

or

to

show

how

the

logical

functions

are

operative

even

in his

new

theory

of

cognition

of the sensible.

He

clearly

saw

only

the

latter

as

an

alter

native.

35

See Peter

Strawson,

The Bounds

of

Sense

(London:

Methuen

&

Co.,

1966).



12/26

CATEGORIES,

OGICAL

UNCTIONS,

ND

SCHEMATA 625

form.

Of

greater

concern

is Kant's

apparent

doctoring

of

the

list of

logical functions; for example, his distinguishing the singular from the

universal

and

the affirmative

from

the

infinite.36

As

long

as

the

doctor

ing,

however,

is

not

done

in terms

of

his

new

rule

theory

of

cognition,

there

is

no

circularity

in the

derivation of

categories

that

relate

to

that

new

theory.

Kant's

ground

for

distinguishing

the

singular

from the

universal

is

that

they

express

different

quantities

of

knowledge.

His

ground

for

distinguishing

the

affirmative

from

the infinite is that

they

express

or

have

a

different

content

of

knowledge.

Whatever

he

means

by these remarks, it is clear that he thinks that they differ in these

ways

already

in

a

context of

abstract

thinking.37

If

judgment

is

in

volved

in

purely

abstract

thinking,

such

as

thinking

purely conceptual

connections,

and

some

of its

forms

(singular

versus

limitative)

in

this

context

go

beyond

mere

logical form, they

are

still forms

of

judgment.

Hence,

the

unitary

character

of

judgment

is then understood

insofar

as

the

forms of

judgment,

in

relation

to

Kant's

new

account

of

judg

ment

as

rule

cognition,

should cohere with

the forms

of

judgment

in

two other contexts

Qogical

reasoning

and

abstract

thinking),

which is

no

circularity.

Finally,

the

supposed

idea that

general

logic

depends

on

transcendental

logic,38

so

that the

former

cannot

be the

source

of

the

latter,

is

also,

I

believe,

harmless.

As

far

as

the

unitary

nature

of

judgment

goes,

all

that

matters

is

that the

forms

cohere

between

both

contexts

(reasoning

and Kant's

new

theory

of

cognition

by rules).

Kant

states

the

supposed

priority

of

transcendental

logic

in

a

footnote

to

B133-4.

Even

here

all

he

says

is that

general

concepts

presuppose

a

synthesis,

and

(supposedly)

general logic

requires

general

concepts

(since syllogistic logic

is a

logic

of

concepts).

This much

by

no means

implies

that

judgment

forms

are

involved

in

this

presupposed

synthe

sis.39

If

they

are

not,

then the

synthesis

presupposed by general

logic

36

See

Henry

Allison,

Kant's

Transcendental Idealism

(New

Haven:

Yale

University Press,

1983),

128.

37

Nowadays,

the

distinction between

singular

and universal is

purely

logical,

and the distinction

between

negation

(rather

than

affirmation

as

per

Kant)

and

limitation

can

be made

out

logically, perhaps,

in

multivalued

log

ics.

38

See Norman

Kemp

Smith,

Commentary

to

Kant's

Critique

of

Pure

Reason

(London:

Macmillan

and

Co., 1918),

184-5,

and 196.

39

For

example,

I

can

represent

different reactions of

red

as

different

for

being

proper

at different

stages

of

(a synthesis

of)

actual

temporizing

cum

tracking,

and

so

come

to

a

conceptus

communis

or

general

concept

of

red,

without

any

employment

of the

categories

of

substance

or

causation.



13/26

626

ARTHUR

MELNICK

does

not

imply

that

general logic

(and

its

forms)

presuppose

the

cate

gories (the forms of judgment involved in Kant's new account).40

We

turn

now

to

the

Metaphysical

Deduction

proper

in

section

10

(A72/B102-A83/B109).

In

this

section

Kant

first rehearses

or

outlines

his

theory

of

cognition

from

the

Transcendental

Deduction.

The

rea

son

for

this is

simply

that

he

is

leading

up

to

the idea

of

logical

forms

of

judgment

also

being

forms of

judgment

according

to

this

new

the

ory

of

cognition

or

judgment.

The

key

passage

is the

paragraph

at

A79/B105

(112-13).

In

this

paragraph

Kant

identifies the

logical

func

tions as, indeed, functions that have

a

role in his new account of cog

nition

as

synthetic

unity

of

intuitive

representations.

That

is,

these

functions of

reasoning

also

bring

sensible

intuitions

to

the

unity

of

ap

perception

(or, equivalently,

these

functions

operate

to

yield

rules

for

proper

reactions).

I

contend,

however,

that

although

they

are

charac

terized

as

having

this

intellectual

cognitive

role

of

bringing

sensible

intuitions

to

apperception,

Kant is

here

purposely

abstracting

from

the

idea that this

unity

of

representations

is

via

the

unity

of

the

pure

manifold

of

space

and

time.

First,

the

concepts

he

comes

up

with in

the

following

table

of

categories

are

exactly

the

concepts

that he later

schematizes,41

and

it is

only

the

logical

functions

as

schematized that

transcendentally

determine

the

pure

manifold of

time.

Second,

he

chides Aristotle

for

confusing

modes

of

pure

sensibility

with

catego

ries,42

which

suggests

that

he

is

understanding

the

role

of the

logical

functions

apart

from

pure

sensibility. Third,

in

the B

edition

Deduc

tion where he refers

back

to

the

present

sections

and its

categories,

he

says

since

the

categories

have

their

source

in the

understanding

alone,

independent

of

sensibility,

Imust abstract from the modes in

which the manifold

for

an

empirical

intuition

is

given. 43

The

significance

of the fact that

Kant identifies these functions

as

giving

unity

to

representations

in

an

intuition in

the

first

sentence

while

he

relates

them

to

the

unity

of

the manifold

of

an

intuition

in

general

in

the second

sentence,

is,

I

believe,

that

his

new

theory

of

40

As to the problem of the supposed lack of fit between the disjunctive

judgment

and

the

category

of

community

to

follow,

replacing

disjunction

with the biconditional

would suffice.

41

Compare

this table with the

passage

from

183-5;

A142/B182-A145/

B184.

42

CPR,

114;A81/B107.

43

CPR,

160-1;

B144.



14/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

627

cognition

has

two

components.

First,

as

in

the

first

preparatory

sec

tion of the A edition Deduction, the unity of reactions under rules is

objective unity,

which

pertains

to

constraining

what is

actually

given

(how

we

actually

react)

in

an

intuition.

Second,

as

in

the second

pre

paratory

section of

the A

edition

Deduction,

the

unity

of reactions

un

der rules is the

unity

of

(merely)

possible

reactions

beyond

what is

ac

tually

given

in

an

intuition, by

which all

perceptions

belong

to

one

and the

same

general

experience. 44

For Kant the

power

or

nature

of

thought (judgment

or

intellectual

cognition)

is

that it

goes

beyond

mere

passive reception (actually reacting) by constraining that recep

tion

(objectivity),

and

also

by

representing

it

as

part

of the full

scope

of

proper

reactions

(unifying possible experience

in

general).

In

this

paragraph,

then,

Kant

is

identifying

the

logical

functions

as

having

both these roles

in

his

new

theory

of

cognition.

In

sum,

then,

Kant

is

saying

that

the

logical

functions

or

the

forms

of

judgment

in

reasoning

are

also forms of

judgment

as

cognition,

that

is,

forms for

objective cognition

constraining

actual

experience

and

forms

for

cognizing

beyond

actual

experience.

Indeed,

they

are

forms

for

bringing

sensible

intuition

to

the

unity

of

apperception,

where the

unity

of

apperception

is

objective

unity

(as

per

the

first

preparatory

section

of the A

edition

Deduction45)

and also that

unity

which stands

in relation

to

all

possible

appearances

(as

per

the second

preparatory

section46).

The

table

of

categories, then,

is

a

table of the

logical

func

tions of

judgment,

only

conceived

as

having

the role of

bringing

reac

tions under

the

unity

of

rule. The

basis

of

this

conception,

and

so

this

derivation,

is

simply

the

assertion

of the

unity

or

integrity

of

the

no

tion of

judgment

itself; namely,

judgment

is both the unit of

reasoning

and

the unit of

cognition,

so

that

if

there

are

forms of

judgment,

these

are

forms of

judgment

both for

reasoning

and

for

cognition

(where

cognition

is

bringing

sensible

intuition

under

the

unity

of

appercep

tion).

This,

I

claim,

is the

Metaphysical

Deduction.

Of

course

Kant

is

not

showing

that

these

concepts

have

applica

bility.

The

concept

of

a

form

of

judgment

as

cognition

(as

bringing

sensible

reactions

under rule

unity)

is

still, by

itself,

a

mere form of

thought, without objective reality. 47 If they have applicability then

?See

CPR, 138;

Al

10.

45

See

CPR, 135;A105.

46

See

CPR, 139;

A112.

47

CPR,

163;

B148.



15/26

628

ARTHURMELNICK

they

will

apply

a

priori

since their

origin

and

their

very

content

as

con

cepts

is not in the sensible

given,

but in the nature of

cognition

(judg

ment)

itself.

However,

it

is

only

via

their

schemata

that

they

could

ap

ply

or

that

they

could

be

concepts

that

bring

sensible intuition under

rule

unity.

Not

only

is

Kant

not

deducing

that

they

do

or

must

apply;

he is

not

even

deducing

that

they

can

apply.

All

he is

deducing

is

that

there

are

purely

intellectual

concepts

(namely,

concepts

of

forms

of

judgment)

purportedly effecting

intellectual

cognition,

where that

cognition

is

a

matter of

bringing

sensible

intuitions

under

rules.

Roughly, then, in theMetaphysical Deduction Kant ismerely asserting

that

judgment

is

a

unitary

integral

capacity.

His

full

proof

or

defense

of

this

assertion

(in

relation

to

his

new

theory

of

judgmental

cogni

tion)

takes the

whole Transcendental

Analytic.

IV

Kant

says

that

in

applying

a

category

to

appearances,

we

set

its

schema

alongside

the

category,

as

its

restricting

condition. 48

Thus

both

the

logical

function

of

judgment

and

the

schema

are

components

of the

cognition

of

appearances.

In

our

representation

of

substance

above,

we

had the

permanence

of the

real,

which

is the

schema

of

the

logical

function

of

subject-predicate.

If

we

now

put

this

schema

alongside

the

logical

function

we

get:

(3)

With

respect

to

what

presently

affects,

it is

proper

to

be

up

to

stage

k

in

a

temporizing

cum

tracking procedure

that

begins

with

reacting

red

and saying That is red.

Now

the

procedure

we are

up

to

stage

k

in

begins

not

just

with

react

ing

to

what

is

trackable,

but

also

saying

(or thinking)

That is

red.

In

(3)

this

logical

function

of

subject-predicate

is

indeed

functioning

to

express

the

relation

of

sensible

intuitions

(proper

reactions)

to

the

unity

of

apperception

(to

the

unity

of

a

present

rule).

That

is,

it is

functioning

as

a

judgment

or

cognition

according

to

Kant's

new

con

ception

of

cognition,

and

according

to his

characterization

in

the

Metaphysical

Deduction.

48

CPR,

212;

A181/B224.

See also

211-12;

A181/B223,

where Kant

says

that

appearances

are

subsumed

not

simply

under

the

categories,

but

[also]

under

their

schemata.



16/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

629

In

(3)

I

am

not

now

making

the

judgment

That

is

red.

Indeed,

I

cannot make that judgment with that significance (of pertaining to

past

reality)

because

I

am

not

situated

in time

so

as

to

make that

judg

ment.

I cannot

go

back

in time

and

say

That is

red.

Although

I

can

not make

that

judgment,

I

can

license

making

it if

I

can

presently

rep

resent

the

significance

of

making

it

(namely,

its

significance

as

pertaining

to

past reality),

which in turn

is

a

matter

of

representing

the

situation

in

which

it

can

be

made. This

requires

a

determination

of

time,

that

is,

a

determination

of

my

present

situation

as

the Zrth

stage

of

a

temporizing procedure whose first stage

is

the

situation for mak

ing

the

judgment.

In

this

manner,

a

formal and

pure

condition

of

sen

sibility (namely,

time)

restricts,

as

it

enables,

the

employment

of the

logical

function.49

This

time

determination

enabling

the

logical

func

tion,

further,

is

in

conformity

with

the

unity

of

apperception, 50

in

that

representing

the

significance

of

the

judgment

involves

bringing

past

time

to

the

unity

of

apperception,

or

the

unity

of

a

present

rule.

In

(3),

indeed, past

time

is determined

by

a

rule

(the

propriety

of

being

up

to

stage

k

in

temporizing).

Finally,

what enables

the

sense

of the

logical

function

is

not

only

a

determination

of time

in relation

to

a

rule,

but

a

determination

in

accord

with

a

concept

(permanence

of the

real).

Kant

says

that

the

schema

is

a

pure

synthesis [time

determina

tion]

determined

by

a

rule of

unity [apperception]

in

accordance

with

concepts. 51

In

(3)

above

it is

the

concept

of

the

permanence

of the

real

(that

what

presently

affects

is

also

what

is

proper

to

be

in the

course

of

tracking)

in accordance

with which

past

time is

determined

in relation

to

the

unity

of

apperception

(in

accordance

with

which

it is

proper

to be in the course of

temporizing).

Again,

Kant

says

the

schema

contains and

makes

capable

of

representation

only

a

determi

nation

of

time. 52

In

(3)

the

permanence

of the real

(the

propriety,

with

respect

to what

presently

affects,

of

being

up

to

k

in

tracking)

contains

or

makes

capable

of

representation

a

determination

of time

(the

propriety

of

being

up

to

stage

k in

temporizing)

or,

equivalently,

the

permanence

of

the

real

is

the

concept

that contains the

pure syn

thesis

of

time in

relation

to

apperception.

49

CPR,

182;

A140/B179.

50

CPR, 183;

A142/B181.

51

CPR,

143;

A142/B181.

52

CPR,

185;

A145/B184.



17/26

630

ARTHURMELNICK

Although

the transcendental

determination of time is what

is ho

mogeneous as between logical functions and sensible intuitions, Kant

does

not

identify

the schema with

the

transcendental determination

but

rather with

a

concept

that

contains it

or

with

which it is

in

accord.

If the schema then is

a

concept

containing

a

determination

of

time,

or,

equivalently,

if

the

schema is

a

pure

synthesis

determined

by

a

rule of

unity

in

accordance

with

concepts,

then

it is the

entire

representation

in

(3),

other than

the

subject-predicate

judgment

itself,

which

is the

schema

of

that

judgment.

It is

then

this schema which mediates the

subsumption of appearances under the category, 53 where the cate

gory

is the

logical

function

of

judgment

as

cognition

(as employed

in

relation

to

unity

of

sensible

intuitions).

That

is,

the

subject-predicate

judgment

is

represented

as

pertaining

to

that

possible

appearance

(that

proper

reaction

red )

via

bringing

that

possible

appearance

to

the

unity

of

apperception

by

the

permanence

of

the

real.

In

effect,

the

judgment

pertains

via the entire

representation

in

(3)

other than the

judgment

itself.

In

relation

to

the

Metaphysical Deduction,

we

note

that

in

(3),

not

only

does the

unity

of

apperception

(rule unity)

extend

to

possible

ap

pearances,

but

the

subject-predicate

form of

judgment

does

too

as

giving expression 54

to

the

schema.

Indeed,

in

(3)

the

judgment

that

is

licensed

signifies

or

expresses

the

permanence

of

the real since

the

term that

pertains

to

a

real

that

is

trackable

into the

present.

Kant's

new

theory

of

intellectual

cognition

or

thought

as

rules is

now

consis

tent with

intellectual

cognition

as

judgment

having

logical

form.

What

the

schema effects

is

not

just

cognitive

unity

but

cognitive

unity

as

unity

for

logical

functions of

judgment.

Kant's characterization of the

derived

logical

functions

(the categories)

in

the

Metaphysical

Deduc

tion

is

now

finally

realized

since

the

subject-predicate

form

of

judg

ment

expresses

the

relation

of

reacting

red

(that

possible

experi

ence,

or

that

empirical

intuition)

to

the

unity

of

apperception.

I believe what

Kant

says

of

the

schemata

of

pure

concepts applies

to

causation

as

well.

If

we

add

the

logical

function of

the

hypothetical

judgment

to

(2)

above,

we

get:

(4)

With

respect

to

what

presently

affects,

it is

proper

to

be

in

the

course

of

a

series

of reactions

each of

which

determines

the

next,

while

53

CPR, 181;

A139/B178.

54

CPR,

183;

A142/B182.



18/26

CATEGORIES,

LOGICAL

FUNCTIONS,

AND

SCHEMATA

631

being

in

the

course

of

saying

of

each

pair (of

states of

the

substance),

If

that is so-and-so, then that is such-and such.

Since each of the

proper

reactions is with

respect

to

what

presently

af

fects,

each is

a

determination

of

substance,

which

gives

sense

to

the

occurrences

of

that

in

(4).

The

representation

in

(4)

minus the

hypo

thetical

judgment signifies

the

succession

of

the

manifold,

in

so

far

as

that

succession

is

subject

to

a

rule

(the

rule

that

each determines

or

necessarily

advances

to

the

next).55

Each

hypothetical,

then,

ex

presses

that

the

antecedent

necessarily

determines the

consequent,

that is, that the substance being so-and-so is causally connected to its

then

being

such-and-such.

Once

again,

the

schema

contains

and

makes

capable

of

representation only

a

determination of

time, 56

or

the schema

is

a

pure

synthesis

determined

by

a

rule

of

unity

in

accor

dance

with

concepts. 57

The

pure

synthesis

or

the time

determination

in this

case

is the

necessary

advance of

the time

order,

and

the

con

cept

which

brings

the

necessary

advance to

present

rule

(to

the

unity

of

apperception)

is causation

(that

is,

that each

proper

reaction

neces

sarily advances to the later proper reaction).

Kant's

characterization

of

a

schema,

as

a

transcendental

product

of

imagination,

which

concerns

bringing

representations

to

the

unity

of

apperception

by

a

concept,58 exactly duplicates

his

characterization

of

a

category

in the

A

edition Deduction

where

he

writes,

In

the

un

derstanding

there

are

pure

a

priori

modes

of

knowledge [concepts]

which contain the

necessary

unity

of the

pure

synthesis

of

imagination

in

respect

of

all

possible

appearances,

and

these

are

the

categories.59

Compare

this

with

his statement

in

the Schematism where

he

writes,

the schema is

simply

the

pure

synthesis

[of imagination]

determined

by

a

rule

of

[that]

unity

in

accordance with

concepts. 60

Of

course

in

the

Schematism,

the

concept

(such

as

the

permanence

of the

real)

that

contains

or

determines

the

unity

of

the

pure

synthesis

of

imagination

is also

given expression61

by

the

category (the

logical

function

as

it

55

CPR,

185;

A144/B183.

56

CPR,

185;

A145/B184.

57CPR, 183;A142/B181.

58

CPR,

183;

A142/B181.

59

CPR,

143;

A119.

In the

Schematism

he

even uses

the

same

term

when

he

says

the

schema

contains and

makes

capable

of

representation

only

a

de

termination

of

time.

See

CPR,

185;

A145/B184.

60

CPR,

183;

A142/B181.

61

Ibid.



19/26

632

ARTHUR

MELNICK

pertains

to

cognition)

that it

is

a

schema of. In

the A

edition

Deduc

tion there isn't this relation to a logical function. Even when Kant

talks

of

the

mediating

function

of

the

imagination

in

the

A

Deduc

tion,62

it does

not

mediate

between

logical

functions and

sensible

intu

ition

as

it

does

in

the

Schematism,

but rather

between the

necessary

unity

of

apperception

as

such

(rule

unity)

and

sensible

intuition.

The

pure

concepts

of

the

A

edition

Deduction,

then,

are

essentially

equiva

lent

to

the

schemata.

The

only

difference

is

that

in

the

Deduction

they

are

not

characterized

as

schemata

(that

is,

as

related

to

logical

func

tions of judgment). This is certainly not the case in the B edition De

duction,

where

the

logical

functions

of

judgment initially

(up

through

section

20)

play

the

only

role

and

where

even

the

unity

of the

synthe

sis

of

imagination (in

section

26)

is

characterized

in

relation

to

logical

functions.

What

I

contend

is

that

this

difference

in

characterization is

basically

the

only

difference

between

the

deductions.

Whereas

the A

edition Deduction

supplies

a

method

for

deducing

pure

concepts,

where

that method

is to

show

they

are

concepts

containing

or

en

abling

the

unity

of

imagination

(time)

in

relation

to

apperception,

the

B

edition Deduction

supplies

a

method

for

deducing

pure

concepts,

where that method

is

to

show

they

are

concepts

characterizable

as

the

applicability

of

logical

functions of

judgment

containing

or

en

abling

the

unity

of

imagination

in

relation

to

apperception.

It is the

exact

same

method and

so

the

exact

same

deduction, only

the charac

terization

of the

conce

Documents

Categories, Logical Functions and Schemata in Kant