carnap conventionalism

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Carnap's ConventionalismAuthor(s): Richard CreathSource: Synthese, Vol. 93, No. 1/2, Carnap: A Centenary Reappraisal (Nov., 1992), pp. 141-165Published by: SpringerStable URL: http://www.jstor.org/stable/20117711 .

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RICHARD

CREATH

CARNAP'S CONVENTIONALISM

When Herbert

Feigl

spoke

at

the memorial

session

for

Rudolf

Carnap

in

1970

he

recalled

an

incident

that

was

especially

revealing:

he

and

Carnap

were

walking in

a

park in Vienna, and Carnap described the

first ideas that later became The

Logical

Syntax of

Language.

Feigl

responded

that the

syntax

that

Carnap

formulated

in

a

metalanguage,

amounted

to

a

'Hilbertization'

of

Principia

Mathematica .

Carnap

smiled and

accepted

this

description

as

essentially

correct

(Feigl,

1975,

p.

xvi).

Feigl

was

right,

of

course,

perhaps

righter

than

he knew. For

the

Logical

Syntax

owed far

more

than its

metamathematical form to Hil

bert. The

book's central

idea is

an

epistemic

doctrine that

shaped

Carnap's

philosophy

until the

day

he

died. And that central

idea is

a

development of Hubert's work as well. Ironically this Hilbertization of

content

beyond

that

of

form

probably

did

not

occur

until

the

syntax

project

was

well under

way,

and

hence

was

probably

not

part

of

the

sketch

that

Carnap

presented

to

Feigl.

But who knows?

Perhaps

that

crucial

epistemic

doctrine

was even

then

forming

in

the back of

Carnap's

mind.

Could that be

why

he smiled

at

Feigl's

remark?

In

any

case

what I

want to

do

here

is

to

explore

that

epistemology

of

Carnap

in

order

to

see

what it

was,

why

it

was

such

a

step

forward

in the

1930s,

and what it has

to

teach

even now.

To

do that

my

remarks

will

divide into three

parts.

In

the first

I

shall

sketch

Carnap's

new

epistemology;

in the second I shall

say

something

of its

sources;

and in

the

third,

after

some

brief remarks

about

methodology,

I

shall

try

to

apply

the view

to

some

enduring problems

of observation.

1. CARNAP'S

EPISTEMOLOGY

One

tends

to

think of

Carnap

as a

well-known

figure,

but

if

those

paragraphs

on

logical

empiricism

that

are

apparently

de

rigueur

in

recent

philosophy

of science books

count

as

evidence of the

received

view of

Carnap's epistemology,

then

most

philosophers

have

only

a

Synthese

93:

141-165,

1992.

?

1992 Kluwer Academic Publishers. Printed

in

the Netherlands.



142

RICHARD CREATH

hazy

idea of

Carnap's

work,

and their criticisms

are

often

directed

against

a

straw

man.

We would do well

to

begin

afresh.

The chief business of

epistemology

is

to

provide

a

theory

of

justifi

cation;

it

must

tell

us

what beliefs

are

justified,

and in

what

manner

and

to

what

degree they

are so.

Usually

when

we

are

asked

to

justify

our

beliefs

we

do this

by

giving

reasons: we

bring

forward

one

or more

other beliefs

which

(1)

are

themselves

justified,

and

(2)

stand in the

right

sort

of

relation

to

the belief for which

justification

was

sought.

Both features

are

important.

It is the

special

province

of

logic,

deductive

and

inductive,

to

specify

further

the

second

requirement.

But it

is the

first

requirement,

that

the

justifying

beliefs

themselves be

justified,

that

concerns

us

at

this

moment.

Assuming

that

justification

is

not to

be

circular,

that first

requirement

involves

us

in

a

regress

which,

if

it is

not to

be

vicious,

must

stop

somewhere.

In

other

words,

if

reason-giving

is

to

succeed

in

justifying

anything,

there

must

be

some

beliefs

which

are

justified

in

some

way

other than

inference;

there

must

be

some

non-inferentially

warranted

beliefs. This fact is quite separate from any issue between foundational

ist and coherentist

epistemologies.

It is

generally

conceded

that

one

such alternative mode of

justification

is observation.

We

may

set

aside

questions

of whether

one

observes

physical

objects

or

one's

own

interior

(mental)

states

or

both. Whatever

the

content

of observation

might

reasonably

be taken

to

be,

observation

cannot

by

itself be sufficient

to

generate

either what

we

think

we

know

or even

any

useful

body

of

justified

belief

at

all. This

is due

chiefly

to

the

fact that

we

cannot

observe

the

validity

of

any

principle

of

inference,

and

without inference

even

certainty

within

the observational domain

will not

carry

us

very

far. There are also other reasons for

doubting

the

sufficiency

of observation.

In

some

cases,

such

as

mathematics and

set

theory,

the

objects

are

not

of

a

sort

to

be

observed.

Moreover,

even

where the

objects

in

question

are

observable,

the claims

to

be

justified

may

be such that

they

cannot

be

justified

on

the

basis

of observation

or

else

cannot

be

justified

to

the

requisite

degree,

i.e.,

to

the

degree

that

we

generally

believe that these

beliefs

are

justified.

In this latter

category

might

fall,

not

only geometrical

beliefs,

but also beliefs about

the causal

structure

of the

world,

and

certain

other 'fundamental'

be

liefs,

such

as

that red

is

a

color and that

nothing

is both

red

and

green

all

over

at

the

same

time.

Indeed,

many

if

not most

of the claims of

interest

to

philosophers

fall

into

this

category.

Consider

especially

a



CARNAP'S

CONVENTIONALISM

143

belief

that observation is

to

be

trusted. How could this be

justified

on

the basis

of

observation

alone without

begging

the

question

at

issue?

If

observation alone

is

not

enough

to

initiate

a

suitable

body

of

justified

belief,

where else

can we

turn?

Russell's

answer

is

straightfor

ward:

we can

and

must

rely

on

direct

metaphysical

intuition,

though

he tends

to

call it direct

acquaintance (Russell,

1912,

p.

105).

Axiomat

izing

a

body

of belief is useful because it reveals which

beliefs

rely

(for

their

justification)

on

which

other

beliefs. But

axiomatization does

not

tell

us

how

the

axioms

are

justified;

at

best

it

reveals

which beliefs

are

in

need of

a

special

mode of

justification.

Where

our

beliefs

concern

principles

of

inference,

mathematics,

logic,

or

universals

more

gen

erally,

observation

cannot

sufficiently

warrant

the axioms and hence

cannot warrant

the

rest

of

our

beliefs which

depend

on

those

axioms.

We do have such

knowledge,

so

it

must

rely

on

intuition

-

there is

no

alternative.

This

Russellian

epistemology

is

worse

than

a

crime,

it is

a

blunder.

There

is,

for

example,

wide

disagreement

among

intuitions

concerning

the existence and character of universals. There is, unfortunately, no

plausible

way

to

resolve such

disagreements,

and

some

intuitions,

such

as

those

underlying

naive

set

theory,

are

flatly

contradictory.

Even when

intuitions

coincide,

such

as

in

mathematicians'

intuitions

concerning

arithmetic,

this

coincidence

is

more

readily

explained

by similarity

of

training

than

by

intuitions which

are

independently

reliable. In

this

respect,

the

matter

is

like

explaining

the coincidence

of beliefs

on

the

Trinity

among

Anglican

bishops: presumably

the

best

explanation

would

stress

the

efficiency

of the

seminaries rather than

a

happy

reiter

ation

of divine

revelation.

In

mathematics,

no

less than in

religion,

intuitions

diverge

with differences in

time,

training,

and

culture,

as well

as

in

more

idiosyncratic

ways.

The

situation is

actually

worse

than

this.

Even

if

intuitions

agree,

they

need

not

be

right,

and

even

if

some

of

them

are

right,

then in

general

there neither would

be

nor

could be

an

explanation

of this

phenomenon.

To

see

why,

contrast

the

case

of

intuition

with

ordinary

observation. The

story

that observation

supports

includes

an

explana

tion of

how

it

is,

say,

that

in

certain

circumstances

a

certain

paper's

being

white

can

bring

about

a

belief that

that

paper

is

white.

Such

explanatory

stories

are

still

rather

sketchy (though

they

are

being

fleshed

out

more

and

more)

and

even

if

complete

would

not

prove

the

truth

of

our

observational

judgments.

But

our

stories of the world



144

RICHARD CREATH

would be

poorer

without such

explanations,

and

Russell has

no

even

sketchy

account

of

why

intuitions would be

likely

to

be

correct.

Nor,

of

course,

does

anyone

else.

Where the

intuitions

concern

objects,

such

as

numbers,

which

are

said

not

to

be in

the causal

order

(or

alternatively

not

in

space

and

time),

it

is difficult

to

imagine

how

there

even

could

be

an

explanation

for

intuitions

corresponding

to

our

explanations

of

the

reliability

of

ordinary

perceptual judgments.

This

dissimilarity

be

tween

so-called mathematical

intuition and

ordinary perception

is

one

of the

chief

roadblocks

in

the

way

of such writers

as

G?del,

who would

attempt

to

assimilate mathematical

intuition

to

homely

observation.

In

the face

of

all these difficulties the

only

defense

for

metaphysical

in

tuition

is

precisely

the

one

that

Russell offers:

metaphysical

intuition

must

be

a

source

of

justification

because there is

simply

nothing

else

that

can

provide

the

required

warrant.

Russell is driven

to

intuition

by

the

lack of

a

satisfactory

alternative.

Carnap

was

militantly

opposed

to

the

idea that intuition could be

a

source

of

justification,

though

this

opposition

was

expressed

as a

rejec

tion of metaphysics. Metaphysics, according to Carnap, was a suppos

edly

trans-empirical

access

to

a

domain of

supposititious

entities

or

to

mysterious

features

of

ordinary objects,

features

beyond

the reach

of

justification

based

on

observation

(Carnap,

[1932a]/1959,

pp.

76-77;

Carnap,

1935,

p.

15).

Carnap's

rejection

of

metaphysics

is well

known.

Less

widely

discussed

is

the fact that the elimination of

metaphysics

specifically

includes

the elimination of the

direct

metaphysical

in

tuitionism that Russell embraced.

An

explanation

of

why

Carnap

was

so

indirect in his

rejection

of

Russell's intuitionism would call for

a

study

of

the

personal

rather

than

the scientific relations

between

these

men.1 At

any

rate, Russell's solution is not

open

to

Carnap.

Against

this

background

Carnap

made

a

refreshing

and

welcome

suggestion:

the axioms

can

be

construed

as

definitions

(implicit

defi

nitions)

and

their assertion

as

commitment

to

a

language containing

the

terms

so

defined. The axioms

or

postulates

need

no

further

epistemic

justification

because

a

language

is neither

true

nor

false,

and

one

is

free

to

choose

a

language

in

any

convenient

way.

If

someone

else should

choose

other

apparently

conflicting

postulates,

there is in fact

no

dis

agreement

because

each

postulate

set

is

constitutive of the

concepts

it

employs,

and hence

the

one

body

of

postulates

is

not

denying

what the

other is

asserting.

In

this

manner

the

postulates

are

not

even

intended



CARNAP'S

CONVENTIONALISM

145

to

reflect

an

antecedently

and

independently

existing reality,

but rather

literally

to create

the

claims

they

express.

It

may

be

that

some

postulate

sets

are

better

than others.

But

the

'betterness'

in

question

concerns

their

practical

usefulness:

some

are

more

powerful

or

easier

to

use

than others.

In

terms

of

epistemic

justification

or

cognitive

warrant

they

are

all

on

a

par.

Indeed,

they

are

the 'meter

sticks' for

the

justification

of

anything

else.

Epistemically

the

choice

among

them is

conventional, though

the

constraints

imposed

by

pragmatic

utility

can

be

significant.

For

example,

an

inconsistent

postulate

set is

not

very

useful.

For

most

logicians

of the

period,

includ

ing

Carnap,

every

sentence

as

well

as

its

negation

would

trivially

follow

from

a

contradiction.

An inconsistent

postulate

set

would therefore

fail

to

draw

any

cognitively

interesting

distinctions

among

sentences

or

beliefs.

Though

the

preference

for consistent

systems

is

treated

as a

pragmatic

one,

the

pragmatic

considerations

are

powerful

indeed.

Even

so,

just

because

a

postulate

set

includes

as

consequences

some

sentence

and

that

sentence

preceded

by

a

'-i',

the

postulate

set

is

not

thereby inconsistent. The sin , as Quine would later put it, would at

most

be

against

the

ordinary

(logicians')

use

of the

'?i'.

The

postulates

would constitute

implicit

definitions

of the

symbols

involved,

but the

sense

thus

constituted

for the

'-i'

would

not

be that of

negation (Quine,

1936,

p.

90).

This

suggests

another

sense

in which alternative

postulate

sets

can

be

compared:

some

will

provide

explications

of

ordinary

concepts

while

others

will

not. I shall

not

enter here

into

a

technical

discussion

of

the

demands

on an

adequate

explication

(Carnap,

1950,

pp.

5-8),

but

suffice

it

to

say

that

if the

postulates

(construed

as

implicit

definitions

of the terms

they contain)

assign

meanings

which are

sufficiently

close

to

the

meanings

that these

terms

ordinarily

enjoy,

then the

postulates

can

be

thought

of

as

providing

a

clarification of and

hence

an

explication

of those

ordinary

concepts.

There

are

sometimes

reasons

of intellectual

economy

for

wanting

explications

of

familiar

notions,

but

the failure

to

provide

such would

not

by

itself be

a

defect.

After

all,

the novel

concepts

may

in

point

of

practical

utility

be

equal

or even

superior

to

the

ordinary

ones.

This

discussion

of

pragmatic

usefulness and

explication

must not

obscure,

however,

the

epistemic

core

of

Carnap's

doctrine.

The

choice

among

alternative

postulate

sets

is

epistemically

arbitrary;

the

choice



146

RICHARD CREATH

is

a

matter

of

convention.

Moreover,

the

postulates

themselves

are

the

fundamental

epistemic

doctrine. This fact

is

easily

obscured

even

by

Carnap's

own

way

of

putting

his view.

Carnap

did

not

like the word

'epistemology'

-

it smacked

of

psychology.

So,

he avoided

it.2

Writers,

then

as

now,

often

ran

such

empirical

topics

as

the

qualitative

character

of inner

experiences

or

habits of their association

together

with

the

more

properly philosophic

questions

that

Carnap

wanted

specifically

to

isolate. Instead of

'epistemology', Carnap preferred

the

word

'logic'.

This

break

with tradition is

important,

and it is

signalled by

a

termino

logical change.

But there is still

a

point

to

be

made

in

calling

the

new

logic

epistemological.

Remember that this

logic

was

to

replace

traditional

epistemology

within

philosophy.

It

was

to

tell

us

what is

observable

and what

may

be

inferred from what.

This

is the

pure

structure

of

an

epistemology,

and

it

is

the

purely

structural character

of the

enterprise

that

Carnap

highlights

with the word

'logic'.

Indeed,

when

Carnap's

logic

is

generalized

to

include inductive

logic,

the

re

lation

sought

is that of

confirmation,

a

relation which is

transparently

epistemological. Finally, if we are ever to give empirical meaning to

the notions

of this

logic,

we

must

look

to

community

practices

of

justification.

For

all

of these

reasons

we

must

recognize

the

enterprise

as

epistemological.3

That the choice

among

postulate

sets

is

a

matter

of

convention

is

made

plausible

by saying

that the

postulates

implicitly

define the

terms

that

they

contain. The

definitions

are,

of

course,

partial;

in modern

terminology they

reduce the

family

of models while

imposing

only

very

loose restrictions

on

the

extensions

of

the

terms

involved.

But

even

such

partial

definitions

are

sufficient

to

guarantee

that all of the theorems

are

true in each of the models.

There is also

a

further

consequence

of

calling

the conventions

linguis

tic.

When

we

refer

to

someone's

belief that Finland

is

forested,

the

that-clause

describes the

belief

in

terms

of

a

certain sentential

structure.

Thus,

when

Carnap

says

that the conventions endow

the

sentences

with

meaning

and

provide

the

identity

conditions

for what is

expressed

thereby,

he could likewise

have said that those conventions

provide

the

identity

conditions

for

beliefs.

That

a

belief

is

to

be

justified

in

such

and

such

ways

is what

makes it the

belief

that

it is. If the

system

of

justification

were

altered

it would

no

longer

be the

same

belief. Thus

when

we

refer

to

a

specific

belief,

we

implicitly

refer

to

the

system

of

justification

which constitutes

it.

Carnap's approach

here

is in marked



carnap's

conventionalism

147

contrast

to

those who would

identify

a

belief

simply

as

a

disposition

to

utter

a

certain

sequence

of

words,

independently

of

how

those beliefs

are

to

be

justified.

Obviously,

this

feature

of the view will have

impor

tant

consequences

for the issues of

skepticism

and

of the

objectivity

of

belief.

At

this

point

it

would be well

to

say

a

bit

more

about

convention,

for it is

not

always

clear what is

at

stake

in

saying

that

something

is

a

matter

of convention

(Quine, 1936). Plainly,

when

Carnap speaks

of

the semantic and

epistemic

features of

our

language

as

conventional,

he does

not

mean

to

suggest

that

they

are

the

products

of

some

actual

legislative assembly

convened

in

antiquity.

But

shorn

of such

unhelpful

metaphor,

what does

conventionality

come

to? The

answer,

in

essence,

is that

to

lay

down

a

linguistic

convention

is

to

adopt

a

certain scheme

of

justification.

This scheme involves

two

specific

features:

first,

there

are

alternatives

to

certain

aspects

of the

justificatory

system;

and,

sec

ond,

the

choice

among

these alternatives

is

arbitrary

in

the

sense

that

no

justification

is

required

for the choice.

In

particular,

to

say

that

postulates are laid down by convention commits one to the idea that

there

are

alternative

postulates

that

could

have

been

chosen,

but

were

not.

It commits

one

likewise

to

the

idea

that

no

further

epistemic

justification

for the choice of

postulates

is

required.

Conventions

are

not

designed

to

reflect antecedent and

independent

facts;

if

they

were

thus

designed

one

would

have

to

show that

they

had done

so.

Rather,

the

postulates

(together

with

the other

conventions)

create

the truths

that

they,

the

postulates,

express.

Calling

the

choices conventional also

reminds

us

that

they

are

r?vis

able.

Again,

to

say

that

something

is conventional is

to

say

that there

are alternatives. That no further

justification

can be

required

for the

postulates

should

not

be

taken

to

suggest

either that

they

are

unrevis

able

or

that

as a

matter

of fact

we

are

unlikely

to

revise

them. We

can

and do

constantly

adjust

our

conceptual

system

in order

to

maximize

its usefulness. Such

revisions, however,

would

not

be

cases

where

a

given

claim

was

first believed and later disbelieved.

In

abandoning

a

postulate

the

system

of

justification

is revised and therewith the

identity

conditions for the belief.

The

words

may

not

have

changed

between

the

postulate

and

its

apparent

denial,

but

their

significance

has.

Carnap

embraced various conventionalist views from his earliest writ

ings,

but

it

was

not

until The

Logical

Syntax

of

Language

that

the

full

theory

appeared.

Until

then he

seemed

to

be

looking

for the

correct



148

RICHARD CREATH

logical

system

or

the

correct

construction of the

world.

Indeed,

in

an

early

version

of

Logical

Syntax

this

was

still the

case.

The

fully

conventionalist

theory

described above

and

hereafter

appeared

with

the

Principle of

Tolerance:

It

is

not

our

business

to

set

up

prohibitions,

but

to

arrive at

conventions.

. . .

In

logic,

there

are

no

morals.

Everyone

is

at

liberty

to

build

up

his

own

logic,

i.e.,

his

own form of

language,

as he wishes. All that is

required

of him is that, if he wishes to

discuss

it,

he

must

state

his methods

clearly,

and

give

syntactical

rules instead

of

philo

sophical

arguments.

(Carnap, [1934J/1937,

pp.

51-52)

Of

course,

in

saying

that

in

logic

there

are no

morals

Carnap

is

not

denying

the

normative

force

of

logic.

Rather,

he

is

emphasizing

that

there is

no

one

uniquely

correct

normative

story

to

be told.

When

constructing

an

artificial

language,

one

begins

as

above

by

laying

down

conventions which determine

how

various claims

may

be

justified.

When

we

study

natural

languages

the

connection

goes

in the

other direction: evidence about what the conventions are lies in how

various beliefs

are

justified

(Carnap,

1950,

p.

37).

Of

course,

it is

no

easy

task

to learn what claims

are

taken

to

justify

what

other

claims

and

thereby

to

discover what the

principles

of

inference

are

and

what

claims,

if

any,

need

no

further

justification.

Here,

too,

the

claim of

conventionality

consists

in

the

dual

thesis

that there

are

alternatives,

i.e.,

that the

system

of

justification might

have been otherwise

con

structed,

and

that the chosen alternative needs

no

further

justification.

That the

conventions

constituting

the

system

of

justification

are

at

bottom

arbitrary

poses

no

threat whatever

to

the

objectivity

of the

postulates

and their

consequences.

This was of

particular

concern to

Carnap

because

he

thought

that all

of

logic

and

mathematics,

insofar

as

the

claims

thereof

can

be

assessed

at

all,

is

to

be

justified

as are

postulates

and their

consequences.

Once

a

system

of

justification

is

chosen,

i.e.,

once

the various

terms

of the

language

are

given

a

definite

sense,

it is

a

completely

objective

matter

whether

B

is

a

consequence

of A. It in

no

way

depends

on

what

any

person

may

happen

to

imagine,

think,

believe,

or

know about these

sentences

(Carnap,

1950,

p.

38).

It is likewise

a

completely

objective

matter

whether

or

not

a

given

claim

needs further

justification.

These

things

are

no

more

subjective

than

the truth

value

of the

claim All

swans are

white ,

given

of

course

that

the

meanings

of the

terms

are

fixed.

If

the

word 'white' has

a

sense



CARNAP'S

CONVENTIONALISM

149

different

than it in fact

does,

then

the

truth value of the claim

might

be

different,

but

this

in

no

way

impugns

the

objectivity

of All

swans are

white .

Whatever its

truth

value,

it does

not

depend

on our

believing

it

to

be

so.

Carnap's

epistemology

as

I

have

presented

it

so

far

has

a

number of

significant advantages.

It

provides

a

way

of

resolving

foundational

de

bates in

logic

and mathematics. It is

no

longer

necessary

to

worry

whether, say,

Brouwer's

intuitionism

or

classical

mathematics

is the

correct

mathematical

system

(Carnap, [1934J/1937,

p.

305).

Each

can

be construed

as a

separate

proposal

for

structuring

language,

in

short

as

a

system

of

implicit

definition. Each

can

be understood

and

its

practical

consequences

noted. The

proposals

do

not

conflict

with

one

another

so

the foundational debate

can

end.

It

is

similarly

an

advantage

that the

system

provides

an

epistemology

for mathematics

which

ac

cords

well with

our

ordinary

convictions about

how

to

justify

mathema

tical claims: the

justification

of theorems

involves

deriving

them

from

axioms;

their

justification

is

independent

of

experience

and

not

subject

to experimental disconfirmation; and the theorems are objectively true.

That

Carnap

is able

to

achieve all this

without

venturing

into

the

quagmire

of

metaphysical

intuitions

represents

a

tremendous advance

over

the

previously

described view

of

Russell. The

conventionality

at

stake

in

Carnap's epistemology

turns out to

be

a

virtue,

and it is

one

to

which

we

shall have

reason

to return

a

little later in

this

paper.

In

the meantime let

us

look

more

closely

at

the

historical

antecedents of

this conventionalist

and

pragmatist

theory

of

knowledge.

2. carnap's

SOURCES

The

prevailing

view is

that

Carnap's philosophy

comes

directly

from

the work of

Frege

and

Russell.

If

I

am

right

that conventionalism and

pragmatism

are

at

the heart of

Carnap's philosophy

from about 1932

onward,

then that

prevailing

view

is

very

misleading.

To be

sure,

Car

nap

studied

at

Jena with

Frege,

and he

came

away

not

only

with

a

love

of

logic

but also

with

Frege's

intense

anti-psychologistic

convictions.

But

as

we

shall

see

in

a

moment

Frege

was

hardly

an

epistemologist,

and the views he did

hold

were

the

exact

antithesis of

Carnap's.

Russell

by

contrast

did

care

about

epistemology,

but

he

was

also

an

out-and

out

metaphysician

(even

if

Carnap

could

never

quite

admit

the

fact).



150

RICHARD CREATH

As

we

have

already

seen,

the whole

point

of

Carnap's philosophy

was

to

reject

intuition of

a

Russellian

sort.

So,

where

does the

core

of

Carnap's

epistemology

come

from?

The

kernel

of

the

idea

of

implicit

definition has

been around for

a

long

time.

It

goes

back

at

least

to

the work of

Gergonne

at

the

beginning

of the nineteenth

century

(Quine,

1936,

p.

81n.).

At

the

end

of that

century

definition

was

the

subject

of

two

famous debates: Russell

vs.

Poincar?,

and

Frege

vs.

Hilbert.

In

these,

Poincar? and Hilbert

had

defended

forms of

implicit

definition,

while Russell and

Frege

had

attacked

it. Here

I want to

examine the latter of the

two

debates. There

are

two

chief

reasons

for this.

First,

it shows how

enormously

difficult

it

sometimes

is,

even

for

someone

of

Frege's

perspicacity,

to

grasp

the

idea of

a

set

of

axioms

defining

the

terms

they

contain and thus in

a

sense

creating

the truths

they

express.

Second,

a

review

of

this

earlier

episode

will

show

the

magnitude

of

the shift that

Carnap

is

undertaking,

not

only

from

Frege

and Russell but

as we

shall

see even

from

Hilbert.

Carnap's

view

is

a

descendent

of Hubert's. But it

is also much

more;

for the notion of implicit definition is expanded to cover all of philos

ophy

and

to

provide

the

source

of

meaning

in

physics

and

ordinary

life

as

well

as

geometry

and

mathematics.

The

Frege-Hilbert

controversy

appears

in

their

correspondence

be

tween

1895

and

1903

(Frege,

1980,

pp.

31-52).

The

tone

of their

letters

is

quite

remarkable. The usual stock

phrases

of academic

politeness

aside,

they

are

not

friendly

letters.

It

is worth

noting

that while

Frege

was

the older

man

he

held

a

lesser

position

at

a

lesser

university.

In

fact,

Edmund Husserl

wrote

in

1936:

I never got to know G. Frege personally, and I no longer remember the occasion for

our

correspondence.

At the time he

was

generally regarded

as an

outsider who had

a

sharp

mind but

produced

little

or

nothing,

whether

in

mathematics

or

in

philosophy.

(Husserl,

in

Frege,

1980,

p.

61)

At the time

of

Husserl's

correspondence

with

Frege,

or

at

least the

second

part

of

it,

Husserl

was

Hubert's

colleague

in

G?ttingen

and had

seen

the

Frege-Hilbert correspondence.

By

contrast

with

Frege,

Hil

bert

was

at

the

peak

of his

career,

and he could

legitimately

claim,

along

with

Poincar?,

to

be

one

of the

two

greatest

mathematicians in

the world. It

was

not

until the 1940s

that

Frege's

reputation

among

logicians

rose

to

the level of Hubert's

among

mathematicians.

Frege

began

the

correspondence

by

explaining

his view

on some



CARNAP'S

CONVENTIONALISM

151

minor

issues from

a

previous

conversation with Hilbert.

Hilbert

politely

replied

that

there

was no

difference

of

opinion

between them.

A few

years

later

Frege

wrote

again,

claiming

that

Hilbert's Foundations

of

Geometry

was

unclear

in

crucial

respects:

Here the

axioms

are

made

to

carry

a

burden that

belongs

to

definitions.

To

me

this

seems

to

obliterate the

dividing

line

between

definitions

and

axioms

in

a

dubious

manner,

and beside

the old

meaning

of

the word

'axiom',

which

comes out

in the

proposition

that

the axioms

express

fundamental facts of

intuition,

there

emerges

another

meaning

but

one

which

I

no

longer quite

grasp.

(Frege,

1980,

pp.

35-36)

Note that

for

Frege

the

axioms

express

intuitions.

What

Frege

says

he

does

not

quite

grasp

was,

of

course,

the whole

point

of

Hilbert's

enterprise.

To

Frege

the

problem

was

worse

than the lack of

complete

clarity.

For

him,

one

must

understand

the

concepts

completely

before

one can

entertain

any

propositions

or

consider

any

as

axioms.

Only

after

we

understand

the

concepts

and

propositions

can

we

ask of

a

given

proposi

tion

whether

its

truth

depends

on

the truth of

any

other

proposition.

In

this

way

we

trace

that

truth

dependence

back

to

those

propositions

(the axioms)

which do

not

rest

on

any

others.

Naturally,

definition

is

permissible;

but definitions

are

merely

devices

of

abbreviation.

Abbreviatory

definition, however,

presumes

that

some

terms

(the

primitives)

already

have

meaning.

Oddly,

therefore,

Frege

went

on

to

insist

that all

terms

in

our

propositions

be

fully

defined,

apparently

in

this

abbreviatory

way.

That

is

just

not

possible.

On

Fre

ge's

account

how

one

learns

the

meanings

of the

primitive

terms

must

remain

forever

an

utter

mystery.

Once

we

do learn the

meanings,

how

do

we

learn

which

propositions

are

true? Our

knowledge

of

the theor

ems

flows

through

inference from

our

knowledge

of the axioms.

But

our

knowledge

of

the

axioms

is

quite

different

(and

I

might

add

also

mysterious).

In

speaking

of

geometry

Frege

says:

I call axioms

propositions

that

are

true

but

are

not

proved

because

our

knowledge

of

them

flows from

a source

very

different from the

logical

source,

a

source

which

might

be

called

spatial

intuition. From the

truth

of the axioms it

follows

that

they

do

not

contradict

one

another. There is therefore

no

need

for

a

further

proof. (Frege,

1980,

p.

37)

Hilbert's whole

program,

or

at

least

the central

part

of

it,

had been

to

prove

the

consistency

of

various

groups

of axioms

or

as

a

part

of

this the

independence

of

various axioms

(i.e.,

the

consistency

of

a

given



152

RICHARD

CREATH

axiom

as

well

as

of its

negation

with

a

given

group

of other

axioms).

Frege

was

here

suggesting

that this main

body

of Hilbert's

work

was

quite

unnecessary

because

the

truth

of the axioms

could

be

determined

directly

by

intuition and

thereby

the

mutual

consistency

of the

various

axioms

could

be established

effortlessly.

If

Hilbert

was

not

annoyed

by

this dismissal

of his

work,

Frege's

tone

toward the end

of the letter

would

have been

sufficiently

irritating.

What

Frege

said

was:

I

would

not

regard

your

work

as

a

valuable

one

if

I

did

not

believe I could

see

roughly

how such

objections

could be rendered

harmless;

but this will

not

be

possible

without

considerable

reshaping.

(Frege,

1980,

p.

38)

Such

a

tone

would

have

been

more

appropriate

in

addressing

a

graduate

student

than the

most

prominent

mathematician

in

Germany.

Hilbert

did

reply,

however,

and his letter

covers

four basic issues.

First,

meaning

is

given by

the

totality

of

axioms.

Hilbert

is,

in

effect,

a

meaning

holist.

Second,

the

only

thing

one

can

do

to

give

the

meaning

of

a

primitive

term,

such

as

'point',

'line',

etc.,

is

to

give

axioms;

anything

else is

fruitless,

illogical,

and futile .

Third,

Frege's

point

that

first

we

know the truth

of

the axioms

and then

infer

their

consistency

has

the

matter

exactly

backwards.

Fourth and

finally,

of

course

definition

via

a

set

of

axioms does

not

irrevocably

fix

reference,

but that is

perfectly acceptable.

It

does, however,

fix

enough

of the

meaning

for

the mathematical

purposes

at

hand.

One

senses

from this letter

of Hilbert that

he

is

fundamentally

at

cross-purposes

with

Frege,

and

Frege's

long

reply

reinforces

this

view.

Frege

still does

not

understand

the

central

idea of

implicit

definition.

Frege

goes

on

to

raise

several

objections,

one

of which is

important

and

deserves

a

reply.

Hilbert

never

did

provide

such

an answer.

While

there

are

several

later letters

in the

Frege-Hilbert correspondence,

none

is

really

substantive,

and neither

man

felt

compelled

to

alter his

view. Hilbert

said he

was

too

overburdened

with work

to

make

any

detailed

reply,

and the

correspondence

ended

with

an

unpleasant

letter

from

Hilbert:

Many

thanks

for the second

volume of

your

Basic

Laws,

which

I find

very

interesting.

Your

example

at

the end of the book

(p.

253)

was

known

to

us

here;*

I found other

even more convincing contradictions as long as four or five years ago; they led me to the

conviction

that traditional

logic

is

inadequate

and that the

theory

of

concept

formation

needs

to

be

sharpened

and refined.



carnap's

conventionalism

153

*I

believe Dr Zermelo

discovered it three

or

four

years

ago

after

I

had communicated

my

examples

to

him.

(Hilbert,

in

Frege,

1980,

p.

51)

If

this

deprecation

of

Frege's

work

were

insufficient

to

annoy,

Hilbert

added

an

invitation:

It

is

a

pity

that

you

were

neither

in

Cassel

nor

in

G?ttingen;

perhaps

you

will

decide

to

visit

G?ttingen

between

terms.

Since

rail

travel

is

so

comfortable

today,

personal

communication is surely preferable to the written kind. I at least lack time for the latter.

There

are

a

number of

younger

scholars here interested

in

the 'axiomatization of

logic'

(Hilbert,

in

Frege,

1980,

p.

52)

Such

an

'invitation'

to

travel

away

from the

provinces

in

order

to

talk

with the

junior

faculty

and

graduate

assistants

can

hardly

have

appealed

to

Frege.

It

is

not

surprising

that there

were

no

further letters between

the

two.

What do

we

learn from all

this

(besides

the facts

that

great

logicians

do

not

always

understand

alternative

points

of view and that

neither

great

mathematicians

nor

great logicians

are

uniformly very pleasant)?

We

learn,

first,

that there

was a

precedent

for the

central

conven

tionalist

core

of

Carnap's philosophy.

Second,

this

precedent

is

not

to

be found

in

the

Frege-Russell

tradition from

which

Carnap

is

usually

thought

to

arise,

but rather

in

the tradition

that

Frege

and

Russell

attacked

(often bitterly).

Third,

Carnap

went

considerably

beyond

Hil

bert. Neither in the

correspondence

with

Frege

nor

anywhere

else did

Hilbert

give

any

hint of

Carnap's

theory

of

pragmatic

constraints

on

convention. Nor does Hilbert

give

any

general theory

of

analyticity.

Moreover,

Carnap

greatly

generalized

the

theory

of

implicit

definition.

Not only did he extend it to all of logic, mathematics, and philosophy,

but

as

we

shall

see,

he extended its relevance

to

the

concepts

of

empiri

cal science

as

well.

In

this

respect

particularly,

Feigl's

remark that

Carnap's

work

amounts

to

the Hilbertization of

the

language

of science

is

especially prescient.

3.

EXTENDING THE STORY TO

SCIENCE: METHODOLOGY

In

describing

Carnap's

conventionalism

and

pragmatism

I

have

spoken

thus

far

of axioms and definitions

in

a

way

appropriate

to

mathematics

and other

very

abstract

domains. These

are

domains of

our own

making,

and insofar

as

claims

concerning

these domains

are

acceptable,

it is



154

RICHARD CREATH

because

our

postulates

have made them

so.

In

contrast,

Carnap

thought,

the

world

of

empirical

science

is

not

wholly

of

our own

making,

and

one

of

Carnap's

chief aims

in

framing

his

epistemic

view

was

to

provide

an

account

of

our

knowledge

of the external world.

So

far,

however,

no

provision

has

been

made in the

story

either

for scientific

methodology

or

for observational

knowledge,

and

to

this

we

must

now

turn.

As

we

shall

see,

implicit

definition

by

the

epistemic

structure

is

still

an

important part

of

Carnap's approach. Moreover,

the

epistemic

structures

are

to

be laid down

by

convention

and

justified only

by

the

pragmatic

utility

of

doing

so.

Finally,

we

shall

see

that

despite

this

Carnap

is

no

advocate of unbridled conventionalism

in

a

way

that

would

threaten the

objectivity

of

our

scientific

beliefs

about the world.

There

is much

to

be said about scientific

methodology,

but here

I

want to

make

only

a

few

very

brief

remarks

so

that

I

can

leave

more

room

for

methodology's

much

neglected

cousin,

observation. Even

these brief

remarks

will

be

restricted

to

a

single

topic:

induction.

We

have

already

seen

that

Carnap's

account

of

mathematics

and

deductive logic is conventionalist. There is no question of justifying

deduction;

there

is

no

question

of

finding

the

correct account.

Instead

there is

only

the

engineering

task

of

examining

the

practical

conse

quences

of

adopting

this

or

that

system.

So

it is with induction.

The

traditional

question

of

justifying

induction

simply

drops

away.

One

could choose

to

have

no

inductive rules whatever. But the

pragmatic

costs

would be

high:

one

could make

no

prediction

and

this would be

followed

by

frequent

bruises and

quick

starvation. So the

question

is

not

whether

to

have inductive

rules,

but

which.

Here

again

the

matter

is

one

of

pragmatic

comparison.

If

the rules

are

too

weak,

then

we

foreclose or

complicate

useful inferences. If the rules are too

strong,

then

there

is

an

increased

chance that

one

inference will conflict with

another,

thus

requiring

constant

and

costly

revision.

The

virtues of

security

as

contrasted

with

those

of

educational

adventure

will

be

weighed differently by

different

people,

but

we

need

not

all

agree

so

long

as we

make

our

respective

choices clear. There is

no

uniquely

correct

system,

and the choice

among

the alternatives is

pragmatic.

Carnap

himself

occasionally

flirted

with

a

strategy

of

minimal risk

(Car

nap,

1936,

pp.

445-46),

that

is,

of

avoiding

any

empirical

content

for

postulates

and other

interpretative

devices,

and in

general making

the

whole

interpretive, (epistemic)

machinery

as

weak

as

possible.

He

did,

however,

recognize

that

it

is

never

possible

to

provide

absolute

guaran



CARNAP'S

CONVENTIONALISM

155

tees

that

inconsistency

will

be

avoided,

and he

recognized

that

it is

often

more

convenient

to

adopt

a

stronger

epistemology

even

if

doing

so

is riskier.

He,

therefore,

usually

adopted

a

strategy

of

maximizing

freedom

in

laying

down

language

forms,

that

is,

epistemic

structures.

This

freedom

is still constrained

by

the

demands of

pragmatic utility,

and those constraints

are

sufficient

to

rule

out

(absolutely

or

empiri

cally)

inconsistent

systems

of belief.

It

might

be

thought

that because

I

have touched

only

on

deductive

and inductive inference

I have

omitted

all

of the

really

interesting

questions

of scientific

methodology,

such

as

the

structure

of

theories,

scientific

realism,

theoretical

concept

formation,

holism,

underdeter

mination,

etc.

This is

not

really

true.

These latter

questions

are

simply

absorbed

by

Carnap

into

a

general theory

of

scientific

inference.

For

example,

the issue of scientific realism

can

be

expressed

as

the

question

of what conclusions

to

draw from the

belief that the

observational

consequences

of

a

theory

are

true.

Shall

we,

with

the

realists,

conclude

that the

theory

is

true?

Or,

shall

we

with,

say,

van

Fraassen

conclude

something weaker? Carnap thinks that one is free to choose either

strategy,

either

principle

of inference.

Typical

realists

are

wrong

in

thinking

that there is

only

one

correct

inference. But

van

Fraassen

would

be

similarly

wrong

if

he

thought

that

a

weaker

principle

of

inference

was

the

one

uniquely

correct

principle.

So,

which choice does

Carnap

make? Does he

not

prejudice

the

case

against

scientific realism

by

emphasizing

the

conventionality

of

theoretical

concepts

and infer

ence?

The

answer

to

this

latter

question

is

no,

for

as we

shall

see

he

insists

on

the

conventionality

of observational

concepts

and

inferences

as

well.

The

two

domains of

discourse

are

thus

on a

par,

and

thus,

unsurprisingly,

Carnap

typically

adopts

the

principle

of inference that

he takes

to

be

constitutive of realism. This

discussion of realism is

only

an

example

of

the

ways

in

which various

methodological

issues

can

be

absorbed

into

a

theory

of scientific

inference,

but it is

at

least

a

highly

typical example

(Carnap,

1966,

pp.

247-56; Creath,

1985).

One

final

note

on

induction is

in

order. That

is that

Carnap's

actual

proposals

for inductive inference

get

expressed

as a

theory

of

probabil

ity.

I

cannot

even

begin

to

address the

controversies

surrounding

it,

but there is

one

feature that

will

crop

up

later.

Strictly,

probabilities

for

Carnap

are

supposed

to

be rational

betting quotients,

i.e.,

measures

of

the

degree

of confidence that is

warranted for

a

given

proposition.

Thus,

if

we

are

warranted

in

being

certain of

the truth

of

some

proposi



156

RICHARD CREATH

tion,

then

that

proposition

has

a

probability

of

one.

If

we

should

be less than

certain,

then the

probability

should

be less than

one.

Unfortunately,

what

Carnap

actually

presents

is

not

a

theory

of

rational

degrees

of

belief

but

a

theory

of the

extent to

which

a

given

proposition

is

supported

by

the evidence.

These

are

not at

all the

same

thing,

as

is

shown

when

we

ask about the evidence itself. To

what

extent

is

the

evidence

supported

by

the evidence?

Well,

completely;

so

the

probabil

ity

of

the evidence

must

be

one.

But

Carnap

is

a

fallibilist

about

observation,

so

the

degree

of confidence

we

have

in

the evidence should

be less

than

one.

Carnap

fully

understood the

magnitude

of his diffi

culty,

but

he

never

saw a

way

around it

(Carnap,

1957).

In the

end

he

accepted

Richard

Jeffrey's suggestion

that does

not

in fact

solve

Carnap's problem.

It

may

do what

Jeffrey

needs it

to,

but

not

what

Carnap

needs

(Carnap, 1971).4

I think

Carnap

could have done

better,

and

ironically

the

way

to

do

so

is

to

develop

the

conventionalist and

pragmatist

theory

of observation

that he

already

(implicitly)

had. If

I

can

suggest

how that

can

be

done,

then

I

shall

not

only

have

helped

Carnap but enriched our understanding of observation as well.

4.

EXTENDING THE STORY TO SCIENCE: OBSERVATION

In

turning

to

observation

the

most

surprising

thing

is

how

little

Carnap

gives

us

in

the

way

of sustained discussion.

True,

there is 'On Protocol

Sentences',

produced

in

1932

just

as

his conventionalism

was

emerging

(Carnap,

[1932b]/1987).

There

he made

it

plain

that the

questions

of

what

things

were

observable

and

how

much observational

judgments

should be trusted

were

to

be answered

by

conventions.

He

also

sug

gested

some

of the

conventions he would

propose.

Even here the

discussion is

sketchy,

but

thereafter

we

get

even

less

(Carnap,

1936,

pp.

454-56).

All

told,

we are

given

many

hints,

but

no

well-worked

out

theory.

If

we

'connect the

dots',

however,

the outline of

a

general

theory

does

emerge.

Let

us

begin by laying

down

some

desiderata,

i.e.,

some

features

that

Carnap

wanted his

theory

of

observation

to

exhibit.

Some

con

ditions

will

turn out to

be

deeper

than

others,

but

that is

perfectly

acceptable.

(1)

Fallibilism:

As

previously

mentioned,

Carnap

thought

that

we



carnap's

conventionalism

157

could be mistaken

in

any

of

our

beliefs about

contingent

matters

of

fact,

including

in

our

observational

reports.

(2)

Physicalism:

While

Carnap's

physicalism

is

somewhat

broader,

here I

mean

only

that

it

should be

possible

to

observe

physical

objects

directly,

rather than

merely

to

infer their

presence,

from

beliefs about

our

mind. Let

me

emphasize

that this

physicalism

is

a

substantial

break

from both the Au?au and from Russell's brand of Cartesianism.

(3)

Objectivity:

There

are

objective

facts

about the

world,

indepen

dent of what individuals

may

think.

Thus,

observation

reports

cannot

themselves be conventions.

(4)

Non-circularity:

One

cannot

use

observation

in

order

to

show

that observation is

to

be

trusted.

Trying

to

do

so

would

presuppose

that

we

have

independent

evidence

to

judge

the truth

of the obser

vational

beliefs,

but such

independent

evidence

is

just

what

we

do

not

have. The

most

that

a

psychologist

could discover is that

her

own

observational

evidence,

however

refined,

coincides with

or

fails

to

coin

cide with

the observational

beliefs

of her

subject.

Observation will

have

its role

to

play,

but

not

this

one.

(5)

Sensitivity:

The

question

of what

things

are

observable and how

trustworthy

various observational

judgments

are

must

somehow

be

sen

sitive

to

contingent

matters

of fact. The

wholly

a

priori

accounts

of

the

Cartesian will

not

do.

Should

we

add

to

this list

a

sixth

condition,

namely,

a

condition

of

naturalism? The

answer

is

no,

but

not

because

Carnap

rejects

natural

ism.

Unfortunately,

the

word

'naturalism' has

come

to

mean

everything

to

everybody,

and

some

writers

use

it

in

various

ways

simultaneously

without

distinguishing

them. If it

means

merely

that human

beings,

their

judgments,

and the

rest

of their

mental lives

are

all

objects

and

processes

in

the natural

world and

properly

to

be studied

by

science,

then

naturalism is

just

a

weaker

version of

Carnap's

physicalism.

As

such it is

adequately

addressed

by

conditions

(2)

and

(5).

If, however,

naturalism is

meant

in

a

stronger

sense

according

to

which science

can

straightforwardly

answer

every

question,

not

only

about what is but



158

RICHARD creath

about what

ought

to

be,

then

Carnap

rejects

this

naturalism.

This

rejection

is

expressed

in

condition

(4).

So,

how did

Carnap

propose

to

satisfy

these conditions?

His

dominant

impulse

was

to

isolate

an

observational

vocabulary.

This,

of

course,

was

a

dreadful

mistake. The distinction wanted is

at

the level

of

judg

ments,

not

words,

and

as

Carnap

fully

understood that the distinction

must

be somehow

a

matter

of

degree.

Even

so

the words used in

observational

judgments

will

get part

of

their

meaning

in

previously

described

ways,

i.e.,

via

various

postulates

and

principles

of inference.

Thus,

'red'

will

get

some

of

its

meaning

from

Nothing

is

both red

and

green

all

over

at

the

same

time construed

as a

postulate,

and from

' x is

colored'

is

directly

derivable

from 'x is

red' construed

as a

principle

of

inference.

Still,

this

is

not

enough.

We

need

rules

to

connect

judgments

involv

ing

'red'

directly

with the

world.

A

general

schema

for such

a

rule

might

be:

In

conditions

Q,

you may

assert

proposition

Pi

with

degree

of

justification

Ji.

As

a

first

approximation, perhaps

an

assertion that there is

a

red

truck

will be

assigned

a

certain

degree

of

justification, regardless

of

conditions.

Perhaps

under

the

conditions

that the

sun

is

shining

and

the

believer's

eyes

are

open,

itwould

get

a

higher degree

of

justification.

Under

the conditions that the believer has taken

a

narcotic

or

that

there is

a

billboard between the

believer and the

purported

location of

the

truck,

the

assertion would

get

a

lower

degree

of

justification,

and

so on.

Learning

a

language requires

acquiring

the

appropriate

habits. This

is

likewise

true

of

learning

the observational

parts

of

language.

If

you

have

not

learned

to

respond

to

red

objects

in

the

right

circumstances

with the

appropriate

degree

of belief

in

This

is

red ,

then

you

have

not

fully

grasped

the

meaning

of the

word

'red'.

If

you

have

not

learned

to correct

others'

observational

reports

of This

is

red

or

to

acknowledge

such

criticism

when

appropriately

made

against yourself,

then

you

have

not

fully

learned

the

meaning

of the word

'red',

either.

The

totality

of these

epistemic

rules

governing

the

use

of

the

word

'red'

or

alternatively governing

beliefs

whose

expression

uses

the word

'red' in effect defines the

word.

In

the

implicit

definition of mathema

tical

terms,

the freedom

to

lay

down

postulates

and

inference rules



carnap's

conventionalism

159

arbitrarily

was

part

and

parcel

of

our

freedom

to

define

our

terms in

whatever

way

we

desire.

So

it

is

with

terms

which have observational

uses.

Our freedom

to

construct

our

epistemology

so

that

a

non-inferen

tial belief that

something

is red is

justified

to

a

certain

degree

arises

from

our

freedom

to

define 'red'

(and 'justified')

as

we

wish.

Again,

as

in the mathematical

case,

what definitions

we

choose, i.e.,

what

precise

way

we

choose

to

fill

out

the schema

for various

conditions,

will

be

influenced

by pragmatic

considerations.

As

we

shall

see

presently,

these

pragmatic

considerations

will insure

that

the

theory

will

satisfy

the

desiderata

outlined

above.

While the

meanings

of

words

in

observational

reports

are conven

tional,

the

content

of those

reports

is

not.

That red is

a

feature

that

can

be

directly

reported

rather

than

merely

inferred is

a

fact

about

its

meaning,

and it is

a

result of

a

convention. Once

the

meaning

is

fixed,

however,

it

is

no

longer

a

matter

of choice

what

degree

of

belief

one

should

have in

a

specified

circumstance.

Thus,

this

account,

so

far,

satisfies both the

objectivity

condition and the

non-circularity

condition.

In order to see how the account might satisfy the sensitivity condition,

an

analogy

with

measurement

concepts might

be

helpful.

When

we

first

establish

a

concept

of

length

we

could choose

as

our measure

of linear

congruence

a

metal rod without

making

any

adjustments

for thermal

inhomogeneity.

Such

a

choice

might

prove

inconvenient

in

comparison

with

our

usual

'temperature

corrected'

procedures

of

measurement,

but

neither choice would

be

incorrect.

The

differences

are

only

pragmatic.

Indeed,

to

say

that

one

procedure

gave

incorrect results

presupposes

that

we

already

have

an

independent

procedure

for

determining

what

the

correct

results

are.

But

ex

hypothesi

we

do

not

yet

have such

a

procedure.

If there were a

uniquely

correct standard of measurement,

we

could

not

discover that

it

was

so even

in

principle.

Thus,

it

seems

best

to

abandon this

assumption

that there could

be such

a

uniquely

correct

standard

and

say

instead

merely

that there

are

different avail

able standards

giving

different

results

and

defining

(in

part)

different

concepts

of

length.

We

must

begin by choosing

a

standard of

measure

ment,

and

that choice

cannot

be

anything

but conventional. This should

not

suggest,

however,

that

there

can

be

no reasons

for

preferring

one

standard

over

another. We

can

discover that

some

standard is

more

convenient

to

use

overall.

The

uncorrected

rod

might

seem

to

be the

most

convenient,

but

we

have

to

consider

our

convenience

in

using

the

physics

to

be built

on

it

as

well.

If

we

wish

to

take

the

uncorrected

rod



160

RICHARD creath

as our

standard,

then

we

are

forced

to

say

that when

the

rod

is

brought

near a

flame

the

rest

of the universe

shrinks. This is

a

perfectly

consist

ent

claim,

but such

a

physics

would be

extremely

cumbersome. Our

desire

to

avoid

a

clumsy

physics supplies

a

reason

for

preferring

a

given

standard,

but

it is

a

pragmatic

reason,

for

it

purports

to

show

at most

that

one

choice

serves our

overall

aims

and

purposes

better

than the

other choice of standard. These

pragmatic

claims

provide

the

only

sense

that

can

be made of the assertion

that

a

temperature

corrected

measuring

rod is

a

better

indicator of

length.

The

definition is

non

circular,

but

it

is also sensitive

to

contingent

matters

of fact

(Carnap,

1966,

pp.

91-95).

So

it is

with human

observation;

indeed

human

beings

can

be

thought

of

as

measuring

devices for certain features of

the world.

But

just

as

measuring

rods

can

be read

in

a

number

of different

ways,

so

can

human observers.

If

we

were

to

set

up

for

the first time

a

concept

of

color

we

could

choose

to

take

human beliefs

about

the

colors

of

objects

in

the

vicinity

as

evidence, i.e.,

take them

as

warranted

to

some

degree

even though those beliefs were not inferred from other beliefs. Alterna

tively,

just

as we

could 'correct' the

metal rod for

changes

in

tempera

ture,

so we

could

correct

the

person's

beliefs,

either

by

letting

the

beliefs

vary

in

what

degree

of

warrant

they enjoy

in

diverse

circum

stances

(e.g.,

beliefs about the colors of

objects

in

broad

daylight

are

more

justified

than

those about

objects

illuminated

by

mercury

vapor

lamps),

or

even

by taking

them

as

phenomena

providing

evidence

for

quite

different claims

(e.g.,

under these

lights

a

report

that

an

object

is

blue indicates

that it is

green,

or

more

colloquially,

under these

lights

green

things

look

blue).

The

point

is

that there

are

alternative

procedures

for

determining

what the color of an

object

is,

and it is

misleading

to

talk about the

right

procedure

apart

from

our

already

having

chosen

a

standard of

judging.

Even

so,

just

as

there

can

be

reasons

for

preferring

a

measuring

rod

corrected for

temperature

changes,

there

can

be

reasons

for

preferring

to correct

our

non-inferential

judgments

about

color for

changes

in

lighting

conditions.

And the

reasons are

still

pragmatic.

If

we

choose

'uncorrected

observers',

then either

justified

judgments

must

be

fre

quently

revised

or

else

we

must

conclude that the colors of

things

are

highly

unstable and

changes

in

color do

not

correlate

in

any

tidy

way

with

other

changes

interior

to

the

objects

themselves. There is

nothing

inconsistent about such

a

position,

but

many

will find

it

unnecessarily



CARNAP'S

CONVENTIONALISM

161

and

undesirably

cumbersome.

In

any

case

the

argument

for

preferring

a

given

way

of

judging

color

can

show

at

most

that

one

choice

serves

our

overall

aims and

purposes

better

than another.

For

such

pragmatic

reasons

there

are

several

general

features

that

we

might

wish for in

our

rules of non-inferential

justification:

the

results

should be stable

enough

so

that the

properties

we

attribute

to

things

change

only

in

simple,

regular

ways.

The

rules should be cautious

enough

so

that

we

need

not

constantly

revise

our

most

highly

warranted

judgments.

Correspondingly,

however,

the

rules should be

strong

en

ough

to

allow useful

prediction.

Sometimes the

cost

of

making

our non

inferential

judgments

less

open

to

disconfirmation

(perhaps

by

re

stricting

them

to

claims about

our

mental

states)

is

to

make reasonable

predictions

about future

events

extremely

complex

and

difficult.

Finally,

the

rules should

permit

shared results

to

allow

for

joint

investigation

and action. For

all

these

pragmatic

reasons

Carnap

thinks that

it is

highly

prudent

to

adopt

a

language

in which

no

observational

reports

are

certain and

in

which the basic

observational

reports

are

genuinely

about public, i.e., physical objects. Carnap's physicalism represents,

therefore,

not

a

deep

insight

into the

metaphysical

nature

of the

world,

but

a

proposal

governing

what

epistemic

structures

to

set

up;

it is

a

recommendation about what is the

most

fruitful and useful

way

of

fashioning

our

epistemology.

Such

pragmatism

is the basis for

Carnap's

fallibilism

as

well.

In

this

way

conditions

(1)

and

(2)

are

satisfied,

not

by

any

possible

language

but

by

the

language

that

Carnap

recommends

on

pragmatic

grounds.

Now

we

really

can

take

probabilities

as

Carnap

wanted,

as

degrees

of rational belief. The evidence

statements

are

conventionally assigned

a

probability

(rational

degree

of

belief)

less than one. In

differing

circumstances

they

are

assigned

differing

probabilities.

From the

'out

side' these

assignment

rules

can

be viewed

as

rules of criticism.

From

the 'inside' the circumstance mentioned

in

the rules will

refer

to

items

in

the believer's

background knowledge.

Once the

evidence

is in

place

and

properly

fallible,

then

Carnap's

own

theory

of

evidential

support

will

finish

assigning probabilities

to

other

beliefs,

including

theoretical

ones.

I

have been

speaking

as

though

what

happens

in

observation

is that

a

degree

of

belief

comes

into

being

where

none

existed

before,

and

thus that

the

rules of rational belief

in

these

cases

govern

such initiation

of belief. This

may

be

a

convenient

way

of

speaking,

but it is also



162

RICHARD CREATH

misleading.

It

would be

more

accurate to

say

that in

observation

we

adjust

previously

existing

degrees

of

belief. To

accomplish

this

the

conventional rules will have

to

contain

a

parameter

for

these

prior

probabilities

and

then

indicate how

in

varying

circumstances

these

priors

may

be

adjusted

non-inferentially.

It

may

seem

that the

enterprise

is

utterly

a

priori

and

hence

insensitive

to

contingent

facts about

our

observational

powers

and

reliability.

This

is

not

so.

As

with standards of

spatial

and

temporal measurement,

the

conventional standards

are

highly

constrained

by

pragmatic

consider

ations.

Let

us see

how

this

might

work.

We

begin

with observation

having

suitably,

albeit

conventionally,

assigned

rational

degrees

of

belief. Note that

in

using

this

word 'ration

al'

I

am

highlighting

the normative character of the

probabilities.

From

these

we

build

up

and confirm

theories

which

ultimately explain

both

the

very

processes

of observation

on

which

their

confirmation

rests

and

the

reliability

of

our

observational

judgments.

This notion of

reliability

here

is

also

a

probability

relation,

this

time understood

as a

frequency,

i.e., as a

descriptive

relation.

It

seems

fitting

that

the

degree

of

reliability

should match the

degree

of

justification

(that

is,

rational

degree

of

belief).

To

insist

that

they

must

match

moves

one

a

giant

step

further

away

from

classical

foun

dationalism

and toward

a

modest coherentism. Let

me

here

announce

Creath's

conjecture

(which

I

suspect

and

certainly

hope

is

provable,

though

I

do

not

pretend

to

have

proved

it):

if

the

degree

of

reliability

of observation

and the

degree

of its rational

credibility

do

not

match,

then

the

language

is

decision-theoretically

unstable, i.e.,

a

decision

theoretic

argument

can

be

given

from within

the

language

that

one

ought

to choose a different

language.5

If this

conjecture

is

right,

then

Carnap

needs

no

additional

requirement

beyond

the

pragmatic

con

straints

he

already

has.

Moreover,

the

system

is

highly

sensitive

to

the

contingent

facts addressed

by empirical

psychology.

If

we

concentrate

solely

on

these

explanations

of

reliability,

we

might

be

tempted

to

suppose

that

empirical

psychology by

itself

can answer

the fundamental

questions

of

epistemology.

But such

a

supposition

would be

circular,

as we

have

seen.

It would

also confuse the normative

and

descriptive

interpretations

of

probability.

Some

have

been

tempted

to

give reliability

theories of

justification

and

knowledge (Goldman,

1986).

Such

theorists,

however,

have been

hard

pressed

to

pick

out

the

relevant

conditions for

measuring reliability.

The

current

proposal



carnap's

conventionalism

163

helps

these reliabilists

by

specifying

in

the conditions

(Q),

mentioned

in

the

epistemic

rules,

what the relevant conditions

are.

At

the

same

time that it shows what

is

right

about

reliabilism,

the

current

proposal

shows how that view

must

be

embedded

in

a

larger

context.

Carnap's philosophy

began

with

a

rejection

of

intuition

as

a source

of

knowledge.

From

the

current

vantage

point

we can now see

that

the

objections

were

pragmatic.

Intuitive

judgments

are

unreliable,

conflict

ing,

and unshared.

In

short,

no

explanation

of the

reliability

of such

a

process

was

(or

could

be)

forthcoming.

The

same can

be

said

of

any

trans-empirical

(i.e.,

metaphysical)

mode

of

knowing.

Thus,

even

em

piricism

is

a

proposal

to

be

defended

pragmatically,

and

Carnap

says

just

that

in

'Testability

and

Meaning'

(Carnap,

1937,

p.

33).

We have

come

full circle:

starting

with

a

rejection

of

intuition,

Carnap

constructed

a

vast

conventionalist

and

pragmatic epistemology.

Our

job

was

to

unearth

it and

to

extend

it

a

bit.

Carnap

could then

not

only

avoid

relying

on

intuition,

but also

(pragmatically)

justify

in

detail

his

having

done

so.

That is

no

small

accomplishment

for

Carnap's

Hilbertization of the language of science. If Feigl could have foreseen

what it would lead

to,

perhaps

he

would have smiled

right along

with

Carnap.

NOTES

1

Carnap

found

it

nearly

impossible

to

criticize

anyone

he

deeply

admired,

but

clearly

Russell

was

a

special

case.

From

very

early

in his

career

Carnap

devoured

the work

of

Russell,

and from it

he

drew the

reassurance

of

a

kindred

spirit

as

well

as

inspiration

for

his

own

work. To this Russell

responded

with

help

and

generosity; Carnap

would have

described the older

man as

a

'father

figure'.

Furthermore,

as

is well

known,

Russell

frequently changed

his mind

even on

major

issues. As

it

happens

the

book of Russell

that

most

influenced

Carnap

was

Our

Knowledge of

the External World

(George

Allen

and

Unwin,

London,

1914).

That book

was

plainly

the

inspiration

for the

Au?au

as

well

as

for

Carnap's

conviction that the task of

philosophy

was

strictly

the

logic

of science.

Indeed,

Carnap

penciled

in

at

the end of the

third

chapter

of his

personal

copy:

This

...

is

my

task

(see

copy

in the Rudolf

Carnap

Collection,

University

of

Pittsburgh,

p.

97).

But

the first

chapter

of

Russell's book is

a

vigorous

attack

on

the

very

idea that

intuition

is

a source

of

knowledge.

Thus,

Carnap

could,

not

implausibly,

believe

that

Russell had

repented

his

previous

error

and hence

no

longer

needed the criticism

that

Carnap

didn't

want

to

give

anyway.

2

Carnap usually

avoided

describing

his work

as

epistemology

for

reasons

to

be

given

presently.

But

not

always.

In

scattered

passages throughout

his

writing

he conceded its

epistemic

character.

Quine,

too,

intermittently

has

described

Carnap's

basic

notions

as

epistemological.



164

RICHARD

CREATH

3

Perhaps

it

is

unnecessary

to

belabor

this

point

as

I have

done,

but

Burton Dreben

has

reached

a

contrary

conclusion.

He is

often

insightful

in

these

matters,

so

he

may

be

right.

In

any

case,

it

is unwise

to

disagree

with

him without clear and

cogent

reasons.

4

I

do

not

mean

to fault

Jeffrey

here. His intentions

differ

from

Carnap's,

and

the

theory

he advances

together

with

whatever

problems

it faces

likewise differ. Even

so,

Jeffrey's

suggestions

are

constructive,

and

Carnap

finds them

helpful.

If it does

not

fully

solve

Carnap's

difficulty,

that is

a

problem

for

Carnap,

not

Jeffrey.

5

As

Robert

Nozick

has

pointed

out

in

conversation,

there

is

no

guarantee

here

that

a

language

for

which

the

degree

of

reliability

of observation and the

degree

of its rational

credibility do match will be normal from our usual perspective. A sufficiently weird

original assignment might

support

a

weird

theory

which

would

explain

the odd

reliability.

In

fact, however,

all of this is

pretty

harmless. As with all

measurements,

the

results

would be relativized

to

the

procedures

of

measurement

at

hand. For

example,

one

can

measure

the universe

with

a

rubber

measuring

rod;

the results

will

be weird from

our

current

perspective;

but

because the results have

to

be relativized

to

the method of

using

a

rubber

rod,

those

results

are

not

really

in conflict with

our

usual

measurements.

This

should

also

suggest

that

even

if

degrees

of

reliability

and rational

credibility

match,

there

may

be other

pragmatic

considerations that would

make the

language

decision

theoretically

unstable. We

all

assume

that this is the

case

for the

use

of

a

rubber

measuring

rod. Doubtless

it is

also

true

with

many

weird initial conventions of observational

justifi

cation.

Finally,

there

would be

nothing

wrong

if

it should be discovered that

there

is

more

than

one

decision-theoretically

stable

language.

This is

just

what

one

would

expect

under the

assumption

that

these

are

conventions.

REFERENCES

Carnap,

Rudolf:

[1932a]/1959,

'The Elimination of

Metaphysics

Through

the

Logical

Analysis

of

Language',

in

A.

J.

Ayer

(ed.),

Logical

Positivism,

trans,

by

Arthur

Pap,

Free

Press,

New

York,

pp.

60-81.

Carnap,

Rudolf:

[1932b]/1987,

'On Protocol

Sentences',

Nous

XXI,

457-70.

Carnap,

Rudolf:

[1934J/1937,

The

Logical

Syntax

of

Language,

trans,

by

Amethe Smea

ton,

Routledge

&

Kegan

Paul,

Ltd.,

London.

Carnap,

Rudolf:

1935,

Philosophy

and

Logical Syntax, Kegan

Paul,

Trench,

Trubner

&

Co.,

London.

Carnap,

Rudolf:

1936,

'Testability

and

Meaning',

Philosophy of

Science

III,

419-71.

Carnap,

Rudolf:

1937,

'Testability

and

Meaning',

Philosophy of

Science

IV,

1-40.

Carnap,

Rudolf:

1950,

Logical

Foundations

of

Probability,

University

of

Chicago

Press,

Chicago.

Carnap,

Rudolf:

1957,

Letter

to

Richard

Jeffrey

of 17

July,

unpublished;

examined with

permission

of Professor

Jeffrey.

Carnap,

Rudolf:

1966,

Philosophical

Foundations

of

Physics,

Basic

Books,

New York.

Carnap,

Rudolf:

1971,

'Inductive

Logic

and Rational

Decisions',

in Rudolf

Carnap

and

Richard Jeffrey (eds.), Studies in Inductive Logic and Probability, Vol. 1, University

of California

Press,

Berkeley,

pp.

5-31.

Creath,

Richard:

1985,

'Carnap's

Scientific

Realism: Irenic

or

Ironic?',

in Nicholas

Re



carnap's

conventionalism

165

scher

(ed.),

The

Heritage of Logical

Positivism,

University

Press of

America,

Lanham,

MD,

pp.

117-31.

Feigl,

Herbert:

1975,

'Homage

to

Rudolf

Carnap',

in

Jaakko Hintikka

(ed.),

Rudolf

Carnap,

Logical

Empiricist,

D.

Reidel, Dordrecht,

pp.

xiii-xviii.

Frege,

Gottlob:

1980,

Philosophical

and Mathematical

Correspondence,

ed.

by

Brian

McGuinness,

trans,

by

Hans

Kaal,

University

of

Chicago

Press,

Chicago.

Goldman,

Alvin

I.:

1986,

Epistemology

and

Cognition,

Harvard

University

Press,

Cam

bridge,

MA.

Quine,

W.

V.

O.:

[1936]/1966,

'Truth

by

Convention',

in

Ways

of

Paradox and Other

Essays, Random House, New York, pp. 70-99.

Russell,

Bertrand:

[1912J/1959,

The Problems

of Philosophy,

Oxford

University

Press,

London.

Department

of

Philosophy

Arizona State

University

Tempe,

AZ

85287

U.S.A.

carnap conventionalism

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