Susan Haack - Justifications of Deduction

7/26/2019 Susan Haack - Justifications of Deduction

1/9

Mind Association

The Justification of DeductionAuthor(s): Susan HaackSource: Mind, New Series, Vol. 85, No. 337 (Jan., 1976), pp. 112-119Published by: Oxford University Presson behalf of the Mind Association

Stable URL: http://www.jstor.org/stable/2253263.Accessed: 29/06/2011 13:07

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at.http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=oup..

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

Oxford University PressandMind Associationare collaborating with JSTOR to digitize, preserve and extend

access toMind.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/action/showPublisher?publisherCode=mindhttp://www.jstor.org/stable/2253263?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/2253263?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=mindhttp://www.jstor.org/action/showPublisher?publisherCode=oup


2/9

The Justificationf Deduction'

SUSAN HAACK

(i)

It is often aken for grantedby writers

who propose-and, for that

matter, y

writerswho

oppose-'justifications'

of nduction,hatdeduction

either

does not

need,

or

can readilybe providedwith, ustification.

he

purpose

of

this

paper is

to

argue that,

ontrary o this commonopinion,

problems analogous to those which, notoriously,

rise in the attempt o

justify nduction, lso arise n the attempt

o ustify eduction.

Hume presented us with

a

dilemma:

we cannot justify nduction

deductively,because to do so would be to show that whenever he

premisses f an inductive rgument re

true, he conclusionmustbe true

too-which

would

be too

strong; nd

we cannot ustify

nduction

in-

ductively, ither, ecause such a 'justification' ould be circular. propose

anotherdilemma: we cannot ustify eduction

nductively, ecause

to do

so

would

be,

at

best,

to

show that usually,when

the

premisses

of a

deductive argument

re

true, the

conclusion

s

true too-which

would

be too

weak;

and we

cannot

ustify

eductiondeductively, ither,

ecause

such

a

justification ould be circular.

The

parallel between he old and

the new dilemmas

an

be illustrated

thus:

Hume's

dilemma

induction

deductive inductive

justification

justification

too

strong

-circular

The new

dilemma

deduction

inductive

deductive

justification justification

-too

weak -circular

(2)

A

necessarypreliminary

o

serious discussion

of

the problems

of

justifyingnduction/deduction

s a

clear statement

f

them.

This means, first, iving some

kind of characterisation f 'inductive

argument'

nd

'deductive

argument'.

This

is

a

more

difficult

ask

than

seems to be generally ppreciated. It will hardly do, for example, to

characterise eductive rguments

s 'non-ampliative' Salmon [i966])

or

I have profited rom ommentsmade when an earlierversionof this

paper

was read to

the Research Students' Seminar in

Cambridge, May

1972.

I

I2


3/9

THE

JUSTIFICATION

OF DEDUCTION

II3

'explicative' Barker

I965]),

and

inductive rguments s 'ampliative'

or

'non-explicative';

for

these

characterisationsre apt to turn out either

false, if the key notion of 'containingnothing n the conclusion not

already

ontained

n the

premisses'

s taken

iterally,

r

trivial,

f t

is

not.

Because of the difficultiesf

demarcating inductive' and 'deductive'

inference,t seems more profitable o

define n argument:

An

argument s a sequence

Al

.

..

An of

sentences (n

> i),

of

which

A1.

. .

An_1

re the premisses

nd

An

is the conclusion

-and then to tryto distinguish

nductivefromdeductive standards

of

a 'good

argument'.

It

is

well known that deductive

standards of validitymay be put

in

either

f

two

ways: syntacticallyr

semantically. o:

D1

An argumentA1 ..

An

1

F An is deductively alid (in

LD)

just

in case the

conclusion,

An,

is

deducible

from

he premisses,

A1

..

An-,,

and the axioms ofLD, if

any,

n virtue f

the

rules

of inference f

LD

(the

syntactic efinition).

D2 An argumentA1 ..

An

1

H

An is deductivelyvalid just in

case it is impossible that the

premisses,

A1

. . .

An-,

should be

true, nd the conclusion,An,

false the semanticdefinition).

Similarly,

we can

express

standards

of

inductive

strength

either

syntactically

r

semantically;

he

syntacticdefinition

would follow D1

butwith LI' for

LD';

thesemanticdefinition ouldfollowD2 butwith

'it

is

improbable, iventhat the

premisses re true, hatthe conclusion s

false'.

The

question

now

arises, which of these kinds of characterisation

should

we

adopt

n our

statement f

the

problems

f

ustifying

eduction/

induction?

This

presents difficulty.f

we adopt semanticaccounts

of

deductive

validity/inductive

trength,

he problem of justificationwill

seem to

have

been

trivialised.

The

justification roblem will reappear,

however,

n a

disguisedform, s the question Are there ny deductively

valid/inductivelytrongarguments?'. f,

on

the other hand, we adopt

syntacticccountsofdeductivevalidity/inductivetrength, he natureof

the

justification roblem

is

clear: to

show that argumentswhich

are

deductively valid/inductively trong

are also truth-preserving/truth-

preservingmost

of

the

time i.e.

deductively alid/inductivelytrong

n

the semantic

ccounts).

On

the other

hand, there s

the

difficultyhat

we

must

somehow

specify

which

systems

re

possible values

of

'LD'

and

'LI',

and

this will

presumably equire

appeal

to

inevitably ague

con-

siderations

oncerning

he intentions

f

the authors

of

a formal

ystem.

A

convenient

ompromise s this. There are certain orms

f

nference,

such as

the rule:

RI From: m/nfall observedA's havebeen B's

to

infer:

m/n

f

all

A's are

B's

which are

commonly taken

to

be

inductively trong, and similarly,

certain

forms

f

inference, uch as

MPP

From:

A

- B,A

to infer:

B


4/9

114

SUSAN

HAACK:

which

re

generally

aken o be

deductively

alid.

Analogues

of

the

general

justification

roblems

an

now

be set

up

as

follows:

theproblemof the ustificationfinduction: howthat RI is truth-

preserving

most of

the

time.

the

problem of the

justification

f

deduction:

show

that MPP

is

truth-preserving.

My procedurewill

be,

then,

o

show

that

difficulties

rise

n the

attempt

to

ustify

MPP which

re

analogous

to

notorious

ifficulties

rising

n

the

attempt

o

ustify

RI.

(3)

I

consider

first he

suggestion

hat

deduction

needs

no

ustification,

that

the

call

for a

proof

that MPP

is

truth-preserving

s

somehow

mis-

guided.

An

argument

orthis

position

might

go

as

follows:

It is

analytic hat

a

deductively

alid

argument s

truth-preserving,

for

by

valid'

we mean

argument

whose

premisses ould

not

be

true

without ts

conclusion

being

true

too'. So

there

can

be no

serious

question

whether

deductively

alid

argument

s

truth-preserving.

It

seems

clear

enough that

anyone who

argued ike this

would

be the

victim of a

confusion.

Agreed,

if we

adopt

a semantic

definition

f

'deductively

alid'

it

follows

mmediately

hat

deductively

alid

arguments

aretruth-preserving.uttheproblemwas,to showthat particular orm

of

argument,

form

deductively

valid in the

syntactic

ense,

is truth-

preserving;

nd this

s a

genuine

problem,

which

has

simply een

evaded.

Similar

arguments

how the

claim,

made

e.g.

by

Strawson n

[I952],

p.

257,

that

nduction

needs no

justification,

o be

confused.

(4)

I

argued

in

Section

i) that

justifications' f

deduction

re

liable

either

o

be

inductive nd too

weak,

or to

be

deductive

nd

circular.The

former,

nductive

kind

of

ustification as

enjoyed ittle

opularity

except

with

the

Intuitionists? f.

Brouwer

I952]).

But

arguments f

the

second

kind

are not hard

to

find.

(a) Considerthefollowingttempt o ustifyMPP:

Ai

Suppose that A'

is

true,

nd

that A

D

B'

is

true.

By

the

truth-

table for

D',

if

A' is true and

'A

D

B'

is

true,

hen

B'

is true

too.

So 'B'

must be true

too.

This

argument

as

a

serious

drawback: t

is of the

very

form

which

t

is

supposed

to

ustify.

For

it

goes:

Ai'

Suppose

C

(that

A'

is

true

nd thatA

D

B'

is

true). f

C then

D

(if

'A'

is

true and

'A

D

B'

is

true,

B'

is

true).

So,

D

('B'

is true

too.

The

analogy

with

Black's

'self-supporting' rgumentfor

induction

[I954]

is

striking. lack

proposes

to

support

nduction

by

means of

the

argument:

A2

RI

has

usually

been

successful

n

observed

nstances.

.'.

RI

is

usually

successful.


5/9

THE JUSTIFICATION

OF

DEDUCTION

II5

He defendshimself gainst

the charge of circularity

y pointingout

that this argument s not a simple

case of question-begging:

t does not

contain ts conclusionas a premiss. t might, imilarly, e pointedout

thatAi' is not

a simple case

of question-begging: or t does not

contain

its conclusion

s

a

premiss, ither.

One is inclined

to feel that

A2

is objectionably

ircular,

n spite

of

Black's defence;

nd this ntuition

an be supportedby an argument,

ike

Salmon's [I966],

to show that

f

A2

supports RI, an exactly

analogous

argumentwould

support counter-inductiveule,

say:

RCI

From: most observedA's have not been

B's

to infer:

most A's

are

B's.

Thus:

A3 RCI

has

usually been

unsuccessful n thepast.

RCI is

usually

successful.

In a similarway, one can support

the intuition

hat there s something

wrong

with

Ai',

in

spite

of

its

not being straightforwardlyuestion-

begging, by showing that if

Ai'

supports MPP,

an exactly analogouis

argument

would

support

deductively

nvalid

rule, say:

MM

(modus

morons);

From:

A

D)

B

and

B

to

infer:A.

Thus:

A4 Supposing that

A

D

B'

is true and

'B' is true, A

D

B'

is true

v 'B' is true.

Now, by the truth-table

or

::',

if A' is true, hen, f A

D

B'

is

true,

B'

is

true.

Therefore,

A'

is true.

This

argument,

ike

Ai,

has the

very

ormwhich t s

supposed

to

ustify.

For it

goes:

A4' Suppose

D

(if A

D

B'

is true,

B'

is true).

If C, thenD (if A' is true, hen, f A

D

B' is true, B' is true).

So,

C

('A'

is

true).

It

is no

good

to

protest

hat

A4'

does

not

ustify

modusmorons

ecause

it

uses

an invalidrule of

nference,

hereas

A4'

does

ustify

modus

onens,

because

it uses

a

valid rule

of

nference-for

o

ustify

ur

conviction

hat

MPP

is

valid

and

MM is

not

is

precisely

what s at issue.

Neither

s

it any

use

to protest

hat

Ai'

is

not

circularbecause it

is an

argument

n the

meta-language,

whereas

he

rule which

t

is

supposed

to

justify

s a

rule

in the

object

language.

For

the attemptto save

the

argument

orRI

by taking

t

as

a

proof,

n

level2,

of

a rule of evel i,

also

fallsprey o the difficultyhatwe could withequal justice give a counter-

inductive

rgument,

n level

2,

forthe

counter-inductive

ule at

level i.

And

similarly,

f

we

may give

an

argumentusing MPP,

at

level

2,

to

support

the

rule MPP at

level

i,

we

could, equally,

give

an

argument,

using MM,

at

level 2,

to

support

he rule

MM at level i.

(b)

Another

way

to

try

to

justify MPP, which promises

not to be


6/9

II6 SUSAN

HAACK:

vulnerableto the difficultyhat, f it is

acceptable, so is an

analogous

justification f

MM, is suggestedby Thomson's discussion I963] of the

Tortoise's argument.Carroll's tortoise, n

[i895],

refuses o draw the

conclusion,

B',

from A - B' and 'A',

insisting hat a new premiss,

'A

( (A -

B) - B)' be added; and when thatpremiss s grantedhim,

will stillnot

draw the conclusion, ut insists n a further remiss, nd so

ad indefinitum.homson argues hatAchilles

hould neverhave

conceded

that

n

extra

premisswas needed; for,he argues, f the original nference

was

valid

(semantically) he added premiss

s true but not needed,

and

if the original

nferencewas invalid

semantically) he added premiss s

needed

but false.There is an analogy,here,

gain,with ttempts o ustify

inductionby

appending

premiss-something, sually, o the effect hat

'Nature is uniform'-which turns nferencesn accordancewith RI into

deductively alid inferences. he required

premisswould, presumably,

be true but not

needed if RI were

deductively

alid,

false but needed

if

it

is not.

Thomson's

idea suggeststhat we should contrast his picture n

the

case of MPP:

A5

(i)

A

D

((A

D

B)

D

B)

(true

but

superfluous

remiss)

(2)

A

assumption

(3) (A

B)

B

I,

2,

MPP

(4)

A

B

assumption

(5) B 3, 4, MPP

withthis picture n the case of MM:

A6 (i)

B

D

( (A

D

B)

D

A) (false but

needed premiss)

(2)

B

assumption

(3) (A B) A I,

2,

MPP

(4)

A

B

assumption

(5)

A

3,

4,

MPP

Thomson's

point s that n As premiss

i)

is

a tautology, o true; but it

is not

needed, since

ines

2),

(4)

and

(5)

alone constitute valid argument.

In A6, by contrast, remiss

i)

isnot tautology; ut t sneeded, because

lines

2),

(4)

and

(5)

alone

do

not constitute valid

argument.

ut

this s

to assume

that

MPP,

which

s

the rule

of

nference n virtue

f

which n

As (2) and (4) yield

(5),

is valid; whereas

MM, which is the rule

of

inference n

virtueof which, n A6,

(2)

and

(4)

would yield

(5),

is not

valid.

But

this s

just

what

was to have been

shown.

If

As justifiesMPP, which,after ll, it

uses, then the following rgu-

ment

equally ustifiesMM:

A7

(i)

(A- B)

(A

:D

B) (true

but superfluous remiss)

(2)

A

B

assumption

(3)

A

B

I, 2,

MM

(4)

B

assumption

(5)

A

3,

4,

MM

In

A7

as in

As

the

first remiss s a

tautology, o true,but it is super-

fluous, ince ifMM is accepted) ines

2),

(4)

and

5)

alone onstitute

valid

argument.


7/9

THE

JUSTIFICATION

OF DEDUCTION

I17

(c)

Nor will it do to

argue that

MPP is, whereasMM

is not,

ustified

'in virtue

f

the

meaning

of

D

'.

For how

is the meaningof

D

'

given?

There are threekinds of answer commonly iven: that the meaningof

the

connectives s given

by the rules

of inference/axioms

f the

system

in which

theyoccur;

thatthe meaning

s given

by the interpretation,

r,

specifically,

he

truth-table, rovided;

that the

meaning s given

by the

English

readings

of the connectives.

Well,

if

D'

is supposed

to be at

least

partially

defined by the rules

of inference

governing entences

containing

t (cf.

Prior

[I960], [I964]) then

MPP and MM

would be

exactly

on a

par.

In a

system

containingMPP the

meaning

of

'2)'

is

partially

definedby the

rule, from A

=)

B'

and 'A',

to infer B'.

In a

systemcontaining

MM

the meaning of

D

'

is partially

definedby the

rule,fromA - B' and B', to inferA'. In either ase the rule nquestion

would be justified n virtue

of the

meaning of

'-', finally,

ince the

meaning

of

D'

would be

given by

the rule. If, on the

other

hand, we

thought

of

'v'

as partially

defined

by its truth-table

cf. Stevenson

[i96i1]),

we are in the difficulty

iscussed earlier (a)

above)

that argu-

mentsfrom he

truth-table

o the ustification

f a rule

of inference re

liable to employ

the rule

in question. Nor

would it do

to appeal to the

usual

reading

of

D'

as

'if

..

then

. .

',

not ust because

the

propriety

of

that

reading

has been doubted,

but also

because the question,

why

'B'

follows

rom

if

A

then

B'

and 'A' but

not A' from

if A then

B'

and

'B',

is

precisely

nalogous

to the question

at

issue.

(d) Our arguments against attempted ustificationof MPP have

appealed

to the fact that

analogous

procedureswould

justify

MM. So

at

this point it

might be

suggested that we

can produce

independent

arguments gainst

MM.

(Compare attempts

o diagnose

ncoherence n

RCI.)

In

particular,

t

might

be supposed

that it

is

a relatively

imple

matter

o

show that MM cannot

be truth-preserving,

ince with

MM

at

our disposal we

could argue

as follows:

A8

(i) (P

&-P)

=D

(Pv-P)

(2)

Pv -P

(3) P&-P

1,2MM

So

that a

system

ncluding

MM

would be

inconsistent.

This

idea

is

suggestedby

Belnap's paper

on

'tonk'.)

However,

this

argument

s inconclusive

because

it

depends

upon

certain ssumptions

bout what

else we

have

in the

system

o which

MM

is appended-in

particular,

hat

i)

and

(2)

are theorems.

Now

certainly

if

a

system

ontained

i)

and

(2)

as

theorems,

hen

3)

could

be

derived

by

MM,

and the

system

would

be

inconsistent;

ut a

system

llowing

MM

can

hardly

be assumed

to

be

otherwise

onventional.

After

ll, many

systems ack 'Pv

-

P' as a theorem, nd minimal ogic also lacks P

D

(-P

Q)'.)

(5)

It

might

be

suggested

at

this

point

that to direct

our

search

for

justification

o

a

form

f

argument,

r

argument

chema,

uch

as

MPP,

is

misguided,

hat

the

ustification

f

the

schema

lies in

the

validity

f

its

instances.

o the answerto the

question,

What

ustifies

he conclusion?'


8/9

I

I8

SUSAN HAACK:

is simply The

premisses'; and

the

answerto the further

uestion,

what

justifies

he argument

chema, s

simply hat ts instances

re valid.

This suggestion s unsatisfactoryor everalreasons.First, tshifts he

justification

roblem

from

he

argument chema to its

nstances,

without

providing ny

solution o the

problem f the

ustification

f the nstances,

beyond the bald assertion hat

they

re

ustified.The

claim

that

one can

just see

that the

premisses ustify he

conclusion s implausible

n the

extreme n view

of

the

fact hat

people can

and do

disagree bout which

arguments re

valid. Second,

there s

an

imiplicit

enerality

n

the

claim

that a particular

rgument s valid. For to

say that

an

argument s valid

is not

ust

to

say

that

ts

premisses

nd

its

conclusion are true-for that

is neithernecessary

nor

sufficient

or

semantic)

validity.

Rather, t is to

say that tspremisses ouldnot be truewithout tsconclusionbeingtrue

also, i.e. that

there s

no

argumentf

that ormwith rue

remissesnd

false

conclusion.

ut if the claim

that

a

particular

rgument

s

valid

is to be

spelled

out

by appeal

to

other

arguments

f

that

form,

t is

hopeless

to

try to justifythat form

of

argumentby appeal

to

the

validity

of

its

instances. Indeed, it

is not

a

simple matter

o

specify

f

what schema

a

particular rgument

s an

instance.

Our

decision about what the

logical

formof an

argument s may

depend upon our

view

about whether he

argument

s

valid.)

Third,

since

a

valid schema

has

infinitelymany

instances, f

the

validity f the schema

were

to

be

provenon the basis of

the validity f ts

instances, he

ustification f theschema wouldhave tobe inductive,and would in

consequence

inevitably

fail to

establish

a

resultof the desired

strength.

Cf. Section .)

In

rejecting

his

suggestion

do

not,

of

course,

deny

the

genetic

point,

that

the

codification

f

valid

forms

of

inference,

he

construction

f a

formal

ystem,may

proceed n

partvia

generalisation ver

cases-though

in

part,

I

think,

he

procedure

may

also

go

in

the

opposite

direction.

(This

geneticpoint s, I think,

elated

o

the one Carnap [I968] is

making

when he

observes hat

we could not

convince

man

who

is

'deductively

blind'

ofthe

validity

f

MPP.)

But

I do

claimthat he

ustification

f form

of nference

annot

derive from ntuition f

the

validity f its

instances.

(6) What I havesaid in thispapershould, perhaps,be alreadyfamiliar

-it is

foreshadowedn Carroll I895],

and more

or

less

explicit n

Quine

[1936] and Carnap I968

('.

.

. the

epistemological ituation n

inductive

logic .

.

.

is not

worse than that

in

deductive

logic,

but

quite

analogous

to

it', p. 266).

But

the

point

does

not

seem

to

have been

taken.

The

moral

of the

paper might

e

put,

pessimistically,s that

deduction

is no

less in need of

ustification

han

induction; or,

optimistically,

s

that induction s

in no

more need

of

justification

han

deduction.

But

howeverwe put t,the

presumption, hat

nduction s shaky

but deduction

is

firm,

s

impugned.

And this

presumption

s

quite crucial,

e.g.

to

Popper's proposal

[I959]

to replace inductivism y deductivism.Those

of us who

are

sceptical about the

analytic/syntheticistinction

will,

no

doubt,

find

these

consequences

less

unpalatable

than

will

those

who

accept it.

And those of

us who

take

a

tolerant ttitude o

nonstandard

logics-who regard

ogic

as a

theory, evisable, ike other

heories,

n

the

light

of

experience-may

even find

hese

consequences welcome.


9/9

THE JUSTIFICATION

OF

DEDUCTION

II9

BIBLIOGRAPHY

Barker, S. F. [I965]. 'Must every nference e eitherdeductive or inductive?'

in Philosophy n America, d. Black, M.,

Allen and

Unwin, I965.

Belnap, N. D.

[ig6i].

'Tonk, plonk

and

plink', Analysis

I96I,

and in Philo-

sophicalLogic, ed. Strawson,P. F., O.U.P., I967.

Black, M.

[I954].

Inductive support

of

induction',

in

Problemsof Analysis,

Routledge and Kegan Paul,

1954.

Brouwer, L. E. J.

[I952].

Historical

Background, Principles

and Methods of

Intuitionism', outh African

Journal

of Science, 1952.

Carnap, R. [I968].

'Inductive

logic

and

inductive

ntuition'

n The

Problemof

Inductive ogic, ed. Lakatos, I., North-Holland, 1968.

Carroll, L.

[I895].

'What the Tortoise said to Achilles', Mind, I895.

Popper, K. R.

[I959].

The logic of Scientific iscovery,Hutchinson, I959.

Prior, A. N. [I960].

'The

runabout

inference

icket', Analysis, 1960,

and in

Philosophical ogic,

ed.

Strawson,

P.

F., O.U.P., I967.

Prior,A. N. [I964]. 'Conjunctionand Contonktion evisited',Analysis,1963-4.

Quine, W.

V.

0. [1936].

'Truth

by

convention'

I936),

in

Ways of Paradox,

Random House, I966.

Salmon, W. [I966].

The

Foundations of Scientific nference,University of

Pittsburgh, 966.

Strawson, P. F. [I952]. Introduction

o

logical theory,Methuen, I952.

Strawson, J. T.

[I96I].

'Roundabout the runabout nference icket',Analysis,

196I.

Thomson, J. F. [I963]. 'What Achilles should have said to the Tortoise', Ratio,

I963.

UNIVERSITY OF WARWICK

Susan Haack - Justifications of Deduction

Documents

Transcript of Susan Haack - Justifications of Deduction