Teller, Logic

8/19/2019 Teller, Logic

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P UL TELLER

Shimony's

A Priori Arguments for

Tempered Personalism

1. Introduction

In his

essay, Scientific Inference , A bne r Sh im ony presents

an

analy-

sis

of scientific con firm ation wh ich t ies together tw o twentieth-century

proposals for treating the

justification

of our scien tific m ethodology. To

characterize

th e

first

of

these proposals,

to be

referred

to as the method

of pragmatic justification, scientific inference is analyzed as an activity

wh ich w e un de rtak e in o rder to ach ieve certain m ore or less specifically

described ends. It is adm itted

that

w e cannot be sure of achieving those

ends. But, on this view, if we desire th e ends and if we have no reason

to suppose them unattainable, w e are

justified

in assuming tha t the ends

can be

achieved. This assumption

is

then used

as a

premise

for an

argu-

m ent con cern ing the na tur e or structure o f scientific investigation. Peirce

originated

this

pattern of argument, and

Reichenbach,

discovering it

independently, presented

it in its

best kn ow n form

as his familiar

vindi-

cation

or

pragmatic just ifica tion

of

induct ion.

One might refer to the second proposal as the seafarer's doctrine

since it is so suggestively sum m arized by

Neurath 's

simile which com-

pares

our efforts to s tudy and correct methods of scientific inference

with

th e efforts of

sailors rebuilding their ship

at

sea.

On

this view,

th e

only means we have for judg ing which methods of investigation will

result in reliable beliefs are our cu rren tly accepted m ethods of arg um ent

and our scien tific theories (a n d perhaps o ther beliefs) about the na ture

of

th e

universe. These methods

of

argument might turn

out to be un-

reliable,

and the

theories might turn

out to be

wrong;

but at any

given

time they are the only things w e have as a basis for judg ing, m odifying,

and extending our view of the world and our methods of evaluating be-

liefs. Quine suggests some view

o f

this kind

at the end of

Two Dogmas

of Em piricism (1963, pp.

42-46),

and the doctrine bears more than a

AUTHOR'S

NOTE:

Work

on

this article

w as

supported

by National

Science Founda-

t ion graduate and postdoctoral fellowsh ips.

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SHIMONY S PRIORI RGUMENTS

superficial similarity

to

Goodman's view

in

Fact, Fiction

and Forecast

(1965,

pp.

62-65) that inductive rules

are

both developed

and

justified

through a process of mutual adjustment with inference cases. Closely

related points are made by Suppes (1966, pp. 62,

64),

and the whole

position

has

many points

of

similarity

to

Dewey's views

in his

Logic

(1949) .

Shimony uses his versions of the pragmatic justification and seafarer's

doctrine in tandem. H e describes a set of condit ions which one might

hold to be

reasonable constraints

on the

structure

and interpretation of

scientific

investigations. H e then hopes to argue that

scientific

inference, thus formulated,

is a

method

of

reasoning which

is

sensitive

to the

truth, whatever

th e

actual constitution

of the

universe

m ay

be. In

this [first] stage very little will

be

assumed about

th e

place

of

hu m an be ings

in

nature ,

but the

result

of

such austerity

is that

scien-

tific method is only minimally just ified, as a kind of counsel of despera-

tion [because

it is

only shown

to

hold

out

hope

of

reaching true beliefs

i f human be ings are capable of reaching true beliefs]. In the second

stage . . . the justification is enlarged and made more optimistic by

noting the biological and psychological characteristics of human beings

which permit them to use induction as a discriminating and efficient

instrument.

Thus

the second stage . . . evidently presupposes a con-

siderable body of

scientific

knowledge about men and their natural en-

vi ronment . . . (1970, p. 81).

Shimony's paper presents a valuable contribution toward th e goal of

developing an adequate version of the seafarer's doctrine by describing

many specific ways

in

which scientific conclusions

and

methodological

principles may support and supplement one another. I believe

that

a

program

of this kind m ay provide the best way out of m a n y of our

present-day problems

in

confirmation theory,

and I

hope that

the

view

will

be

fur ther developed.

On the

other hand,

I

believe

that

Shimony's

at tempts to incorporate vers ions of Peirce's and Reichenbach's arguments

are misguided and

that

his view would be improved if

freed from

all

attempts

to

argue

in

favor

of his

outline

of

scientific investigation

on

strictly

a priori grou nds, that is , w itho ut appeal to contingent premises.

The aim of the present paper is to sustain this belief by showing that

those

o f

Shimony's arguments which

can be

said

to be a

priori,

and

their

plausible modifications, fail to support h is conclusions. In preparation

for

this criticism, the next two sections will be devoted to describing

tempered personalism and Shim ony's proposed analysis of scientific in -

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Paul

Teller

ference,

and to explaining Shimony's strategy for just ifying tempered

personalism a priori.

2. Tempered

Personalism

2.1. The

.Bayesian

analysis of Carnap and the

personalists.

Tempered

personalism is a Bayesian analysis of scient if ic inference. It wil l be well

to

su mmar ize

the

features common

to all

fo rms

of

Bayesianism

and to

state certain dist inct ive characterist ics of other Bayesian theories; this

will help to m a k e the impor tant fea tu res of Shimony's analysis clear, by

giving both points of agreement and points of contrast .

A

B ayesian desc ript ion chara cterizes reasona ble belief

or

credence

as

a variable quantity,

the

magni tude

of

which

can be represented by a

func t ion

from proposi t ions

(o r

sentences) onto numbers be tween zero

and one, inclusive. The f u n c t i o n , P(h/e), has two arguments , h and e.

T he va lue of the func t ion is usu ally interpreted as a co nd i t iona l betting

rate;

if P

describes

the beliefs of an

agent ,

P(h/e)

de te rmines

the

odds

at which the agent would be ind iffere nt between accepting

either

side

of

a bet on the truth of h, where the bet wil l be cal led off if e should

tu rn

out to be

false.

If e is a

tautology, such

as p v ~p, the bet is un-

condit ional , P(h/e) is interpreted as the be t t ing ra te of an un con dit iona l

bet on h, and

<

T(h/e) is

abb reviated

to P(h). P(h/e) is

read

as

th e

degree of rational belief (or credence) in h given

(the

t ru th of) e.

In a Bayesian descr ip t ion P satisfies the axioms of condit ional proba-

bility, of which Bayes's

theorem

is a trivial consequence:

P(h)

is

of ten

referred to as the prior

degree

of

belief

in h, or

simply

the

prior probability of h.

P(e/h)

is of ten referred to as the likelihood of e

on h. I f h is taken to be a hypothesis and e fully describes new ly acq uired

evidence,

then

Bayes's

theorem

gives

a

plausible account

of how one's

degree of belief should change from P to a new fu nc t io n P'; B ayes ians

hold

that

P'(h)

=

P(h/e) if e has

been

f o u n d

to be

t rue.

In other

words,

the new degree of bel ief in h is taken to be the old degree of

belief

in h

given

th e

t ru th

of e.

This process

is

called con dit ional izat ion.

H owever, for a Bayesian theory fully to characterize the degrees of belief

wh ich ar ise by cond it ional izat ion, the theory m ust

specify

the bel ief

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S HI M ON Y S PR I OR I R GU M E N T S

func t ion

from

which

to

s tar t . This in i t ia l func t ion

is

called

the

prior

probabi l i ty funct ion.

A

ma j o r difficulty faced

by any Bayesian analysis is the problem of giv-

ing an acceptable specif ica t ion of pr ior probabi l i ty funct ions; and vari-

a n t s

of

B ayesianism

can be classified by the

an sw ers they propose

to

this

problem. One form of Bayesianism, known as personalism, holds that

the prior probabili ty func t ion is to be de te rmined by the agent 's subjec-

t ive j udg m e n t s a bou t w ha t odds

he

would take

in

bets, subject

to the

sole constraint

that

th e pr ior p robabi l i ty func t ion mus t

satisfy

the prob-

ab i li ty ax ioms. The sub jec t ive jud gm ent of d i f fe ren t people may give

rise

to

very

d i f fe ren t

pr ior probabi l i ty funct ions ,

but the

personalists

a rgue

that as

long

as the

f u n c t i o n s

satisfy the

probabi l i ty axioms there

is no j udg ing one to be m o r e or less rational than any other (c f . Savage,

1967b, p.

597,

and

p a s s i m ) . Another view, advanced

by

Carnap, holds

that it should be possible to put addi t ional constra ints of rationali ty on

the prior probability function. Ideally, according to Carnap, we should

be

able

to f ind suffic iently

s t rong cons t ra in ts

on al l

rational belief

to

enable us to d e f i n e th e pr ior probabi l i ty funct ion complete ly. The re -

su l t ing func t ion would g ive a logical concept of the degree of belief

it is

ra t ional

to

have

on any

given evidence,

in the

sense

that the

rational

degree

of

belief

on any

given evidence could

always be

calculated

from

the exp licit

def ini t ion.

1

If

it would be

possible

to find justif iable constraints on a prior proba-

b i l i ty func t ion suff ic ien t

to

d e f i n e

it

completely,

all

changes

in

rational

belief could hencefor th be described by con di t ional iza tion on new obser-

vat ions .

In

other words ,

the

ini t ia l constra ints would once

and for a l l

de te rmine co nf i rm at ion re la t ions be tween any possible hypothesis and

any

possible

observations.

2

Many personal is ts dif fer from C a r na p

in

this

respect also. They recom m end the ir doc t r ine on ly for use in restricted,

relatively well-defined situations

in

which

an

agen t

is

conf ron ted wi th

a

pract ica l decis ion-making problem in face of un cer ta in ty (c f . Savage,

1954,

pp. 16, 82-91;

1967a,

pp.

306-7). Examples

are the

wildcatter 's

problem

of

where

to

drill

an oil

well

and the

manufac ture r ' s

problem

of

how m u c h to produce . The personal is ts advise the wildcat ter and the

ma n ufa c t u r e r

to estimate their init ial degrees of belief subjectively for

1

Cf. Carnap, 1963, p. 971ff. Also 1962, p. 307. It should be added that Carnap

seems

to

show some vacil la t ion

on

these points

in his

C o n t in u u m

of

Induct ive

Methods ( 1 9 5 2 , pp. 5 3 - 5 5 ) .

2

C f .

references

of the las t foo tnote .

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Paul Teller

any

one

such problem,

but if a

similar

problem

arises years

later

under

considerably different circumstances they are advised to make new evalu-

ations rather

than to try to

conditionalize their

old

estimates

on the

vast

body of

intervening observations

of

uncertain relevance

to the

problem.

Furthermore, personalists recommend that

in

preparation

for a

Bayesian

analysis, a problem should be structured in terms of possible states of

th e

world, possible available acts,

and

possible consequences

of these

acts.

In

order

to

make

the

problem manageable this structur ing m ust

be

highly idealized,

and

personalists recommend

that one

simply ignore

states, actions,

and

consequences,

th e

possibility

of

which have

not oc-

curred

to the agent or which seem,

prima

facie,

to be irrelevant to the

problem. Savage

has

attempted

to

describe

how

such

a localization

and

specialization

of a

problem -description should proceed

(Savage,

1954,

pp. 82-91; 1967a, pp.

306-7),

but to the best of my know ledge no per-

sonalist

has tried to describe condit ions which determine when an agent

should continue condit ionalization

on his old

probability

function and

when

he

sho uld start from scratch, restructuring

h is

problem

and

m aking

new

subjective evaluations

of a

prior probabil ity function.

2.2. T he first

distinctive

feature

o f Shimony's

Bayesian analysis.

Shim-

ony's first departure from the views o f both Carnap and the personalists

results from

his

desire

to

give

an

account

of scientific

inference, viewed

as an enterprise un derta ken to achieve the theoretical [end] of learning

the

t ruth about

various

aspects

of the

wo rld . . .

but not the

practical

ends of special concern in problems of making decisions in

face

of un-

certainty (1970,

p. 81). For the

purpose

of

giving such

an

account

Shimony rejects the interpretat ion of P(h/e) as a bett ing quotient for

h

given e:

The source

of the

difficulties [with this interpretation]

is the

indispensability

of

general

theories

in

natural science

as it is now

studied

and, indeed, as it conceivably could be studied if the ideal of general

insight

into the

nature

of

things

is not to be abandoned (1970, p. 9 3 ) .

T he

personalists could interpret

P h/e)

as a betting

quotient

insofar as

they

restricted

application of

their theory

to

practical decision-making

problems

in

face

of

uncerta inty,

in

which

the

outcome

of

acts

are ob-

servables such as a drilling operation resulting in a gu sher or a dry

hole.

Bu t if the subject of concern is the t ruth of theories, th e bett ing quotient

interpretation is no

longer directly

applicable, as

plainly

there is no

bett ing on the t ruth of theories such as quantum mechanics or general

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relativity.

Moreover, even

if the

func t ion

P(h/e) is freed from its

inter-

pretation as a

fair

be tting quotient, in m an y cases it cannot plausibly be

interpreted

as the

rational degree

of

belief

in the

truth

of h,

given evi-

dence e (1970, pp.

93-94).

For if h is a general and precise theory, such

as quantum mechanics ,

it

does

not

seem rational

to

have

a

high degree

of belief

in its

literal truth:

the

his tory

of

science

has had too

m a n y

upsets

fo r that. Yet there is a

sense

in

which such theories

can be

said

to be highly or poorly confirm ed, and S him ony w ould l ike his inter-

pretat ion of P(h/e) to be as close to this sen se as possible.

T he

history

of

science suggests

an

alternative explicandum

to

Shimony.

H e proposes that

P(h/e)

be called a rational degree of commitment

to h

given

e and

that

this should

be interpreted as the

rational degree

of belief in the claim

that

the propo sition h is near to the

truth

when

th e

evidence

is e. A

proposit ion whose truth

can be

established

by

observation is

near

to the

t ruth

if and

only

if it is

t rue.

A ny

other

prop osition, h, is near to the tru th if it is related to the tru th in the

following

way:

(i)

within

th e

domain

of

current experimentation

h

yields

almost the same observational predictions as the t rue theory; ( i i )

the concepts of the true theory are generalizations or more complete

realizations of

those

of h;

( i i i ) among

the

current ly form ulated theories

competing with h there is none w hich

better satisfies

condit ions (i) and

(ii) (1970, pp. 94-95).

This characterization

is far

from complete

and

Shimony

presents

an

interest ing discussion

of the

difficulties

to be ex-

pected

in

filling

out the

description (1970,

pp.

95-97).

But

since

the

points

I

have

to

make will quite clearly

be

independent

of any

plausible

attempt to

clarify

further

the interpretation o f near to the

truth,

w e

m ay

rely

on the

in tui t ive unders tanding

of the

phrase suggested

by

con-

di t ions ( i ) ,

( i i ) ,

a n d ( i i i ) .

By way of

abbreviation,

and in

conformity with

Shimony's

usage,

I

will

henceforth

refer

to

P(h/e)

as the probability of h on e, when it is

clear

that probability

is to be und erstood as rational degree of com-

mitment .

2.3.

The

second distinctive feature

of

Shimony's

Bayesian

analysis.

Shimony gives

his

Bayesianism

its

second distinctive feature

by

stipulat-

ing

that

probability evaluations are to b e m ade o nly for the p roposit ions

of

a

limited

and

well-defined investigation.

A n

investigation

is

deter-

mined by:

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Paul Teller

(1) A set of hypotheses

hi,

. . . , h

n

(of which the last may be a

catch-all

hypothesis equivalent

to ~[li

1

v . . . v h

w

_ i ] )

which

have been suggested as worth investigating. [H enceforth , hy-

potheses wh ich have been suggested

as

worth investigating

will

be

referred

to by

Shimony's frequently used expression,

seriously proposed hypotheses. ]

3

(2 ) A set of

possible outcomes

e

if

. . . ,

e

m

of

envisaged observa-

tions;

and

(3 ) T he information,

i,

initially available. This information in ac-

tual circumstances

is

very heterogeneous, consisting partly

of

vague

experience concerning the matter of

interest,

partly of

experience which may be sharp but is of dubious relevance,

partly of sharp evidence which does not seem to bear directly

on the question at hand b ut is relevant to othe r questions in

th e same

field,

and partly of propositions which are regarded

as established even though they

go

beyond

the

actual evidence

and , therefo re have been accepted b ecause of previous investiga-

tions (1970,

p.

9 9 ) .

In Shim ony's accou nt, probabilities are specified for all the propo sitions

of an investigation, namely the proposition in S, the truth

funct ional

closure of (h

{

, . . . , h

n

,

ei,

. . . ,

e

m

)

and for no thin g else. An investi-

gation begins with

the

specification

of its

prior probability funct ion

P.

For

every m em ber,

d, of S,

P ( d ) must represent ,

at

least approx ima tely,

the investigator 's intuitiv ely judg ed initial degree of com m itm ent to d,

subject

to the restriction tha t P satisfy the probability axioms and to one

fur ther

restriction to be discussed a t length below. T he planned observa-

t ions are then made, and the invest igat ion terminates by determining

the posterior probability of the investigation. This is done by condition-

alizing

the prior probability

funct ion,

P, on the observed outcome of

the observations, e. A hypothesis,

h

{

,

is said to be preferred to a second

hypothesis, h

h

at the end of an investigation with observed outcome e

ifP(h«/e)/P(Ve)islargq*

3

Al though Shimony here says

that h

n

may be a

catch-all hypothesis,

in the

rest

of

his

discussion

he

seems

to

assume

that

it

always

is .

4

Since th e publicat ion of Scientif ic Inference Shimon y has decided

that

h

n

,

th e catch-all hypothesis, should be treated

differently

from hi,

I ?

i < n . This

shift

is necessitated by

difficulties which arise

in

explicating

th e notion of

near

to

th e

truth ;

since the catch-al l hypothesis is only specified as the n egation of the

disjunction of the

other hypotheses

of the

invest igat ion,

it is

highly unclear

in

w h a t

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SHIMONY S

PRIORI RGUMENTS

Shimony does not exclude the possibility tha t the concept of rational

degree of com m itm ent might be extended to broader applications, and

he

makes some general remarks about such

a

possibility

(1970,

pp.

118-21).

B ut

tempered personalism

itself

deals only with

the

specifica-

tion of rational degrees of commi t men t to the propositions of specific

investigations,

in the form of the prior and posterior probabilities de-

scribed above.

Shimony at t r ibutes to Jeffreys the suggestion that scientific investiga-

tions

be

localized

for the

evaluation

of

probabilities.

As I

remarked

earlier,

th e

personalists have similarly recom m ended application

of a

Bayesian

theory only to isolated and well-defined practical decision-

making problems;

and

they have at tempted

to

explain

how

such localiza-

tion of a problem might best be described. It was also noted tha t

personalists have

said

li t t le about deciding when old probabili ty func-

tions should

be

abandoned

in

favor

of a new

subjective evaluation, while

guidelines for such decisions are at least implicit in the formula t ion of

tempered personalism: an investigation ends when th e investigator has

made

the

observat ions that

he

envisaged

in

setting

up the

problem.

If

fur ther

examina t ion

of any

hypotheses

is

desired,

new

observations

should be planned and a new

subjectively

evaluated prior probability

funct ion

de te rmined .

Shimony's main motivation

for

stipulating that probability calculations

be limited to

narrowly specified

investigations is tha t it permits prob-

ability

to be a

manageable instrument

in

scientific inferen ce (1970,

p.

99; see

also

p. 100). If not

restricted

in

some such

way the

problem

of

assigning and

up da t ing probabi li ty evaluat ions would

be

hopelessly

d i f f i -

cult; m oreover

there

is no reason to suppose that an individual investiga-

t ion would gain from

a

global assignment

of

conf irmation re la t ions.

Quite to the

contrary,

it is

surely

overoptimistic to suppose

that

m en

could,

following

Carnap's prescription, once

and for all

settle

on a

per-

fectly general prior probabili ty funct ion which hencefor th need only

change

by

cond i tional ization.

5

From t im e

to

tim e

w e

seem

to be in

need

of

revising

our

opinion about

the

con firm atio n relation between evidence

and hypotheses. This is made possible by Shimony's localized investiga-

sense

th e

catch-all hypothesis

can be

said

to be

near

to the

truth,

or

whether this

makes sense

a t

all.

5

In

fact

Putnam has proved that there cannot be such a f un c t ion . See Pu tnam

(1963).

173


9/38

Paul

Teller

tions w ith their freshly assigned p rior probabilities, w hich give scien tific

investigations greater openness

to the

contingencies

of

inqu iry than pos-

sessed by

Carnap's c-functions

(1970, p.

9 7 ) .

2.4.

The

third

distinctive

feature

of

Shimony's

Bayesian

analysis.

As

so fa r described, Shimony's position differs from that of the personalists

only

in that he rejects the betting quotient interpretation of the proba-

bil ity fu nc tio n. The theory is to apply on ly to m ore or less narrow ly

specified problem situations, and the prior probabil ity function is to be

determined by the investigator's subjective judgment. Both Shimony

and

the

personalists agree that

the

prior probabil ity evaluation must

be

subject

to the

constraint

of the

probability axioms.

B ut

orthodox per-

sonalism holds that

the

probabil ity axioms

are the

only rational con-

straint that

can be placed on

P,

while Shimony goes so far in agreeing

with Carnap as to say that there is at least one other rational con straint:

The only kind o f irration ality wh ich [the personalists] explicitly discuss

is

incoherence [failure o f the probability axioms], but there are surely

other properties

of

belief systems w hich

are

characterizable

as

irrational,

and which would

inhibit

th e progress of natural science if they were

universal. In particular, the assignment of extremely small prior prob-

abilities to unfamiliar hypotheses is compatible with coherence, but may

be

irrat ional

in the

sense

of

being

th e

result

of

prejudice

or of

obeisance

to a uth ori ty or of narrow ness in envisaging possibilities. But unless a

hypothesis is assigned a non-negligible prior probability, Bayes' theorem

does

not

permit

it to

have

a

large posterior probability even upon

th e

grounds of a very large body of favorable observational data, and thus

th e theorem does not funct ion as a good instrument fo r learning from

experience (1970,

p . 92 ) .

In keeping w ith these rem arks Shim ony imposes the following condit ion

on the prior probability evaluation: fo r every seriously proposed hypothe-

sis of an investigation,

h , P ( h ) m u s t

be

sufficiently

high to allow th e

possibility that it will be preferred to all rival seriously proposed hy-

potheses as the result of the envisaged observations . . . (1970, p .

101).

This condit ion

is

called

th e

tempering condit ion,

and

accordingly

Shimony calls his description of scientific inference

tempered

person-

alism.

In

effect,

the

tempering condit ion requires

the

prior probabilities

and

likelihoods

of an

investigation

to

satisfy

th e

condit ion

that for

each seri-

ously proposed hypothesis h

{

of the investigation, there is some possible

outcome,

e,,

of the

envisaged observations,

so

that conditionalization

of

174


10/38

SHIMONY

S

PRIORI RGUMENTS

th e

hypotheses

on e _

w ill result

in hi

being preferred

to all

rival seriously

proposed hypotheses. This is to requ ire that

TC For each hi of an investigation, there is a possible outcome,

e ^

of

th e

envisaged observations such that P (hi/e

;

-)

— 1 — e

where

e is the

number such that

a

hypothesis, h,

is

said

to be

preferred

to its rivals at the end of an investigation just in case its posterior prob-

ability

is as

large

as 1 — e.

Although

th e

tempering condit ion

is

stated

as a

requirement

on the

prior probabilities of the seriously proposed hypotheses, it should be

noted that it is really a collective req uire m en t on the prior probabilities

and

th e

likelihoods.

T he

tempering condit ion places

the

strict require-

ment on the prior probabilities that P ( h i ) 7^ 0, for all h*; for if P(h{) =

0

then

P(hi/e,)

=

0,

whatever

the

likelihoods.

But

even

if P ( h ^ ) is

quite

large,

it

does

not

follow

that there is

some

e - fo r

w hich

P(hi/e,-) is suffi-

ciently

large to g uara ntee that hi wil l be preferred to all rival hypotheses.

As a

glance

at (1 )

will show,

if

P ( h i )

= 5 ^ 0

calculation

of

P (h

i

/e

j

-) pal-

pably depends on the value of P (e

3

/ h i ) .

6

It is

easy

to give examples in

which a prior probability distribution

fails

to

satisfy

th e tempering condi-

tion and in

which

the

distribution

can be

modified

to

satisfy

th e

require-

ment by changing either th e prior values for the seriously proposed

hypotheses

or the

values

of the

likelihoods.

The tempering cond it ion is imposed to en sure

that

every hypothesis

of an investigation has a possibility of receiving a high evaluation at the

end of the investigation; but it is w orth rem ark ing

that

the condit ion

also imp lies a parallel exclusion

condition

on the possibility of a hy-

pothesis receiving a low evaluation:

EC For

each hypothesis,

hi, of an

investigation

there is an e -

among

th e possible outcomes of the inves tigation's envisaged observa-

tions such

that

P(hi/e,-) ̂

e.

T he exclusion condit ion follows from the tem pering condit ion and the

8

P ( h i / e j )

appears

to

depend

on

P(e;).

B ut

since

for any

conditional probability measure P,

the

values

of P(h

t

/e>) can be

calculated

without using P(e^) by normalizing P ( h i ) X P ( e j / h i ) taken as a function of h

(

.

H enceforth I shall speak of P ( h

t

/e^) being

fully

determined by P ( h i ) and P(e//hi)

by Bayes's formula,

although strictly speaking normalization is also required. The

possibility of normalization or the method of normalizing may be affected by the

changes mentioned in fn. 4.

175


11/38

Paul Teller

assumption

that

fo r every hypothesis, h*, of an investigation there is a

rival hypothesis, hj,

i.e.,

a hypo thesis, hj, such that hi hj is logically

false. In the present fo rm ula tion of tempered personalism this cond ition

is

always satisfied since the catch-all hypothesis

(the

negation of the dis-

junct ion of the other hyp otheses) rivals all the other hypotheses. A l-

though this might

no

longer

be the

case

for the

revised treatment which

Shimony

plans

to

give

th e

catch-all hypothesis,

th e

assumption will

generally still

be

satisfied, since

as a

rule

an

investigation considers rival

hypotheses.

T o

show

that th e

exclusion condit ion follows from

th e

tempering con-

dition, th e probabil ity axioms, and the assumption given above, suppose

that th e

exclusion condit ion,

EC,

fails. Then there

is a

hypothesis,

h

{

,

of the

invest igat ion such that

for all

envisaged observations,

e

;

>

Let

h

k

be a

hypothesis which rivals

hi.

Then

for all

Q

by the axiom of total p robab ility. Then by ( 2 )

w hich co ntradicts

TC, the

tem pering condit ion.

3.

An

Outline

of

Shimony's Proposed

A

Priori Justification

of Tempered Personalism

3.1. Antecedents in the pragmatic form of a rgument . The impasse

created by H um e's skeptical arg um en ts led Reichenbach and

Feigl

to

develop ideas o rigina lly suggested by Peirce into a form of justification

which seemed to them appropriate for use in

discussion

of nond educ t ive

means

of reaching conclusions about the unob served. They saw induc -

tion

as a specific policy or program of action and interpreted th e prob-

lem of induction as the question of how one could

justify

following

the policy. Moral problems aside,

one's

reason for follow ing a course of

action is to achieve some desired

end,

w hich in the case of indu ction is

taken

to be the end of

obtaining true beliefs. Reichenbach

and

Feigl

conceded

to

H u m e th at

it is

impossible

to

give

a

noncircular argument

in support of the claim

that

fol lowing the policy will lead to true beliefs

or frequently true beliefs. But a weaker claim seemed to

them

to justify

176


12/38

SHIMONY S PRIORI

R G U M E N T S

a

person

in

under taking

th e

proposed course

of

act ion.

Let us

call

the

end of reaching true or at least frequently true beliefs the inductive

aim. Let us suppose, as is

usually

th e case, tha t w e desire to achieve the

induc t ive a im . Suppose w e knew w ith cer ta inty

tha t

if the induct ive aim

can be

achieved

by any

course

of

action

at

all, then

it can be

achieved

by following

th e

proposed inductive course

of

action.

7

Suppose, further,

that

w e

have

no

reason

to

believe

the aim

cannot

be

achieved. Then,

ac-

cording to Reichenbach and Feigl, we are

justified

in choosing the in-

duct ive course

of

action over

any

other course

of

act ion ( intend ed

to

realize

th e

same aim)

of

w hich

we do not

have similar knowledge.

3.2.

Shimon y's

form of argu m ent . Shim ony indicates the natu re of the

justification

he

intends

by

w riting that my t reatme nt

of

scientific infer-

ence is instrumentalist ic, in the sense tha t the

justif ication

for certain

prescriptions is their conduciveness to achieving certain ends, but the

ends admit ted are only the theoretical ones of learning the t ru th about

various aspects of the world . . . (1970, p . 81) .

Thus,

Shimony's pro-

posed pattern of

justif ication

is like the last in tha t he hopes to justify

tempe red person alism as a cou rse of action, by appealing to certain end s

which

one

might hope

to

achieve

by

fol lowing

th e

tempered personal-

ist's prescriptions for the conduct and interpretation of scientif ic investi-

gations.

The ends concerned are, as he says, the theoretical ones of

learning

the t ruth

about various aspects

of the

world.

B ut

unlike Reich-

enbach and Feigl, he does not argue that this end can be achieved by

his proposed course of action if by any; ra ther he argues that tempered

personalism

is

just if ied

by

vi r tue

o f

certain

of its

properties which make

it

conducive

to

achieving

the

stated ends.

I

take Shimony

to be

mak-

ing the following

claim:

of two

possible courses

o f

act ion,

if the first has

one of the

properties

in

quest ion while

the

second does not, then, other

things being equal, there is more reason to suppose that the

first

course

of

action will lead to the stated end than will the second. Shimony wil l

argue

that tempered personalism

has

such properties. Consequently,

other things being equal, there

is

more reason

to

suppose that

the

tempered personalist cou rse of action w ill achieve the stated end than

will

some other course of action which lacks these properties. Finally,

Shimony holds that these claims can all be established without appeal to

contingent premises, and in tha t sense his justification is a priori.

7

Reichenbach's method

of proving such a conditional state m ent will be described

in sec. 5.

77


13/38

Paul Teller

T he

properties

in

question

are

described

by the

fol lowing

three

state-

ments

:

(1 )

Invest igat ions conforming

to the

prescriptions

of

tempered

personalism

are open m inded.

That

is to say, wh en true hypoth-

eses

(or hypotheses close to the truth) are seriously

proposed,

they have a chance of being accepted as t rue (or close to the

truth):

the tempering condition

is

only

a way of

prescribing

open m indedness w ithin a probabilistic scheme of inference;

and open mindedness is a necessary condit ion for the accept-

ance

of

true hypotheses

in

case they should ever

be proposed

(1970, p. 158; see also pp.

130-33).

(2) Investigations co nfo rm ing to the prescriptions of tempered

personalism

m ainta in

a

critical

attitude (1970,

p. 130)

toward

proposed hypotheses. That is, no hypothesis receives a high

posterior evaluation

or is

accepted w ithou t ca reful comparison

with competing hypotheses

in

their agreement with observa-

tions. Tem pered personalism's receptivity tow ard seriously

proposed hypotheses is adequately balanced by a capacity to

evaluate them critically

(1970, p.

133;

see

also

pp.

133-36,

pass im).

(3 )

Invest igat ions conforming

to the

prescriptions

of

tempered

personalism can incorpo rate any methodological device w hich

analysis or

experience indicates

to be

valuable (1970,

p.

122;

cf . also

pp. 130-33). In

other words tempered personalism

is

claimed

to be h igh ly flexible.

Shimony holds

that

one

m ay

fairly

sum up these

claims

by

ascribing

'sensitivity

to the t ru th ' to the

tempered personalist formulation

of

sci-

entific inference and also to the info rm al processes of confirm at ion used

by

scientists

from

which tempered personalism

is

extracted

(1970, p.

122), and

that

a

sensitivity

to the

truth

can be

claimed

for

scientific

inference

on a priori

grounds, though

th e

exact content

of this

sensitivity

was not

determined

[by his

examinat ion

of a

priori

considerations]

(1970,

p.

158).

3.3. Antecedents of conditions (1) and (2). Conditions (1) and (2)

might be seen as at tempts on Shimony's part to incorporate and make

m ore precise several attractive ideas appearing

in the

work

of

Peirce

and

Reichenbach. Condit ion

(1 )

can be seen as m otivated by Peirce's obser-

vation

that it

hardly makes sense

to

under take

the

task

of

discovering

178


14/38

SHIMONY

S PRIORI RGUMENTS

general

truths about the

world unless

we

suppose ourselves

to

have

the

power to propose hypotheses which are true or at least sufficiently near

to the

t ruth

to

suit

our

purposes.

This is

so, according

to

Peirce, for

th e

same reason

that

a

general

w ho has to

capture

a

position

or see his

coun-

try

ruined, must go on the hypothesis that there is some way in which

he can and shall capture it (Collected Works, 7.219). But, speaking

intuitively, the pow er of suggesting true or nearly true hypotheses is of

no v alue unless w hen proposed they are treated w ith an open m ind .

T he

tempering condit ion

and

sta tement

(1) can be

seen

as an

at tempt

to make this intuition more precise.

Secondly, Shim ony reads in Peirce the recom m enda tion that scientific

method should systematically

and self-critically

correct current

beliefs in

th e light of experience

(1970,

pp. 126-27).

This

idea is refined (at the

expense of na r rowing its appl icat ion) by Reichenbach and others w ho

argue that the straight rule of induc t ion , the rule of always positing

observed frequencies

to be

long-run frequencies,

has the

advantage

of

correcting

our beliefs about long-run frequencies by adjust ing them in

th e light of new observat ions, in a w ay guaranteed to be successful in

th e

long run.

For

reasons detailed

by

Black (1954,

pp.

168-73) past

efforts

to make out these arguments have all

failed.

B ut sta tement (2)

can

be seen as another a t tem pt to make good use of this prima facie ap-

pealing

idea.

3.4.

T he

program

for

examining

Shimony's

main

a

priori arguments.

I do not dispute that investigations conforming to the prescriptions of

tempered personalism have properties like those indicated

by ( 1 ) , ( 2 ) ,

and

( 3 )

and

that

having such propert ies does

in

fact

const i tute grounds

for

preferr ing

a

tempered personalist formulation

of

scien tific investiga-

tions to others. But I mainta in that Sh imony has not succeeded in sup-

porting these claims

by

arguments which appeal

to no

contingent pre-

mises, and that it is doubtful whether this task could be accomplished.

Statements

( 1 ) ,

( 2 ) ,

and

( 3 )

are far from

perfectly clear,

so that it is

not yet evident wh ether or not a m ethod hav ing the three intended

properties is conducive to achieving th e stated end, in the sense of

there

being m ore reason

to

suppose

the

m ethod

to be

able

to

achieve

the

stated

end than could

an

al ternat ive method which does

not

have

the

proper-

ties. In particular I shall argue that when ( 1 ) , ( 2 ) , an d (3 ) are clarified,

in the way Shimony clearly intends, to leave no doubt that tempered

personalism

is conducive to achieving the end by v i r tue o f h aving these

179


15/38

Paul

Teller

properties, then

it is not

possible

to

argue

a

priori that tempered person-

alism h as the properties in quest ion. On the other hand, when ( 1 ) , ( 2 ) ,

and (3 ) are

interpreted

in a

m a n n er

that

makes such

a

prior i argum ents

possible,

there

is no

longer

any

reason

to

suppose

that

th e

properties

make tempered personalist investigations conducive to the desired end.

To facilitate th e exposition of these arguments I will henceforth use

th e phrase,

Q

is a desirable property for a method of scientific investi-

gation exchangeably with Q, as a property of scientific investigations,

is conducive to the end of reach ing true or nea rly tru e beliefs of the sort

usually considered th e concern of science. Q is conducive to end

E

is

in

turn

to be

interpreted,

as

explained above,

as

there

is

m ore reason

to suppose that end E can be at tained by using scientific investigations

having property

Q

than

by

using ones

no t

having property

Q ,

other

things being equal.

4.

C onsideration

of the

Main

A

Pr ior i A rgum ents

4.1. Examination

of the

first condition. Tempered personalism

is

claimed to have the

first

property,

that

of being open-minded, because

tempered personalist investigations must conform to the tempering con-

dition, that a seriously proposed hypothesis be given a sufficiently high

prior probability to allow i t a chance to be preferred at a n investigation's

termination to all other rival hypotheses of the investigation. Shimony

argues

for the

desirability

of

this condition

by the

observation that

it

rules out the skepticism toward hu m an abductive powers [in Peirce's

sense] implicit

in any

formal scheme which treats

on the

same footing

seriously proposed hypotheses, frivolou sly proposed hypotheses,

and un-

suggested h ypotheses. B y giving prefe rential trea tm en t to se riously pro-

posed hy potheses but insisting on open m ind ed ne ss w ithin this prefe rred

class,

the

tempering condit ion provides

a

safeguard against

one of the

major types

of

error that could

be

commi t ted

by a

method

of confi rma-

t ion:

th e

error

of

reject ing, because

of a priori

commi tmen ts ,

a

true

hy-

pothesis which som eone has been f or tun ate enoug h to put for th

(1970,

pp.

132-33) .

T o evaluate the tempering condit ion and the suggested argument for

its desirabili ty we must examine the application and effect of the condi-

tion in further detail . From th e infinite collection of hypo theses, stated

and

unstated,

th e

va riou s existing processes

of

proposing hypotheses

se-

180


16/38

SHIMONY

S PRIORI RGUMENTS

lect

a subset, com prisin g hypotheses such as those proposed by scientists,

crackpots,

eccentrics, small children,

and so on.

From this

set a

smaller

subset

is

designated

as the set of

seriously proposed hypotheses; tem-

pered personalism prescribes

that

all i ts members are to be considered

by

scientific invest igat ions.

A

full statement

of

this condition would

require an explicit characterization of the properties determining these

tw o nested subsets, however flexible th e properties might

be.

8

For ex-

ample,

th e

property determining

th e

subset

of

seriously proposed

hypothe-

ses

might

be as

follows:

a

hypothesis

is

seriously proposed

if

(a ) someone

with a Ph.D. regards it wor thy of research, or (b ) it is categorized as

worthy

of

research

by

some method

of

hypothesis proposing which

has

been highly confirmed to be useful by previous investigations. In order

for the refere nce to som ething called seriously proposed hypotheses

to be a non vac uou s part of the characterization of tempered personalism,

not only must the condition be explicitly described, but as described it

must

be

genuinely restrictive,

in the

sense that from

all hypotheses

sug-

gested

or

recognized

by any

human agency whatsoever

th e condition

must pick out a proper subclass.

Clearly, the tempering condition is desirable only if the restriction

m a d e

by the

reference

to

seriously proposed hypotheses

is a

desirable

one for scientific investigations. The only plausible consideration which

would make the restriction desirable would be

that

seriously proposed

hypotheses are, in some sense, more likely to include hypotheses which

are true or closer to the

truth

than hypotheses proposed by

other

means.

But

how can we

establish

that this is the

case, that seriously proposed

hy-

potheses

are

more likely

to

include close approximations

to the truth

than frivolously or ran do m ly proposed hypotheses? G rou nd s for this

conclusion

are to be found , no

doubt ,

in the

long history

of

man's search

fo r knowledge,

but

g rounds

of

that k ind

are

clearly

a posteriori.

9

If we

are to forgo reliance on

facts

about which methods of proposing hypothe-

ses have proven particularly successful

in the

past

or on

other

facts

about

th e world which lead us to have greater trust in one rather

than

some

other

method

of

generating hypotheses,

it is to be

doubted

whether

w e

are any longer in a position to justify th e claim that one set of

proposed

8

In sec. Ill, D (1970, pp.

110-14)

and sec. V, D (1970, pp. 150-58) Shimony

discusses

at

length

th e

considerations which

may be

relevant

to

def in ing

the

class

of

seriously proposed hypotheses. B ut he does not form ulate a specif ic def in i t ion.

9

Shim ony discusses these considerations in sec. V, B, 3 (1970, pp. 143-48).

181


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Paul Teller

hypotheses

is

more likely

to

contain close approximations

to the truth

than some other set.

That

such a choice cannot be

justified

a priori

follows

as a

special case

of

H um e's conclusion

that

propositions about

th e unobserved are logically independent of propositions about what is

known

by

observation.

Let X be the

class

of

hypotheses which

do not

logically conflict

with what

is

k n o w n

and

which have been suggested

or

recognized by any human agency whatsoever. Let C be the subset of K

which constitutes seriously proposed hypotheses, and let C'

=

K — C.

T he foregoing rem arks m ake i t reasonable to assume

that both

C and

C'

are nonem pty. By the very

fact that

the m embers of C' are logically con-

sistent with what

is

known ,

it is

logically possible

that

more t ruths

(or

better

approximations

to the

truth) wil l

be found in C' than in C.

Whether

or not

this

is the

case

is a

matter

of

nondemonstrat ive

infer-

ence

from

our

present body

of

knowledge.

In

particular, whether

th e

intuit ive

screening

of

hypotheses performed

by Ph.D.'s is

advantageous

in admit t ing

a

greater number

of

true

(or

nearly true) hypotheses than

some other method

of

screening depends

on the

contingency

of

trained

scientists h aving good intuit ion for good hypotheses. A similar comment

holds

for

methods

of

hypothesis-proposing confirmed

to be useful by

previous scientific investigations.

The

foregoing a rgumen t

can be

recast

in the form of a

dilemma which

is easily stated by considering th e passage

from

Shimony (1970, pp.

132-33) quoted above: By giving preferential treatment to seriously

proposed hypotheses but insisting on open mindedness within this pre-

ferred class, the tempering condition provides a safeguard against one

of the major types of error

that

could be committed by a method of

confirmation:

th e

error

of

rejecting, because

of a

priori commitments,

a true hypothesis which someone

has

been fortunate enough

to put

forth.

W e must ask, to begin with, whether the proposed condition really

gives preferential treatment to some class of hypotheses. If not, the con-

dition is not at all

what

it is set out to be, and we may fairly ask for a

restatement before considering

th e

question

of

justification.

If

there

is

a class

of

hypotheses

to

which

th e

tempering condition gives p referential

treatment,

we mu st fu rthe r ask on w hat g rounds is this preferential

treat-

ment given. If th e grounds are a priori it seems that, after all, hypotheses

which might be true are rejected (or at least excluded

from

present in-

vestigations) as a result of a priori considerations. Thus any

attempt

to

182


18/38


just ify the condition a priori undermines the

very

advantage that is

claimed

for it.

This does

not

show

th e

condition

to be

undesirable,

for

the alternative answer to the second question may be, and I believe is,

perfectly

acceptable

— a given preferen tial

treatment

can be justified on

a

posteriori grounds.

10

At one

stage

of

inquiry some hypotheses

are ex-

cluded

from

consideration,

but on

principles which

are subject to re-

vision precisely becau se they

are not

justified

on a

priori groun ds. Since

th e principles of selection may be revised, errors made in selecting hy-

potheses for consideration at the present stage of inquiry may be cor-

rected at a later stage.

Although

th e

distinction between proposed

and

seriously proposed

hypotheses

is of no

help

in

making

out an a

priori justification

o f

scien-

tific methodology, one might retreat to the first horn of the dilemma

and restate th e tempering condition in a way which m akes no pretense

of giving preferential treatment

to any

class

of

proposed hypotheses.

11

I

suppose the suggestion to be spelled out along these lines:

from

th e field

of

all statable hypotheses

very

few are actually thou ght

of.

Of

those

that

are thought of or explicitly formulated, many are not really proposed as

scientific hypotheses. For example, they may have only been put down

as didactic or philosophical examples, or they m ay have been discarded

in

th e

process

of

fo rm ulat ion. Even taking

a very

liberal attitude

in de-

ciding wh ich hypotheses are to classify as hav ing been actually proposed,

our

innate capabilities, limitations,

and

intuitions severely restrict

th e

range

of hypotheses

that

we in fact put forward. Let us use the term

actually proposed

hypotheses to

refer

to

hypotheses which

are fully

formulated and put forward for

consideration.

W e m ay now inquire w hether anyth ing is to be gained by revising the

tempering condition in the following w ay: replace the requiremen t

that

all seriously proposed hypotheses are to be assigned nonnegligible prior

probabili ty w ith the req uire m en t that all actually proposed hypotheses

are

to be

assigned nonnegligible prior probability.

I

will call

the

revised

condition th e total tempering condition, and investigations which

satisfy

it

totally open-minded investigations.

It

might

be

supposed

that

this

form

of the tempering condition consti tutes true open-mindedness for

a

Bayesian formulat ion of scientific confi rmat ion and that such t rue

10

Shimony discusses this possibility in ibid., V, D (1970, pp. 150-58).

Professor

Shimony

has

suggested

this as a

possible

way out of the

present dif-

ficulty.

183


19/38

Paul

Teller

open-mindedness

is

pr ima

facie

desirable,

in the

sense

of

being conducive

to

reaching scientific

t ruths . Shimony

appears

to

have something

of

this

sort

in

mind when

he writes, The

tempering condition

is

only

a way

of

prescribing open mindedness within

a

probabilistic scheme

of

infer-

ence,

and

open mindedness

is a

necessary condit ion

for the

acceptance

of

true hypotheses

in

case they should ever

be

proposed [N.B.

not

'seri-

ously

proposed'] (1970,

p.

158) .

I

believe that such

a

revision w ould

be a

step

in the

wrong direct ion.

Indeed,

if one

were

to

agree

to

test

all

hypotheses w hich were actual ly

proposed, m ost in ves tigation s could quickly

be

brough t

to a

halt

by

proposing

spurious correlations which w e intuitively judge not to be

worth subjecting

to

direct examination.

T o

make

the

point,

I

hereby

propose

(not seriously of course)

that

the observed frequency of all

pulsars would be double their presently observed values if

the

U .S .

Senate

had two

hundred members ins tead

of one

h un dr e d .

If we

were

required

to give al l truly proposed hy potheses a nonnegligible prior prob-

ability,

this hypothesis w ould s tand

in

compet i t ion

to our

present, well-

confi rmed

belief

in the

near cons tancy

of

pulsars '

frequency,

and the

progress of

astrophysics w ou ld have

to

await const i tut ional reforms. Such

examples support

the

claim

that

on ly seriously proposed hypo theses

meri t

serious consideration, even though

it may be far

from clear

how

th e

term

seriously

proposed

hypothesis

is to be

defined.

In

part

V of

Scientific Inference Sh im on y fur the r supports this claim w ith an in-

teresting discussion

of

relevant contingent facts about

man and his en-

vironment . For example : to first approximat ion w e have a good sense

of th e

relevance

and

irrelevance

o f

various factors

to

phenomena

of in-

terest . This crude sense

of

relevance

is

often

wrong,

and

some

of its

errors,

such

as

over es tima t ing

the

inf luence

of 'wonders ' in the

heavens

upon terrestrial events, have hampered

the

deve lopment

of

knowledge.

Nevertheless, when this sense

of

relevance

is

controlled

by

critical

in -

telligence, it

makes crucial observations possible

by

enabling

men to

disregard

th e

innumerable details

that

are

potentially distracting

in ex-

perimentat ion

(1970,

p.

143).

Were

w e

required

to be

rigidly open-

minded about

all

actually proposed hypotheses, such considerations

would be

beside

the

point.

But in

point

of fact

they

are

extremely

im -

portant in un ders tan ding , expla in ing, and

just i fying

our conf idence in

our

me thods

of scientific

invest igat ion. Consequent ly,

the

total temper-

ing

condi t ion

and the

open-mindedness

to

which

it

could

be

said

to

8


20/38

SHIMONY

S PRIORI

RGUMENTS

give rise would

not be a

desirable feature

of

tempered personalism.

I have argued

from

contingent premises

that

the

total

tempering con-

dition is, as a mat ter of fact, not a desirable feature of scientific investi-

gations;

and if in

fact

the

condition

is not

desirable,

it is not an a

priori

t ru th that it is desirable. A different line of analysis

clarifies

these con-

siderations,

and

provides

an

independent argument

in

support

of the

claim tha t the total tempering condition can not be shown to be desir-

able on a priori grounds. In the total process of an investigation we start

with the set of all actually proposed hypotheses and conclude with some

selection among

th em .

In other words, the actually proposed hypotheses

m u s t go through a filtering process which excludes some hypotheses by

giving them a very low valuation, and retains others by giving them a

relatively

high valuation. In a Bayesian formulation this f i l tering can

take place in two wa ys: by assig nm en t of prior probabilities to the hy-

potheses and by the processes of conditionalization (which depends in

part on the assessment of l ikelihoods and in part on the results of the

observa t ions) . H ow ever one chooses to m eas ure selectivity, if the degree

of

final selectivity is fixed, then a decrease (increase) in the first filtering

process m us t be accom panied by an increase (decrea se) in the selectivity

of

the second filte rin g process. If we are equally ignorant about th e e f f i -

cacy of

both

filtering processes as m eans to the end of true or nearly true

beliefs,

then there is no g rounds for opting to eliminate one filter in

favor of the other. And as long as we forswear appeal to cont ingent

premises,

we are

completely ignorant about

the

efficacy

of both

filters.

Above,

we

considered

th e

possibility

of

determining

th e

first filter

by

reference

to

seriously proposed hypotheses,

and w e saw it to be

logically

possible that it would select false hypotheses or hypotheses far from the

t ruth. Consequently, contingent premises would be required to con-

clude that such a

filter

is desirable. The same a rgumen t is eas ily seen to

work for other criteria which might plausibly be substituted for seri-

ously proposed. Below I will argue

that

we have also been given no

reason to suppose, on strictly a priori grounds,

that

the second

filter

is

desirable.

The total tempering condition seemed to be a desirable feature of

scientific investigations because it ensures t h a t if a t rue or nearly true

hypothesis

is

proposed

it has a

chance

of

surviving.

But it is now

clear

tha t

imposing this condit ion

has a

price;

for if it is

imposed,

and if an

investigation is to resu lt in a selection of hypo theses, the selection m u st

185


21/38

Paul Teller

be fully carried out by the second filter. Thus th e total tempering con-

dition

is

desirable only

if it is a

desirable feature

of

scien tific investiga-

tions that th e process of selection among proposed hypotheses is fully

carried out b y conditionalization, the second filtering process. I tur n now

to consider whether we have been given any a priori reasons to suppose

that conditionalization is desirable, that is, w he ther the process of select-

ing hypotheses by cond itionalization is cond ucive to the end of reach ing

t rue

or

nearly true beliefs.

It

will follow

from the

complete absence

of

any

such reasons that there are no a priori reasons for the desirability of

selecting hypotheses by con ditionalization alone.

4.2. Examination of the second

condition.

As explained in section 2,

the hypotheses which have been admitted to an investigation are evalu-

ated by conditionalization of the prior probability on the outcome of

the observations. We will first ask whether Shim ony succeeds in giving

any a priori support for the claimed desirability of using conditionaliza-

tion of a probability measure, rather than some

other

method, as the

means of critically evaluating hypotheses. Then, granting that eva luation

is

to be

carried

out by

conditionalization

of a

probability measure,

w e

will ask what conditions must hold to warrant description of the evalua-

tion

as

critical

in a

clearly desirable sense,

and we

will inquire whether

it is

possible

to

argue without appeal

to

contingent premises

that

these

con ditions obtain for the probab ility me asure s of tempered personalist

investigations.

A s

for the

first quest ion, Shimony maintains that

an

investigation

should have a B ayesian evaluation structure by arguing that the funct ion

specifying the degree to which it is rat ional to be committed to the

t ruth of propositions must satisfy th e axioms of cond itional probability.

Bayes's theorem follows from the probability axioms, thus making con-

ditionalization

th e

natural means

to

describe change

of

belief within

an investigation.

12

Shimony holds

that

the axioms of probability are

necessary conditions

for

orderly thinking about propositions with

un-

known

truth

values

(1970,

p. 158). H e supports

this

claim with an in-

genious combination

of the

Cox-Good argument

and the

Dutch

book

argum ent which avoids m any of the shortcom ings of each and makes it

u

It is open to question whether conditionalization can be justified on the grounds

that th e belief function satisfies th e probability axioms (cf. H acking,

1967).

A l-

though

Shimony

says

no thing on this

point,

I will no t press th e issue since I believe

there

are

ways

th e

claim

can be

substantiated.

186


22/38


possible

to

derive

th e

probability axioms from exceedingly weak assump-

tions (1970, pp. 104-9). Still several assumptions are required and it is

at least unclear how one could argue, strictly a priori,

that

these

assump-

t ions must be true of an yth ing w e would call orderly thinkin g ab out

propositions with unknown truth values.

This

is most clearly th e case

for the fifth and

sixth assumptions from which

Shimony

argues,

and

which are stated as follows (with Shimony's n u m b e r i n g ) : a s

before,

hi,

. . . ,

h

n

are the hypotheses of an investigation and

ei,

. . . , e

m

the

possible outcomes of the investigation's envisaged observations.

Then

for

any e from a m o n g

ei,

. . . , e

m

and any c and d from th e truth func-

tional closure

of

(h^

. . . ,

h

n

,

e

b

. . . ,

e

m

):

( 5 ) There

is a funct ion F

e

such

that

(6 ) There is a

funct ion

G

6

which is cont inuous and monotonically

increasing in

both

its variables such

that

if e logically implies

( c & d ) then

As Shimony observes (1970,

pp.

106-7), these conditions

are

intuitively

very compelling for any plausible interpretation of the notion rational

degree of commitment ; but it is hard to see how we might turn this

strong intuitive appeal into an a priori argument in support of the claim

that any method for which ( 5 ) and (6) fail will be less conducive to

the aim of learning abo ut the w orld than a m ethod of which ( 5 ) and (6)

are true.

Let us suppose, however,

that

the proposed hypotheses of an

investi-

gation

are to be

evaluated

in the

Bayesian m anner ,

by

conditionalization.

Let u s then ask w hat con ditions m ust hold to w ar ran t description of such

an evaluation as critical in a clearly desirable sense. And let us ask

whether

it is possible to argue a priori that

these

conditions do hold.

In a

trivial

sense posterior evaluations of the hypotheses of an investiga-

tion are determined by the outco m e of the envisaged observations, since

th e

posterior probability

of a

hypothesis,

h,

is

determined

by

condition-

alization on the

outcome,

e; mo re exactly by m ultiplying the prior prob-

ability P ( h )

by the

likelihood P(e/h).

But the

investigation

can

insofar

Documents

Teller, Logic