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Transcript of Teller, Logic
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1/38
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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SHIMONY S PRIORI RGUMENTS
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).
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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
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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.
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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
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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.
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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
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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
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Paul
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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-
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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).
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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
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SHIMONY S PRIORI RGUMENTS
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.
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Paul
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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
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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
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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.
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SHIMONY S PRIORI RGUMENTS
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