adams, truth values & the value of truth [16 pgs]

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2002 University of Southern California and Blackwell Publishers Ltd.

TRUTH VALUES AND THE VALUE OF TRUTH 207

Pacific Philosophical Quarterly 83 (2002) 207222 02790750/00/01000000

2002 University of Southern California and Blackwell Publishers Ltd. Published by

Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and

350 Main Street, Malden, MA 02148, USA.

207

TRUTH VALUES AND

THE VALUE OF TRUTH

ERNEST ADAMS

Abstract: This paper explores the ways in which truth is better than falsehood,

and suggests that, among other things, it depends on the kinds of propositionto which these values are attached. Ordinary singular propositions like It is

raining seem to fit best the bivalent scheme of classical logic, the general

proposition It is always raining is more appropriately rated according to

how often it rains, and a practically vague proposition like The lecture

will start at 1 is appropriately rated according to its nearness to exactness.

Implications for logic of this rating system are commented on.

1. Introduction

Pure reason, which is what most modern Logic is concerned with, gener-

ally assumes that truth is bivalent: there are the true and the false,

and Logic studies the laws to which bearers of these values conform, e.g.,

the law of double negation. But it is not concerned with the values of

these values, with why the true is better than the false, and why it should

be the goal of scientific inquiry, as Frege and others have held.

The reason for this neglect is perhaps not far to seek. There are too

many and competing theories of truth semantic, correspondence, coher-

ence, and all the varieties of pragmatism, which above all ought to teach

us the value of truth. Better to leave the meaning of truth to the philo-

sophers and study truth values independently of their value, just as science

studies the motions of material bodies without overly concerning itself

with the definitions of space, time, and matter.

But recent developments, even in pure Logic, should make us wonder

whether it can consistently maintain its olympian unconcern with the

value of truth. Too many theories have recently been put forward thatcall bivalence and other dogmas of classical Logic into question, and in

PAPQC01 pages: 16


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208 PACIFIC PHILOSOPHICAL QUARTERLY

consequence call for a re-examination of the very idea of truth. And to

deal with the controversies to which these theories have inevitably given

rise, I would argue that we must cross the threshold from pure to pract-

ical reason, and ask ourselves: what makes the truth that is adopted byone theory better than the truth that is adopted by another? Failing to

address this question, we are too apt to fall into empty formalism and

simply assert, for instance, that vague statements have degrees of truth

subject to these or those formal laws, or, mea culpa, that conditional

statements have no truth values but only probabilities that are also sub-

ject to certain seemingly arbitrary formal laws. And why not say that

these probabilities are truth values?1

But now we are going to examine an example that suggests a prag-

matic diagram and a formula that reconciles all of the theories of truthmentioned above within a narrow domain, but which also suggest how

they might be generalized outside of that domain to accommodate vague

statements and other constructions whose laws shouldbe questioned, but

which are often assumed without question.

2. An example, a pragmatic diagram,

and a pragmatic formula2

The example is as follows: Sam, a student, is anxious to register for the

same class that his girl friend, Jane, will take, and believing that she will

take Logic, registers for Logic. This processfits thepractical syllogism

pattern of practical reason, which can be diagrammed thus:

Although this is a causal process, considered as a syllogism it appears

to have two premisses, one a belief and the other a desire. However

only what is believed, that Jane will take Logic, is an object of pure Logic

that can be true or false. Neither what is desired, to take the same class as

Jane takes, nor the conclusion, the action of taking Logic, is something

that can enter into inferential processes of the kind that pure Logic deals

Diagram 1: Practical Syllogism


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with.3 But if we extend the picture and bring in not only the action but

the results that follow from it, together with certain facts that determine

whether these results are desired, we get a pragmatic diagram that has

elements of concern to Logic:

Diagram 2: Simple Pragmatic Diagram

Note that now we have added another pair of causal arrows, leading

from the action, 3, and the facts, 4, to the result, 5. We have also added

two vertical arrows representing something like semantic relations, one

between the belief, 1, and the facts, 4, and the other between the desire,

2, and the results, 5. The first determines whether the beliefcorresponds

to the facts and is true, and the second determines whether the desire cor-

responds to the results and is satisfied. Details of these correspondences

will be returned to, including whether they are properly called semantic,but first let us note that there is a correspondence between the correspond-

ences that allows us to state simple pragmatic principles, or formulas:

The results of actions based on beliefs correspond to what is desired if and only if the beliefs

correspond to the facts.

or more simply:

Results satisfy desires if the actions that lead to them are based on true beliefs.

Broadening the above diagrams and principles to add linguistic ele-

ments to the picture would lead to an almost endless series of remarks

tying it into classical, even ancient views on relations between thoughts,


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words, and the world, but here we will confine ourselves largely to

what might be called the pragmatic aspects of the picture. First and

foremost, to the extent that these pragmatic principles are valid, they give

truth a practical value and suggest a motive for seeking it i.e., forseeking to arrive at conclusions that are true.4 But even within these

limits, which will be transgressed shortly, the principles do not define

a pragmatic concept of truth. Obviously the first, more elaborate

pragmatic principle is stated in terms of a correspondence between beliefs

and facts, between something in the mind and something in the world,

and therefore it can with equal right be held to embody a correspondence

concept of truth.5 It also makes a possibly intriguing departure in involv-

ing a parallel correspondence between a desire and a result, and therefore

to embody a correspondence concept of satisfaction.Note too that if linguistic elements were added to the picture it could

be regarded as embodying directly semantic concepts of both truth and

desire. Thus, Sams belief that Jane will take logic is true if Jane takes

logic, so essentially the same words are used to refer both to the belief

and to the fact, and his desire to take the same class as Jane is described

in essentially the same words as the result he aims for: to take the same

class as Jane.6 Leaving these elements out of the picture leaves only the

unstructured belief and desire as the bearers, respectively, of truth and

satisfaction.In any case, the diagram and the principles are very limited, and two

kinds of limitation will be discussed at some length in what follows. We

will pass quickly over limitations like the following, cited by Nicholas

Rescher (Rescher, 1977 and 1998), in which a person mistakenly believ-

ing that an apple before him is a Gravenstein and wanting to eat an

apple, satisfies his desire by eating the apple, even though the belief on

which this action is based is mistaken. What this shows is that to make

the principles or formulas work, there must also be a correspondence

between the belief and the desire. One must be apposite to the other, sothat if the belief is that the apple is a Gravenstein then the desire must be

for a Gravenstein apple.

Much more serious are the personal and temporal limitations of our

pragmatic principles. It is Sam who has the motive for seeking the truth

about Janes plans, and he has that motive now. Not, say, a year from

now. I regard it as important in developing a theory of practical reason

to take limitations of this kind into account in a systematic way, since

failing to do so we are too apt to regard the truth as an abstract good,

of equal interest to all persons at all times.7 I would argue that even

Science, which pretends to seek the truth for its own sake, doesnt

really ignore human interests. However these are very complex matters,

and the temporal limitation of our pragmatic principles will be returned

to, relating to beliefs about the non-present, and the past and future.


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But before turning to that, we will comment on less severe limitations

that nevertheless show that the principles need to be revised significantly

in application to beliefs of special kinds.

3. The value of accuracy

One limitation relates to statements of a kind that can said to be theoretic-

ally precise, but practically vague. An example is The lecture will begin at

1 pm. Trying to put that into the framework of Diagram 1 might lead to:

The problem here is with the inference from 3 and 4b to 5b: Sam s

arriving at 1 and the lectures not beginning at 1 do not entail that Sam

will not arrive in time for the lecture. If the lecture started at 10 seconds

after 1, then, taken literally, Sams belief that it would begin at 1 would

be false. But even so his action of arriving at 1 would probably succeed.

Therefore we couldnt say that

The result of Sams action, based on the belief that the lecture would start at 1, will

correspond to what he desires if and only if the belief corresponds to the facts.

Rather, we might say that:

The result of Sams action, based on the belief that the lecture would start at 1, will cor-

respond to what he desires if and only if the belief corresponds closely enough to the facts.

Diagram 3


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This closely enough suggests accuracy and degrees of correspondence

with the fact, perhaps as theorized about in Fuzzy Logic. One is even

tempted to formulate a general pragmatic principle of fuzzy truth,

thus:

Results of actions based on beliefs correspond to what is desired if and only if the beliefs are

sufficiently true.

This formula still doesnt quite fit the facts of human action, since it

seems to suggest that there is a sharp line of division between beliefs that

are sufficiently true and those that are not. Is there an exact degree of

truth such that Sam will arrive at the lecture on time if and only if the

belief he acts on has that degree of truth? Fuzziness is not that sharp.Thus, our formula still doesnt correctly capture a practical value that

might attach to beliefs that only correspond approximately or fuzzily

to the facts. But these observations do bring out something.

When we go beyond the values of beliefs like the one in the example

of the class that Jane will take, and consider ones whose values only

correspond to the facts roughly, or to a degree, the problem of char-

acterizing an appropriate measure of this degree becomes acute. Nor is it

one that we should leap to conclusions about, since all too often this

leads to empty mathematical formalism. We may assume that these meas-ures should be componential, so that the degree of truth of a conjunc-

tion is some precisely defined mathematical function of the degrees of

truth of its conjuncts. Why? What is the value of these truth values; what

evidence do we have that some practical advantage attaches to arriving at

conclusions that score high on these measures? My view is that we would

be better advised to give up this empty mathematizing, and look at the

details of practical reasoning and acting on beliefs such as are expressed

as The lecture will begin at 1. Further remarks on this will be made in

section 6, but there are other domains to consider, including one in whichI have violated my own precepts in theorizing about degrees of truth.

4. Approximate generalizations

A belief that seems more like the kind that classical pragmatists like

Pierce had in mind is typically expressed as a generalization, e.g., that

dogs bark, or that red blackberries are unripe. These typically are less

subject to temporal limitations than beliefs expressed by singular sent-

ences, such as This dog barks, or Those red blackberries are unripe.

One reason why the motive for seeking the truth about the generalization

is less restricted than it is for seeking the truth about the singular state-

ment is that the former may be acted upon repeatedly, and for this reason


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a person may want to store it, much as she might put a tool in a

toolbox against future uses that she only anticipates in a general way.

The fact that one may act repeatedly on beliefs in generalizations

also suggests that they do not conform to the same pragmatic prin-ciples as do beliefs in singular propositions. We cannot say that allsuch

actions have desired results if and only if the beliefs acted on correspond

to the facts. Thus, we cannot simply substitute Red blackberries are

unripe for Jane will take Logic in Diagram 1 to arrive at something

like:

But replacing a belief about something particular, e.g., that these red

blackberries are unripe, by a belief about agenerality (a general belief)

demands corresponding changes in the other factors in the diagram, asfollows (numbering the changes to correspond to the entries in the dia-

gram). (2) The desire should not be for ripe blackberries on a particular

occasion, but then again, it should not be for ripe blackberries on all

occasionswe cant suppose that Sam desires them all the time. (3) Nor

do the general belief and desire influence a particular action, but rather

something more like a policy for actionsay to refrain from eating red

blackberries.8 (4) The possible facts as described in Diagram 4 are no

longer exhaustive. The logical opposite ofred blackberries are unripe is

not red blackberries are ripe, but something more like red blackber-

ries are sometimes ripe. (5) One of the results given in Diagram 4 no

longer corresponds to one of the facts, since if red blackberries are some-

times ripe and Sam refrains from eating them he will sometimes not eat

ripe blackberries. Incorporating the suggested changes leads to:

Diagram 4


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Diagram 5

Crude as this diagram is, it nevertheless suggests a correspondence

between the general belief that it involves and the facts, that is in

some ways more like the one involved in the approximate, or fuzzy prag-

matic formulas that correspond to Diagram 3 than it is like the simplesemantic correspondence that corresponds to Diagram 1. Thus, first

approximations topragmatic principles for generalizations might go:

The results of acting on in accord with policies based on general beliefs correspond to what

is desired to the extent that the beliefs correspond to the facts.

or more simply:

The truer general beliefs are, the more desirable the results of acting in accord with them

are.

Let us briefly compare and contrast the principles stated above with

those stated in section 2. Like the earlier principles, the present ones also

suggest a practical motive for trying to arrive at beliefs that correspond

to the facts, and therefore they are pragmatic. But while the motive for

arriving at beliefs that correspond to the facts is less ephemeral than the

one that applies, for instance, to the proposition that Jane will take Logic,

it is less sharply defined. That is because in the present case the cor-

respondence with the facts, rather than being all or none, is a matter of

degree. Whatever this is, it is surely not bivalent. But like the degrees that

enter into the pragmatic formulas that apply e.g., to the lecture will start

at 1 p.m, they are what matter. What matters is significance, and an


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exact degree oftruth ofred blackberries are unripe doesnt matter as

long as it is significantwhich is related to the fact that satisfaction is no

longer a matter of all or none, but rather of more or less.

A final point about the degrees of correspondence of generalizationspertains to the way these degrees are measured in my theory of approximate

generalizations (Adams, 1974, and elsewhere), which is as proportions.9

E.g., the degree of correspondence of Red blackberries are unripe is

the proportion of unripe berries among all red blackberries. Admittedly

there is a good deal of arbitrariness in the choice of this measure, as is

usually the case with numerical terms of art.10 But if it is agoodmeasure

it contributes by refiningreasoning involving approximate generalizations.

An example involves the syllogism Barbara though it doesnt involve

blackberries.Barbara has traditionally been rendered in the form All As are Bs

and all Bs are Cs; ergo all As are Cs.All As are Bs,All Bs are Cs,

and All As are Cs are universal generalizations, but it is common to

idealize and apply Barbara to generalizations that have exceptions,

e.g., as in All Greeks are men and all Athenians are Greeks, therefore all

Athenians are men.11 But these are really approximate generalizations,

and proportionality analysis shows that when they are this kind of

reasoning isnt always valid, and it brings counterexamples to light, e.g.,

All penguins are birds and all birds fly, ergo all penguins fly. Evenmore importantly, we will see that this analysis tells us when approx-

imate reasoning of the form of Barbara is valid. This will be returned to

in the concluding section, but first we will comment very briefly on three

kinds of propositions and possible associated pragmatic principles that

are not among those covered so far.

5. General themes, and pragmatic principles not yet covered

The investigation on which we have embarked has barely begun, but

already certain themes have already begun to emerge. One is that the

correspondences that determine the values of different beliefs vary widely

with the beliefs in question. Most importantly, what determines these

values are pragmatic. They depend on how the beliefs influence actions

or policies, and how much the results of these actions, or actions in

accord with these policies, are desired. These things can only be ascer-

tained by reference to the facts of human behavior, and no one or a few

pragmatic principles should be expected to cover all cases.

So far we have very cursorily considered three cases, no two of which

conform to the same pragmatic principles: (1) beliefs expressed by simple

singular statements, (2) beliefs expressed as singular quantitative state-

ments, and (3) beliefs expressed as generalizations. The first might be


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held to be the model assumed in current logical theory, since it involves

a bivalent correspondence that in its semantic guise conforms to Conven-

tion T. The second and third involve degrees of correspondence that are

measured in different ways in the two cases. This will be returned tobelow, but first we must stress that our three cases are far exhausting all

cases that are humanly important.

Here are four more cases that are not included among the ones com-

mented on above, which may be noted partly to show how limited the

little that has been done so far is. These are: (1) propositions concerning

the past and other remote things, (2) theoretical propositions, (3) moral

claims, and (4) conditional propositions. My personal view is that what

are often called the true or the right, pertaining to these propositions

have important pragmatic dimensions. As to the past, clearly the truthabout it can be a matter of practical importance. The simple pragmatic

formula often holds, since the correspondence between beliefs about the

past and the facts often determines the desirability of the results of

actions that are guided by these beliefs. For example, whether the action

of looking for a coat in the closet, guided by the belief that the coat was

hung in the closet, succeeds in finding the coat depends on whether the

coat was hung in the closet. However, this success really depends on the

coats remaining where it was hung. It is more immediately dependent on

what ispresently the case, and where it was hung is only important as aguide to that. More generally, what matters, and what we aim to influ-

ence, are the present or the future, and the past or otherwise remote only

matters insofar as it bears on those. Therefore I am inclined to think that

a pragmatic account of the truth about the past or the remote must

bring in broadly inductive factors that lead from them to the present.12

As to theories, all the brou-ha-ha and dispute over the rightness of

theories, e.g., the theory of evolution, the labor theory of value, and so

on, seems to me to show that the rightness or wrongness of claims about

them makes very little practical difference. If anything, they become thefoci ofmovements or in the scientific case, ofparadigms that influ-

ence programs of action or research whose long-term consequences may

be important, but whose influence cannot be evaluated in the short term.13

As to moral propositions, clearly hardly anything can be more pract-

ically important. But we cannot say, e.g., that doing to others what one

would have them do to oneself yields rewards in proportion to its degree

of truth. My view is that such benefits as derive from holding true

moral beliefs are societal and not individual. But that does not mean that

it is not worthwhile to look at those benefits in detail, and to attempt to

formulate principles that describe the relation between them and some

sort ofrightness that pertains to the moral beliefs that guide them.

Despite their formal similarities and even logical connections to gener-

alizations, conditional propositions bring in a host of new pragmatic


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issues at least, assuming with me that the practical aim of reasoning

about them is not direct correspondence with the facts, i.e., truth, but

rather probability.14 Although it is intuitively evident that persons often

do aim, not just to arrive at true conclusions but also to arrive at prob-able ones, the question becomes: what is the practical value of success

in this endeavor? What is the practical value of knowing that a coin

that is about to be tossed has a 50% chance of coming down heads if

in fact it is goingto come down tails? This question is examined in sec-

tions 47 of Adams, 1998, and a pragmatic motive for being right

in probability judgments is found, but the matter is too complicated

to enter into here.15 The only lesson to be drawn here is that truth-as-

correspondence, or closeness to it, is not the only pragmatically useful

value that can attach to conclusions reached in reasoning. Probabilityis another one, and, at a still greater leap, it is the only one that attaches

to conditionals.

This ends our speculations on a pragmatic research program. Finally,

we shall comment very briefly on another issue related to pragmatism,

and to another kind of proposition.

6. Addendum concerning truth and logic

We must not take it for granted that the kind of pragmatic, utilitarian

truth that we have been attempting to characterize has any simple con-

nection with deductive logic. Now consider the syllogism Darii, which

may be rendered as Some As are Bs and all Bs are Cs; therefore some

As are Cs, and which, like Barbara, has exceptions when All Bs are

Cs is only approximately true. Thus, it is just as invalid to reason Some

penguins are birds and all birds fly; therefore some penguins fly as to

reason All penguins are birds and all birds fly; therefore all penguins

fly. But the following proportionality formula throws light both onthe validity of exact Darii and exact Barbara, and on when their

approximate versions are valid. Letting P, B, and F symbolize is a

penguin,is a bird, and flies, respectively, and letting p(P,B), P(B&P,F),

and p(P,F) be the proportions of penguins that fly, of birds which are

penguins that fly, and of penguins that fly, it is easily demonstrated that

no matter what these proportions are, it is the case that:

(P) p(P,F) p(P,B) p(B&P,F).

The proportion of penguins that fly must be at least as great as the

proportion of penguins that are birds, multiplied by the proportion of

birds which are penguins that fly. This does not apply directly either to

Barbara or Darii, since their common minor premise is All birds fly,


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and (P) involves not the proportion of birds that fly, but rather the

proportion of birds which are penguins that fly. But (P) relates to these

syllogisms in two ways.

Suppose first that All birds fly is exactly true. This would entail thatAll birds which are penguins fly is also exactly true: i.e., p(B&P,F) = 1.

This together with (P) would entail that p(P,F) p(P,B): i.e., the propor-

tion of penguins that fly must be at least as great as the proportion of

penguins that are birds. This would validate both Barbara and Darii,

since ifallpenguins are birds the proportion of penguins that are birds

must equal 1 and so must the proportion of penguins that fly. And if only

some penguins were birds, the proportion of penguins that flew would

still have to be at least as great as the proportion that were birds, so at

least some penguins would have to fly.16

But the foregoing assumes that All birds fly is exactly true, whatever

the truth of the other premise is, and the examples at hand show us that

idealization is not always tenable. On the other hand, we do not want

argue that we can never idealize Barbara and Darii when their com-

mon universal premise is not exactly true. Thus, substituting parrot

for penguin, it does not seem unreasonable to idealize and argue either

All parrots are birds and all birds fly; therefore all parrots fly, or

Some parrots are birds and all birds fly; therefore some parrots fly.

Moreover the proportion p(B&P,F) in inequality (P) makes clear whatthe difference between these cases is. While a high proportion ofbirdsfly,

and a high proportion of birds which areparrotsfly, a very low propor-

tion of birds that are penguins fly. Inequality (P) is always valid, and

Barbara and Darii are valid at least as idealizations when p(B&P,F) is

high, but not when this proportion is not high.

Now, Barbara and Darii only give us that all Bs are Fs, hence p(B,F)

is high, but except in the ideal case in which p(B,F) = 1 they dont entail

that p(B&P,F) is high. However, recent work of Donald Bamber, 2000,

proves that when p(B,F) is close to 1, while it is not certain that p(B&P,F)is high, it is a statistical near certainty that it is high. Slightly more ex-

actly, as p(B,F) approaches 1 the proportion of predicates, P, for which

p(B&F,P) is arbitrarily high also approaches 1. Therefore it is a plaus-

ible statistical default to assume, when almost all Bs are Fs, that almost

all Bs which are Ps are also Fs, and therefore Barbara and Darii apply.

Parrots are typical and penguins are rare and untypical in the birds

and flying examples, which goes far towards explaining the acceptability

of Barbara and Darii in most cases even when their universal premisses

are not exactly true.

The foregoing considerations will be developed further, and applied

to more general syllogistic reasoning in a paper now in preparation, but

let us conclude the present paper with some reflections on the method

employed here in analyzing Barbara and Darii.


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First, note that whereas inexact Barbara and Darii are vague and

subject to exceptions, inequality (P) that is applied in analyzing them is

exact and has no exceptions. Also, the analysis is more general than the

syllogisms analyzed in that it explains not only why the syllogisms arevalid when their universal premisses are exactly true, but why and under

what circumstances they can be idealized and applied when these

premisses are only approximately true.

Second, notice the way in which inequality (P) applies to particular

premisses and conclusions of the form Some Ps are Bs and Some Ps

are Fs that enter into applications of Darii. These correspond to the

proportions p(P,B) and p(P,F) that enter into (P), but the proportions

dont measure the degrees of truth ofSome Ps are Bs and Some Ps

are Fs. They measure the proportions of Ps that are Bs and Ps that areFs, but the proportion, say, of parrots that fly is no more a measure of

how trueSome parrots fly is than it is a measure of the degrees of

truth either ofAll parrots fly or ofNo parrots fly. In other words,

p(P,F) measures something that is common to a range propositional forms

including All Ps are Fs,Some Ps are Fs, and No Ps are Fs, and so

on, many of which are themselves vague. But p(P,F) cannot be regarded

as measuring the degrees of truth of all of these forms simultaneously,

which would be absurd, since this would entail that the alleged

contradictories Some Ps are Fs and No Ps are Fs were equally true.At most section 4 of this paper suggests that p(P,F) might measure the

degree to which it is desirable to believe and act on the approximate

generalization Parrots fly a pragmatic degree of truth. But Some

parrots fly is not a generalization, approximate or otherwise, nor is it

an approximation of anything else. We may say that Some parrots

fly is true, even that it has a degree of truth, but as yet we have no clear

idea of what it is to act on this belief, hence no clear idea as to why it

might be such actions should have beneficial consequences. And lack-

ing that we have no justification for assuming that the proportion ofparrots that fly is a good measure of how good a policy it is to act on

the belief that some parrots fly. But let us conclude with some general

observations on the relation between inequality (P) and the syllogisms

Barbara and Darii.

The key fact is that (P) applies to Barbara and Darii not by formal-

izingthem, but rather by explainingthem. That (P) doesnt formalize the

syllogisms is clear from the fact that the syllogisms involve terms like

all, some, and and therefore, while (P) involves three proportions,

one of which is stated to be at least as great as the product of the other

two. But (P) explains the syllogisms both by showing that they are always

valid when their universal premisses are true without exception, and

by showing that they are usually valid when these premisses have few

exceptions.


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Recall too the relation between the proportion p(P,F) and the con-

clusions All Ps are Fs and Some Ps are Fs of Barbara and Darii. We

have argued that in the former case is it plausible to take the proportion

as a measure of the desirability of believing the conclusion, but lackinga pragmatic analysis of propositions of the form Some Ps are Fs,

we have hesitated to suggest that the proportion might be a good meas-

ure of the desirability of believing them. But given that (P) does not

formalize inferences involving these propositions, that p(P,F) may not

measure their degrees of truth does not militate against analyzing infer-

ences involving them in terms of these proportions. In fact, this gives us

a way of dealing with at least one kind of vague proposition, namely ones

of the form Some Ps are Fs, without formalizing them or inferences

involving them. Of course it is questionable how much light this mightthrow on vague propositions in general, but it is suggestive.

A final point is that there is an analogy between our approach to the

logic of practical syllogistic and the approach of Physics to informal

reasoning about measurable quantities like weight, length, and tempera-

ture. In ordinary language we say things like Mrs. Smith is light and

Mr. Smith is heavy, but Physics or medicine would be more apt to

say something like Mrs. Smith weighs 120 lbs. and Mr. Smith weighs

220 lbs. That would not be regarded as a formalization or even a regime-

ntation ofMrs. Smith is light and Mr. Smith is heavy, but it conveysall of the information in it and more besides. Similarly, in ordinary lan-

guage we may say Some parrots fly, but though it would not formalize

that statement, saying that at least 10% of parrots fly conveys at least this

much information and more besides.

If the foregoing approach has some validity it suggests that it may be

possible to explain informal reasoning without formalizing it, by intro-

ducing appropriate measures of logical quantities that are related to

the propositions involved. But choosing appropriate measures is no

easier in logic than it is in Physics (cf. Adams, 1966, and Adams andAdams, 1987), and while the degrees of truth that the Fuzzy Logicians

theorize about might seem plausible a priori, it is less so in the case of

statements of the Some Ps are Fs form that enter into syllogistic reason-

ing than the proportions that are related to them.17

Department of Philosophy

University of California-Berkeley

NOTES

1 In fact, Brian Ellis did something very like this in an early work (Ellis, 1973), but only

gave this up when David Lewis showed that his formal laws entailed that there could only

be four possible probability values.


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2 I apologize to readers familiar with my work for using the example, diagram, and

formula to be discussed here elsewhere.3 Jeffreys logic decision (Jeffrey, 1983) does treat propositions as objects of desire, but

we will ignore that here since it is not relevant to the developments to follow.

4 This is a motive for seeking truth in our world, not truth in a world.5 Thus also, our simple pragmatic principles are far from William James pragmatism,

e.g., as expressed as Principally, the truth of a state of mind means . . . a leading that is

worthwhile (Pragmatism, 1907). Also, our principles have nothing to do with alleged feel

good benefits of holding beliefs of one or another kind. Endnote 9 will comment briefly on

a correspondence with a kind ofPeircian pragmatism.6 Bringing linguistic elements into the picture also adds elements to the world, since

the Sams belief, described as that Jane will take Logic, involves the names Jane and

Logic, and these are presumed to refer to things, objects, in the world.7 This suggests the distinction between practical and disinterested values of the

information, discussed in Rosenkrantz, 1977.8 Changing the belief to something general, and changing what it influences from a

particular action to general policy makes the picture more like Peirces The feeling of

believing is a more or less sure indication of there being established in our nature some

habit which will determine our actions (from The Fixation of Belief, 1877). Our picture

thereby moves closer to Peircian pragmatism.9 Proportions suggest probabilities, since both obey the same formal laws. But the two

ought not to be confused, since proportions are matters of fact while probabilities, at least

of the sort that are relevant to reasoning, are matters of belief. The author s analysis of

conditional propositions (Adams, 1975, and elsewhere) evaluates them in terms of probabil-

ity, e.g., that a particular bird flies, not of the proportion of birds that fly. Sections 47 ofAdams, 1998, are concerned with probabilities, particularly of conditionals, and with for-

mulating appropriate pragmatic principles that apply to judgments about them.10 Cf. my paper On the Nature and Purpose of Measurement (Adams, 1966) and my

paper with William Y. Adams Purpose and Scientific Concept Formation, (Adams and

Adams, 1989).11 Copi, 1972, p. 185. It might be argued that even though there are many non-Greek

residents of Athens, All Athenians are Greeks is true without exception because these

people could not be Athenian citizens. But if Barbara could only be applied to general-

izations that are rendered universally true by definition, its practical usefulness would be

limited in the extreme.12 It is in the details of this that I am inclined to see the practical importance of the

coherence that sometimes figures in accounts of the nature of truth. We only have traces

or records, and not direct sensory access to the past, and we often have to reconcile

conflicts between these items of testimony. But I am inclined to think that going into

detail concerning these matters will require us to confront the problem of time directly.13 It seems to me that the efforts of the praxis philosophers are directed primarily at

the theoretical case. But if the present remarks are correct these efforts must be fruitless.

There are no clear practical principles that apply to beliefs of this sort, and to demand that

they should be discovered, formulated, or created is as pointless as to demand that the

center of the universe should be discovered.14 Cf. my book The Logic of Conditionals, Adams, 1975.15 My ideas are largely inspired by very cryptic suggestions in parts (4) and (5) of Ramsey s

great paper Truth and Probability (Ramsey, 1950). I think that even more than the earlier

parts of this paper, upon which modern ideas of subjective probability are based, the last

parts, which attempt to link that to a pragmatically useful concept of objective probability,


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are the most profound ones in the paper. So far as I can see, to date these parts have hardly

been commented on at all, and so we can say that Ramsey is still ahead of our time.16 Note that this would be somewhat stronger than the conclusion of Darii, which is only

that some penguins must fly, and not that the proportion that fly must be at least as great

as the proportion that are birds.17 It is particularly questionable to assume with Fuzzy Logic that the truth of Some

parrots fly should equal 1 minus that ofNo parrots fly, assuming that that is the logical

contradictory ofSome parrots fly (cf., Nguyen and Walker, 2000, p. 67).

REFERENCES

Adams, E. W. (1966). On the Nature and Purpose of Measurement, Synthese 16,

pp. 225269.

Adams, E. W. (1974). The Logic ofAlmost All , Journal of Philosophical Logic 3, pp. 3

17.

Adams, E. W. (1975). The Logic of Conditionals, Dordrecht, D. Reidel and Company.

Adams, E. W. (1996). Four Probability-preserving Properties of Inferences, Journal of

Philosophical Logic 25, pp. 124.

Adams, E. W. (1998). The utility of truth and probability, in P. Weingartner, G. Schurz,

and G. Dorn (eds.), The Role of Pragmatics in Contemporary Philosophy, Holder-Pichler-

Tempsky, Vienna, pp. 1761994.

Adams, E. W. and Adams, W. Y. (1987). Purpose and Scientific Concept Formation with

W. Y. Adams, British Journal for Philosophy of Science 38, pp. 419440.

Bamber, D. (2000). Entailment with near surety of scaled assertions of high probability,

Journal of Philosophical Logic 29, pp. 174.

Ellis, B. (1973). The logic of subjective probability,British Journal for the Philosophy of

Science 24 (2), pp. 125152.

James, W. (1907). Pragmatism, a New Name for Old Ways of Thinking, New York, Longmans,

Green & Co.

Jeffrey, R. (1983). The Logic of Decision, 2nd Edition, Chicago, the University of Chicago

Press, 1983.

Jevons, W. S. (1896). Studies in Deductive Logic, Third Edition, New York, The Macmillan

Company, Limited.

Nguyen, H. T., and Walker, E. A. (2000). A First Course In Fuzzy Logic, Second Edition,

Boca Raton, Chapman and Hall/CRC.

Peirce, C. S. (1877). The fixation of belief,Popular Science Monthly.

Ramsey, F. (1950). Truth and Probability, in R.B. Braithwaite (ed.), The Foundations of

Mathematics and Other Logical Essays, New York, The Humanities Press, pp. 156198.

Rescher, N. (1977). Methodological Pragmatism, New York, New York University Press.

Rescher, N. (1998). Pragmatism in crisis, in P. Weingartner, G. Schurz, and G. Dorn

(eds.), The Role of Pragmatics in Contemporary Philosophy, Holder-Pichler-Tempsky,

Vienna, pp. 2438.

Rosenkrantz, R. D. 1977. Inference, Method and Decision, Dordrecht, D. Reidel Publishing

Company.

adams, truth values & the value of truth [16 pgs]

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