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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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TRUTH VALUES AND THE VALUE OF TRUTH 209
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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210 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 211
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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212 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 213
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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214 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 215
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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216 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 217
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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218 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 219
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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220 PACIFIC PHILOSOPHICAL QUARTERLY
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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TRUTH VALUES AND THE VALUE OF TRUTH 221
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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222 PACIFIC PHILOSOPHICAL QUARTERLY
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).
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