A possible extension of logical theory

PHILOSOPHICAL STUDIES

Edited by WILFRID SELLARS and HERBERT FEIGL with the advice and assistance of PAUL MEEHL, JOHN HOSPERS, MAY BRODBECK

VOLUME XVI Contents December 1965 NUMBER 6

A Possible Extension of Logical Theory? by Geothey Hunter, UNIVERSITY OF LEEDS AND UNIVERSITY OF NORTH CAROLINA

Beliefs Which Are Grounds for Themselves by John Turk Saunders, SAN FERNANDO VALLEY STATE COLLEGE

Necessity, Contingency, and Punishment by David BIumenfeld and Gerald Dworkin, UNIVERSITY OF CALIFORNIA, BERKELEY

A Possible Extension of Logical Theory? by GEOFFREY HUNTER

UNIVERSITY OF LEEDS AND UNIVERSITY OF NORTH CAROLINA

"Even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience."

Hume, Treatise, 1.3.12

THE ~EART of my paper consists of the following two propositions: 1. A man who knows of at least one case of an X being a Y, and who does

not know of any positive reason for thinking that an X might not be a Y, has some reason for thinking that all X's are Y's.

2. The contradictory of proposition (1)--i.e., "A man who knows of at least one case of an X being a Y, and who does not know of any positive reason for thinking that an X might not be a Y, has no reason at all for

81

82 PHILOSOPHICAL STUDIES

thinking that all X's are Y's"--is absurd in virtue of the meaning of what is said, absurd in virtue of the concepts employed being what they are. If by "analytic proposition" you mean "true proposition that is true simply and solely in virtue of the concepts that occur in it being what they are (or being what they are made to be by the propounder of the proposition) and not in virtue of any other facts," then proposition (1) is analytic. It is certainly not merely contingently true.

An article by Lewy in Analysis for September 1939 provides a convenient starting point for the explanation and defense of these two propositions. In that article Lewy claimed that inductive conclusions logically follow from inductive premises, and he gave the following example: The premisses are:

(1) Whenever I have heard barking in the past there was always a dog somewhere near; and

(2) I am hearing barking now;

and the conclusion is: (3) I have good reason to believe that there is a dog somewhere near

nOW.

Lewy claimed that (1) and (2) together entail (3). Why? Simply because it seems to me that the following proposition "Whenever I have heard barking in the past there was always a dog somewhere near, I'm hearing barking now, but I have no reason whatever to believe there is a dog in the neighbourhood" is self-contradictory. I can not prove that this is so, but I should ask you to reflect on how we use expressions like "I have good reason to believe," "It's probable," "It's very likely" etc. If you reflect on how these expressions are actually used, I'm sure you will see that the proposition I've just stated is self-contradictory in the very same way in which it is self-contradictory to say "All men are mortal, Smith is a man but Smith is not mortal."

Now I believe that Lewy was very nearly right. But his example was a bad one. It is easy to show that ( 1 ) and (2) together do not in fact entail (3).

Imagine a situation in which the propositions that follow are true: When- ever I have heard barking in the past there was always a dog somewhere near (Lewy's premise (1)). I am familiar with radio and tape-recording, but I happen never to have heard barking on any radio or tape-recorder. I am in a small boat in the middle of the Atlantic, with my wife. It is a clear day, and there is no land or ship or other boat in sight. I happen to know that there is no dog on board. My wife says, "Did I ever play you the recording I made of the sheep-dog trials I went to last year in Wharfedale?" I say "No"; she plays me the recording; and I hear barking now (Lewy's premise (2)). In

A POSSIBLE EXTENSION OF LOGICAL THEORY? 83

that situation I do not have good reason to believe that there is a dog somewhere near. (This is the contradictory of Lewy's conclusion (3).)

Thus Lewy's premises (1) and (2) could be true while the conclusion (3) was false. So (1) and (2) together do not entail (3).

What was wrong with Lewy's example? He failed to take into account the requirement that the arguer must know of no positive reason for thinking that an X might not be a Y. Lewy was, I believe, right in thinking that the fact that all known X's are Y's affords a presumption that all X's are Y's. But what he failed to see was that this presumption may be weakened, and even canceled out altogether, by other considerations. 1

The first person I know of to state clearly the importance in inductive arguments of the clause nisi ratio positiva obstet ("unless there is a positive reason against") was Roger Joseph Boscovich in his De Lege Continuitatis (1754). He also makes use of the legal notion of "presumption." This is what Boscovich says in Article 40 of his Theoria Philosophiae Naturalis (first edition, 1758). A marginal note to Article 40 says that it deals with "ubi & cur vim habeat induetio incompleta" ("where and why incomplete induction may have force") : 9 . . As regards the nature & validity of induction, & its use in Physics, I may here quote part of Art. 134 & the whole of Art. 135 from my dissertation De Lege Continuitatis. The passage runs thus: "Especially when we investi- gate the general laws of Nature, induction has very great power; & there is scarcely any other method beside it for the discovery of these laws . . . . Now, induction should take account of every single case that can possibly happen, before it can have the force of demonstration; such induction as this has no place in establishing the laws of Nature. But use is made of an induction of a less rigorous type; in order that this kind of induction may be employed, it must be of such a nature that in all those cases particularly, which can be examined in a manner that is bound to lead to a definite conclusion as to whether or no the law in question is followed, in all of them the same result is arrived at; & that these cases are not merely a few. Moreover, in the other cases, if those which at first sight appeared to be contradictory, on further & more accurate investigation, can all of them be made to agree with the law; although, whether they can be made to agree in this way bet- ter than in any other whatever, it is impossible to know directly anyhow. If such conditions obtain, then it must be considered that the induction is adapted to establishing the law . . . (Art. 135). In addition, whatever absolute properties, for instance those that bear no relation to our senses, are generally found to exist in sensible masses of bodies, we are bound to attrib- ute these same properties also to all small parts whatsoever, no matter how small they may be. That is to say, unless some positive reason prevents this (nisi positiva aliqua ratio obstet) . . . When we consider absolute, not relative, properties, whatever we perceive to be common to those contained


within the limits that are sensible to us, we should consider these things to be still common to those beyond those limits. For . . . if there should be any violation of the analogy, this would be far more likely to happen between the limits sensible to us, which are more open, than beyond them, where indeed they are so nearly nothing. Because then none did happen thus, it is a sign that there is none. This sign is not evident, but belongs to the princi- ples of investigation, which generally proves successful if it is carried out in accordance with certain definite wisely chosen rules. Now, since the indica- tion may possibly be fallacious, it may happen that an error may be made; but there is presumption against such an error, as they call it in law, until direct evidence to the contrary can be brought forward. Hence we should add: unless some positive reason is against it. Thus, it would be offending against these rules to say that large bodies indeed could not suffer compene- tration, or enfolding, or be deficient in inertia, but yet very small parts of them could suffer penetration, or enfolding, or be without inertia. On the other hand, if a property is relative with respect to our senses, then, from a result obtained from the larger masses we cannot infer that the same is to be obtained in its smaller particles; for instance, that it is the same thing to be sensible, as it is to be coloured, which is true in the case of large masses, but not in the case of small particles; since a distinction of this kind, accidental with respect to matter, is not accidental with respect to the term sensible or coloured . . .-2

That passage illustrates something of the wide range and variety of things, short of knowledge of an actual refuting instance, that could in a given case be "positive reasons against." Perhaps this is the place to say that the bare logical possibility of an X not being a Y is not to be counted as a positive reason against thinking that all X's are Y's: the bare logical possibility of something's being the case is no reason at all for thinking that it is the case.

What I am maintaining is this: The premises (1) I know of at/east one case of an X being a Y and (2) I know of no positive reason for thinking that an X might not be a Y taken together stand in a logical relation to the conclusion (3) I have some reason for thinking that all X's are Y's, a relation such that the conjunction (1) and (2) but not (3), though not self-contradictory, is absurd in virtue of the meaning of what is said.

If (1) and (2) are both true, then (3) cannot be false; and this is not iust a physical impossibility. If someone asserted (1) and (2) and yet denied (3), then I should not know what he was suggesting, and this would be because his words mean what they do.

There is a general point of logical theory involved here. Consider the possible Iogi~al relations between a conjunction of propositions, say p & q & r, and another proposition, say s. What I am claiming is that there are not just two possibilities, viz. either (i) p & q & r & ,~s involves a contradiction, or (ii) p & q & r dr ,~s is perfectly all right so far as logic is concerned. There


is a third possibility, viz. (iii) p & q & r has a logical relation to s such that p & q & r & ~s, though not involving a contradiction, is absurd in virtue of the meaning of what is said. If someone asserted p & q & r & ,~s, then we should not know what he was suggesting, and this in virtue of the meaning of what was said: for p and q and r could not all be true while s was false, and this impossibility is created by the meanings of the words used; it is in some sense a logical and not a merely physical impossibility.

Neither (1) nor (2) by itself entails (3). It is obvious that I could know of at least one case of an X being a Y (premise (1)) and yet have no reason at all for thinking that all X's are Y's (contradictory of (3)). It is equally obvious that (2) does not entail (3) : for it might be true that I knew of no positive reason for thinking that an X might not be a Y, and yet that I had no reason at all for thinking that all X's are Y's; this would be the case, for instance, if I knew nothing at all about X's and Y's. It is only the conjunction of (1) and (2) that stands in the logical relation I have described to the conclusion (3).

The occurrence of even one case of an X being a Y affords the man who knows of it a presumption that all X's are Y's, provided he knows of no positive reason against. Throughout when I speak of "some reason" I mean the contradictory of "no reason at all."

So far I have considered only that form of argument in which one of the premises is that the arguer knows of at least one case of an X being a Y, and the conclusion is that the arguer has some reason for thinking that all X's are Y's (where All X's are Y's is a merely de facto universal proposition). I shall call arguments of this kind "simple inductive arguments."

There are conclusions which we should like to be assured of that cannot be reached by simple inductive arguments alone; for instance, the conclusion that we have some reason for thinking that a moving body not acted on by any external force would continue in uniform motion in a straight line. There are no bodies not acted upon by any external force, so we cannot in this ease use arguments that start from the premise "We know of at least one case of a body not acted on by any external force that . . ." etc.

In such cases the following form of argument seems to me to be a sound form: (11 ) I have good reason for thinking that if p then q and r and s . . . and (12) I have good reason for thinking that q and r and s . . . and (13) I have no good reason for thinking that any definite suggestion that I know of, other than the suggestion that p, is a true explanation of the facts that q and r and s . . . Therefore: (14) I have some reason for thinking that p.

A premise of the form (11) may be known to be true even when the proposition p contained in it is not known to be true, for the hypothetical contained in such a premise may be analytic. For example, let "p" be "Ele-


ments consist wholly of atoms, for each element its own kind of atom, and every atom of a given element has the same weight as every other atom of that element; and any given compound consists wholly of certain discrete portions every one of which consists wholly of a whole number of atoms of various kinds and has the same number of atoms of each kind as every other discrete portion (in the sense explained above) of the compound." Then though p itself could hardly be known to be true (unless it is taken as analytic), the hypothetical "If p is true, then the proportions by weight in which the elements enter into a given compound are constant for that compound" could be known to be true, for it is (so far as I can see) analytic.

Again, a premise of the form (12) may be known to be true, where q and r and s are suitably chosen; they could, for instance, be propositions about particular conjunctions of observable things.

The importance of premise (13) can be brought out in the following way. Suppose we did not require a premise of the form (13), but allowed instead that all arguments of the form "(11) and (12), therefore (14)" were sound ones. Let "p" be "There exist imperceptible malicious demons with a spite against the human race, who have no moral scruples and are not punished for anything they do, and who have limited powers but are able to make cars break down." Then we should have to allow the soundness of the argument (11) I have good reason for thinking that if p were true, my car would occasionally break down in bad weather miles from anywhere; and (12) My car does occasionally break down in bad weather miles from anywhere; and therefore (14) I have some reason for thinking that there exist imperceptible malicious demons with the specified qualities and powers--for both premises are true, since the hypothetical contained in (11) is so nearly analytic that I have good reason for thinking

This is only the beginning of should be possible to go on to forms of premises that stand in their conclusions. For instance,

it true. a possible extension of logical theory. For it give, for other kinds of conclusions, sets of the logical relation that I have described to if the conclusion I want a reason for is that

something or other is a law of nature, then one of the premises might be "I know that properly controlled experiments designed to test the hypothesis that it is a law of nature that . . . have been carried out and that they have not falsified the hypothesis." (I am not saying that I can have no reason for thinking that something is a law of nature unless a premise of that form is true; only that a premise of that form, together with certain others that the reader can work out for himself, and that could be known by the arguer, would stand in the logical relation I have described to the conclusion "I have some reason for thinking that it is a law of nature that . . .")

To finish, consider the quotation from Hume at the head of this article.


Is it true, understood in the sense in which it would most naturally be taken by anyone who knew nothing of its original context (I do not want to discuss the textual question of exactly what Hume meant by it)? It is not true. If we have observed the constant conjunction of objects, then, provided we know of no positive reason for thinking otherwise (and the mere logical possibility of things being otherwise is not a positive reason for thinking that they are otherwise), we have some reason for thinking that any unobserved objects of those kinds will also be conjoined; and this proposition (i.e., the whole hypothetical from "If we have observed . . ." to " . . . will also be conjoined") is in some sense logically true. Similarly, if we have observed the frequent but not constant conjunction of objects, then, provided we know of no positive reason for thinking otherwise, we have some reason for thinking that if there are any unobserved objects of those kinds then some of them will be conjoined, and this proposition too (the whol." hypothetical) is in some sense logically true. So if Hume intended to deny either of those propositions, what he himself says must be logically absurd.

It might be objected that what Hume says cannot be logically absurd, because it is possible for a person to believe it and to act in accordance with his belief, as Pyrrho is said to have done: "He led a life consistent with this doc- trine, going out of his way for nothing, taking no precautions, but facing all risks as they came, whether carts, precipices, dogs or what not, and, generally, not letting himself be guided by his senses. But he was kept out of harm's way by his friends who . . . used to follow close after him . . . He lived to be nearly ninety. ''a

There are two possible replies to this objection, either a simple one that is probably right, or a more sophisticated one. The simple reply is to say that the objection presupposes that it is impossible either to believe what is logically absurd or to act on such a belief, and that such episodes in history as, say, Spinoza's claim that there must be an explanation for absolutely every- thing, and Hobbes's publications on squaring the circle, as well as the exist- ence of several twentieth-century publications that the reader may think of, are at least prima facie evidence that there is no such impossibility. The other reply is this: "Pyrrhonian and Humean skeptics do not believe the logically absurd things they say or write, for it is logically impossible to believe what is logically absurd (since there is nothing there to believe). All that happens is that they speak or write or rehearse to themselves, or have a tendency to speak or write or rehearse to themselves, various groups of words. And the Pyrrhonian acts, not in accordance with a logically absurd belief, but in accordance with some such belief as that expressed by the words 'I never have any reason at all for drawing any inference about objects I have not experienced,' a belief that taken on its oven is not logically absurd. The


logically absurd 'proposition' is 'Past experience gives me no reason at a11 for drawing any inferences about objects I have not experienced.'"

Received April 17, 1964

NOTES An example of the way in which a very strong presumption afforded by a mass of facts

may be upset by the addition of one further piece of evidence occurs in Vance Packard's The Status Seekers (London: Longman's, 1960), p. 47: "Sociologist Raymond W. Mack told me of an interesting exercise he sometimes gives his students in stratification. He asks them to 'place' in the class structure a man with these characteristics: "He is a graduate of Indiana University and has a law degree from Ohio State. His father, a small business- man, was a high-school graduate. His mother had two years of college. He drives a 1958 Buick . . . he has his own law office . . . he is a Methodist . . . he has a $12,000 income . . . his two children are university students." At this point Mack asks the students if they now have the man pretty well pegged as to status. Usually they nod that they have. Then he adds: 'Oh, yes, and one other thing. He is a Negro.' "

Quoted from the 1763 edition, translated by J. M. Child (La Salle, IlL: Open Court t'ublishing Co., 1922), pp. 57 and 59.

Diogenes Laertius ix. 62.

Beliefs Which Are Grounds for Themselves by JOHN TURK SAUNDERS

SAN FERNANDO VALLEY STATE COLLEGE

CAN BELIEFS ever be grounds for themselves? More specifically, can the fact that I believe that P be one of my grounds for believing that P? I wish to show that it can, and thereby to refute the contrary dogma which is abroad these days, for example: " . . . I cannot be said to rely on my beliefs at all. It is absurd to speak of my believing that P on the basis of the fact that I believe that p.,,1 "My belief cannot be included among the grounds for itself. ''2 I use the term "dogma" advisedly, for I have seen no arguments of- fered by its proponents in behalf of this thesis.

It is possible that no defense has been provided because the thesis has been viewed as self-evident. It may have been thought, that is, that its denial com- mits one to the legitimacy of circular reasoning. You ask me my reasons for P and I cite N, O, and P. But this, of course, would be a mistake: the thesis is not that P cannot be one of my grounds for believing that P, but that the fact that I believe that P cannot be one of my grounds for believing that P. And such a commitment is entailed by the denial of the former, but not by the denial of the latter.

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A possible extension of logical theory