2′. But if Q′ is true, then it is not within my power to do O (for a similar reason).
3′. But either Q is true, or Q′ is true.
∴4′. Either it is not within my power to do O, or it is not within my power to do O′;
and (B) is accordingly false. Another way of expressing this is to say that what sort of order I issue depends, among other things, on whether a naval battle takes place tomorrow—for in this situation a naval battle tomorrow is (by our fourth presupposition) a necessary condition of my doing O, whereas no naval battle tomorrow is equally essential for my doing O′.
Considerations of time. Here it might be tempting, at first, to say that time makes a difference, and that no condition can be necessary for any other before that condition exists. But this escape is closed by both our fifth and sixth presuppositions. Surely if some condition, at any given time, whether past, present, or future, is necessary for the occurrence of something else, and that condition does not in fact exist at the time it is needed, then nothing we do can be of any avail in bringing about that occurrence for which it is necessary. To deny this would be equivalent to saying that I can do something now which is, together with other conditions prevailing, sufficient for, or which ensures, the occurrence of something else in the future, without getting that future occurrence as a result. This is absurd in itself and contrary to our second presupposition. And if one should suggest, in spite of all this, that a state of affairs that exists not yet cannot, just because of this temporal removal, be a necessary condition of anything existing prior to it, this would be logically equivalent to saying that no present state of affairs can ensure another subsequent to it. We could with equal justice say that a state of affairs, such as yesterday’s naval battle, which exists no longer, cannot be a necessary condition of anything existing subsequently, there being the same temporal interval here; and this would be arbitrary and false. All that is needed, to restrict the powers that I imagine myself to have to do this or that, is that some condition essential to my doing it does not, did not, or will not occur.
Nor can we wriggle out of fatalism by representing this sort of situation as one in which there is a simple loss of ability or power resulting from the passage of time. For according to our sixth presupposition, the mere passage of time does not enhance or diminish the powers or abilities of anything. We cannot, therefore, say that I have the power to do O′ until, say, tomorrow’s naval battle occurs, or the power to do O until tomorrow arrives and we find no naval battle occurring, and so on. What restricts the range of my power to do this thing or that is not the mere temporal relations between my acts and certain other states of affairs, but the very existence of those states of affairs themselves; and according to our first presupposition, the fact of tomorrow’s containing, or lacking, a naval battle, as the case may be, is no less a fact than yesterday’s containing or lacking one. If, at any time, I lack the power to perform a certain act, then it can only be the result of something, other than the passage of time, that has happened, is happening, or will happen. The fact that there is going to be a naval battle tomorrow is quite enough to render me unable to do O′, just as the fact that there has been a naval battle yesterday renders me unable to do S′, the nonoccurrence of those conditions being essential, respectively, for my doing those things.
Causation. Again, it does no good here to appeal to any particular analyses of causation, or to the fact, if it is one, that causes only “work” forwards and not backwards, for our problem has been formulated without any reference to causation. It may be, for all we know, that causal relations have an unalterable direction (which is an unclear claim in itself), but it is very certain that the relations of necessity and sufficiency between events or states of affairs have not, and it is in terms of these that our data have been described.
The law of excluded middle. There is, of course, one other way to avoid fatalism, and that is to deny one of the premises used to refute (B). The first two, hypothetical, premises cannot be denied, however, without our having to reject all but the first, and perhaps the last, of our original six presuppositions, and none of these seems the least doubtful. And the third premise—that either Q is true, or Q′ is true—can be denied only by rejecting the first of our six presuppositions, that is, by rejecting the standard interpretation, tertium non datur, of what is called the law of excluded middle.
This last escape has, however, been attempted, and it apparently involves no absurdity. Aristotle, according to an interpretation that is sometimes rendered of his De Interpretatione, rejected it. According to this view, the disjunction (Q v Q′) or, equivalently, (Q v -Q), which is an instance of the law in question, is a necessary truth. Neither of its disjuncts, however—i.e., neither Q, nor Q′—is a necessary truth nor, indeed, even a truth, but is instead a mere “possibility,” or “contingency” (whatever that may mean). And there is, it would seem, no obvious absurdity in supposing that two propositions, neither of them true and neither of them false, but each “possible,” might nevertheless combine into a disjunction which is a necessary truth—for that disjunction might, as this one plainly does, exhaust the possibilities.
Indeed, by assuming the truth of (B)—i.e., the statement that it is within my power to do O and it is also within my power to do O′—and substituting this as our third premise, a formal argument can be rendered to prove that a disjunction of contradictories might disjoin propositions which are neither true nor false. Thus:1”. If Q is true, then it is not within my power to do O′.
2”. But if Q′ is true, then it is not within my power to do O.
3”. But it is within my power to do O, and it is also within my power to do O′.
∴ 4”. Q′ is not true, and Q is not true;
and to this we can add that, since Q and Q′ are logical contradictories, such that if either is false then the other is true, then Q is not false, and Q′ is not false—i.e., that neither of them is true and neither of them false.
There seems to be no good argument against this line of thought which does not presuppose the very thing at issue, that is, which does not presuppose, not just the truth of a disjunction of contradictories, which is here preserved, but one special interpretation of the law thus expressed, namely, that no third value, like “possible,” can ever be assigned to any proposition. And that particular interpretation can, perhaps, be regarded as a more or less arbitrary restriction.
We would not, furthermore, be obliged by this line of thought to reject the traditional interpretation of the so-called law of contradiction, which can be expressed by saying that, concerning any proposition, not both it and its contradictory can be true—which is clearly consistent with what is here suggested.
Nor need we suppose that, from a sense of neatness and consistency, we ought to apply the same considerations to our first situation and to proposition (A)—that, if we so interpret the law in question as to avoid fatalism with respect to the future, then we ought to retain the same interpretation as it applies to things past. The difference here is that we have not the slightest inclination to suppose that it is at all within our power what happened in the past, or that propositions like (A) in situations such as we have described are ever true, whereas we do, if we are not fatalists, believe that it is sometimes within our power what happens in the future, that is, that propositions like (B) are sometimes true. And it was only from the desire to preserve the truth of (B), but not (A), and thus avoid fatalism, that the tertium non datur was doubted, using (B) as a premise.
Temporary efficacy. It now becomes apparent, however, that if we seek to avoid fatalism by this device, then we shall have to reject not only our first but also our sixth presupposition; for on this view time will by itself have the power to render true or false certain propositions which were hitherto neither, and this is an “efficacy” of sorts. In fact, it is doubtful whether one can in any way avoid fatalism with respect to the future while conceding that things past are, by virtue of their pastness
alone, no longer within our power without also conceding an efficacy to time; for any such view will entail that future possibilities, at one time within our power to realize or not, cease to be such merely as a result of the passage of time—which is precisely what our sixth presupposition denies. Indeed, this is probably the whole point in casting doubt upon the law of excluded middle in the first place, namely, to call attention to the status of some future things as mere possibilities, thus denying both their complete factuality and their complete lack of it. If so, then our first and sixth presuppositions are inseparably linked, standing or falling together.
The assertion of fatalism. Of course one other possibility remains, and that is to assert, out of a respect for the law of excluded middle and a preference for viewing things under the aspect of eternity, that fatalism is indeed a true doctrine, that propositions such as (B) are, like (A), never true in such situations as we have described, and that the difference in our attitudes toward things future and past, which leads us to call some of the former but none of the latter “possibilities,” results entirely from epistemological and psychological considerations—such as, that we happen to know more about what the past contains than about what is contained in the future, that our memory extends to past experiences rather than future ones, and so on. Apart from subjective feelings of our power to control things, there seem to be no good philosophical reasons against this opinion, and very strong ones in its favor.
2
PROFESSOR TAYLOR ON FATALISM
JOHN TURK SAUNDERS
IN A recent article1 Richard Taylor presents us with a problem the solution to which, he suggests, requires either the acceptance of fatalism or the rejection of the traditional interpretation of the logical law of excluded middle. I wish to point out that the problem is solved when one notices an error in Taylor’s reasoning, and that once this error is uncovered it is clear that no reason has been provided on behalf of either fatalism or a reinterpretation of the law of excluded middle.
The gist of the problem may be presented as follows. Suppose that I am a naval commander who is about to issue an order to his fleet. Suppose also that, other conditions being what they are, order O is a sufficient condition for there being a naval battle tomorrow, whereas another order, order O′, is a sufficient condition for there being no naval battle tomorrow. It follows that if the proposition Q (“A naval battle will occur tomorrow”) is true then a necessary condition for O′ is lacking, whereas if the proposition Q′ (“No naval battle will occur tomorrow”) is true then a necessary condition for O is lacking. But, according to the law of excluded middle, either Q is true or Q′ is true. Hence, either a necessary condition for O is lacking, or else a necessary condition for O′ is lacking. But, says Taylor, no agent can perform an act if a necessary condition for that act is lacking. And he concludes: Either it is not within my power to issue order O, or it is not within my power to issue order O′. Thus the problem is capped by the undesirable fatalistic implications of the last mentioned statement (implications which are not detailed by Taylor).
ANALYSIS, VOL. 23, NO. 1, 1962.
Taylor errs, however, in supposing that no agent has within his power an act for which a necessary condition is lacking. I suspect that he is led to make this supposition by equivocal reasoning of the following sort. He sees that (1) no agent can perform an act if a necessary condition for that act is lacking. But this means only that (2) as a matter of logic, if condition x is necessary for the occurrence of act y and x is lacking, then no agent performs y. The expression “can” functions only to indicate that the consequent of the second formulation follows logically from its antecedent. Taylor may then have equivocated with respect to “can,” taking it this time to mean the same as “has the power to.” In this way he may have become convinced that no agent has the power to perform an act if a necessary condition for that act is lacking. The latter is another way of putting his erroneous supposition that no agent has within his power an act for which a necessary condition is lacking.
Now to point out that this supposition is, indeed, erroneous. My knocking upon a thin wooden door with my fist is a sufficient condition for the door’s shaking. Hence the door’s shaking is a necessary condition for my knocking upon the door. But the door’s shaking is not a necessary condition for my ability to knock upon the door. (If it were, then my mere ability to knock upon the door would suffice to make it shake.) I may decide not to knock and the door may not shake, but it does not follow that I did not have it in my power to knock. On the other hand, my having a certain muscle structure is a necessary condition for my ability to knock upon the door. E.g., if my tissues were damaged in certain ways, I could not knock. Suppose that my tissues are damaged in one of these ways. Then I do lack the ability to knock upon the door, since a necessary condition of that ability is lacking. And, a fortiori, I do not knock upon the door. Thus, while a necessary condition for an ability to do something is always a necessary condition for doing it, the converse does not hold. Often a necessary condition for an act is not a necessary condition for our having the power to perform that act. To suppose otherwise is to adopt a position which logically implies that our mere abilities are sufficient conditions of everything which our acts suffice to produce. In that case we need never perform an act in order to benefit from its results. We need only possess or acquire the ability to perform it. E.g., to work up a sweat I need not exercise: I have only to possess or acquire the ability to exercise.
Now we may solve (or dissolve) Taylor’s problem by noting that he is not entitled to conclude: Either it is not within my power to issue order O, or it is not within my power to issue order O′. The occurrence of a naval battle on the morrow is a necessary condition of O but not of the ability to issue O; and the non-occurrence of a naval battle on the morrow is a necessary condition of O′ but not of the ability to issue O′. (To suppose otherwise, as Taylor does, is to adopt a position which logically implies that my ability to issue O is a sufficient condition for a naval battle on the morrow and that my ability to issue O′ is a sufficient condition for the non-occurrence of a naval battle on the morrow.) Thus fades the spectre of Taylor’s fatalism, leaving in tranquility the law of the excluded middle.
NOTE
1 Richard Taylor, “Fatalism,” The Philosophical Review, Vol. LXXI, No. 1, January 1962.
3
FATALISM AND ABILITY
RICHARD TAYLOR
IF THERE is an error in my defence of fatalism1 I am sure John Turk Saunders has put his finger on it.2 His rejoinder is so familiar that I have come to anticipate it every time I hear this discussed, but no one else has put it so well.
The thing at issue is my presupposition that no agent can perform any given act in the absence of some condition necessary for its accomplishment. Saunders says this means only that it is impossible, as a matter of logic, both that an agent should perform a certain act y, and that there should be lacking some condition, x, necessary for doing y. It does not follow that he is unable to do y, but only that he does not do y—which is consistent with his having the ability to do y.
Now this is true in the usual sense of ability, which consists in having the skill, strength, equipment, or knowing how. But to make that point is really to miss the point. If there is lacking some condition, x, which is necessary for my doing y, or which is such that y cannot occur without it, then not only do I not do y, I cannot do it, no matter what my natural or acquired abilities might be. This is very obvious when one considers necessary conditions which are lacking in the past. It is less obvious when one considers necessary conditions which are lacking in the future, as Saunders does.
ANALYSIS, VOL. 23, NO. 2, 1962.
For example, if conditions are such that a naval battle yesterday is a necessary condition for my reading a certain kind of headline today, then, given that no such battle occurred, we can conclude not only that I do not read such a headline, but that I cannot, that it is not within my power. This is consisten
t with my knowing how to read it, having the requisite skill and vision, and so on, and thus being able, in that sense. But if it were in my power to read such a headline, then it logically follows that it would be within my power to make a naval battle occur yesterday which, we are supposing, did not occur; and this is absurd.
No one doubts that fatalism with respect to the past is true, i.e., that we have no power to make happen what did not in fact happen. My argument showed that we have the same reasons for saying it is true with respect to the future, given the usual interpretation of the law of excluded middle. One does not answer that argument by simply assuming that it is not true with respect to the future.
The issue now turns on the notion of ability. Saunders says that one often has the ability to do something, y, even though there is lacking some condition, x, necessary for its accomplishment. This is true, in the sense of ability that involves skill, strength, requisite organs, or knowing how, which is, admittedly, the ordinary sense. But note that, if we press this sense, then we need no longer be fatalists about the past, for we will then have the ability to do things that are sufficient for the occurrences in the past of things which did not in fact occur—for instance, to make a battle occur yesterday which did not occur. I still have the ability, in this sense, to read a certain kind of headline—my vision is all right, I know how to read, etc.—even though, due to the absence of some condition necessary for there being any such headline, I cannot do it.