The mortality of Socrates is so often asserted in books on logic that it may be as well briefly to consider what it means. The phrase “Socrates is mortal” may be thus defined: “There is at least one instant t such that t has not to Socrates the one-many relation R which is the converse of the relation ‘exists at,’ and all instants following t have not the relation R to Socrates, and there is at least one instant t´ such that neither t´ nor any instant preceding t´ has the relation R to Socrates.”

This definition has many merits. In the first place, no assumption is made that Socrates ever lived at all. In the second place, no assumption is made that the instants of time form a continuous series. In the third place, no assumption is made as to whether Socrates had a first or last moment of his existence. If time be indeed a continuous series, then we can easily deduce[58] that there must have been either a first moment of his non-existence or a last one of his existence, but not both; just as there seems to be either a greatest weight that a man can lift or a least weight that he cannot lift, but not both.[59] This may be set forth as follows: for the present we will not concern ourselves with evidence for or against human immortality; I will merely try to present some logical questions which persistently arise whenever we think of eternal life. One of the greatest merits of modern logic is that it has allowed us to give precision to such problems, while definitely abandoning any pretensions of solving them; and I will now apply the logico-analytical method to one of the problems of our knowledge of the eternal world.[60]

We will start from the generally accepted proposition that all men are mortal. Clearly, if we could know each individual man, and know that he was mortal, that would not enable us to know that all men are mortal, unless we knew, in addition, that those were all the men there are. But we need not here assume any such knowledge of general propositions; and, though most of us will admit that the proposition in question has great intrinsic plausibility, it is not strictly necessary for our present purpose to assume anything more than the still more probable proposition “Socrates is mortal.” This last proposition, quite apart from the fact that we have a large amount of historical evidence for its truth, has been repeated so often in books on logic that it has taken on the respectable air of a platitude while preserving the character of an exceedingly probable truth. The truth also results from the fact that it is used as the conclusion of a syllogism. For it is a well-known fact that syllogisms can only be regarded as forming part of a sound education if the conclusions are obviously true. The use of a syllogism of the form “All cats are ducks and all ducks are mice, therefore all cats are mice,” would introduce grave doubts into the University of Oxford as to whether logic could any longer be considered as a valuable mental training for what are amusingly called the “learned professions.”

If, then, we divide all the instants of time, whether past, present, or future, into two series—those instants at which Socrates was alive, and those instants at which he was not alive—and leave out of consideration, for the sake of greater simplicity, all those instants before he lived, we see at once, by the simple application of Dedekind’s Axiom, that, if Socrates entered into eternal life after his death, there must have been either a last moment of his earthly life or a first moment of his eternal life, but not both.

Logic alone can give us no information as to which of these cases actually occurred, and we are thrown back on to a discussion of empirical evidence. It is no unusual thing to read of people who thought “that every moment would be their last.” In this case it is quite obvious that they consequently thought that eternity would have no beginning.

Now here we must consider two things: (1) It is plainly unsafe to conclude from what people think will happen to what will happen; (2) even if we could so conclude, it would be unsafe to deduce that there was a last moment in the life of Socrates: we could only make the guess plausible, as we should be using the inductive method.

There are two other pieces of evidence that there is a last moment of any earthly existence, which we may now briefly consider. That this was so was held by Carlo Michaelstaedter; but since he apparently only believed this because he wanted, by attributing a supposed ethical value to that moment, to give support to his theory of suicide, we ought not to give great weight to this evidence. Secondly, Thomas Hobbes objected to the principle “that a quantity may grow less and less eternally, so as at last to be equal to another quantity; or, which is all one, that there is a last in eternity” as “void of sense.” Now, the principle meant is true, so that, although the other proposition mentioned by Hobbes does not follow logically from the first, there is some evidence that this other is true. In fact, that Hobbes thought that such-and-such a proposition followed from another proposition which he wrongly believed to be false, is far better evidence for the truth of such-and-such a proposition than any we have for the truth of most of our most cherished beliefs.

Thirdly, Leibniz, in a dialogue[61] written on his journey of 1676 to visit Spinoza, raised the question whether the moment at which a man dies may be regarded as both the last moment at which he is alive and the first at which he is dead, as it must be by Aristotle’s theory of continuity. Agreement with this view violates the law of contradiction; denial of it implies that two moments can be immediately adjacent. By the denial, then, we are led to regard space and time as made up of indivisible points and moments, and thus, since we can draw one and only one parallel from any point in the diagonal of a square to a given side, the diagonal will contain the same (infinite) number of points as that side, and will therefore be equal to it. In this Leibniz repeated an argument used by the ancient Arabs, Roger Bacon, and William of Occam. This Leibniz considered to be a proof that a line cannot be an aggregate of points. Indeed, their number would be “the number of all numbers” of the greatest possible integer, which is not.

It does not seem, further, that any light is thrown on the logical question of human mortality or immortality by legal decisions. It would appear that one can, legally speaking, be alive for any period less than twenty-four hours after one is dead and be dead for any period less than twenty-four hours before one’s death. At least, according to Salkeld, i. 44, it was “adjudged that if one be born the first of February at eleven at night, and the last of January in the twenty-first year of his age, at one of the clock in the morning, he makes his will of lands, and dies, it is a good will, for he was then of age.” In Sir Robert Howard’s case (ibid., ii. 625) it was held by Chief Justice Holt that “if A be born on the third day of September; and on the second day of September twenty-one years afterwards he make his will, this is a good will; for the law will make no fraction of a day, and by consequence he was of age.” But it is hardly necessary to remark that in this way the problem with which we are concerned is merely shifted and not solved. For the question as to whether there is or is not a last moment of a man’s life is not answered by the decision that he dies legally twenty-four hours before or after he dies in the usual sense of the word, and the problem arises as to whether there is or is not a last moment of his legal age.[62]

So assuming that there was a last moment of Socrates’s earthly life, and consequently no first moment of his eternal life, we see, further, that, unless the possibility of infinite numbers is granted, it would be quite possible for us logically to doubt the possibility of an eternal life for Socrates on the same grounds as those which led Zeno to assert that motion was impossible and that Achilles could never overtake the Tortoise. If, on the other hand, it be admitted that eternity, at least in the case of Socrates, had a beginning, these same arguments of Zeno would lead any one who denies the possibility of infinite number to conclude that Socrates, like the worm, can never die. Thus is it quite plain that the difficulties about immortality which meet us at the very outset of our inquiry can partly be solved only by the help of the theory of infinite numbers and partly, it would seem, not at all.

There is another difficulty about immortality which is quite distinct from this and is analogous to another argument of Zeno. If, indeed, all the instants of time be divided, as before, into the two series of instants at which Socrates was alive and instants at which he was not alive, it follows at once that no instant of time is not accounted for. At none of these instants, however, does Socrates die; obviously he cannot die either when he is alive or when he is dead. Thus it would appear that Socrates never died, and that we ought to re-define the term “mortal” to mean “a human being who is alive at some moments and dead at some.” Consequently we must avoid the very tempting conclusion that, because Socrates never died, he was therefore immortal.

It is very important carefully to distinguish between the two arguments I have just set forth. The second argument proves quite rigidly that Socrates and, indeed, anybody else, never dies, whether there is or is not a last moment of his life on earth. The first argument proves that, if there is a first moment of Socrates’s eternal life, his life on earth never ends. But we have seen that we cannot conclude that this unending life proves that he never is or will be in a state of eternity.

CHAPTER XXIII