THE MORTALITY OF SOCRATES
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.
FOOTNOTES:
[58] By "Dedekind's Axiom," _E. N._, p. 11.
[59] _M._, vol. xx., 1910, pp. 134-5.
[60] [Here, again, Mr. R*ss*ll's work seems to anticipate some of Mr.
Russell's later work, e.g. in _Our Knowledge of the External World as a
Field for Scientific Method in Philosophy_, Chicago and London, 1914,
pp. 3-4, 55-6, _et passim._--ED.]
[61] "Pacidius Philalethi" in Louis Couturat, _Opuscules et Fragments
inedits de Leibniz_, Paris, 1903, pp. 594-627, especially pp. 599, 601,
608, 611. Cf. [A. E. Taylor, Hastings' _Encyclopaedia of Religion and
Ethics_, vol. iv., Part 2, Edinburgh, 1912, p. 96.--ED.]; Robert Latta,
_Leibniz: The Monadology and other Philosophical Writings_, Oxford,
1898, pp. 21 ff, 29 (note); Couturat, _La Logique de Leibniz d'apres des
documents inedits_, Paris, 1901, pp. 130, 132; and Russell, _Ph. L._,
pp. 108-16, 243-9.
[62] [It may be remarked that, according to _The Times_ of December 20,
1917, Mr. Justice Sargant, in the Chancery Division, also held that "the
law did not recognize fractions of a day," and that Lord Blackburn, in
his decision (9 _App. Cas._, 371, 373) that a man born on the thirteenth
of May 1853 attained the age of twenty-one on the thirteenth of May 1874
"was not speaking strictly."--ED.]