THE UNKNOWABLE
According to Mr. S. N. Gupta,[88] the first thing that every student of
Hindu logic has to learn when he is said to begin the study of inference
is that "all H is S" is not always equivalent to "No H is not S." "The
latter proposition is an absurdity when S is _Kebalanvayi_, i.e. covers
the whole sphere of thought and existence.... 'Knowable' and 'Nameable'
are among the examples of _Kebalanvayi_ terms. If you say there is a
thing not-knowable, how do you know it? If you say there is a thing
not-nameable, you must point that out, i.e. somehow name it. Thus you
contradict yourself."
Mr. Herbert Spencer's doctrine of the "Unknowable" gives rise to some
amusing thoughts. To state that all knowledge of such and such a thing
is above a certain person's intelligence is not self-contradictory, but
merely rude: to state that all knowledge of a certain thing is above all
possible human intelligence is nonsense, in spite of its modest,
platitudinous appearance. For the statement seems to show that we do
know something of it, viz. that it is unknowable.
To the last (1900) edition of _First Principles_ was added a "Postscript
to Part I," in which the justice of this simple and well-known criticism
as to the contradiction involved in speaking of an "Unknowable," which
had been often made during the forty odd years in which the various
editions had been on the market, was grudgingly acknowledged as
follows:[89]
"It is doubtless true that saying what a thing is not, is, in some
measure, saying what it is;... Hence it cannot be denied that to affirm
of the Ultimate Reality that it is unknowable is, in a remote way, to
assert some knowledge of it, and therefore involves a contradiction."
The "Postscript" reminds one of the postscript to a certain Irishman's
letter. This Irishman, missing his razors after his return from a visit
to a friend, wrote to his friend, giving precise directions where to
look for the missing razors; but, before posting the letter, added a
postscript to the effect that he had found the razors.
One is tempted to inquire, analogously, what might be, in view of the
Postscript, the point of much of Spencer's Part I. It is, to use De
Morgan's[90] description of the arguments of some who maintain that we
can know nothing about infinity, of the same force as that of the man
who answered the question how long he had been deaf and dumb.
But the best part of the joke against Mr. Spencer is that he, as we
shall see in Chapter XXXVIII, was refuted by a fallacious argument, and
thus mistakenly asserted the validity of the refutation of remarks which
happen to be unsound.
The analogy of the contradiction of Burali-Forti with the contradiction
involved in the notion of an "unknowable" may be set forth as follows.
If A should say to B: "I know things which you never by any possibility
can know," he may be speaking the truth. In the same way, [Greek: o] may
be said, without contradiction, to transcend all the _finite_ integers.
But if some one else, C, should say: "There are some things which no
human being can ever know anything about," he is talking nonsense.[91]
And in the same way if we succeeded in imagining a number which
transcends _all_ numbers, we have succeeded in imagining the absurdity
of a number which transcends itself.
All the paradoxes of logic (or "the theory of aggregates") are
analogous to the difficulty arising from a man's statement: "I am
lying."[92] In fact, if this is true, it is false, and _vice versa_. If
such a statement is spread out a little, it becomes an amusing hoax or
an epigram. Thus, one may present to a friend a card bearing on both
sides the words: "The statement on the other side of this card is
false"; while the first of the epigrams derived from this principle
seems to have been written by a Greek satirist:[93]
Lerians are bad; not _some_ bad and some _not_;
But all; there's not a Lerian in the lot,
Save Procles, that you could a good man call;--
And Procles--is a Lerian after all.
This is the original of a well-known epigram by Porson, who remarked
that all Germans are ignorant of Greek metres,
All, save only Hermann;--
And Hermann's a German.
FOOTNOTES:
[88] _Md._, N. S., vol. iv., 1895, p. 168.
[89] _First Principles_, 6th ed., 1900, pp. 107-10. The first edition
was published in 1862.
[90] Note on p. 6 of his paper: "On Infinity; and on the Sign of
Equality," _Trans. Camb. Phil. Soc._, vol. xi., part i., pp. 1-45 (read
May 16, 1864).
[91] The assertion of the finitude of a man's mind appears to be
nonsense; both because, if we say that the mind of man is limited we
tacitly postulate an "unknowable," and because, even if the human mind
were finite, there is no more reason against its conceiving the infinite
than there is for a mind to be blue in order to conceive a pair of blue
eyes (cf. De Morgan, _loc. cit._).
[92] Russell, _R. M. M._, vol. xiv., September 1906, pp. 632-3, 640-4.
[93] _The Greek Anthology_, by Lord Neaves (Ancient Classics for English
Readers), Edinburgh and London, 1897, p. 194.