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 KebalÁnvayi, i.e. covers the whole sphere of thought and existence.... ‘Knowable’ and ‘Nameable’ are among the examples of KebalÁnvayi 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, ? 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.

CHAPTER XXXV