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: ô] 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).