In fact, the world of things falls into various sets of things of the same "type." For every propositional function [Greek: ph](_x_) there is a range of values of _x_ for which [Greek: ph](_x_) has a signification as a true or a false proposition. Until this theory was brought forward, there were occasionally discussions as to whether an object which did not belong to the range of a certain propositional function possessed the corresponding property or not. Thus, Jevons, in early days,[114] was of opinion that virtue is neither black nor not-black because it is not coloured, but rather later[115] he admitted that virtue is not triangular.[116] FOOTNOTES: [113] _Pa. Ma._, p. 40. [114] _S. o. S._ pp. 36-7. [115] _E. L. L._, pp. 120-1. [116] [It may perhaps be added that, some years after Mr. R*ss*ll's death, Dr. Whitehead stated, in an address delivered in 1916 and reprinted in his book on _The Organisation of Thought_ (London, 1917, p. 120), that "the specific heat of virtue is 0.003 is, I should imagine, not a proposition at all, so that it is neither true nor false...."--ED.] CHAPTER XXXIX THE HIERARCHY OF JOKES Jokes may be divided into various types. Thus a joke or class of jokes can only be the subject of a joke of higher order. Otherwise we would get the same vicious-circle fallacy which gives rise to so many paradoxes in logic and mathematics. A certain Oxford scholar succeeded, to his own satisfaction, in reducing all jokes to primitive types, consisting of thirty-seven proto-Aryan jokes. When any proposition was propounded to him, he would reflect and afterwards pronounce on the question as to whether the proposition was a joke or not. If he decided, by his theory, that it was a joke, he would solemnly say: "There _is_ that joke." If this narration is accepted as a joke, since it cannot be reduced to one of the proto-Aryan jokes under pain of leading us to commit a vicious-circle fallacy, we must conclude that there is at least one joke which is not proto-Aryan; and, in fact, is of a higher type. There is no great difficulty in forming a hierarchy of jokes of various types. Thus a joke of the fourth type (or order) is as follows: A joke of the first order was told to a Scotchman, who, as we would expect, was unable to see it.[117] The person (A) who told this joke told the story of how the joke was received to another Scotchman thereby making a joke about a joke of the first order, and thus making a joke of the second order. A remarked on this joke that no joke could penetrate the head of the Scotchman to whom the joke of the first order was told, even if it were fired into his head with a gun. The Scotchman, after severe thought, replied: "But ye couldn't do that, ye know!" A repeated the whole story, which constituted a joke of the third order, to a third Scotchman. This last Scotchman again, after prolonged thought, replied: "He had ye there!" This whole story is a joke of the fourth order.