^{page 234 note 1} Adventures of Ideas, p. 125Google Scholar.

^{page 234 note 2} Modes of Thought, chap. i.

^{page 235 note 1} Ethics II, iii (c).

^{page 236 note 1} Modes of Thought, p. 16.

^{page 236 note 2} ibid., p. 20.

^{page 236 note 3} ibid., p. 19.

^{page 234 note 4} ibid., p. 16.

^{page 237 note 1} Aims of Education, p. 106. (New York, 1929.)Google Scholar

^{page 238 note 1} Quoted by Laird, , The Idea of Value, p. xviiiGoogle Scholar, from Lotze, , System of Philosophy, English translation, Vol. II, p. 319Google Scholar. In the edition I have consulted (Oxford, 1884), the reference is Vol. II, p. 536.

^{page 238 note 2} Philosophy as a Science (New York, 1941) p. 148Google Scholar. I owe this reference to Prof. Laird. Cf. his article in Mind N.S. Vol. LI, No. 203, p. 251.

^{page 239 note 1} I find this hard, by the way, to reconcile with what he says later in the book, on p. 234, concerning the need that any definition of “real” should explain our “spontaneous appraisals” of what is real, and he instances “What definition of real would explain our spontaneous assertion that Spain is a real country but Utopia is not?” On the former count, should we not have to say that to a metaphysician Utopia is real when he finds it interesting?

^{page 239 note 2} We should probably many of us have to own, if we were pressed, to detecting a similar distinction, psychological but not logical, between “Is your journey necessary?” and “Is your journey really necessary?”

^{page 241 note 1} G. H. Hardy in A Mathematician's Apology has an interesting discussion of why we should say some mathematical theorems are “serious” whereas chess problems are “trivial.” (He prefers the word “serious” to “important” because of the ambiguity of the latter. Perhaps he is wise.) He suggests that our criterion of the “seriousness” of a mathematical theorem lies in the significance of the mathematical ideas which it connects. “We may say, roughly, that a mathematical idea is significant if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself, and even in other sciences” (p. 29). Chess problems, on the other hand, though intricate and ingenious, have no linkages beyond themselves. Another criterion of seriousness is that of “depth,” an elusive notion to define, but which has something to do with the way in which the idea reaches to a more complex level of thought. Thus, the idea of an irrational is “deeper” than that of an integer (p. 50).

My attention was called to this passage by my friend Miss R. M. Wrong after this paper had been written.