¹ In preparing this paper for publication, I owe much to the criticism of my friend Mr. Lawrence Kagan.

² This was my belief two years ago. My present belief involves a change but it is not essential to the main thesis. Undefinable“ was used loosely. For in one important sense of ”definition,“ clearly no term is intrinsically undefinable: definability is a systematic question. I was thinking of traditional definition per genus et differentiam. In this sense, perhaps, there are terms which are undefinable—those terms which are not species of wider genera, the widest terms. But I am not even sure of this.

³ Cf. Dewey, Quest for Certainty, p. 137.

⁴ By Ernest Nagel in Lecture.

⁵ No one has called Mr. Wittgenstein the Mystery Man of Modern Philosophy. I have no explanation to offer for this.

⁶ Wittgenstein: Tractatus 4.0312, 4.041, 4.12; Wisdom: “Logical Constructions;” Stebbing: Mod. Introd. Log., p. 127; Russell: passim. Mr. Wittgenstein however is not always consistent. See his article on “Logical Form” in the Proceedings of the Aristotelian Society, Supplem., Vol. IX.

⁷ See Mr. Ryle's very lucid paper in the Proc. Arist. Society, Vol. 30, called “Are There Propositions?” Mr. Ryle decides that there aren't any propositions. If we accept this analysis our task may be considerably simplified. For it would then be easy to demonstrate that all propositions are isomorphic with the facts represented, since, as all students of the class algebra know, the null class is included in any class. And so we might end here. The proof is rigorous but I feel that the reader may not be entirely satisfied. I shall go on.

⁸ Stebbing: Mod. Introd. Log., Ch. IV & P. 115; Cohen & Nagel: ILSM, Ch. II; Eaton: General Log., Part I; Mace: Principles of Logic, Ch. III. I do not discuss Mr. Mace's theory or the proposition as the “objective factor in the judgment,” since Mr. Mace says that he is oversimplifying the matter and indicates that he might accept the interpretation of the proposition as a logical construction.

⁹ Eaton, op. cit., p. 12; Stebbing, p. 32 & p. 115; Cohen & Nagel, pp. 27 & 28. See Ryle, op. cit., pp. 100 & 101.

¹⁰ Eaton, p. 22; See Ryle, pp. 92–96. The theory of course is not modern. It goes back to Plato.

¹¹ Dr. Nagel seems to advance a slightly different theory also, on pp. 28 & 29 of I.L.S.M. “For propositions are at most only the abstract and selected relations between things. When we affirm or deny the proposition THE MOON IS NEARER TO THE EARTH THAN THE SUN, neither the moon alone, nor the earth, nor the sun, nor the spatial distance between them is the proposition. The proposition is the relation asserted to hold between them.” On this view the proposition is equated with what W. E. Johnson calls the “Tie” of the fact. How this can be said to represent the fact or be true or false, I don't know. And I don't see how it is compatible with Dr. Nagel's views as stated recently in “Verifiability, Truth, and Verification,” Jl. of Philos., vol. 31, p. 142: “When true, a proposition states relations between processes, but never is them.”

¹² Symbolism and Truth, Ch. V.

¹³ Collected Papers, Vol. 2, Bk. II.

¹⁴ Nagel: “Peirce's Guesses at the Riddle.” Jl. of Philos., Vol. 30, p. 375.

¹⁵ A more complete analysis of proposition requires the concept of “meaning.” This concept is developed in connection with “fact.” And the analysis of proposition is completed in Part III.

¹⁶ If a R b, R is the component.

¹⁷ Eaton: Gen. Logic, page 58. Eaton says “every proposition.” As the title of this section makes clear, I offer here an analysis only of atomic propositional form.“ Most of the logicians cited have not been clear on this point. Witness the passages quoted.

¹⁸ Eaton: Gen. Logic, page 58, and Russell: Knowledge of Ext. World, page 54. For a fuller presentation of this view see the works mentioned. Also Stebbing: Modern Introduction to Logic, page 126.

¹⁹ I don't know why Russell does not employ his principle of abstraction here. The definition of propositional form as a class is clearly possible.

²⁰ Op. cit., p. 126.