The Principles of Mathematics (1903)

§ 477

Truth values and Judgment. The problem discussed under this head is the same as the one raised[115] in § 52, concerning the difference between asserted and unasserted propositions. But Frege's position on this question ismore subtle than mine, and involves a more radical analysis of judgment. His Begriffschrift, owing to the absence of the distinction between meaning and indication, has a simpler theory than his later works. I shall therefore omit it from the discussions.(§ 477 ¶ 1)

There are, we are told (Gg. p. x), three elements in judgment: (1) the recognition of truth, (2) the Gedanke, (3) the truth-value (Wahrheitswerth). Here the Gedanke is what I have called an unasserted proposition--or rather, what I called by this name covers both the Gedanke alone and the Gedanke together with its truth-value. It will be well to have names for these two distinct notions; I shall call the Gedanke alone a propositional concept; the truth-value of a Gedanke I shall call an assumption[116]. Formally at least, an assumption does not require that its content should be a propositional concept: whatever x may be, the truth of x is a definite notion. This means the true if x is true, and if x is false or not a proposition it means the false (FuB. p. 21). In like manner, according to Frege, there is the falsehood of x; these are not assertions and negations of propositions, but only assertions of truth or of falsity, i.e. negation belongs to what is asserted, and is not the opposite of assertion[117]. Thus we have first a propositional concept, next its truth or falsity as the case may be, and finally the assertion of its truth or falsity. Thus in a hypothetical judgment, we have a relation, not of two judgments, but of two propositional concepts (SuB. p. 43).(§ 477 ¶ 2)

This theory is connected in a very curious way with the theory of meaning and indication. It is held that every assumption indicates the true or the false (which are called truth-values), while it meansthe corresponding propositional concept. The assumption 22 = 4 indicates the true, we are told, just as 22 indicates 4[118] (FuB. p. 13; SuB. p. 32). In a dependent clause, or where a name occurs (such as Odysseus) which indicates nothing, a sentence may have no indication. But when a sentence has a truth-value, this is its indication. Thus every assertive sentence (Behauptungssatz) is a proper name, which indicates the true or the false (SuB. pp. 32-4; Gg. p. 7). The sign of a judgment (Urtheilstrich) does not combine with other signs to denote an object; a judgment indicates nothing, but asserts something. Frege has a special symbol for judgment, which is something distinct from and additional to the truth-value of a propositional concept (Gg. pp. 9-10).(§ 477 ¶ 3)

§ 477 n. 1. This is the logical side of the problem of Annahmen, raised by Meinong in his able work on the subject, Leipzig, 1902. The logical, though not the psychological, part of Meinong's work appears to have been completely anticipated by Frege.

§ 477 n. 2. Frege, like Meinong, calls this an Annahme: FuB. p. 21.

§ 477 n. 3. Gg. p. 10. Cf. also Bs. p. 4.

§ 477 n. 4. When a term which indicates is itself to be spoken of, as opposed to what it indicates, Frege uses inverted commas. Cf. § 56.