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)