4.063 A picture to explain the concept of truth: a black spot on white paper; one can describe the form of the spot in that one can answer for each point on the sheet whether it is white or black. To the fact that a point is black corresponds a positive fact, to the fact that a point is white (not black), a negative one. If I indicate a point on the sheet (a Fregean truth-value) then this corresponds to the assumption that is proposed for judgment, etc. etc.
In order though to be able to say whether a point be black or white, I must first know when one calls a point black and when one calls it white; in order to be able to say “p” is true (or false), I must have determined under which conditions I call “p” true, and thus I determine the sense of the proposition.
The point at which the simile breaks down now is this: we can indicate a point on the paper without knowing what white and black are; to a proposition without sense however nothing whatsoever corresponds, because it signifies no thing (truth-value) whose properties are called false or true; the verb of a proposition is not “is true” or “is false”—as Frege believed—but rather that which “is true” must already contain the verb.
Anscombe (note 1 on pp. 105-106) says that Wittgenstein’s reference to “the Fregean Annahme” (assumption) is really a reference to what Russell says about Frege in Principles of Mathematics Appendix A, §477. She argues that Russell and Wittgenstein get Frege (in “Function and Concept”) wrong, and mistakenly attribute to him a technical meaning of ‘assumption.’ Assumption in this sense means something like the assertion of a proposition as either true or false, so that the truth-value of the proposition can be thought of as a verb, meaning the checking of an imaginary box next to “is true” or “is false.” Anscombe notes that Frege did say that the verb of the proposition is “is true” in the Begriffsschrift, but he never said this of “is false” and he rejected this earlier view of his in “Sense and Reference.”
Anscombe pp. 152-153 notes that Wittgenstein’s talk of determining the conditions under which I call a proposition true sounds like verificationism to some people, but it is just a reference to truth-conditions. The emphasis is on logic, not epistemology.
Ostrow (p. 84): “What is important in the notion of the assumption for Wittgenstein is that it brings out how the possibility of saying something determinate about the world depends logically on a prior inner connection between language and reality, a form that is common to both. At the same time, a clear understanding of this idea makes evident that we have no holds on that form apart from our capacity to make true and false statements about the world.”
See comment on 4.442 for Proops on this. On pp. 40-42 he gives reasons for rejecting Anscombe’s account of what “verb” means for Wittgenstein/Frege here. Proops (p. 41, note 122) points to Begriffsschrift § 2 as a likely source of Wittgenstein’s belief that Frege’s assertion sign (|-) marks something as an assertion, when in fact, as Frege explains elsewhere, it is the vertical stroke that does this, the horizontal stroke merely marking a potentially assertable proposition, what Wittgenstein appears to be calling an assumption. Proops (pp. 50-57) notes that Wittgenstein links talk of the ‘assumption’ in his Notebooks (January 11th 1915, pp. 37-38) with a yardstick: “Could we not ask: What has to be added to that yardstick in order for it to assert something about the length of the object? (The yardstick without this addition would be the ‘assumption’ [Annahme].” A yardstick marks a certain length, as if in readiness for objects one yard long (Proops assumes, for the sake of argument, that it has no finer gradations marked), but does not actually say of its own accord that this or that object is one yard long. Similarly, an unasserted proposition marked only by a horizontal stroke stands, as it were, ready to be asserted as a proposition, but does not assert itself. We might then wonder what needs to be added to it to make it an assertion, an actual proposition rather than mere content. But this content must already have sense. I cannot even consider asserting something unless it is already a proposition. Proops (p. 56): “The Annahme is treated as the notational embodiment of the “showing” aspect of the proposition (picking out a situation while saying nothing about it), while the assertion sign is treated as embodying the proposition’s “truth-claiming” or “saying” aspect (saying of the possible situation thus picked out that it actually obtains). I have wanted to suggest that Wittgenstein’s critique of the assertion sign is best seen as part of an attack on the coherence of such a conception of the proposition.” See 4.022. Proops (p. 57): “In the end, then, the thought that a proposition cannot assert its own truth is best seen not as a direct criticism of any view that Frege or Russell actually hold, but as the denial of a crucial presupposition of the coherence of the notion of logical assertion.”
Marie McGinn (p. 50): “The judgement stroke is not itself a function, but it is only by placing the name of a truth-value in the context of a judgement stroke that we move from naming an object to expressing something with the bipolarity which Wittgenstein takes to be the defining feature of sense. This is what Wittgenstein means when he says that Frege believes the verb of a proposition is “is true” or “is false”: it is only when we assert, by means of the judgement stroke, that the proposition designates the True that we achieve something with the essential bipolarity of a proposition.”