3.11 We use the physically perceptible token (audible or written, etc.) of the proposition as a projection of a possible state of things.
The method of projection is the thinking of the proposition’s sense.
This is tricky and important. How do we use sentences (sensibly perceptible representatives of propositions) as projections (representations?) of possible states of things? A possible state of things is a state of affairs. A proposition is a picture of a state of affairs. A sentence is a physical version of a proposition, i.e. (I suppose) a proposition with additional, physical characteristics. Since this is the form in which (it seems) we must deal with propositions, we could identify the two, but the proposition is the sentence conceived under the aspect of logic. Its external features (font, language, etc.) are irrelevant. Perhaps this is where the earlier talk of “external properties” of objects comes in. If objects are quasi-fictional ‘entities’ that we get by analyzing propositions, and we only ever encounter propositions in a form where they have external properties, then perhaps one might talk of the external properties of objects. To do so would surely be at best misleading though, since to think of a sentence as a proposition is precisely to think of it without its external properties, or not to think of those properties, or to think of it as if they were irrelevant.
Anyway, the first sentence of 3.11 seems to say no more than that we use sentences in place of (or as) propositions. The second equates doing this with thinking (of) the sense of the proposition. If thinking means doing something with (or having) a thought (as this term has been used and understood up to now) then this cannot be a psychological matter. But Wittgenstein could be using das Denken (“the thinking”) to mean something other than the thought (der Gedanke). So let’s not jump the gun. If thinking in a psychological (metaphysical, not logical) sense is a method for using sentences to get at or convey propositions, then 3.11 tells us that sentences get hooked up to propositions by means of a psychological act. There are multiple problems with this idea. Some have to do with Wittgenstein’s Fregean opposition to psychologism. But perhaps saying so begs the question. More obviously, the theory under consideration is massively implausible. If I use a sentence to convey a thought to another, how does that person know what I’m thinking? Language use (i.e. successful language use) would seem to not only require but be a kind of telepathy. Surely Wittgenstein cannot have meant this.
The other way to take the second sentence of 3.11 is as an equation or definition: thinking of the proposition’s sense is (means, equals) using the sentence that expresses or corresponds to it. What I say or write, I also (thereby) think. This seems to make insincerity impossible, but it does not do so if “thinking” is simply being (re-)defined in this way.
Anscombe says (p. 69, note 1) that “Wittgenstein’s use of ‘projection’ is a metaphorical extension of the mathematical use, which may be explained thus: ‘The drawing of straight lines through every point of a given figure, so as to produce a new figure each point of which corresponds to a point of the original figure.’”