Whether or not it is ultimately defensible and this is an absolutely crucial question for Wittgenstein's Philosophy of Mathematics this strongly counter-intuitive aspect of Wittgenstein's account of algorithmic decidability, proof, and the sense of a mathematical proposition is a piece with his rejection of predeterminacy in mathematics.
Wittgenstein's second reason for rejecting an undecidable mathematical proposition is that it is a contradiction-in-terms.
If a genuine mathematical proposition is undecided, the Law of the Excluded Middle holds in the sense that we know that we will prove or refute the proposition by applying an applicable decision procedure (PG 379, 387).
Given linguistic and symbolic conventions, the truth-value of a contingent proposition is entirely a function of how the world is, whereas the "truth-value" of a mathematical proposition is entirely a function of its constituent symbols and the formal system of which it is a part.
Philosophers have a tendency to step outside the framework of mathematics and ask "from the outside" whether mathematical objects really exist and whether mathematical propositions are really true.
In particular, if there are undecidable mathematical propositions (as Brouwer maintains), then at least some mathematical propositions are not propositions of any existent mathematical calculus.
Second, "there do not exist any mathematical objects or facts," and therefore mathematical propositions are void of content.
"The concepts of infinite decimals in mathematical propositions are not concepts of series," says Wittgenstein (RFM V, §19), "but of the unlimited technique of expansion of series".
Thus, from the Tractatus to at least 1944, Wittgenstein maintains that "mathematical propositions" are not real propositions and that "mathematical truth" is essentially non-referential and purely syntactical in nature.
Normative ethical conclusions are justified through first-order ethical reflection and argument, just as mathematical propositions are justified through mathematical reasoning, rather than through learning more about our evolutionary past or about what is happening in our brains when we engage in these forms of reasoning (Rachels, 1990).
