## Notes to Wittgenstein's Philosophy of Mathematics

1. In his posthumously
published (1953*, 334-335), Kurt Gödel says that the
“syntactical viewpoint,” “a combination of
nominalism and conventionalism,” was developed “[a]round
1930” by “R. Carnap, H. Hahn, and M. Schlick, largely
under the influence of L. Wittgenstein” (i.e.,
“*Wittgenstein 1922*”).

2. Defenders of the Logicist
interpretation of the *Tractatus* also ignore Wittgenstein's
expressed contempt for Russell's Second edition of *Principia
Mathematica* (McGuinness and von Wright, 1995*, 186: Letter from
F. Ramsey to his mother, Sept. 20, 1923) and his disdain for, and
criticism of, Ramsey's defence of Logicism in “The Foundations
of Mathematics” [see the Waismann version of Wittgenstein's 1927
letter to Ramsey (*WVC* 189, Footnote #1)].

3. I would like to thank Dr. Timothy Pope (University of Lethbridge) for the translations that appear here. Any errors in the translations are entirely my responsibility.

4. Wittgenstein probably
adapted this example (beginning in 1929 at (*PR* §132) and
(*WVC* 71)), which he articulates in various similar ways, from
Brouwer, who first stated similar ‘propositions’ in his
(1908, 110); see §2.4 above.