Abstract
I want to start by giving some quotes from Wittgenstein. It is part of his conception of what the foundations of Mathematics are about, a conception which many people have found peculiar and one of my defects is that I am not able to find it peculiar anymore, but find it perfectly sensible.
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Ludwig Wittgenstein, Remarks on the Foundations of Mathematics, revised edition, edited by G.H. von Wright, R. Rhees and G.E.M. Anscombe, Cambridge, Mass, the MIT Press, 1983.
Saul Kripke, Wittgenstein on Rules and Private Language Cambridge, Mass, Harvard University Press, 1982.
Ludwig Wittgenstein, Lectures on the Foundations of Mathematics, edited by Cora Diamond, Cambridge, Mass, Harvard University Press, 1980.
Juliet Floyd, “On Saying What You Really Want to Say: Wittgenstein, Gödel and the Trisection of the Angle” in J. Hintikka, editor, The Foundations of Mathematics in the Early Twentieth Century, Boston Studies in the Philosophy of Science, Reidel 1995.
Georg Kreisel, “review of Wittgenstein’s Remarks on the Foundations of Mathematics”, British Journal for the Philosopy of Science 9 (1958) pp. 135–158.
Michael Dummett, “Wittgenstein’s Philosophy of Mathematics”, in Truth and Other Dilemmas, Cambridge, Mass, Harvard University Press, 1980, pp. 248–268.
Ludwig Wittgenstein, Philosophical Investigations, translated by G.E.M Anscombe, Oxford, Basil Blackwell, 1953.
Alfred Tarski, “On Some Fundamental Concepts of Metamathematics”, Logic,Semantics, Metamathematics, edited by John Corcoran, Indianapolis, Indiana, Hackett publishing company, 1983, pp. 30–37.
Rohit Parikh, “Monotonic and Non-monotonic Logics of Knowledge”, in Funda-mentaInformatica special issue, Logics for Artificial Intelligence vol XV (1991) pp. 255–274.
Michael Dummett, “Wang’s Paradox”, in Truth and Other Dilemmas, Cambridge, Mass, Harvard University Press, 1980, pp. 248–268.
Rohit Parikh, “Existence and Feasibility in Arithmetic”, Jour Symbolic Logic 36 (1971) 494–508.
Rohit Parikh, “Vagueness and Utility: the Semantics of Common Nouns”, in Linguistics and Philosophy 17, 1994, pp.521–535.
W, is a little like a space of senses as in Frege.
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Parikh, R. (1995). How Far Can We Formalize Language Games?. In: Depauli-Schimanovich, W., Köhler, E., Stadler, F. (eds) The Foundational Debate. Vienna Circle Institute Yearbook [1995], vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3327-4_7
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