Preproceedings 2006 - Austrian Ludwig Wittgenstein Society

and language arise after mathematics and the
mathematical systems do not depend on logic. Thus, on
the one hand, the mathematics do not depend on logic, on
the other, logic is applied mathematics.
Parts of mathematical practice are a product of the
cognitive “make up” and in those parts where our
idealizations exist laid the possibilities of antinomies,
paradoxes and illusions.
Just as traditional rationalistic metaphysics existed,
so the parts of mathematical practice that cannot be
constructively justified actually do exist. Sometimes their
distinction cannot be described in terms of usual (but
transitory) oppositions between the “classical” and the
“constructive”.
Humans are bound to project their knowledge
beyond their actual or even possible experience but there
is an intersubjective agreement in doing so, even if the
specific views that result from this are sometimes very
different.
About Wittgenstein’s mathematical epistemology - Olga Antonova / Sergei Soloviev
References
Bernays, Paul 1959-1960. Comments on Ludwig Wittgenstein,
Remarks on the Foundations of Mathematics, Ratio II.
Brouwer, L.E.J. 1948. : Consciousness, philosophy and
mathematics. 1 In Philosophy of mathematics. Selected readings.
Second edition. P. Benacerraf and H. Putnam (eds.). pp. 90-96
Dummett, Michael 1959 Wittgenstein’s Philosophy of Mathematics,
Philosophical Reviews, V. 68(3).
Glock, H.G. 1996 A Wittgenstein Dictionary. Oxford University
Press.
Heyting, Arendt 1974. Intuitionistic views on the nature of
mathematics. Synthese, 27. pp. 79-91.
Martin-Lof, Per 1996. On the meaning of the logical constants and
the justifications of the logical laws. Nordic Journal of Philosophical
Logic, Vol. 1, No. 1, pp. 11–60. Scandinavian University Press.
Stern, David 1995. Wittgenstein on Mind and Language. Oxford
University Press,
Wittgenstein, Ludwig 1922. Tractatus Logico-Philosophicus.
German text with an English translation by C.K. Ogden; with an
introduction by Bertrand Russell. Routledge and Kegan Paul,
London.
Wittgenstein, Ludwig 1953. Philosophical Investigations, G.E.M.
Anscombe and R. Rhees (eds.), G.E.M. Anscombe (trans.),
Oxford: Blackwell.
Wittgenstein, Ludwig 1956. Remarks on the Foundations of
Mathematics, G.H. von Wright, R. Rhees and G.E.M. Anscombe
(eds.), G.E.M. Anscombe (trans.), Oxford: Blackwell, revised
edition 1978.
(Significs 1989). Essays on Significs. Papers presented on the
occasion of the 150th anniversary of the birth of Victoria Lady
Welby (1837–1912) Edited by H. Walter Schmitz . Foundations of
Semiotics 23. 1989. xv, 313 pp.
19