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Biographical Notes: Friedrich Waismann
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[5. Biographical Notes.]

Friedrich Waismann.

The philosopher Friedrich Waismann (Vienna 1896 - Oxford, UK, 1959) studied mathematics and philosophy at Vienna. In 1929, he became an assistant to Schlick. He was one of the few members of the Vienna Circle admitted to the meetings with Wittgenstein. Waismann recorded several conversations which were published posthumously in F. Waismann, Wittgenstein und der Wiener Kreis, 1967 (English translation Wittgenstein and the Vienna Circle: Conversations Recorded by Friedrich Waismann, New York: Barnes & Noble Books, 1979). Waismann proposed a logical interpretation of probability inspired by Wittgenstein in his work "Logische Analyse des Wahrscheinlichkeitsbegriffs" (Erkenntnis, 1, 1930). In 1936 he published his only book Einführung in das mathematische Denken, about the philosophy of mathematics. He immigrated to England in 1937, where he taught philosophy of mathematics and philosophy of science at Cambridge and, from 1940, at Oxford. In England he contributed to the development of analytic philosophy. His book, The Principles of Linguistic Philosophy, Oxford, 1965, an exposition to the philosophy of the late Wittgenstein, was also posthumously published.
The only book he published during his life dealt with the interpretation of mathematics. Waismann criticized both Logicism and Formalism. Logicism argues that all mathematical truths are logical truths, and it is based on Frege and Russell’s definition of natural numbers, namely a natural number is the class of all equinumerable classes. According to Waismann, this definition introduces an element of contingency in mathematics, thus disturbing its a priori character. Moreover, formal logic is by no means a privileged calculus to which all mathematics is reducible. Logic itself is a part of mathematics. Waismann also rejected the formalistic interpretation, because it is not interested with the meaning of mathematical concepts. According to Formalism, a natural number is whatever fulfils the axioms of mathematics. But this approach neglects a very important problem, namely the question whether the axioms of mathematics identify the natural numbers we really employ. The solution consists in the study of the role that natural numbers play in ordinary language (note the evident analogy with Wittgenstein's assertion that meaning is use).

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