Online research in philosophy

Understanding Wittgenstein's Tractatus is essential reading for anyone wishing to further their insight into one of the most influential works of twentieth ...

The philosophy of arithmetic of Wittgenstein's Tractatus is outlined and the central role played in it by the general notion of operation is pointed out. Following which, the language, the axioms and the rules of a formal theory of operations, extracted from the Tractatus, are presented and a theorem of interpretability of the equational fragment of Peano's Arithmetic into such a formal theory is proven.

Wittgenstein played a vital role in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, Pasquale Frascolla examines the three phases of Wittgenstein's reflections on mathematics, considering them as a progressive whole rather than as separate entities. Frascolla discusses the development of Wittgenstein's views on mathematics from the Tractatus up to 1944. He looks at the presentation of arithmetic in the theory of logical operations, the presence of a strong verificationist orientation and the (...) rule-following considerations in Wittgenstein's writings. Frascolla identifies a unifying key--a "quasi-formalism"--to the development of Wittgenstein's reflections on mathematics. (shrink)