By Felix Kaufmann (auth.), Brian McGuinness (eds.)
ISBN-10: 9027708487
ISBN-13: 9789027708489
ISBN-10: 9400997957
ISBN-13: 9789400997950
The major merchandise within the current quantity was once released in 1930 lower than the identify Das Unendliche in der Mathematik und seine Ausschaltung. It was once at the moment the fullest systematic account from the perspective of Husserl's phenomenology of what's often called 'finitism' (also as 'intuitionism' and 'constructivism') in arithmetic. due to the fact that then, very important adjustments were required in philosophies of arithmetic, partially as a result of Kurt Godel's epoch-making paper of 1931 which validated the basic in completeness of mathematics. within the mild of that discovering, some of the claims made within the publication (and within the accompanying articles) are demon strably incorrect. however, as a complete it keeps a lot of its unique curiosity and cost. It offers the problems within the foundations of arithmetic that have been below debate while it was once written (and on occasion nonetheless are); , and it bargains one replacement to the at the moment dominant set-theoretical definitions of the cardinal numbers and different arithmetical strategies. whereas nonetheless a scholar on the college of Vienna, Felix Kaufmann was once vastly inspired by way of the early philosophical writings (especially through the Logische Untersuchungen) of Edmund Husser!' He was once by no means an uncritical disciple of Husserl, and he built-in into his mature philosophy principles from a large collection of highbrow resources. yet he considered himself as a phenomenologist, and made common use in all his significant courses of a lot of Husserl's logical and epistemological theses.
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Extra resources for The Infinite in Mathematics: Logico-mathematical writings
Sample text
Without using the thesis that logic is a matter of truth connections, one might try to justify the view just stated by saying that the proposition 'p and not-p' asserts everything so that everything is derivable from it. However, this would not hold water: for a contradiction asserts nothing at all, it offends against sense. In general we may say that the concept of implication stipulated in the terminology of symbolic logic merges in a misleading manner specifically logical implication with empirical 'implication'.
For what follows the most important application of this insight is the observation that the sign of equality in mathematics relates not to the mathematical objects (numbers) themselves, but to mathematical symbols. 44 If by way of conclusion and summary, we are to specify the relation between logic and the world, we can say that while logic says nothing about the world, it presupposes the world. 45 For as we have seen, logical concepts constitute the schemata for describing the world. Moreover, the analysis of connections between the meanings of statements, which is a main theme of logic, presupposes an existence which as object of these statements constitutes their meaning.
T. p. 286]. , p. T. p. 287]. 2. Cf. Wittgenstein, Tractatus Logico-Philosophicus, with an introduction by Bertrand Russell, 1922 London (English-German); p. ] A detailed account and analysis of Wittgenstein's doctrine will be given in a book by F. Waismann, Logik, Sprache, Philosophie, to be pubhshed shortly in the collection Schriften zur wissellschaftlichell WeltaujjassulIg, Springer, Vienna. ] .. Cf. Section II, note 16. 27 The extensionality thesis goes back to Wittgenstein and, following him, was maintained above all by F.
The Infinite in Mathematics: Logico-mathematical writings by Felix Kaufmann (auth.), Brian McGuinness (eds.)
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