Abstract
This article is a philosophical study of mathematical proof and provability. In contrast with the prevailing tradition in philosophy of mathematics, we will not so much focus on “proof” in the sense of proof theory but rather on “proof” in its original intuitive meaning in mathematical practice, that is, understood as “a sequence of thoughts convincing a sound mind” as Gödel (1953, p. 341) expressed it. Call provability in the former sense formal provability and provability in the latter sense informal provability.Soour aim is to investigate informal provability, both conceptually and extensionally. However, our main method of doing so will be, on the one hand, to demarcate informal provability from formal provability, and on the other hand, to study informal provability by formal means. Moreover, the whole investigation will be carried out in a somewhat restricted setting: our primary focus will be on informal provability in pure mathematics rather than in applied mathematics, and within pure mathematics we will concentrate just on informal provability in the more mundane areas of mathematics, such as number theory and analysis, rather than in the more foundational areas.1 Furthermore, we will only deal with informal proofs as far as their justificatory role in mathematics is concerned, disregarding other roles that proofs can have (see Auslander (2008) on other roles; see Detlefsen (2008) for a general discussion on the significance of proofs in mathematics and of a variety of different methods of proof).
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© 2009 Hannes Leitgeb
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Leitgeb, H. (2009). On Formal and Informal Provability. In: Bueno, O., Linnebo, Ø. (eds) New Waves in Philosophy of Mathematics. New Waves in Philosophy. Palgrave Macmillan, London. https://doi.org/10.1057/9780230245198_13
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DOI: https://doi.org/10.1057/9780230245198_13
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