Beschreibung
Abstract:Formalism in the philosophy of mathematics is, roughly put, the view that mathematics is purely syntactic in character and that semantic concepts are not relevant or reducible to purely syntactic ones. The focus in this talk will be on a particular version of formalism, namely instrumental formalism and its emphasis on “non-representational roles” of symbolic languages in mathematical reasoning. David Hilbert’s foundational work from the 1920s is usually viewed as a culmination point in the development of such a formalist position (Detlefsen 2005). Interestingly, both in Hilbert’s work as well as in and in related contributions to instrumental formalism, one can identify two relevant criteria of reliability for the use of formal languages or theories, namely (i) the consistency and (ii) the conservativity of sets of rules or axiom systems. The latter condition requires that a formal theory in use presents a conservative extension of an interpreted base theory. In Hilbert’s own proof theoretic work, this central but implicit assumption has been described as his “conservativity program” (cf. Zach 2004). The focus of this talk will be on Hilbert’s instrumental formalism, its mathematical roots, and its more general philosophical context. Specifically, following an exposition of Hilbert’s program, I will first survey different contributions to formalist thinking and to conservativity in nineteenth-century mathematics and discuss the impact of these results on Hilbert’s logical work. Secondly, I will investigate the more general “intellectual context” of Hilbert’s program (cf. Giaquinto 1983, Hallett 1900) and discuss how his results on the foundations of mathematics relate to forms of scientific instrumentalism and early contributions to the logic of science in Logical Empiricism.
| Zeitraum | 1 Dez. 2022 |
|---|---|
| Ereignistitel | APSE-CEU-IVC Talks: Philosophy Department of the Central European University, Institute Vienna Circle and Unit for Applied Philosophy of Science and Epistemology of the Department of Philosophy of the University of Vienna |
| Veranstaltungstyp | Sonstiges |
| Ort | ÖsterreichAuf Karte anzeigen |
| Bekanntheitsgrad | International |