6533b835fe1ef96bd129e900
RESEARCH PRODUCT
Realism, metamathematics, and the unpublished essays
Francisco Rodríguez-consuegrasubject
Philosophy of mathematicsPhilosophyMetamathematicsGödelGödel's completeness theoremGödel's incompleteness theoremsPhilosophical realismcomputerRealismEpistemologyExposition (narrative)computer.programming_languagedescription
This initial chapter is divided into two sections. The first is devoted to a brief exposition of the intuitive essence and the philosophical motivation of Godel’s main metamathematical results, namely his completeness theorem for elementary logic (1930) and his incompleteness theorems for arithmetic (1931). Thereafter some discussion of the different ways to confront the relationship between those results and Godel’s philosophical realism in logic and mathematics is offered. Thus, mathematical realism will be successively regarded as (i) a philosophical consequence of those results; (ii) a heuristic principle which leads to them; (iii) a philosophical hypothesis which is “verified” by them. In the second section Godel’s philosophy of mathematics, such as it can be derived from his published writings, is briefly expounded upon. Then the final version of his essay on Carnap is summed up, in order to see how his unpublished philosophical ideas might throw some light on Godel’s published doctrines. Finally, other relevant ideas and authors are briefly surveyed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-01-01 |