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On Gödel’s philosophical assumptions. (English) Zbl 0935.01008

There are some similarities between K. Gödel and his admired hero G. W. Leibniz whose logic and metaphysics he appreciated. Regarding this relation between Gödel and Leibniz the author regards it as strange that Gödel never made use of an idea of Leibniz’s which the author labels as “one of his most central notions, perhaps the most important one”: the idea of a possible world (p. 13). On the contrary, Gödel followed a ‘one-world assumption’ according to which “all that can properly be said to exist must exist somewhere in the actual world and […] therefore all we can meaningfully speak about must in analysis be denizens of the actual world” (p. 14). Given this background the author discusses Gödel’s special (‘actualistic’) type of Platonism, his functional interpretation of first-order number theory, Gödel’s own interpretation of his incompleteness theorem (‘deductive incompleteness’), the completeness proof for first-order logic, the nature of abstract entities as compared to physical objects, and the notion of mathematical intuition.

MSC:

01A60 History of mathematics in the 20th century
03-03 History of mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations

Biographic References:

Gödel, K.
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