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Is there a “Hilbert thesis”? (English) Zbl 1428.03021
The paper is devoted to the so called Hilbert thesis stating that – as J. Barwise put it – “The informal notion of provable used in mathematics is made precise by the formal notion provable in first-order logic”. Different variations of this thesis are discussed. The author also considers whether the very name “Hilbert thesis” is justified. The thesis is compared with Church’s thesis concerning computability. The problem of the possibility of providing arguments towards the considered thesis is discussed.

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