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- W1531434842 abstract "English translation of Moritz Pasch,“Betrachtungen zur Begrundung der Mathematik,” Mathematische Zeitschrift 20 (1924), pp. 231–240. Pasch observes that one axiomatization can be more “natural” than another even if the two systems yield the same theorems. He illustrates this property of naturalness with some examples from geometry. He then considers the metamathematical resources David Hilbert will need to complete his program of consistency proofs and concludes that the Hilbert school will be unable to dispense with any part of the combinatorial theory from Pasch’ s paper “The Origin of the Concept of Number,” a theory at least as strong as Peano Arithmetic." @default.
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- W1531434842 date "2010-01-01" @default.
- W1531434842 modified "2023-09-26" @default.
- W1531434842 title "Reflections on the Proper Grounding of Mathematics II" @default.
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- W1531434842 doi "https://doi.org/10.1007/978-90-481-9416-2_14" @default.
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