gingerly
发表于 2025-3-21 19:03:36
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PRE
发表于 2025-3-21 21:22:10
What Do We Want a Foundation to Do?ious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational.
讨人喜欢
发表于 2025-3-22 02:44:14
Book 2019undations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives..The volume i
CORD
发表于 2025-3-22 04:53:04
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JAMB
发表于 2025-3-22 09:37:00
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鞭打
发表于 2025-3-22 13:37:24
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酷热
发表于 2025-3-22 17:49:53
Proving Theorems from Reflectionthe axioms of set theory, but are of a less ‘problematic’ nature, as they can be solved by adopting the right axiomatic framework. We contend that any foundations for mathematics should be able to simply formulate such questions as well as to raise at least the theoretical hope for their resolution.
coagulation
发表于 2025-3-23 00:47:28
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Ordnance
发表于 2025-3-23 03:23:32
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一条卷发
发表于 2025-3-23 06:03:01
Univalent Foundations and the UniMath Libraryf formalized mathematics implementing the ideas of the Univalent Foundations (Sect. 8.1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (Sect. 8.2). This leads us to a general discussion about the links between architecture and mathematics where