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From foundations to applications: reverse mathematics and philosophy — arXiv:2609.25183

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.25183
License (as archived): CC0-1.0
Archived: 2026-10-08T16:34:13.003Z
SHA-256 of the archived text: d2776e6cc4cffe856387bc6ed40c2f983e4603c45d249e42e8bccd9c69c4d305
Stable URL of this page: https://metraipolis.com/documento/dc_2fb897e9ffdb

How to cite

From foundations to applications: reverse mathematics and philosophy — arXiv:2609.25183 — arXiv (en), https://arxiv.org/abs/2609.25183 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2fb897e9ffdb (Metraipolis archive dc_2fb897e9ffdb, sha256 d2776e6cc4cffe856387bc6ed40c2f983e4603c45d249e42e8bccd9c69c4d305)

BibTeX

@misc{dc2fb897e9ffdb,
  title = {From foundations to applications: reverse mathematics and philosophy — arXiv:2609.25183},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.25183},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2fb897e9ffdb; sha256 d2776e6cc4cffe856387bc6ed40c2f983e4603c45d249e42e8bccd9c69c4d305},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.25183. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Reverse mathematics is a branch of mathematical logic dedicated to determining the minimal set existence principles necessary and sufficient to derive ordinary mathematical theorems about concrete structures like the real line. Since the mid-1970s, reverse mathematics has developed a systematic classification of the strength of theorems in areas of mathematics ranging from real and complex analysis to infinitary combinatorics. This essay will place reverse mathematics in its historical and philosophical context, and reveal its relevance to central issues in the philosophy of mathematics, from the foundational programmes of Hilbert and Brouwer to contemporary debates about realism, determinacy, and applicability of mathematics. In doing so, it will discuss the role of computability theory in measuring the strength of set existence principles, as well as related questions about idealisation when these principles are applied in the physical sciences and in philosophy.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-23 in math.LO).
Categorie arXiv: History and Overview (math.HO) ; Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2609.25183 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T15:54:33.543Z dalla pagina https://arxiv.org/catchup/math.LO/2026-09-23?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).