Colomina-Alminana, Juan (2026) Extensionalism without Logicism: Ambrose and Extensional Logic. [Preprint]

Text Between Extension and Infinity. with author info.pdf Download (389kB)

Abstract

Drawing primarily on her early work (1931-1934), I argue that Alice Ambrose’s
philosophical project at the time centers on preserving the rigor of extensional logic while rejecting
the metaphysical and epistemological endorsements of logicism because of its commitment to the
notion of material infinity. Positioning Ambrose as a transitional figure between Russell’s
formalism and the constructivist turn represented by Brouwer’s and Weyl’s intuitionism, I
demonstrate how Ambrose offers a clever practice‑oriented statement of finitist extensionalism.
Employing only extensional methods—considering classes, relations, and propositions by
reference to their members and truth-values instead of mental processes—, Ambrose reformulates
an existential claim about π as an explicit infinite disjunction of concrete instances insisting,
against intensional projects, that such claims gain meaning only through a finite stopping rule that
produces a witness.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Colomina-Alminana, Juan j.colomina-alminana@northeastern.edu 0000-0002-0518-5361
Keywords:	Extensionalism, Finitism, Witness, First-Order logic, Intuitionism, Logicism, Metalogic
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics
Depositing User:	Juan Colomina-Alminana
Date Deposited:	06 Jun 2026 16:23
Last Modified:	06 Jun 2026 16:23
Item ID:	29708
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics
Date:	January 2026
URI:	https://philsci-archive.pitt.edu/id/eprint/29708

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item