Philosophia Mathematica

CARSON, EMILY

doi: N/Apmid: N/A

In her recent book, Realism in mathematics, Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails to explain the key issue faced by an epistemology for mathematics, namely the step from knowledge of the finite to knowledge of the infinite.

CARSON, EMILY

doi: 10.1093/philmat/4.1.3pmid: N/A

In her recent book, Realism in mathematics, Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails to explain the key issue faced by an epistemology for mathematics, namely the step from knowledge of the finite to knowledge of the infinite.

CORTOIS, PAUL

doi: N/Apmid: N/A

In this expository article one of the contributions of Jean Cavailles to the philosophy of mathematics is presented: the analysis of ‘mathematical experience’. The place of Cavailles on the logico-philosophical scene of the 30s and 40s is sketched. I propose a partial interpretation of Cavailles's epistemological program of so-called ‘conceptual dialectics’: mathematical holism, duality principles, the notion of formal contents, and the specific temporal structure of conceptual dynamics. The structure of mathematical abstraction is analysed in terms of its complementary dimensions: paradigmatic generalization (domain extension, descriptive definitions, creative role of the symbolism…) and thematic reflexivity of concepts (promotion of operations to objects of a higher type).

CORTOIS, PAUL

doi: 10.1093/philmat/4.1.18pmid: N/A

In this expository article one of the contributions of Jean Cavailles to the philosophy of mathematics is presented: the analysis of ‘mathematical experience’. The place of Cavailles on the logico-philosophical scene of the 30s and 40s is sketched. I propose a partial interpretation of Cavailles's epistemological program of so-called ‘conceptual dialectics’: mathematical holism, duality principles, the notion of formal contents, and the specific temporal structure of conceptual dynamics. The structure of mathematical abstraction is analysed in terms of its complementary dimensions: paradigmatic generalization (domain extension, descriptive definitions, creative role of the symbolism…) and thematic reflexivity of concepts (promotion of operations to objects of a higher type).

POLLARD, STEPHEN

doi: N/Apmid: N/A

This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).

POLLARD, STEPHEN

doi: 10.1093/philmat/4.1.42pmid: N/A

This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).

RUSNOCK, PAUL

doi: N/Apmid: N/A

RUSNOCK, PAUL

doi: 10.1093/philmat/4.1.59pmid: N/A

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LINSKY, BERNARD

doi: 10.1093/philmat/4.1.73pmid: N/A

Article PDF first page preview Close This content is only available as a PDF. © Oxford University Press

LINSKY, BERNARD

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