Mathematics Without Numbers
E490369
Mathematics Without Numbers is a philosophical work by Geoffrey Hellman that develops a version of structuralism in the philosophy of mathematics using modal logic instead of traditional set-theoretic foundations.
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf | book ⓘ |
| addresses |
nature of mathematical objects
ⓘ
ontological commitment in mathematics ⓘ role of possibility and necessity in mathematics ⓘ |
| approach | modal-structuralism ⓘ |
| argues | mathematics can be formulated without quantifying over abstract entities ⓘ |
| author | Geoffrey Hellman NERFINISHED ⓘ |
| contrastsWith | set-theoretic foundations ⓘ |
| develops | axiomatic treatments of mathematical theories in modal form ⓘ |
| examines | consistency and possibility of mathematical structures ⓘ |
| field |
logic
ⓘ
philosophy ⓘ |
| framework | second-order modal logic ⓘ |
| hasPhilosophicalStance | anti-platonism (in form of modal structuralism) ⓘ |
| influenced | later work on modal structuralism ⓘ |
| influencedBy | structuralism in mathematics ⓘ |
| isDiscussedIn |
literature on nominalism in mathematics
ⓘ
literature on structuralism in mathematics ⓘ |
| isUsedAsExampleIn | studies of modal approaches to mathematics ⓘ |
| language | English ⓘ |
| mainTopic |
foundations of mathematics
ⓘ
mathematical structuralism ⓘ modal logic ⓘ philosophy of mathematics ⓘ |
| positionOnMathematicalObjects |
nominalist-friendly
ⓘ
structuralist ⓘ |
| proposes | structuralism without commitment to abstract objects ⓘ |
| relatedTo |
model theory
ⓘ
ontology of mathematics ⓘ philosophical logic ⓘ |
| seeksToAvoid | commitment to sets as fundamental entities ⓘ |
| seeksToProvide | alternative foundations for mathematics ⓘ |
| subjectOf | debates on nominalism in mathematics ⓘ |
| uses | modal logic ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.