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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Mathematics Without Numbers canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5063603 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mathematics Without Numbers Context triple: [Geoffrey Hellman, notableWork, Mathematics Without Numbers]
-
A.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
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B.
Ontological Reduction and the World of Numbers
"Ontological Reduction and the World of Numbers" is a philosophical essay by W.V.O. Quine that examines how mathematical entities, particularly numbers, can be understood and justified within a naturalistic and ontologically parsimonious framework.
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C.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
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D.
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics is a philosophical and foundational study in which Friedrich Waismann analyzes how mathematical concepts are formed, clarified, and used in modern mathematics.
-
E.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a landmark 1960 essay by physicist Eugene Wigner that explores why abstract mathematics so powerfully and mysteriously describes physical reality.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mathematics Without Numbers Target entity description: 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.
-
A.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
-
B.
Ontological Reduction and the World of Numbers
"Ontological Reduction and the World of Numbers" is a philosophical essay by W.V.O. Quine that examines how mathematical entities, particularly numbers, can be understood and justified within a naturalistic and ontologically parsimonious framework.
-
C.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
D.
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics is a philosophical and foundational study in which Friedrich Waismann analyzes how mathematical concepts are formed, clarified, and used in modern mathematics.
-
E.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a landmark 1960 essay by physicist Eugene Wigner that explores why abstract mathematics so powerfully and mysteriously describes physical reality.
- F. None of above. chosen
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 ⓘ |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Mathematics Without Numbers Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.