Ontological Reduction and the World of Numbers
E319088
"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ontological Reduction and the World of Numbers canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2996817 — 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: Ontological Reduction and the World of Numbers Context triple: [Ontological Relativity and Other Essays, hasPart, Ontological Reduction and the World of Numbers]
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A.
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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B.
The Logical Structure of the World
The Logical Structure of the World is Rudolf Carnap’s seminal 1928 work in which he develops a rigorous, formal reconstruction of all scientific concepts from a phenomenalist basis, serving as a foundational text of logical positivism.
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C.
Philosophy of Mathematics and Natural Science
Philosophy of Mathematics and Natural Science is a seminal work by Hermann Weyl that explores the conceptual foundations and philosophical implications of modern mathematics and theoretical physics.
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D.
The Logical Basis of Metaphysics
The Logical Basis of Metaphysics is a major philosophical work by Michael Dummett that develops his influential views on realism, anti-realism, and the role of language in metaphysical debates.
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E.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
- 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: Ontological Reduction and the World of Numbers Target entity description: "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.
-
A.
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.
-
B.
The Logical Structure of the World
The Logical Structure of the World is Rudolf Carnap’s seminal 1928 work in which he develops a rigorous, formal reconstruction of all scientific concepts from a phenomenalist basis, serving as a foundational text of logical positivism.
-
C.
Philosophy of Mathematics and Natural Science
Philosophy of Mathematics and Natural Science is a seminal work by Hermann Weyl that explores the conceptual foundations and philosophical implications of modern mathematics and theoretical physics.
-
D.
The Logical Basis of Metaphysics
The Logical Basis of Metaphysics is a major philosophical work by Michael Dummett that develops his influential views on realism, anti-realism, and the role of language in metaphysical debates.
-
E.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
academic article
ⓘ
philosophical essay ⓘ |
| addresses |
how to justify belief in numbers
ⓘ
reduction of talk about numbers to talk about concrete entities or structures ⓘ the role of quantification over abstract objects ⓘ |
| arguesFor |
accepting mathematical entities only as required by best scientific theory
ⓘ
compatibility of mathematics with scientific naturalism ⓘ ontologically parsimonious treatment of mathematical entities ⓘ |
| author |
W. V. O. Quine
ⓘ
linked to:
Willard Van Orman Quine
Willard Van Orman Quine ⓘ |
| contributesTo |
Quinean program of naturalized ontology
ⓘ
debate on existence of abstract objects ⓘ methodology of ontological reduction in philosophy ⓘ |
| examines |
criteria for ontological commitment in mathematics
ⓘ
how mathematical entities can be accommodated in a naturalistic worldview ⓘ status of numbers as abstract objects ⓘ ways to reduce or reinterpret reference to numbers ⓘ |
| focusesOn |
justification of mathematical ontology
ⓘ
ontological reduction ⓘ relationship between mathematics and empirical science ⓘ |
| hasPhilosophicalDomain |
analytic philosophy
ⓘ
logic and foundations of mathematics ⓘ metaphysics ⓘ |
| language | English ⓘ |
| mainTopic |
mathematical entities
ⓘ
naturalism ⓘ numbers ⓘ ontological parsimony ⓘ ontology ⓘ philosophy of mathematics ⓘ |
| philosophicalApproach |
Quinean naturalism
ⓘ
ontological commitment ⓘ ontological reductionism ⓘ |
| relatedTo |
Quine’s criterion of ontological commitment
ⓘ
indispensability argument for mathematics ⓘ nominalism ⓘ ontological relativity ⓘ platonism about numbers ⓘ |
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: Ontological Reduction and the World of Numbers Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Ontological Relativity and Other Essays
→
hasPart
→
Ontological Reduction and the World of Numbers
ⓘ