Frege’s Conception of Numbers as Objects
E927621
Frege’s Conception of Numbers as Objects is a major philosophical work by Crispin Wright that offers an influential interpretation and defense of Gottlob Frege’s view that numbers are abstract objects grounded in logic.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Frege's Conception of Numbers as Objects | 1 |
| Frege’s Conception of Numbers as Objects canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11477253 — 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: Frege’s Conception of Numbers as Objects Context triple: [Crispin Wright, notableWork, Frege’s Conception of Numbers as Objects]
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A.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
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B.
The Interpretation of Frege’s Philosophy
The Interpretation of Frege’s Philosophy is Michael Dummett’s influential book that offers a comprehensive and highly influential analysis of Gottlob Frege’s logical and philosophical thought, especially his philosophy of language and logic.
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C.
Hume’s Principle (derivable, not postulated)
Hume’s Principle (derivable, not postulated) is the numerical equivalence principle in Frege’s logical system that is obtained as a theorem rather than assumed as a foundational axiom.
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D.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
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E.
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.
- 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: Frege’s Conception of Numbers as Objects Target entity description: Frege’s Conception of Numbers as Objects is a major philosophical work by Crispin Wright that offers an influential interpretation and defense of Gottlob Frege’s view that numbers are abstract objects grounded in logic.
-
A.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
-
B.
The Interpretation of Frege’s Philosophy
The Interpretation of Frege’s Philosophy is Michael Dummett’s influential book that offers a comprehensive and highly influential analysis of Gottlob Frege’s logical and philosophical thought, especially his philosophy of language and logic.
-
C.
Hume’s Principle (derivable, not postulated)
Hume’s Principle (derivable, not postulated) is the numerical equivalence principle in Frege’s logical system that is obtained as a theorem rather than assumed as a foundational axiom.
-
D.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
-
E.
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.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
monograph
ⓘ
non-fiction book ⓘ philosophical book ⓘ |
| academicDiscipline |
logic
ⓘ
mathematics ⓘ philosophy ⓘ |
| analyzes |
Frege’s Grundlagen der Arithmetik
ⓘ
linked to:
Die Grundlagen der Arithmetik
Frege’s formal system for arithmetic ⓘ the role of abstraction principles in grounding number talk ⓘ |
| author | Crispin Wright ⓘ |
| critiques |
nominalist views of numbers
ⓘ
psychologistic accounts of arithmetic ⓘ |
| defends |
Frege’s conception of numbers as logical objects
ⓘ
the view that arithmetic is analytic ⓘ |
| focusesOn |
Frege’s abstraction principles
ⓘ
Frege’s logicist reduction of arithmetic to logic ⓘ Frege’s notion of sense and reference as applied to numerical terms ⓘ Frege’s treatment of cardinal numbers ⓘ Frege’s view that numbers are objects ⓘ the epistemology of arithmetic within a Fregean framework ⓘ the status of numbers as abstract objects ⓘ |
| genre | analytic philosophy ⓘ |
| hasPerspective |
Fregean
ⓘ
logicist about arithmetic ⓘ realist about mathematical objects ⓘ |
| influenced |
contemporary debates on abstraction principles
ⓘ
discussions of the ontology of mathematical objects ⓘ neo-Fregean philosophy of mathematics ⓘ |
| language | English ⓘ |
| mainSubject |
Fregean semantics
ⓘ
Frege’s Theorem ⓘ Gottlob Frege ⓘ Hume’s Principle ⓘ
linked to:
Hume’s Principle (derivable, not postulated)
abstract objects ⓘ foundations of arithmetic ⓘ logicism ⓘ neo-Fregeanism ⓘ ontology of numbers ⓘ philosophy of logic ⓘ philosophy of mathematics ⓘ |
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: Frege’s Conception of Numbers as Objects Description of subject: Frege’s Conception of Numbers as Objects is a major philosophical work by Crispin Wright that offers an influential interpretation and defense of Gottlob Frege’s view that numbers are abstract objects grounded in logic.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Frege’s Conception of Numbers as Objects