Proofs and Refutations
E349460
Proofs and Refutations is a seminal work in the philosophy of mathematics that explores how mathematical knowledge develops through a dialectical process of conjectures, criticisms, and revisions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Proofs and Refutations canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T3333500 — 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: Proofs and Refutations Context triple: [Imre Lakatos, notableWork, Proofs and Refutations]
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A.
Conjectures and Refutations
Conjectures and Refutations is a major philosophical work by Karl Popper that develops his theory of scientific knowledge through the ideas of falsifiability, critical testing, and the growth of knowledge via bold hypotheses and their refutation.
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B.
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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C.
From a Logical Point of View
From a Logical Point of View is a landmark collection of philosophical essays by W.V.O. Quine that helped reshape analytic philosophy, especially through its critique of the analytic–synthetic distinction and its naturalized approach to epistemology.
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D.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
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E.
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.
- 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: Proofs and Refutations Target entity description: Proofs and Refutations is a seminal work in the philosophy of mathematics that explores how mathematical knowledge develops through a dialectical process of conjectures, criticisms, and revisions.
-
A.
Conjectures and Refutations
Conjectures and Refutations is a major philosophical work by Karl Popper that develops his theory of scientific knowledge through the ideas of falsifiability, critical testing, and the growth of knowledge via bold hypotheses and their refutation.
-
B.
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.
-
C.
From a Logical Point of View
From a Logical Point of View is a landmark collection of philosophical essays by W.V.O. Quine that helped reshape analytic philosophy, especially through its critique of the analytic–synthetic distinction and its naturalized approach to epistemology.
-
D.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
philosophy of mathematics work ⓘ |
| academicDiscipline |
history of science
ⓘ
mathematics ⓘ philosophy ⓘ |
| arguesThat |
mathematical concepts evolve through counterexamples
ⓘ
mathematical knowledge grows through a dialectical process ⓘ proofs are subject to criticism and revision ⓘ |
| author | Imre Lakatos ⓘ |
| basedOn | Lakatos’s earlier papers on the philosophy of mathematics ⓘ |
| centralConcept |
fallibility of mathematical knowledge
ⓘ
heuristic reasoning in mathematics ⓘ method of proofs and refutations ⓘ quasi-empiricism in mathematics ⓘ |
| contrastsWith |
formalism in mathematics
ⓘ
logicism in mathematics ⓘ strictly axiomatic views of mathematics ⓘ |
| countryOfOrigin | United Kingdom ⓘ |
| examines | Euler’s formula V − E + F = 2 ⓘ |
| focusesOn |
conjectures
ⓘ
criticisms ⓘ dialectical development of mathematical knowledge ⓘ revisions of proofs and concepts ⓘ |
| genre | academic non-fiction ⓘ |
| hasTheme |
evolution of definitions and theorems
ⓘ
fallibilism about mathematical knowledge ⓘ role of counterexamples in mathematics ⓘ |
| influenced |
history of mathematics scholarship
ⓘ
philosophy of mathematical practice ⓘ quasi-empirical approaches to mathematics ⓘ |
| influencedBy |
Hegelian dialectics
ⓘ
Karl Popper’s philosophy of science ⓘ |
| intendedAudience |
historians of mathematics
ⓘ
mathematicians ⓘ philosophers of mathematics ⓘ |
| language | English ⓘ |
| mainSubject |
growth of mathematical knowledge
ⓘ
methodology of mathematics ⓘ philosophy of mathematics ⓘ |
| notableFor |
critique of formalist conceptions of proof
ⓘ
dialogue-based exposition ⓘ integration of history and philosophy of mathematics ⓘ |
| publicationYear | 1976 ⓘ |
| publisher | Cambridge University Press ⓘ |
| setting | fictional mathematics classroom ⓘ |
| structure | dialogue between a teacher and students ⓘ |
| timePeriodDescribed | 18th and 19th century developments in polyhedron theory ⓘ |
| usesExample | Euler’s polyhedron formula ⓘ |
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: Proofs and Refutations Description of subject: Proofs and Refutations is a seminal work in the philosophy of mathematics that explores how mathematical knowledge develops through a dialectical process of conjectures, criticisms, and revisions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Imre Lipschitz