Remarks on the Foundations of Mathematics
E53947
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Remarks on the Foundations of Mathematics canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T429748 — 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: Remarks on the Foundations of Mathematics Context triple: [Ludwig Wittgenstein, notableWork, Remarks on the Foundations of Mathematics]
-
A.
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.
-
B.
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.
-
C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
D.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
-
E.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
- 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: Remarks on the Foundations of Mathematics Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
D.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
-
E.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
philosophical work ⓘ posthumous work ⓘ |
| author | Ludwig Wittgenstein ⓘ |
| basedOn |
Wittgenstein’s later manuscripts
ⓘ
linked to:
Philosophical Investigations
|
| countryOfFirstPublication | United Kingdom ⓘ |
| criticizes |
formalism in mathematics
ⓘ
intuitionism ⓘ logicism ⓘ |
| discusses |
set-theoretic paradoxes
ⓘ
the concept of a rule ⓘ the foundations of arithmetic ⓘ the idea of mathematical necessity ⓘ the nature of mathematical proof ⓘ the practice of calculation ⓘ the role of language in mathematics ⓘ the status of mathematical propositions ⓘ |
| editor |
G. E. M. Anscombe
ⓘ
linked to:
Elizabeth Anscombe
G. H. von Wright ⓘ R. Rhees ⓘ |
| genre |
analytic philosophy
ⓘ
philosophy of mathematics ⓘ |
| hasEdition | English translation by G. E. M. Anscombe ⓘ |
| hasPart | series of numbered remarks ⓘ |
| influenced |
later philosophy of mathematics
ⓘ
studies of rule-following in philosophy ⓘ |
| influencedBy | Philosophical Investigations ⓘ |
| language |
English
ⓘ
German ⓘ |
| mainSubject |
language
ⓘ
logic ⓘ mathematical proof ⓘ mathematical truth ⓘ mathematics ⓘ philosophy of mathematics ⓘ rule-following ⓘ |
| notableFor |
critique of foundational programs in mathematics
ⓘ
emphasis on mathematical practice ⓘ language-game analysis of mathematics ⓘ |
| originalLanguage | German ⓘ |
| philosophicalApproach |
language-centered
ⓘ
ordinary language philosophy ⓘ
linked to:
analytic philosophy
|
| philosophicalTradition | analytic philosophy ⓘ |
| publicationStatus | posthumous ⓘ |
| publicationYear | 1956 ⓘ |
| publisher | Basil Blackwell ⓘ |
| relatedWork |
Philosophical Investigations
ⓘ
Tractatus Logico-Philosophicus ⓘ |
| timeOfWriting | Wittgenstein’s later period ⓘ |
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: Remarks on the Foundations of Mathematics Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.