Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
E462023
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4678548 — 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: Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics Context triple: [Friedrich Waismann, notableWork, Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics]
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A.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
B.
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.
-
C.
A Beginner’s Guide to Mathematical Logic
A Beginner’s Guide to Mathematical Logic is an introductory textbook that explains the fundamental concepts and techniques of mathematical logic in a clear and accessible style.
-
D.
Dialogues on Mathematics
Dialogues on Mathematics is a popular science book by Hungarian mathematician Alfréd Rényi that presents key mathematical ideas through fictional conversations.
-
E.
Proofs and Refutations
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.
- 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: Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics Target entity description: 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.
-
A.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
B.
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.
-
C.
A Beginner’s Guide to Mathematical Logic
A Beginner’s Guide to Mathematical Logic is an introductory textbook that explains the fundamental concepts and techniques of mathematical logic in a clear and accessible style.
-
D.
Dialogues on Mathematics
Dialogues on Mathematics is a popular science book by Hungarian mathematician Alfréd Rényi that presents key mathematical ideas through fictional conversations.
-
E.
Proofs and Refutations
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.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics book ⓘ non-fiction book ⓘ philosophy of mathematics book ⓘ |
| aimsTo |
bridge philosophical reflection and mathematical practice
ⓘ
clarify how mathematical concepts gain meaning ⓘ |
| analyzes |
how mathematical concepts are clarified
ⓘ
how mathematical concepts are formed ⓘ how mathematical concepts are used in practice ⓘ |
| approach |
foundational analysis
ⓘ
philosophical analysis ⓘ |
| author | Friedrich Waismann ⓘ |
| concerns |
criteria for clarity in mathematical concepts
ⓘ
the nature of mathematical thinking ⓘ the relationship between informal and formal mathematics ⓘ |
| context | 20th-century philosophy of mathematics ⓘ |
| examines |
the development of mathematical ideas
ⓘ
the logical structure of mathematical theories ⓘ the role of language in mathematics ⓘ |
| focusesOn |
clarification of mathematical concepts
ⓘ
formation of mathematical concepts ⓘ use of concepts in modern mathematics ⓘ |
| genre | academic monograph ⓘ |
| hasPart |
chapters on applications in modern mathematics
ⓘ
chapters on clarification of concepts ⓘ chapters on concept formation ⓘ |
| intendedAudience |
readers interested in foundations of mathematics
ⓘ
students of mathematics ⓘ students of philosophy ⓘ |
| language | English ⓘ |
| philosophicalTradition |
Vienna Circle tradition
ⓘ
linked to:
Vienna Circle
analytic philosophy ⓘ |
| relatedTo |
concept formation
ⓘ
logical analysis of language ⓘ meaning in mathematics ⓘ modern mathematics ⓘ |
| relatedWork |
Friedrich Waismann's writings on language and logic
ⓘ
works of the Vienna Circle on the foundations of science ⓘ |
| subject |
epistemology of mathematics
ⓘ
foundations of mathematics ⓘ mathematical 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: Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Friedrich Waismann
→
notableWork
→
Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
ⓘ