How is pure mathematics possible?
E91455
"How is pure mathematics possible?" is a central guiding question in Immanuel Kant’s *Prolegomena to Any Future Metaphysics*, where he investigates the conditions that make synthetic a priori knowledge in mathematics possible.
All labels observed (1)
| Label | Occurrences |
|---|---|
| How is pure mathematics possible? canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T765828 — 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: How is pure mathematics possible? Context triple: [Prolegomena to Any Future Metaphysics, section, How is pure mathematics possible?]
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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.
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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.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
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D.
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.
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E.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
- 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: How is pure mathematics possible? Target entity description: "How is pure mathematics possible?" is a central guiding question in Immanuel Kant’s *Prolegomena to Any Future Metaphysics*, where he investigates the conditions that make synthetic a priori knowledge in mathematics possible.
-
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.
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.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
D.
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.
-
E.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
Kantian concept
ⓘ
epistemological problem ⓘ philosophical question ⓘ |
| addresses |
ground of the certainty of mathematical knowledge
ⓘ
problem of the applicability of mathematics to appearances ⓘ |
| aimsToExplain |
how mathematical judgments can be necessary and universally valid
ⓘ
how mathematical knowledge extends our cognition ⓘ |
| answerAccordingToKant |
arithmetic is grounded in the pure intuition of time
ⓘ
geometry is grounded in the pure intuition of space ⓘ pure mathematics is possible because its objects are constructed in pure intuition ⓘ |
| asksAbout |
a priori foundations of arithmetic
ⓘ
a priori foundations of geometry ⓘ possibility of pure mathematics as a science ⓘ relation between mathematics and pure intuition ⓘ |
| author | Immanuel Kant ⓘ |
| centralTheme | synthetic a priori knowledge ⓘ |
| concerns |
conditions of possibility of mathematical knowledge
ⓘ
justification of synthetic a priori judgments in mathematics ⓘ status of mathematical propositions ⓘ |
| discussedIn | Prolegomena to Any Future Metaphysics ⓘ |
| field |
epistemology
ⓘ
philosophy of mathematics ⓘ |
| historicalContext | late 18th century ⓘ |
| influenced |
neo-Kantian philosophy
ⓘ
phenomenology of mathematics ⓘ subsequent philosophy of mathematics ⓘ |
| keyConcept |
a priori versus a posteriori knowledge
ⓘ
distinction between analytic and synthetic judgments ⓘ forms of sensibility ⓘ pure intuition of space ⓘ pure intuition of time ⓘ synthetic a priori judgments ⓘ transcendental ideality of space and time ⓘ |
| language | German ⓘ |
| mainWork | Prolegomena to Any Future Metaphysics ⓘ |
| method | transcendental investigation ⓘ |
| originalTitleContext |
Prolegomena zu einer jeden künftigen Metaphysik, die als Wissenschaft wird auftreten können
ⓘ
linked to:
Prolegomena to Any Future Metaphysics
|
| philosophicalPeriod |
Enlightenment
ⓘ
linked to:
Age of Enlightenment
|
| philosophicalTradition | transcendental idealism ⓘ |
| relatedDoctrine |
Kant’s doctrine of sensibility
ⓘ
Kant’s doctrine of the transcendental aesthetic ⓘ |
| relatedQuestion |
How is metaphysics as a science possible?
ⓘ
How is pure natural science possible? ⓘ |
| relatedWork | Critique of Pure Reason ⓘ |
| statusInWork | central guiding question of the Prolegomena ⓘ |
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: How is pure mathematics possible? Description of subject: "How is pure mathematics possible?" is a central guiding question in Immanuel Kant’s *Prolegomena to Any Future Metaphysics*, where he investigates the conditions that make synthetic a priori knowledge in mathematics possible.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.