Triple

T765828
Position Surface form Disambiguated ID Type / Status
Subject Prolegomena to Any Future Metaphysics E16172 entity
Predicate section P3120 FINISHED
Object How is pure mathematics possible?
"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.
E91455 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: How is pure mathematics possible? | Statement: [Prolegomena to Any Future Metaphysics, section, How is pure mathematics possible?]
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?]
  • 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
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: How is pure mathematics possible?
Triple: [Prolegomena to Any Future Metaphysics, section, How is pure mathematics possible?]
Generated 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.
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

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69a493684ee48190bd43b7c78da4aec8 completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a69fb6ac8190bda41852ea01842c completed March 1, 2026, 8:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69a666760a4c8190afd00dbfc263be28 completed March 3, 2026, 4:41 a.m.
NEDg Description generation batch_69a66a6289a881909a2ada9c8a5ea091 completed March 3, 2026, 4:58 a.m.
NED2 Entity disambiguation (via description) batch_69a66ad0da0081909fc828eccabf5b80 completed March 3, 2026, 5 a.m.
Created at: March 1, 2026, 7:37 p.m.