Triple

T5063603
Position Surface form Disambiguated ID Type / Status
Subject Geoffrey Hellman E114087 entity
Predicate notableWork P4 FINISHED
Object Mathematics Without Numbers
Mathematics Without Numbers is a philosophical work by Geoffrey Hellman that develops a version of structuralism in the philosophy of mathematics using modal logic instead of traditional set-theoretic foundations.
 E490369 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: Mathematics Without Numbers | Statement: [Geoffrey Hellman, notableWork, Mathematics Without Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Mathematics Without Numbers
Context triple: [Geoffrey Hellman, notableWork, Mathematics Without Numbers]
  • A. 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.
  • B. Ontological Reduction and the World of Numbers
    "Ontological Reduction and the World of Numbers" is a philosophical essay by W.V.O. Quine that examines how mathematical entities, particularly numbers, can be understood and justified within a naturalistic and ontologically parsimonious framework.
  • C. 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.
  • D. Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
    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.
  • E. The Unreasonable Effectiveness of Mathematics in the Natural Sciences
    The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a landmark 1960 essay by physicist Eugene Wigner that explores why abstract mathematics so powerfully and mysteriously describes physical reality.
  • 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: Mathematics Without Numbers
Triple: [Geoffrey Hellman, notableWork, Mathematics Without Numbers]
Generated description
Mathematics Without Numbers is a philosophical work by Geoffrey Hellman that develops a version of structuralism in the philosophy of mathematics using modal logic instead of traditional set-theoretic foundations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Mathematics Without Numbers
Target entity description: Mathematics Without Numbers is a philosophical work by Geoffrey Hellman that develops a version of structuralism in the philosophy of mathematics using modal logic instead of traditional set-theoretic foundations.
  • A. 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.
  • B. Ontological Reduction and the World of Numbers
    "Ontological Reduction and the World of Numbers" is a philosophical essay by W.V.O. Quine that examines how mathematical entities, particularly numbers, can be understood and justified within a naturalistic and ontologically parsimonious framework.
  • C. 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.
  • D. Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
    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.
  • E. The Unreasonable Effectiveness of Mathematics in the Natural Sciences
    The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a landmark 1960 essay by physicist Eugene Wigner that explores why abstract mathematics so powerfully and mysteriously describes physical reality.
  • 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_69bd443c0c8c81908663b77afb28e165 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd747756bc8190863c426e6fd6e8f7 completed March 20, 2026, 4:23 p.m.
NED1 Entity disambiguation (via context triple) batch_69bea497fed0819098746fd8917f041c completed March 21, 2026, 2 p.m.
NEDg Description generation batch_69bea5163c78819086d2424ee7b57890 completed March 21, 2026, 2:03 p.m.
NED2 Entity disambiguation (via description) batch_69bea577f4b0819084d579e4d4804947 completed March 21, 2026, 2:04 p.m.
Created at: March 20, 2026, 1:38 p.m.