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Record W2314560663 · doi:10.1017/bsl.2015.2

EXISTENTIAL-IMPORT MATHEMATICS

2015· article· en· W2314560663 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueBulletin of Symbolic Logic · 2015
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Algebra and Logic
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsPredicate (mathematical logic)ExistentialismMathematicsCombinatoricsDiscrete mathematicsPhilosophyComputer scienceEpistemology

Abstract

fetched live from OpenAlex

Abstract First-order logic has limited existential import: the universalized conditional ∀ x [S( x ) → P( x )] implies its corresponding existentialized conjunction ∃ x [S( x ) & P( x )] in some but not all cases. We prove the Existential-Import Equivalence : ∀ x [S( x ) → P( x )] implies ∃ x [S( x ) & P( x )] iff ∃ x S( x ) is logically true. The antecedent S( x ) of the universalized conditional alone determines whether the universalized conditional has existential import : implies its corresponding existentialized conjunction. A predicate is a formula having only x free. An existential-import predicate Q( x ) is one whose existentialization, ∃ x Q( x ), is logically true; otherwise, Q( x ) is existential-import-free or simply import-free . Existential-import predicates are also said to be import-carrying . How widespread is existential import? How widespread are import-carrying predicates in themselves or in comparison to import-free predicates? To answer, let L be any first-order language with any interpretation INT in any [sc. nonempty] universe U. A subset S of U is definable in L under INT iff for some predicate Q( x ) in L, S is the truth-set of Q( x ) under INT. S is import-carrying definable iff S is the truth-set of an import-carrying predicate. S is import-free definable iff S is the truth-set of an import-free predicate. Existential-Importance Theorem : Let L, INT, and U be arbitrary. Every nonempty definable subset of U is both import-carrying definable and import-free definable. Import-carrying predicates are quite abundant, and no less so than import-free predicates. Existential-import implications hold as widely as they fail. A particular conclusion cannot be validly drawn from a universal premise, or from any number of universal premises .—Lewis-Langford, 1932, p. 62.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.718
Threshold uncertainty score0.662

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.043
GPT teacher head0.258
Teacher spread0.215 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it