Why this work is in the frame
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Bibliographic record
Abstract
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.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it