The Metaphysics of Relational States
Bibliographic record
Abstract
A many-faceted beast, the metaphysics of relations can be approached from many angles.One could begin with the various ways in which relational states are expressed in natural language.If a more historical treatment is wanted, one could begin with Plato, Aristotle, or Leibniz. 1 In the following, I will approach the topic by first drawing on Russell's Principles of Mathematics (1903) (still a natural-enough starting point), and then turn to a discussion mainly of positionalism.The closing section contains an overview of the six contributions to this Special Issue.P R O O F 164 Jan Plate D2. 'Loves' expresses a relation distinct from the one expressed by 16 'is loved by'.17 But this last statement might give rise to linguistic qualms; for, given that 'is 18 loved by' is not even a complete phrase, it does not look like an appropriate 19 target for the attribution of a semantic value.We can get around this by 20 adopting the notational expedient of 𝜆-expressions.Instead of 'loves' and 'is 21 loved by', we might speak of '𝜆𝑥, 𝑦 (𝑥 loves 𝑦)' and '𝜆𝑥, 𝑦 (𝑥 is loved by 𝑦)', and 22 lay down a semantics of 𝜆-expressions under which ⌜𝜆𝑥, 𝑦 (𝑥 𝜑s 𝑦)⌝ denotes 23 whatever dyadic relation is such that the instantiation of that relation by 24 any entities 𝑥 and 𝑦, in this order, is just the state of affairs that 𝑥 𝜑s 𝑦. 2 25 Under such a semantics, '𝜆𝑥, 𝑦 (𝑥 loves 𝑦)' denotes the dyadic relation whose 26 instantiation by any entities 𝑥 and 𝑦 (in this order) is the state of affairs that 27 𝑥 loves 𝑦.Analogously for '𝜆𝑥, 𝑦 (𝑥 is loved by 𝑦)', which may also be said to 28 denote the converse of 𝜆𝑥, 𝑦 (𝑥 loves 𝑦).29 Using 𝜆-expressions as names for relations, (D2) becomes: 30 D2 ′ .The relation 𝜆𝑥, 𝑦 (𝑥 loves 𝑦) is distinct from 𝜆𝑥, 𝑦 (𝑥 is loved by 𝑦). 31 And this is hard to deny.As the argument is both straightforward and tedious, 32 I delegate it to a footnote.3 (D2) closely reflects what Bertrand Russell implies 33 From (1) and (2) we can conclude, by Leibniz's law, that 𝜆𝑥, 𝑦 (𝑥 loves 𝑦) is distinct from 𝜆𝑥, 𝑦 (𝑥 is loved by 𝑦).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.030 |
| Scholarly communication | 0.008 | 0.013 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".