Existence, Meaning and the Law of Excluded Middle. A dialogical approach to Hermann Weyl’s philosophical considerations
Bibliographic record
Abstract
Intuitionistic logic is often presented as a proof-based approach to logic, where truth is defined as having a proof. I shall stress another dimension which is also important: that of the constitution of meaning. This dimension of meaning does not reduce to proof, be it actual or potential, as standard presentations of intuitionistic logic put it. The law of excluded middle sits right at the junction between these two dimensions, proof and meaning: in intuitionistic logic, there is no proof for the law of excluded middle, but the law of excluded middle is a proposition that does have meaning. It is thus a problematic case. Better understanding how these two levels, meaning and proof, dissociate and interact is the purpose of this paper. I contend that the dialogical framework, a logical framework developing first and foremost intuitionistic logic (though it can also accommodate classical logic), allows to separate these two levels, meaning and proof, and show how the level of proofs rests on the level of meaning. In this respect, the law of excluded middle becomes a meaning-constitutive principle, even if it is neither proved nor refuted. The dialogical framework can thus integrate the philosophical considerations of Hermann Weyl's "intuitionistic episode" of the 1920s, which, I contend, already present a similar distinction between the level of meaning and the level of existence.
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How this classification was reachedexpand
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 | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".