Rethinking Wittgenstein's Tractatus through Statistics and Quantum language
Bibliographic record
Abstract
For the last quarter century, I have been advocating quantum language (QL). QL should be regarded not only as a linguistic turn of quantum mechanics, but also as the ultimate formulation of epistemology in the sense of Descartes and Kant. Even more importantly, QL naturally and essentially includes statistics. Furthermore, Wittgenstein's dream — namely, a proof of why logic holds in our world, as pursued in his Tractatus Logico-Philosophicus (TLP) — can be realized within QL. In this paper, I propose to replace his picture theory with statistics, and to reinterpret statistics within the framework of quantum language.In doing so, I demonstrate that Wittgenstein's dream can in fact be fulfilled within statistics itself, when properly described in the language of QL.This version corrects two minor typos: (1) "\mathbb{P} \theta" was replaced by the correct form "\mathbb{P}_\theta", and (2) a missing percent sign was fixed by replacing "100%" with "100\%" in LaTeX notation.
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.
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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.021 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".