Brouwer on ‘hypotheses’ and the middle Wittgenstein
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.
Bibliographic record
Abstract
Wittgenstein returned to Cambridge in January 1929. The earliest manuscripts of that period which we possess, MS 105, date from that month, opening on a few personal remarks, including a comment on his conversations with Ramsey, followed by remarks where we see Wittgenstein exploring new ideas about topics not covered in the Tractatus, such as the nature of irrational numbers or the contrast between a physical and phenomenological description of visual space. Whence these new topics and ideas? It is, exegetically speaking, natural to look for an answer in the prehistory of MS 105. Alas, any earlier manuscript, if any, must be assumed either destroyed or lost. An obvious starting point is Brouwer’s lectures in Vienna in March 1928, ‘Mathematik, Wissenschaft und Sprache’ on the 10th (Brouwer 1929A) and ‘Die Struktur des Kontinuums’ on the 14th (Brouwer 1930A)2. It appears that Wittgenstein only attended the first one, but it was reported by a witness, Herbert Feigl, that it spurred him into coming back to philosophy. According to Feigl: When the Dutch mathematician Luitzen Egbertus Jan Brouwer was scheduled to lecture on intuitionism in mathematics in Vienna, Waismann and I managed to coax Wittgenstein, after much resistance, to join us in attending the lecture. When, afterwards, Wittgenstein went to a café with us, a great event took place. Suddenly and very volubly Wittgenstein began talking philosophy—at great length. Perhaps this was the turning point, for ever since that time, 1929, when he moved to Cambridge University Wittgenstein was a philosopher again. (Feigl 1981, p.64)
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 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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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