Bibliographic record
Abstract
Logic is the science of reasoning. Mathematical logic applies to mathematical reasoning – the art and science of writing down deductions . This volume is about the form, meaning, use , and limitations of logical deductions, also called proofs . While the user of mathematical logic will practise the various proof techniques with a view of applying them in everyday mathematical practice, the student of the subject will also want to know about the power and limitations of the deductive apparatus.We will find that there are some inherent limitations in the quest to discover truth by purely formal – that is, syntactic – techniques. In the process we will also discover a close affinity between formal proofs and computations that persists all the way up to and including issues of limitations: Not only is there a remarkable similarity between the types of respective limitations (computations vs. uncomputable functions, and proofs vs. unprovable, but “true”, sentences), but, in a way, you cannot have one type of limitation without having the other. The modern use of the term mathematical logic encompasses (at least) the areas of proof theory (it studies the structure, properties, and limitations of proofs), model theory (it studies the interplay between syntax and meaning – or semantics – by looking at the algebraic structures where formal languages are interpreted), recursion theory (or computability, which studies the properties and limitations of algorithmic processes), and set theory.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.007 | 0.010 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.073 | 0.039 |
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".