Deductive updating is not Bayesian.
Bibliographic record
Abstract
One of the major debates concerning the nature of inferential reasoning is between counterexample-based theories such as mental model theory and probabilistic theories. This study looks at conclusion updating after the addition of statistical information to examine the hypothesis that deductive reasoning cannot be explained by probabilistic inferences. In Study 1, participants were given an initial "If P then Q rule" for a phenomenon on a recently discovered planet, told that "Q was true," and asked to make a judgment of either deductive validity or probabilistic likelihood of the putative conclusion that "P is true." They were then told the results of 1,000 observations. In the low-probability problem, 950 times P was false and Q was true, whereas 50 times P was true and Q was true. In the high-probability problem, these proportions were inverted. On the low-probability problem, probabilistic ratings and judgments of logical validity decreased. However, on the high-probability problem, probabilistic ratings remained high whereas judgments of logical validity significantly decreased. Confidence ratings were consistent with this different pattern for probabilistic and for deductive inferences. Study 2 replicated this result with another form of inference, "If P then Q. P is false." These results show that deductive updating is not explicable by Bayesian updating.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".