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Weber argues that we should understand the quick uptake of Meselson and Stahl's experimental result as an instance of inference to the best explanation (as opposed to Duhem's deductive characterization).
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But there are also instances of inferences comprised of deductive, extrapolative, and sometimes properly inductive reasoning on topics of everyday life as well as philosophy in numerous pre-Dignāga texts of several schools.
An instance of an inference form is produced by replacing all the variables in it by appropriate expressions (i.e., ones that make sense in the context) and by doing so uniformly (i.e., by substituting the same expression wherever the same variable recurs).
Coltheart et al. 2010 argue that the step from abnormal data to belief is an instance of abductive inference, as those who end up endorsing a delusional belief need to select an explanatory hypothesis for their abnormal data from a range of relevant hypotheses.
Thus Paley's use of the term 'inference' in connection with the watch's designer.[2] The watch does play an obvious and crucial role but as a paradigmatic instance of design inferences rather than as the analogical foundation for an inferential comparison.
Line (3) above may be called an inference form, and (1) and (2) are then instances of that inference form.
Also, the instances of such inference rules depend on details of the context of the formula.
An LK-proof is a (hyper) tree of sequents, such that the leaves are axiom sequents of the form F ⊢ FF, where F is an arbitrary formula, and the (hyper) edges are instances of the inference rules specified by the calculus.
This would be an instance of an abductive inference.
Another instance of meta-Bayesian inference (which we have not explored here) that could couple the perceptual model to the response model is when the subject is observing his or herself (cf. meta-cognition).
Similarly, an axiomatic calculus for FOL, for instance, would contain rules of inference in addition to the axioms.
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