Traditionally, philosophers have focused mostly on the logical template of inference. The paradigm-case has been deductive inference, which is topic-neutral and context-insensitive. The study of deductive rules has engendered the search for the Holy Grail: syntactic and topic-neutral accounts of all prima facie reasonable inferential rules. The search has hoped to find rules that are transparent and algorithmic, and whose following will just be a matter of grasping their logical form. Part of the search for the Holy Grail has been to show that the so-called scientific method can be formalised in a topic-neutral way. We are all familiar with Carnap’s inductive logic, or Popper’s deductivism or the Bayesian account of scientific method.
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There is no Holy Grail to be found. There are many reasons for this pessimistic conclusion. First, it is questionable that deductive rules are rules of inference. Second, deductive logic is about updating one’s belief corpus in a consistent manner and not about what one has reasons to believe simpliciter. Third, as Duhem was the first to note, the so-called scientific method is far from algorithmic and logically transparent. Fourth, all attempts to advance coherent and counterexample-free abstract accounts of scientific method have failed. All competing accounts seem to capture some facets of scientific method, but none can tell the full story. Fifth, though the new Dogma, Bayesianism, aims to offer a logical template (Bayes’s theorem plus conditionalisation on the evidence) that captures the essential features of non-deductive inference, it is betrayed by its topic-neutrality. It supplements deductive coherence with the logical demand for probabilistic coherence among one’s degrees of belief. But this extended sense of coherence is (almost) silent on what an agent must infer or believe.

Stathis Psillos