Demonstrative reasoning is what can be loosely called ‘deductive’ reasoning,21 in which the steps of the argument proceed with absolute certainty based on the logical relations between the ideas concerned (e.g. the kind of argument used in mathematics, such as the proof of Pythagoras’ Theorem). Factual reasoning—which Hume also calls ‘moral’ and Locke had called ‘probable’—is now commonly called ‘inductive’ inference, encompassing all sorts of everyday reasoning in which we draw apparently reasonable (but less than logically certain) conclusions based on our personal experience, testimony, our
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