Conatus: THIRD EDITION by Tom Wallace - HTML preview

C O N A T U S

generalisations. An inductive argument can be characterised as one whose conclusion, whilst not following deductively from its premises, is in some way supported by them and rendered plausible in the light of them. Scientific reasoning is held to be the paradigm of inductive reasoning.

When we turn to mathematics and to science, we see the two other foundational truths coming into play — coherence and correspondence.

The correspondence theory of truth suggests there has to be a fact out there in the world to which truth corresponds — and that this is a better guide to the world than ‘provable’ or ‘unprovable’. Since it is held that truth must correspond with facts about the world, the correspondence theory of truth is related to empiricism — observable facts. Scientists hope that the universe turns out to have similar correspondence to their models. If there’s a good enough match between what theory predicts and what is actually our there then that suggests a successful model.

Mathematics uses axioms as its starting point and then uses deduction to derive further truths. Once again, we take axioms as brute facts and we assume that anything logically derived from them will also be true. The truth which mathematics derives from its axioms is coherent within the system (ie., within mathematics itself) but notice that it does not necessarily correspond to events in the external world.

Science, at least in its official version, recognises the contingency of all its discoveries.

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