Inferences and proofs

Since its birth, logic has been concerned with the study of correct reasonings or, more specifically, of proofs. A proof should have the epistemic power to provide us with justification for the judgement or assertion which it ends with. This power is, from a different point of view, the power to compel one to accept the conclusion of the proof. Which forms of reasoning can be said to have such power? And above all, how can they exert an epistemic compulsion? 

According to Descartes, a correct reasoning is nothing but a chain of valid inferences. The epistemic power of proofs should therefore depend on the epistemic power of valid inferences. The problem then becomes: what is an inference? And why valid inferences have an epistemic force? These question, far from being psychological in nature, involve epistemology, logic and mathematics.

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