Philosophical logic
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Philosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with mathematical logic, and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics traditionally treated by logic in general. It is concerned with characterising notions like inference, rational thought, truth, and contents of thoughts, in the most fundamental ways possible, and trying to model them using modern formal logic.
The notions in question include reference, predication, identity, truth, negation, quantification, existence, necessity, definition and entailment.
Philosophical logic is not concerned with the psychological processes connected with thought, or with emotions, images and the like. It is concerned only with those entities — thoughts, sentences, or propositions — that are capable of being true and false. To this extent, though, it does intersect with philosophy of mind and philosophy of language. Gottlob Frege is regarded by many as the founder of modern philosophical logic.