See: Logic, Mathematical Logic, Metalogic, First-Order Logic.
- Philosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with philosophy of logic, metalogic, and 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 characterizing 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.
- 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.
- Not all philosophical logic, however, applies formal logical techniques. A good amount of it (including Grayling's and Colin McGinn's books cited below) is written in natural language. One definition, popular in Britain, is that philosophical logic is the attempt to solve general philosophical problems that arise when we use or think about formal logic: problems about existence, necessity, analyticity, a prioricity, propositions, identity, predication, truth. Philosophy of logic, on the other hand, would tackle metaphysical and epistemological problems about entailment, validity, and proof. So it could be said that philosophy of logic is a branch of philosophy but philosophical logic belongs to the domain of logic (though logic is itself a branch of philosophy).