Philosophical logic

Philosophical logic studies logical systems and their foundations, especially how they represent necessity, possibility, identity, existence, and vagueness.

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Classical logic: A logic governed by principles including excluded middle and noncontradiction. Its principles provide the baseline that philosophical logicians examine and sometimes revise.
Kripke semantics: A possible-worlds semantics that evaluates modal formulas across worlds linked by accessibility relations. It explains how modal systems model which possibilities count as accessible.
Aristotle: An ancient Greek philosopher whose works founded major traditions in logic and metaphysics. His syllogistic and modal writings established enduring questions about necessity and inference.
Intuitionistic logic: A logic that rejects unrestricted excluded middle and interprets proofs constructively. It challenges a classical principle whose validity has philosophical consequences for truth and proof.
The problem of nonexistence: The philosophical puzzle of how meaningful claims can concern things that do not exist. It tests how logic handles names, reference, and existential commitment.
Modal logic: A family of logics that formalizes necessity and possibility. It gives precise systems for the modality at the center of many philosophical debates.
Tarskian semantics: A model-theoretic account of truth defined relative to interpretations and structures. It supplies a general account of how formal sentences receive truth conditions.
Gottlob Frege: A German logician and philosopher who developed modern predicate logic and a theory of sense and reference. His formal language transformed the analysis of quantification, identity, and existence.
Paraconsistent logic: A logic in which contradictions do not entail every proposition. It rejects classical explosion to make inconsistent information logically manageable.
The problem of the many: A puzzle about why many slightly different aggregates seem equally eligible to be one ordinary object. It connects vagueness in language with identity and the boundaries of objects.