Logic

===Epistemology of logic===
The epistemology of logic studies how one knows that an argument is valid or that a proposition is logically true.{{sfnm|1a1=Warren|1y=2020|1loc=6. The Epistemology of Logic|2a1=Schechter}} This includes questions like how to justify that modus ponens is a valid rule of inference or that contradictions are false.{{sfn |Warren |2020 |loc=6. The Epistemology of Logic}} The traditionally dominant view is that this form of logical understanding belongs to knowledge [[A priori and a posteriori|a priori]].{{sfn |Schechter}} In this regard, it is often argued that the [[mind]] has a special faculty to examine relations between pure ideas and that this faculty is also responsible for apprehending logical truths.{{sfn |Gómez-Torrente |2019}} A similar approach understands the rules of logic in terms of [[Conventionalism|linguistic conventions]]. On this view, the laws of logic are trivial since they are true by definition: they just express the meanings of the logical vocabulary.{{sfnm|1a1=Warren|1y=2020|1loc=6. The Epistemology of Logic|2a1=Gómez-Torrente|2y=2019|3a1=Warren|3y=2020|3loc=1. What is Conventionalism}}

Some theorists, like [[Hilary Putnam]] and [[Penelope Maddy]], object to the view that logic is knowable a priori. They hold instead that logical truths depend on the [[empirical]] world. This is usually combined with the claim that the laws of logic express universal regularities found in the structural features of the world. According to this view, they may be explored by studying general patterns of the [[fundamental sciences]]. For example, it has been argued that certain insights of [[quantum mechanics]] refute the [[principle of distributivity]] in classical logic, which states that the formula <math>A \land (B \lor C)</math> is equivalent to <math>(A \land B) \lor (A \land C)</math>. This claim can be used as an empirical argument for the thesis that [[quantum logic]] is the correct logical system and should replace classical logic.{{sfnm|1a1=Chua|1y=2017|1pp=631–636|2a1=Wilce|2y=2021|3a1=Putnam|3y=1969|3pp=216–241}}
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