When speaking in a mathematical context of “logic” – a field with a long history in philosophy – we are really talking about mathematical logic, which takes as its substrate the intersection of logic and mathematical reasoning. This works in two directions – the application of mathematical reasoning to formal logical systems, and the application of these systems back to mathematics. This interplay has been especially important and influential as applied to foundational mathematics – that is, systems in which large parts of mathematics can be formalized. Therefore one often hears “foundational mathematics” and “mathematical logic” as approximate synonyms.

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Logic and foundations courses at Princeton [Show]

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