This lecture discusses key ideas from the 18th century philosopher Immanuel Kant's work, The Prolegomena to Any Future Metaphysics.

Specifically it focuses on his discussion in the Preamble on the peculiarities of all metaphysical knowledge, bearing upon the nature of mathematical judgements, properly speaking. Kant argues, against previous thinkers, that properly mathematical judgements are not analytic but synthetic a priori. There is still scope for analytic judgements within mathematics that help to clarify matters or to show some equivalence or equality.

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