Abstract

Most commentators agree that (part of what) Kant means by characterizing the propositions of geometry as synthetic is that they are not true merely in virtue of logic or meaning, and that this characterization has something to do with his views about the construction of geometrical concepts in intuition. Many commentators regard construction in intuition as an essential part of geometrical proofs on Kant’s view. On this reading, the propositions of geometry are synthetic because the geometrical theorems cannot be proved in purely conceptual or logical terms. Other commentators see the main role of pure intuition and the figures constructed in pure intuition in that they provide a model for Euclidean geometry. On views of this kind, the propositions of geometry are synthetic because the geometrical axioms are substantive truths about one of our forms of intuition. On the interpretation proposed in this essay, what Kant means by claiming that the propositions of geometry are synthetic is not only that the Euclidean axioms and theorems cannot be reduced to tautologies or logical truths, but also that they apply to really possible objects. Construction in intuition plays no essential role in (what we now call) ‘pure’ geometry on Kant’s view. But the fact that the concepts of geometry can be constructed in intuition is of crucial importance in the context of Kant’s transcendental philosophy of geometry, because, among other things, it allows him to explain how Euclidean geometry is possible as an a priori synthetic science in the sense just indicated.