### The Synthetic Nature of Geometry, and the Role of Construction in Intuition

Anja Jauernig

Sala: sala Beccaria

Data: 26 maggio 2010 - 14:30

Ultima modifica: 13 aprile 2010

#### Abstract

Kant famously claims that Euclidean geometry is synthetic. This thesis is usually understood as saying that the Euclidean theorems cannot be derived from the Euclidean axioms in purely logical terms, which is why geometric proofs depend on construction in intuition, or that the Euclidean axioms cannot be reduced to logical truths or tautologies, but should be understood as truths about our pure intuition of space. I argue for a third reading of this thesis, namely, that Euclidean geometry is informative and applies to the actual world. On my reading, construction in intuition is not essential to geometric proofs, but it still plays an important role in Kantâ€™s philosophy of geometry, not least because it allows the transcendental philosopher to explain how Euclidean geometry is possible as an a priori synthetic science.