#mathematic #geometry # Created 2021-12-20 - 06:46 # [[Epistemic status]] #shower-thought # Euclidean Geometry invented by [[Euclid]], still used today, seems to consist of (infallible) axioms combined into theorems. (kind of obvious to me?) **Euclidean geometr**y is a superb attempt to map our physical territory, unfortunately, [[The Map is not the Territory|this map is not the territory]]. Our map which is the closest to our physical territory is [[Minkowskian spacetime]]? #knowledge [[Kant]] holds that **Euclidean** geometry is known a priori, although it is [[Synthetic]], i.e. not deducible from logic alone. Geometrical proofs, he considers, depend upon the figures; we can see, for instance, that, given two intersecting straight lines at right angles to each other, only one straight line at right angles to both can be drawn through their point of intersection. This [[Philosophy/Epistemology/Knowledge]], he thinks, is not derived from experience. But the only way in which my intuition can anticipate what will be found in the object is if it contains only the form of my sensibility, antedating in my subjectivity all the actual impressions. The objects of sense must obey geometry, because geometry is concerned with our ways of perceiving, and therefore we cannot perceive otherwise. This explains why geometry, though [[Synthetic]], is a priori and apodeictic. >In Euclidean geometry all triangles have interior angles equal to two right angles; straight lines meet at most once; and every direction in space determines a collection of parallel lines which never meet, keeping ever a constant distance from one another ~ [[Tim Maudlin]]