Hume on Space and Geometry

Graciela di Pierris (Stanford) gives a talk at the MCMP Colloquium titled "Hume on Space and Geometry". Abstract: Hume’s discussion of space, time, and mathematics in Part II of Book I of theTreatise has appeared to many commentators as one of the weakest parts of his work.I argue, on the contrary, that Hume’s views on space and geometry are deeplyconnected with his radically empiricist reliance on phenomenologically given sensoryimages. He insightfully shows that, working within this epistemological model, wecannot attain complete certainty about the continuum but only at most about discretequantity. Therefore, geometry, in contrast to arithmetic, cannot be a fully exactscience. Nevertheless, Hume does have an illuminating account of Euclid’s geometryas an axiomatic demonstrative science, ultimately based on the phenomenologicalapprehension of the “easiest and least deceitful” sensory images of geometricalfigures. Hume’s discussion, in my view, demonstrates the severe limitations of apurely empiricist interpretation of the role of such figures (diagrams) in geometry.