Meta Ontology

We show how an epistemology informed by cognitive sciencepromises to shed light on an ancient problem in thephilosophy of mathematics: the problem of exactness. Theproblem of exactness arises because geometrical knowledge isthought to concern perfect geometrical forms, whereas theembodiment of such forms in the natural world may beimperfect. There thus arises an apparent mismatch betweenmathematical concepts and physical reality. We propose thatthe problem can be solved by emphasizing the ways in whichthe brain can transform and organize its perceptual intake. Itis not necessary for a geometrical form to be perfectlyinstantiated in order for perception of such a form to be thebasis of a geometrical concept.