The Root of All Dimensions
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This thesis aims to resolve the disjunction of ontology and epistemology in Platonist mathematical philosophy. This disharmony results from the assumption of the non-spatiotemporal existence of abstract mathematical entities, a principle which fails to account both for our knowledge of mathematics, and for the operation of mathematical principles in the tangible universe. In order to address the problem, we will examine the definition and function of mathematical principles as expressed in Plato’s philosophy, referring also to Aristotle in order to identify the logical restrictions governing the Platonist position. Our investigation of the nature and role of mathematical principles within the Platonist cosmos will lead us to the consideration of the geometric structures of matter as described in the Timaeus, and of the role of mathematics in the essential connection of the human intellect to the schematics and algorithms of the natural world.