A Philosophical Inquiry into the Concept of Number

The dissertation is an inquiry into the ontology and epistemology of numbers. As regards the former, the Fregean conception of numbers as objects and the Russellian conception of numbers as higher-level entities are both critically examined. A conception of numbers as modes of existence, that is, ways or manners in which things exist, is introduced and defended instead. As regards the latter, the basic concepts of arithmetic are explicated in terms of pure logic alone, and all the truths of arithmetic are shown to follow from those explications solely by logical means. A new version of logicism in the philosophy of arithmetic is thereby established.