Using Mathematical Modeling as an Example of Qualitative Reasoning in Metaphysics. A Note on a Defense of the Theory of Ideas
Citation: Proceedings of the LQMR 2015 Workshop, Tomasz Lechowski, Przemysław Wałęga, Michał Zawidzki (eds). ACSIS, Vol. 7, pages 65–68 (2015)
Abstract. This is an outline of a defense of the theory of Ideas. I propose-using qualitative reasoning in metaphysics-the new incarnation of the theory of Ideas and I try to defend the theory against traditional counterarguments. The starting point are the theories of Ideas of Plato and Ingarden and an ontology of Ideas proposed by Kaczmarek; these theories are paraphrased-using a modified method of semantic paraphrases of Ajdukiewicz -and presented in terms of the basic concepts of category theory. To paraphrase Ideas as categories I propose recognized category theory as a pattern for the theory of Ideas. This recognition-based on an analogy between mathematical structures and philosophical structures-is the core of the qualitative reasoning in metaphysics. It could also be called a mathematical philosophy or mathematical modeling in metaphysics. I invoke an arrows-like, i.e. no-object-oriented, formulation of a category and I base the proposed theory of Ideas on that formulation. The components of an Idea are arrows and their compositions (equivalents of changes and transformations); objects in this approach are special arrows namely the identity arrows. Using the category of higher dimensions I introduce the concept of the dimension of an Idea (and other concepts) which allows me to refute the argument of the ''third man''.