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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”.

Using Mathematical Modeling as an Example of Qualitative Reasoning in Metaphysics. A Note on a Defense of the Theory of Ideas