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Coherence principle7/23/2023 ![]() ![]() An overview of categorical structuralism is given, as well as the associated views on the foundations of mathematics. In this thesis, we begin by by investigating structuralism to note important properties of mathematical structures. This has led to a programme of categorical structuralism, integrating structuralist philosophy with insights from category theory for new views on the foundations of mathematics. It has been noted that category theory expresses mathematical objects exactly along their structural properties. Structuralism is the view that mathematics is the science of structure. Finally, since such a shift in foundations is motivated by independent mathematical reasons as well, we shall argue that going “normative” and trying to change mathematics in order to save the structuralist insight is not an ad hoc move. We shall show that, once faced within the appropriate conception of mathematics, the former criticisms could be countered. As a consequence, the tenets of structuralism become normative constraints which act at the level of foundations, specifically on the formal language and framework. On the contrary, the core insight of structuralism could be regarded as prescribing what mathematics should be about and on how such mathematics should be expressed. Accordingly, this thesis is not regarded as providing an account of the ontological and metaphysical nature of mathematical objects and their properties in fact, such a view has elicited several objections difficult to dismiss. The aim of this paper is to present a different reading of the structuralist thesis in philosophy of mathematics.
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