Abstract
This paper proposes a new approach to the investigation into aesthetics. Specifically, it~argues that it is possible to explain the aesthetic and its underlying dynamic relations with an~axiomatic structure (the octahedral axiom-derived category) based on contemporary mathematics (namely category theory), and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there were a way to describe the structure of the aesthetic with the language of mathematical structures and mathematical axioms---a~language completely devoid of arbitrariness---then we would make possible a universal argument about the essential human activity of ``the aesthetic'', and we would also gain a new method and viewpoint into the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one mathematical structure as a foundation in constructing the science of dynamic aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the generative structure of the aesthetic.
Highlights
This paper focuses on a new kind of aesthetics, which is made possible by defining the mathematical structure of the aesthetic
Mathematician Saunders MacLane has stated in his work “Categories for the Working Mathematician” [12]: “A category will mean any interpretation of the category axioms within set theory”
This paper extends this statement and attempts the interpretation of category axioms into aesthetics
Summary
This paper focuses on a new kind of aesthetics, which is made possible by defining the mathematical structure of the aesthetic. “Aesthetics” prior to that, regardless of whether it was “the science of sensitivity” or “the philosophy of beauty” was studied exclusively based on the correlation between subject and object, and scholars were attempting to describe the aesthetic experience that comprises the aesthetic objectively, as a universal phenomenon Such subject = object relations are too simplistic. Q, and because M in Q is injected into zero and not tangible, we can call M the environment of Q (of the step) This means that the multifarious works of art Q (e.g., paintings, sculptures, music, and poetry) and their observers P emerge through the aesthetic concept X as an extension of M generating an aesthetic object.
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