I have argued previously that beauty can be defined as roughly symmetry producing an indivisible object. Although multiple symmetries and perspectives can generate this, there is always an underlying pattern (a language) of universal symmetry. In this sense, beauty is a Platonic form.
Neoplasticists sought to describe aesthetics in terms of lines, quadrilaterals, and colour. An ambitious and somewhat grandiose project: they sought a universal grammar that could generate any form of beauty in such an indivisible object. Yet in their severe restrictions on functional form, they left out far too many degrees of freedom.
On the other hand, mathematicians have in effect generalised this project to uncover morphisms across any type of space or structure you can think of. As such, I regard mathematicians as today's neoplasticists creating a universal language of aesthetics for all senses: who else can establish a correspondence between circles and music? If this is not beauty, then what is?
Moreover, isomorphisms and automorphisms are also invoked in formal systems to explicitly define universal truth. This follows the approach of the structuralists, Tarski, et al in response to the postmodernists1 and those challenging the law of the excluded middle2 to cast doubt on the notion of objective truth itself. Then given we can establish the existence of such truth formally (provided we know our Boolean values are correct, and probabilistic inference also follows formal rules via distributions), it follows that rational deduction is sufficient, and empiricists in the style of Locke or Hume have reconstructed one form of such deduction. Therefore, the same language of morphism that acts as a universal grammar for beauty also encodes a universal and objective truth.
It follows then that both beauty and truth are objective abstract concepts that exist independently of ourselves and our perception, given there exists some invariant structure defining these two. Assume an idealist model of the world, where abstract objects carry as much ontological weight as physical objects (and there is no reason why they should not, if they exist in an invariant manner independently to our perceptions), then beauty and truth are Platonic forms.
I cannot resist making this point, albeit it descends into general culture war nonsense which is orthogonal here: the postmodernists had a serious epistemological agenda, and their challenges to the concept of truth were valid. Much of what I discuss here we only know given that others engaged in these questions as a direct response to, and result of, the postmodernists. Hence the right-wing attacks on this school are one reason why I have increasingly distanced myself from such commentary: reflecting their ignorance more than anything. Note that wokeness does not necessarily follow from postmodernism, nor vice-versa, anyhow.
The implications of relaxing this just produces a lattice in Boolean propositional logic anyhow. Nonetheless there exist higher-order systems, so as Tarski rightly argued, if we can establish isomorphisms between them, then we have an objective truth. Tarski's definition also came sometime after the debate between formalists (with Hilbert and Russell the most famous proponents) vs constructivists (Brouwer).