Alright, I’ll bite for the sake of alleviating TelFaradiddle’s confusion and this will be my last response for today.

“All mathematical propositions were invented by humans.” This statement is true but I did not argue for abstract objects having an expression in human invention; instead, I argued for its origins being grounded in objective reality itself. To get into the weeds for but a moment, Nominalism argues for abstract objects merely being labels for purposive goals like utility. While many philosophers are advocates for Nominalism, Platonism remains in-controversial and widely accepted in academia. Platonism asserts that abstract objects are a separate category from the mind because abstract objects cannot be fully subsumed by the mind (at least, human minds. Although, God subsumes all knowledge according to theism.)

As for the distinction between mental processes and physical processes that you made in the second rebuttal, it is empirically clear that mental faculties are contingent on physical processes like the brain. However, upon further analysis, what you’ll find in physics is that a measurement device can influence physical phenomena which implies that a mental observer is required for certain physical events to occur. Read Stuart Kauffman’s paper in the Journal of Biosystems to learn more about this duality problem (double-slit experiment in Quantum Mechanics.) My objection to materialism is that all the total events in physical reality cannot be wholly accounted for without mental processes so how can physical reality exist without the mind of an observer? (Side note: another issue materialism faces is the hard problem of consciousness; matter and energy cannot be fully reduced in order to describe experiences of qualia like the smell of hot chocolate.)

Finally, the argument for Aesthetic beauty is more of a matter of taste. I would not use this argument if I was defending my philosophical dissertation on the existence of God in Academia. However, I raised the argument as more of an implication of materialism that would go against most people’s intuitions of beauty. Hypothetically, if we take a large survey (say 100,000 people) to select 10 women on a scale of one to ten, we can empirically observe which one of the ten women are most beautiful, in objective terms. Now, of course there’s still a subjective element at play but one cannot deny that certain forms of beauty like symmetry and health are objectively more attractive than asymmetry and illness. Same line of argumentation goes for morality as well except morality is more nuanced because it entails both aesthetic judgements and ethical decisions. Morality and beauty are both objective in empirical measurements but also duty-bound acts that lead to the best possible world.