Mathematical Platonism

Contemporary mathematical Platonism is not the Platonism of Plato, which advocates for the existence of many "forms" that include moral virtues, colors, and ideas.  The former merely holds that mathematical truths exist independent of human perception, and nothing more, whereas the latter holds that there are abstract "forms" of everything from chairs to colors.  It is clear that the two doctrines are not identical.  Plato's Platonism is utterly doomed on epistemological grounds [1], and it also fails to be metaphysically valid (though I have yet to explain why there is no "form" of a chair, I have already deconstructed moral Platonism).  Mathematical Platonism, on the other hand, is correct.

Nevertheless, the explanations given for why it is correct are often lacking, and they do not go far enough in detailing either the reason why mathematical truths exist apart from the human mind or how they actually exist independent of all minds and matter.  Regarding the first of these matters, mathematics is nothing but numeric logic, and so has to exist, since logic has to exist.  Regarding the second, logic exists in the absence of all other things, not merely the human mind.  There is a massive distinction between what I mean when I say that logic exists independent of all other things (a truth yet to be elaborated upon by even a single academic "authority," as far as I am aware [2]) and what mathematical Platonists mean when they say that math transcends human awareness.

Logic is far broader and more foundational than mathematics alone is.  Mathematics reduces to logic, but logic does not reduce to mathematics; numbers cannot exist apart from the laws of logic.  Also, mathematical Platonism merely holds that mathematical truths exist without the human mind, but there is an enormous difference between an existence that is independent of human perception and existence that is independent of all other things.  As such, even mathematical Platonism falls short of affirming some of the most important truths about logic, truths that are among those that only an extremely small minority ever discover on their own.

Non-rationalistic Christians often claim that mathematical truths exist in the absence of human minds but not in the absence of the divine mind.  They are grievously mistaken: if there was no deity, there would be zero gods.  Numbers exist without God because they are rooted in logic, and logic exists by intrinsic necessity.  In the same way, the nonexistence of God would mean that it is true that there is no God, meaning that truth exists independent of God--and every law of logic would likewise remain true by necessity in God's absence.  The fact that God could cease to exist [2], leaving only the necessary and uncreated laws of logic (accompanied by mathematical truths) and empty space as creation vanishes, is scarcely emphasized at all, yet it remains true.

The independence of logic from all other things continues to be ignored, denied, or overlooked, even by mathematical Platonists.  They do not tend to go far enough.  Of course, few ever do when philosophical pursuits are concerned.  There is no "form of reason," as an adherent of Plato's Platonism might suppose; there is only reason itself.  Furthermore, regarding mathematical Platonism, not only do mathematical truths exist apart from everything other than the laws of logic, not just human minds, but the laws of logic also exist apart from everything other than themselves.  Reason is the necessary existent, the one thing that cannot not exist, regardless of what else does not, and this and this alone is why numbers exist necessarily.


[1].  https://thechristianrationalist.blogspot.com/2017/11/the-circular-reasoning-of-platonism.html

[2].  https://thechristianrationalist.blogspot.com/2018/11/the-ramifications-of-axioms.html