Mathematical Truths

Everyone must utilize at least some awareness of mathematical truths to function on a practical level, as well as to function on an abstract level where quantities of any kind are involved.  Anyone who sees multiple rocks, vehicles, trees, or any other material object and recognizes the distinction between one item and another that belong in the same broad category grasps basic mathematical facts to some extent.  One can understand some foundational truths about addition or numeric sequences, to name a handful of examples, without having a developed understanding of what follows from the more foundational aspects of arithmetic, but there are far more explicitly metaphysical truths that can be reasoned out by reflecting on the nature of numbers.

Numbers are neither physical objects nor mere linguistic symbols.  Mathematical truths confine physical objects, hence why nine trees will always be nine trees and not six or any other number, and numbers can be assigned words or symbols meant to refer to them.  Thus, physical matter and language still have connections to mathematics despite math transcending them both.  There is also the further, more foundational connection of all things being governed by the truths of logic: logical truths preside over every aspect of reality, including numbers, languages, and material objects.  Equating these three with each other due to a misunderstanding of their connections is still a blatant error.

Because it pertains to the numeric applications of logic, mathematics deals with a particular subset of necessary truths--logic itself is all-encompassing, far broader than numbers alone could possibly be.  Without logic, numbers could not have any conceptual relationship with each other or any sort of inherent truth that forces itself on the material world.  Other than math, however, there is still an enormous amount of logical truths that can be known even if not all of them are known by a single person.  There is nonetheless no aspect of reality that is exempt from truths about numbers because mathematical truths, like all logical truths, cannot be false.

Mathematical truths are not happenstance, contingent constructs of perception or matter.  Even if no minds existed to grasp them and no matter existed to physically reflect them, numerical concepts would still be true and would thus still exist.  Numbers and the relationships between them are not arbitrary or dependent on things that could have been some other way.  It follows that numbers, understood properly, can be used to refute solipsism, strict naturalism, the idea that the uncaused cause (God) created everything in existence (here is a separate post addressing the necessary existence of mathematical truths in a theistic context [1]), and any other philosophy that ultimately contradicts the truth that mathematical facts, as well as any logical fact, exist without reference to matter, minds, or time.

[1].  https://thechristianrationalist.blogspot.com/2018/10/refuting-mathematics-applicability.html