Category Archives: Science

Numbers and other mathematical objects are simply concepts, and not things actually observable in the universe, so we cannot say that statements like 3+2=5 are true in the same way that we can say that the statement “massive objects exert forces on other massive objects” is true. We might like to think that mathematical statements are true by definition, but this idea is complicated by the fact that there is more than one way to axiomatize mathematics, and therefore more than one definition that we might choose in order to define numbers, operators and other mathematical objects. But even if there were truly only one way to axiomatize math, the axioms themselves would still not be provable, and hence it would hardly seem fair to then conclude that mathematical theorems are “True” in some objective and universal sense. These problems are compounded by the fact that we cannot prove that our commonly accepted mathematical axioms do not contradict each other, leading to a still deeper level on which to question the truth of mathematical statements. In the end, while it hardly seems fair to say that math is false, it is also not reasonable to conclude that math is true. Math is probably neither “true” nor “false” in the usual sense of those words, though it does, undeniably, provide extremely useful models for reality. This will perhaps seem less surprising if we remember that mathematics was not originally developed from the ground up using axioms, but rather piece by piece in order to solve problems that appear in the real world. Hence, mathematical definitions and theorems were originally designed by humans to model physical reality so that we could make useful predictions, not to encapsulate universal or metaphysical truth.

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