Mathematically speaking, what is an ‘Axiom’?
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Axioms are essentially things we choose to hold as truth because there is no way to prove that they are true, and they are the building blocks we use to “prove” other things.
There’s a field of philosophy called *epistemology* which is basically the philosophical study of “how we know things” and one of the most famous conclusions reached in this study (and one of the most famous philosophical ideas ever) is that virtually nothing can actually be proven, the only thing that *can* be proven is “I think, therefore I am.” Basically saying that the only thing that you can know with absolute certainty is that because you have a consciousness, you exist in some capacity, everything beyond that can not be proven.
This, as I said, is a very famous conclusion, but it is also impractical, we want to be able to make sense of our world so to get around this idea we create “axioms” which are statements that we hold to be true without any actual proof that they are. These axioms become the building blocks of math, science, and philosophy that we use to “prove” other things. But those proofs rely on the axioms being true, if you can falsify an axiom, you will either falsify or bring into question any things that were “proved” using the axiom.
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