We don’t. At some point we need take things on faith. The good news is we don’t need much faith. For math most people use, there are a few ideas we take on faith called “Peano’s axioms” which are basic things like “1+1=2” and “I can add one to a number”.
We also have a LOT of experience to tell us that those things are true, but that only results in high confidence, not certainty.
For the not 5 year olds:
– check out Godel’s incompleteness theorem
– prove to me the concept of “previous observations are relevant to future events” without recursion.
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