If you put a chair next to another chair, and you found that there were three chairs where before there was one, would it be more likely that 1 + 1 = 3 or that arithmetic is not the correct model to describe these chairs? A true mathematical proposition is a pure conduit between its premises and axioms and its conclusions.
But note that you can never be quite completely certain that you haven’t made any mistakes. It is uncertain whether “S0 + S0 = SS0” is a true proposition of Peano arithmetic, because we may all coincidentally have gotten something hilariously wrong.
This is why, when an experiment does not go as predicted, the first recourse is to check that your math has been done correctly.
If you put a chair next to another chair, and you found that there were three chairs where before there was one, would it be more likely that 1 + 1 = 3 or that arithmetic is not the correct model to describe these chairs? A true mathematical proposition is a pure conduit between its premises and axioms and its conclusions.
But note that you can never be quite completely certain that you haven’t made any mistakes. It is uncertain whether “S0 + S0 = SS0” is a true proposition of Peano arithmetic, because we may all coincidentally have gotten something hilariously wrong.
This is why, when an experiment does not go as predicted, the first recourse is to check that your math has been done correctly.