Can you prove proof works?

[FulhamFan3]

What makes us so confident that a line of argument works at all? Why do you trust statements so much?

[Rainer]

Give an example.

[matt grime]

Do you mean mathematical proof? It is the axioms of logic that tell us when an argument is a correct proof, and they are just axioms.

[loseyourname]

It depends on the logical system in which you prove a statement. Certain systems seem to be based on axioms that are empirically verifiable at least to some extent. The classical laws of identity, non-contradiction, and excluded middle all have some basis in the way we observe nature to operate. Beyond this observation, though, there isn't any formal way I can think of to prove their validity.

[matt grime]

Axioms in mathematics are not really true, or false, they just are. Eg the parallel postulate isn't true, or false. What we do is work in models which satisfy the axioms. In the case of the parallel postulate there a models which satisfy it, and those that do not, and they are all useful in many ways.