Nonetheless, FOL is a very good start to formalizing physics.

[mun]

Hi,

If one were to formalise physics, what would be the appropriate logic to use? Is FOL already sufficient, since the mathematics involved are first-order, e.g., sets, differentials. Or, is a more expressive logic needed?

 

[Tac-Tics]

Hi,

If one were to formalise physics, what would be the appropriate logic to use? Is FOL already sufficient, since the mathematics involved are first-order, e.g., sets, differentials. Or, is a more expressive logic needed?

It really depends what you mean by formalizing physics.

FOL is enough to talk about most meaningful mathematics. In FOL, you can construct proofs of equality between complex-valued functions, which should be enough for almost all physics.

However, regardless of the kind of logic you use, you will run into the problem that most physical systems are not algorithmic. You can give the initial conditions and expect to be able to calculate the final conditions. Though if you had your axioms right and you already knew the answer, you could use such a system to prove you were correct.