I'm trying to learn sentential calculus now and I'm very confused with the following thing.
In many books on logic I've found out that before working with sentential calculus itself we need the FINITE SET of symbols to define the syntax of the sentential calculus. So the concept of set and even of finite set is supposed to be already known.
But for me this fact contradicts with the fact that axiomatic set theory and construction of natural numbers (for example with Peano axioms) supposes that logic is already known: so it appears that we need to know what is a finite set to use the concept of the set itself.
Please, help me understand how these things shoul be learned.
Thanks in advance for any help.