Having never had much exposure to formal mathematical logic, I have decided to embark on a quest to rectify this; unfortunately having been exposed to concepts from Intuitionistic Logic through my dabbles in functional programming, I find myself running into issues understanding "how it all fits together".
I am familiar with the notion of rejecting the law of the excluded middle (LEM); from the little I know of intuitionistic logic, I understand that this is done in the sense that LEM is not treated as an axiom within whatever deductive system is being used. However, looking at the treatments of propositional calculus within pretty much any text that I can lay my hands on, I find that after a discussion of the syntax of a zeroth-order logic, the author starts to talk about "semantics", in many cases illustrating this with truth tables.
At this point I run into an issue, because clearly the semantics presented for example in Goldrei (Propositional and Predicate Calculus: A Model of Argument) mean that LEM is a tautology.
When presenting "the semantics of propositional calculus", is the author in fact presenting a specific "logic" (i.e. classical logic), or are these semantics a fundamental part of of any propositional calculus? It seems to me that the latter cannot be true (as intuitionistic propositional logic definitely exists), but I cannot find an introductory text in which the author addresses this issue.
I am likely falling into the trap of a little knowledge being a dangerous thing and it's quite possible that everything I think I know about this is wrong, but I find myself currently unable to pass beyond this point without serious doubts as to what I'm reading actually refers to.