To even suppose that logic is false is to utter gibberish:
1. Logic is not a proposition that expresses a truth value; rather, it is merely the form that expresses true or false propositions. Logic cannot, itself, be called “false.”
2. A rejection of the laws of logic actually affirms the laws of logic. If one says that logic is incorrect, then by rejecting the fundamental Laws of Thought they say, simultaneously, that logic is actually correct because (1) there is no such thing as an invalid inference (the laws of logic are denied), (2) everything that they say is both true and false in the same respect (no bivalence or non-contradiction), and (3) the statement that they made is identical to every other statement ever uttered (no more identity). Essentially, they just said that their toes smell like green cheese.
3. One cannot actually argue against logic without presupposing logic in order to argue against it. If they, however, reject logic and so argue against logic without presupposing logic, then it merely follows from anything they say that the affirmation of the laws of logic is correct (in the absence of logic, there is no invalid inference). Anything they say simply affirms logic–even if they say that they reject it.
4. To say that logic is false is to form the proposition “logic is false.” However, the presupposed assumptions of a proposition cannot be predicated within that proposition (lest they not be the presupposed assumptions), and propositions presuppose propositional logic. For example, we may attempt to predicate “truth” within some proposition so that by asserting that proposition we presuppose that it is true. Thus, truth is predicated within proposition x and proposition x is thought to be true. However, any predication of truth–any attempt to define truth–presupposes an understanding of truth in order for proposition x predicating truth to be considered true. Thus, “truth” cannot be predicated without presupposing an understanding of truth, and because it is understood by means of a presupposed assumption it cannot be predicated within the proposition itself.
So if you want to reject logic, then feel free to pink up the smelly rainbow so long as you rip the sparkling without catching a yellow. Because, you know, you never know what you’re going to always know what you’re not going to chair.
The next time you doubt logic — or that logic is the bedrock of reason — simultaneously slap yourself and don’t slap yourself with a Logic Textbook.