Paradox of Truth

Philosophy has built for itself a great system of knowledge, bound by an even greater system of logic. The nature of this logic is so purely obvious: if an idea is in self contradiction, it is false; the conjunction of a statement with a false statement is false; the negation of truth is false, and conversely; many simple laws compose our thought.

But why this logic, and not another? I have heard it argued that such logic is only how we speak, and not what we mean. That seems perfectly fine, so long all agree that it is so, but when not all agree that logic is the words and truth the meaning, that they say logic, not ours but theirs, is truth, we would call their logic illogical, by the sacred grounds of our own. Where is the division? If so many people would refuse good logic, and use themselves the poorest reasoning, declaring it the more truthful, who is to say that what we call good logic is not just that?

The dilemma is much worse when it happens that two so disagreeing people must debate each other on some philosophical matter, and the truth of one is not the truth of the other. What is philosophy, if we are unable not merely to speak the same language but to think the same ideas?