The laws of logic are self-evident.

Thanks, Con, and welcome to Round 2. I'll begin by pointing out the idiocy of saying that my link was in any way a "trick." In the last round, I said that axioms were the foundation of classical logic... and then included a link to what classical logic was, simply so my opponent would know the kind of logic that I was talking about (since he doesn't seem to know the rules of them, I figured he might have it confused with something else -- there are, in fact, many different kinds of logic such as propositional logic). However, since my first link describing the kind of logic that I'm talking about is really irrelevant to my actual argument, then we can forget about it all together since it's really irrelevant to this debate. Again, it was just meant as a source to describe the kind of logic in question (classical logic). Meanwhile, my opponent's 2 sources merely relate a search page (which is irrelevant to the debate), and the same exact link that I have already provided in the first round; the Wiki page defining axioms. Let's move on. Con opens his argument by challenging the idea that the concept behind "a finite whole is greater than any of its parts" is not, in fact, self-evident. He claims that we can only be sure of this through 'experience.' However, Con is wrong. The reality that a finite whole is greater than any of its parts would be true whether or not I had ever learned that or "experienced" it, or if anyone else had ever learned or experienced it. It is not true because someone once decided that it's true, but simply because it is true. It is a self-evident truth which cannot be disproved; it is not something we consider true simply because we experience it as true. Con's asserts that we cannot prove that something is really self-evident, and instead that we're just hoping that this is true so in order to preserve our logic system. Well right there, we see that Con agrees that self-evident truths are foundations for classical logic. The resolution is affirmed: the laws of logic are self-evident. But anyway, Con writes, "My opponent also declares that if axioms are not true, then logic would be irrelevant and useless. However, she dismisses the conclusion as false without proving it to be false, therefore dismissing the premise as false without proof." This makes no sense whatsoever. What conclusion did I ever dismiss as false? The conclusion of that statement is simple: If logic axioms are not self-evident, then our logic system would be irrelevant because those axioms are the foundation of logic. If we can violate those laws, then the conclusions and premises of syllogisms would be very different. YOU WOULD NOT BE ABLE TO ARGUE AT ALL. For instance, if premise 1 read, "Socrates is a dog" and premise 2 reads "Socrates is not a dog," it would be acceptable *unless* you realize that these two statements cannot both be sound at the same time. The entire syllogism would be invalid. Similarly, Con claims that the law of identity is evident through proof; however, that is completely false. One cannot actually prove that a book is a book. What proof is there that a book is a book other than to accept it as a self-evident truth? It is certainly not one's 'experience' or 'exhaustion' which determines this fact, but rather its implicit state of being is reasoned through self-evidence. Aristotle explains: "Now 'why a thing is itself' is a meaningless inquiry (for to give meaning to the question 'why'—the fact or the existence of the thing must already be evident—e.g., that the moon is eclipsed—but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, 'because each thing is inseparable from itself, and its being one just meant this" [1]. Moving on to the law of the excluded middle, my opponent offers the same reasoning -- that this law is verified (proven) via the Proof of Exhaustion. However, that is certainly not the case. I'll first point out that nowhere does the SEP describe this law or proof. Does that mean we should not accept it and/or consider this argument a trick? Absolutely not. I'll just dismantle this argument without the SEP, which really isn't all that difficult to do. The proof of exhaustion is a proof which is established by working through EVERY possible case and finding no contradictions. Usually such a proof is only possible if the proposition to be proved has some restrictions placed upon it [2]. In other words, this system allows us to prove something by testing it over and over again to prove its validity. Let's take the four color theorem; it's an example which used this system to prove it to be true. The four color theorem states that only four colors are needed to color in any map without having any of the colors touch. This has been done over and over and over, and has always produced the same successful result [3]. That system is indeed entirely different than the concept behind self-evident truths. Self-evident truths are not proven to be true because trying to counter them repeatedly fails; they are considered self-evident because you CANNOT counter them without first assuming that they're true to begin with. For instance, how can we try to disprove that something is itself without first accepting that something is indeed itself (as in the law of identity)? On the contrary, the four color theorem cannot be proven true merely by assuming its truth -- which you can with self-evident truths. Instead, the proof of exhaustion must be implemented to prove that the theory can actually work. Again, this is NOT the case - or even anywhere near the same thing as self-evident truths. Finally, we have the law of non-contradiction. My opponent writes, "This is practically the same thing as the law of the excluded middle." However, once again my opponent is incorrect. The law of the excluded middle says that anything is either A or not A. For instance, I am either a human or I'm not. I'm either blue or I'm not blue. I'm alive or I'm not alive. Etc. Meanwhile, the law of non-contradiction says that nothing can be both A and not A at the same time. So, while it's true that I have to be either A or not A (i.e. human or not human), it's NOT true and in fact impossible for me to be both at the same time. So, in other words, I cannot be both blue and not blue at the same time (law 3), but I do have to be either blue or not blue (law 2). Con writes, "My opponent claims that the law of identity must be assumed because to attempt to disprove it would establish its truth. However, that is merely a proof for the law of identity." Once again, we are presented with a completely non-sensical statement. The first sentence was correct, but the second sentence did absolutely nothing except verify the first sentence. So we move on to Con's final argument of the round in which he writes, "It is realized that the law of identity is the law of identity, and so, by examples and truth, and not self-evidence, the law of identity is proven, and therefore not self-evident." Alas, we can see that Con has proven absolutely nothing. It is realized that the law of identity is the law of identity? Yes... so what's his point? He continues to say that by examples and truth (and not self-evidence) that the law of identity is proven; however, has not given any examples, and I've dismantled the "exhaustion" argument. Further, how can Con use examples and TRUTH to justify truth itself? Unless, of course, you accept a self-evident truth. Con just completely negated his own non-sensical argument. In conclusion, the laws of logic are self-evident. They prove themselves. [1] Aristotle's Metaphysics, Book VII, Part 17 [2] http://ddi.cs.uni-potsdam.de... [3] http://people.math.gatech.edu...