The Instigator
Danielle
Pro (for)
Winning
58 Points
The Contender
mongeese
Con (against)
Losing
8 Points

The laws of logic are self-evident.

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Post Voting Period
The voting period for this debate has ended.
after 11 votes the winner is...
Danielle
Voting Style: Open Point System: 7 Point
Started: 12/21/2009 Category: Education
Updated: 4 years ago Status: Post Voting Period
Viewed: 9,241 times Debate No: 10539
Debate Rounds (4)
Comments (60)
Votes (11)

 

Danielle

Pro

Many thanks in advance to my opponent for accepting this debate.

Because we've had an issue regarding definitions in the past, I'd like to take this opportunity to address any relevant definitions or clarifications for this debate. The dictionary defines logic as the science that investigates the principles governing correct or reliable inference. In philosophy, logic is used to construct proofs which give us reliable confirmation of the truth of the proven proposition. We derive truthful conclusions from truthful premises. The system of classical logic relies on laws that are self-evident. A self-evident proposition is one that is known to be true by understanding its meaning without proof. I stand in affirmation of the resolution: The laws of logic are self-evident. If my opponent accepts these definitions, he must simply respond to confirm and I will begin this debate in the second round. Thanks again, and good luck!
mongeese

Con

I accept my opponent's definitions.

Here's to a good debate!
Debate Round No. 1
Danielle

Pro

Thanks again to my opponent for accepting this debate.

I'd like to point out that regardless of what my opponent puts forth, the resolution is automatically affirmed given the nature of logic itself. Classic logic [1] relies on self-evident truths called axioms; without these laws, the entire logic system we use would be irrelevant and useless. So, because classical logic absolutely does rely on self-evident truths (whether my opponent agrees with them or not), then I have automatically won this debate based on that brute fact alone. Anyone who knows the rules of logic knows that this is true. However, it is not my intention to win this debate on a semantics level. I will explain how, why and that the laws of logic are self-evident, and see if my opponent can really argue that the laws of logic are not or should not be self-evident as he has claimed on more than one occasion.

In traditional logic, an axiom is a proposition that is not proved or demonstrated, but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted and serves as a starting point for deducing and inferring other (theory dependent) truths [2]. For instance, an example of a self-evident truth is the notion that a finite whole is greater than any of its parts. This is something that seems "obviously true" because it is. So, self-evident axioms exist.

There are three self-evident logic axioms:

1. The law of identity
2. The law of the excluded middle
3. The law of non-contradiction

* The law of identity states that anything is itself. In other words, A = A.

* Tautologies follow the first law, and assert that something is either A, or not A.

* The final law follows the second, and posits that nothing can be both A and not A simultaneously.

These laws are self-evident because they exist to prove themselves. Their truth is inescapable. As soon as you try to disprove any one of them, you find that you must assume it to be true. For example, the law of identity states that A = A; everything is equivalent to itself. If one were trying to disprove the law of identity, then he would not be trying to disprove the laws of gravity or the laws of motion. He would indeed be trying to disprove the law of identity (and it is not the law of gravity or the law of motion). The law of identity is exactly that: the law of identity. Thus, the first axiom must be assumed.

The second law (tautologies) can be explained in the same manner. One cannot both be A and ~A. If A refers to "I am American" then ~A cannot be true. In other words, if I am an American, then I cannot NOT be an American. This is precisely why my opponent's statement that one can be both typing and not typing at the same time is false. Of course if one defines "typing" in two ways then it is possible; however, two separate definitions would mean that you're not referring to the same thing, meaning the law would not apply.

And finally, the law of non-contradiction follows in the same way. If you tried to disprove the law of non-contradiction, then you'd be trying to prove that it was false that something could not be both true and false at the same time and in the same way. However, in doing so, you are assuming the very law that you're trying to disprove! Another example: If I say that my kitchen table is made of wood, then I cannot also say that it is not made of wood (at the same time). In doing so, I would have made two statements that exclude the possibility of the other. As such, we would be presented with an impossible contradiction.

In conclusion, self-evident truths exist. To deny the validity of the inherent (self-evident) laws of logic would result in retortion -- presenting arguments that rely upon the very principles it seeks to overturn. In other words, how does my opponent plan on countering my argument? Any point that he presents will undoubtedly be based on logic. However, if these fundamental laws are not self-evident, then the entire foundation of logic is dismantled meaning his arguments are completely irrelevant.

With that, I send the debate over to Con.

"Those who invalidate reason ought seriously to consider whether they argue against reason with or without reason. If with reason, then they establish the principle that they are laboring to dethrone: but if they argue without reason (which, in order to be consistent with themselves they must do), they are out of reach of rational conviction, nor do they deserve a rational argument." -- Ethan Allen ... not the furniture guy :p

[1] http://plato.stanford.edu...
[2] http://en.wikipedia.org...
[3] http://plato.stanford.edu...
mongeese

Con

Thanks for the reply.

My opponent puts forth axioms as self-evident building blocks of logic. I would first like to point out that my opponent's source for this claim says nothing to support the claim, listing axioms rarely, and not once calling axioms self-evident. In fact, nothing about self-evidence is mentioned at all. The entire SEP itself has no comprehensive pages on both axioms and self-evidence [1]. There isn't even a page for the law of identity. The source should be dismissed as a trick. However, this isn't necessarily true. An axiom is "a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision" [2]. Now, to consider something to be self-evident does not make it so, so in reality, we just hope that axioms really are self-evident, or provable in some other way, to preserve our logic. 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.

My opponent uses, as an example, the statement "A finite whole is greater than any of its parts." However, this is not self-evident. When you read that statement, your mind proves it for you. You realize from past experience that a part is less than a whole. You do some simple math, and realize that if any part where equal to a whole, it wouldn't be a part, but a whole, and if a part were greater than a whole, it couldn't be a part, as nothing could be added to the part to reach a whole, and you know from experience that parts can always be added together to make a whole.
In conclusion, it seems obviously true because you can prove it to be true in such a simple way.

The law of identity is also rather simply proven through experience. You ask yourself, is that lamp a lamp? Yes. Is my watch a watch? Yes. Is this computer a computer? Yes. Is that refrigerator a refrigerator? Yes. Rather quickly, you realize that you cannot even conceive of a situation in which the law of identity could be false. It's somewhat like a proof by exhaustion. And so, the law of identity is not self-evident, but evident through proof.

The law of the excluded middle is much the same way. Through a proof by exhaustion, one realizes that he cannot conceive of a single scenario in which something is both A and not A. Additionally, it can be reasoned that double negatives are equal to a positive (-1 * -1 = 1) by the simple definition of "opposite," and therefore...
If A, then not not A.
If A, then not ~A.

Finally, the law of non-contradiction. This is practically the same thing as the law of the excluded middle. It is soon realized through any conceivable example that A iff not ~A, and ~A iff not A.
A. Therefore, not ~A.
~A. Therefore, not A.
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. 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.

In conclusion, the laws of logic are not self-evident, but rather evidenced by rather simple proof.

1. http://plato.stanford.edu...
2. http://en.wikipedia.org...
Debate Round No. 2
Danielle

Pro

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...
mongeese

Con

Thank you, PRO, for your quick response.

Thank you for the clarification that the source was merely meant for background information of some sort, and not required at all for the argument.

My opponent puts forward the claim that her "self-evident" statement "would be true whether or not I had ever learned that or 'experienced' it, or if anyone else had ever learned or experienced it." However, let's take another fact that we would not consider to be self-evident at all: the fact that carbon sublimates at 3800�C. This would be true despite anybody's knowledge or experience, just like my opponent's "self-evident" statement; however, that fact cannot make something self-evident, or else carbon's sublimation point would be self-evident, and I only know that because a chemistry website (http://chemistry.about.com...) said so, because scientists empirically proved it to be true. Nobody decided to just say that carbon would sublimate at a given temperature; it just does, and we have proven it to do so, and therefore know it to do so. One cannot disprove this scientific fact, but carbon's sublimation point is still not self-evident. Therefore, what my opponent says, while true, does not intrinsically make her statement self-evident.

I have never agreed that axioms are self-evident. I don't see where my opponent gets that conclusion, and she didn't do a very good job at explaining.
My opponent points out that argument necessitates logic. That is all that was required.

My opponent claims that one cannot prove that a book is a book. However, to call something a book requires a definition for book. Let's use, "a set of written sheets bound together into a volume" (http://www.merriam-webster.com...). Now, I am given that A is a book. I must prove that A is a book. Now, I know that A is a set of written sheets bound together into a volume, because it is a book. Therefore, because A matches the definition of "book," it is a book. I have proven A (a book) to be a book. Rather simple, but still proof. I could do this for any object that my opponent would wish to present. I could prove a table to be a table; cinnamon to be cinnamon; an iPod to be an iPod. I can prove the Law of Identity. Anybody and everybody can prove the Law of Identity, and everybody does prove the Law of Identity to themselves, and that is why we know it. Because the Law of Identity is proven, it cannot be self-evident.

As for Aristotle's quote, he explains the Law of Identity to be "because each thing is inseparable from itself, and it's being one just meant this." Sounds like a proof for the Law of Identity. If Aristotle has to be dragged in to explain something, then it's not evidencing itself.

My opponent criticizes my mentioning of proof by exhaustion. This would probably explain it better: one realizes that for any object with definition A, if it is given to be A, then it has the properties of A, and by the definition of A, anything with the properties of A is A, and therefore, A is A. It's more like a substitution of all possible objects A, I guess. Exhaustion of everything at once.
Similarly, one realizes that for any description A, given the definition of "opposite" involving shifting among pairs (http://www.merriam-webster.com...), if an object is A, then it is A, and if it is not A; else, it is ~A. Simple as that.
Finally, one realizes that A is not ~A by realizing that ~ means "not," and we have the Law of Contradiction.

My opponent again claims that if something cannot be countered without assuming it to be true, then it must be self-evident. However, this looks more like a proof of validity than a proof of self-evidence, as a proof of self-evidence by definition cannot exist. Let's take proposition B: anything is either A or not A. First, I assume it to be true (B), and realize that I can possibly argue in favor of B (B). Then I assume it to be false (~B), and realize that I cannot disprove it, and therefore, (~B) cannot be true. Through deductive reasoning, I realize that B must be true (B). This is a rather informal proof, but still a proof. Therefore, I have proven B: anything is either A or not A.

However, most people wouldn't even attempt this informal proof, and prove it by the definition of "opposite" or "not," as explained two paragraphs above.

Now, my opponent criticizes my statement, "However, this is merely a proof for the law of identity." Well, my opponent did prove the law of identity through deductive reasoning, did she not?

Finally, I am criticized for saying, "By examples and truth, and not self-evidence, the law of identity is proven, and therefore not self-evident." The point is that for something to be self-evident, it must be known WITHOUT proof, and as it is known WITH proof, it cannot be self-evident. My opponent claims that I have accepted a self-evident truth. This is false; I've only accepted truths that have been proven.

My opponent claims that the laws of logic "prove themselves." However, for a proposition to be self-evident, it must be "known to be true by understanding its meaning without proof." This is obviously a contradiction, as if something proves itself, then its meaning is understood, with proof. My opponent has contradicted her own definition. She admits that these axioms, "known... without proof," to be proven. Therefore, they are not self-evident. My opponent's entire argument from this point collapses.

In conclusion, I have proven the axioms that my opponent claims to be self-evident, and therefore not proven. My opponent has done nothing, really, to defend her first "self-evident" statement. She has even admitted her axioms to prove themselves, and therefore, they cannot be self-evident. As the axioms upon which classical logic (Why did we even throw "classical" in here? It's not in the resolution...) rests are not self-evident, the laws of logic are not self-evident.
Debate Round No. 3
Danielle

Pro

Thanks, Con.

I'll begin with Con's example regarding carbon sublimating at 3800� C. His point was that this fact would be evident whether anyone had experienced (learned?) it or not, and a such, that alone is not enough to make it self-evident fact. Con is 100% correct. Indeed objective reality exists outside of ourselves, so that fact would be true regardless of our experience. The only reason I mentioned experience in the first place was because my opponent was the one who said in the previous round that experience proves certain laws. I explained how that was not the case, and most certainly not the case in regard to self-evident laws. Nowhere did I ever say that experience proved anything, so Con has completely strawmanned my argument, and actally took his own wrong argument and proved how it was wrong.

On that note, we can see where Con's analogy regarding the carbon fails. He writes, "Nobody decided to just say that carbon would sublimate at a given temperature; it just does, and we have proven it to do so, and therefore know it to do so. One cannot disprove this scientific fact, but carbon's sublimation point is still not self-evident. Therefore, what my opponent says, while true, does not intrinsically make her statement self-evident."

Ladies and gentlemen, that is a complete misrepresentation of my argument. I never said that everything which has been proven true was self-evident. I gave only THREE, count 'em, THREE laws or facts that are proven to be self-evident, therefore Con's example is irrelevant. In the previous rounds, I have explained on numerous occasions that something is self-evident because it proves itself. In no way has the sublimating temperature of carbon ever proved itself. To come up with this information, scientists have used other pieces of evidence and experimentation - perhaps even the Proof of Exhaustion method - and thus Con's point here is moot. He has ignored the reason behind what actually makes something self-evident, and instead presented an analogy which does not fit the criteria at all.

Next, Con writes, "I have never agreed that axioms are self-evident. I don't see where my opponent gets that conclusion, and she didn't do a very good job at explaining." In the last round, my opponent's very first paragraph states: An axiom is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Con provided and sourced this definition. An axiom by its very definition is self-evident.

Now we get to the heart of the debate.

Con responds to the law of identity saying that the definition of "book" is how we can prove that something is a book. However, that is an insufficient argument. In order to define something, there must be something to define. Even if you define book as "a set of written sheets bound together into a volume," the law of identity states that a book is a book because that's exactly what it is: a set of written sheets bound together into a volume. In other words, when we say that something has an identity, we are saying that it has a specific nature. So, in calling something a book, you're acknowledging that it possesses the nature of written sheets bound together in a volume. It's not just applying the definition, but accepting it for what it is.

Aristotle was the first to explicitly formulate the law of identity. He and just about every single major (and minor) philosopher after him accept that this law is axiomatic and self-evident; it is considered the most certain of all principles. It has never been proven untrue in classic logic. Indeed, it forms the foundation of a coherent philosophical system [1]. The law of identity can be described as saying that everything is identical to itself. Obviously utilizing a simple definition does not give you the same result or understanding as the law of identity.

You can define something, but to accept the law of identity as self-evident is to go far beyond implementing or understanding the definition. The definition itself is irrelevant to the role that this law actually serves in philosophy, which is to assert that while a book maybe defined as a set of written sheets bound together in a volume, that it actually IS a set of written sheets bound together in a volume. And, of course, while Book A and Book B may both be books by definition, Book A = Book A, and Book B = Book B; they are both identical to themselves, and while both are books, they are not identical to each other.

Further, Con writes that because Aristotle notes that each thing is inseparable from itself, and it's 'being' alone proved this, that it sounds like a proof for the Law of Identity. He says, "If Aristotle has to be dragged in to explain something, then it's not evidencing itself." However, you'll notice that Aristotle merely explained exactly why the law is self-evident. If my opponent agrees with that - which he should - then it only proves my case. Aristotle didn't provide outside evidence for the law, but merely explained why the law was evidence in and of itself... hence being self-evident!

Moving on to the second and third laws, I'm not sure what Con's explanation regarding the Proof of Exhaustion is. The PoE is already clearly defined, and whatever Con explained it as in the last round is wrong. I've defined and explained the Proof of Exhaustion system in the last round. You cannot change the systematic laws of certain principles to fit an agenda. As I have explained, the PoE is completely irrelevant to the laws of self-identity. You can use the PoE to prove something, and may even use it to prove the 3 axioms I have provided as true; however, simply because those 3 axioms may be proven in other ways in no way negates the fact that they are still evidence for themselves; they are self-evident.

Next Con writes, "My opponent again claims that if something cannot be countered without assuming it to be true, then it must be self-evident. However, this looks more like a proof of validity than a proof of self-evidence, as a proof of self-evidence by definition cannot exist." I would like for Con to please explain or rather prove to me how self-evidence by definition cannot exist. In fact, I will prove to you right now that this is a false statement -- In epistemology, a self-evident proposition is one that is known to be true by understanding its meaning without proof [2]. As you can see, there is a definition for this term and this term does in fact exist. The three laws that I have mentioned prove that self-evidence exists.

Regarding his intended syllogism, you'll notice that Con says, "Through deductive reasoning, I realize that B must be true..." However, all form of reasoning is based on logic, and all logic is based on the 3 self-evident axioms that I have provided. So, when Con asks, "Well, my opponent did prove the law of identity through deductive reasoning, did she not?" The answer is yes - because reasoning is based on logic, and logic is based on these 3 self-evident axioms. Nevertheless, here is an actual comprehensive syllogism derived not from classical logic (since I won't use logic to explain itself - hehe) but rather propositional logic [3]:

1. (A & ~A) [Proposition]
2. A [Conjunction elimination from 1]
3. ~A [Conjunction elimination from 1]
4. ~(A & ~A) [Reductio 1 - 3]

That said, Con's conclusion is FALSE. He writes, "For something to be self-evident, it must be known WITHOUT proof, and as it is known WITH proof, it cannot be self-evident." Again - the axioms I mentioned prove themselves! Yes, they require proof, but if they can prove themselves (which I have demonstrated and Con has not and can not negate), then they are indeed self-evident.

[1] http://talbenshahar.com...
[2] http://en.wikipedia.org...
[3] http://editthis.info...
mongeese

Con

Thanks, PRO, for this debate. It's been fun.

It appears that I only need to mention a few things here.

My opponent criticizes my introducing carbon's sublimation point as a straw man. However, she claimed that her statement, "a finite whole is greater than any of its parts," is self-evident, and went on to describe many things about the statement that would apparently make it self-evident. I merely pointed out that something with the characteristics described by my opponent doesn't intrinsically make that thing self-evident.

My opponent has given no significant difference between her own statement and mine that would make one self-evident while the other not (as I have already shown why her proposition requires a simple proof to compare to the empirical evidence of carbon's sublimation). Therefore, it seems to be an easy conclusion to make that they are both either self-evident or not self-evident. Seeing as carbon's sublimation point requires proof to be known, they are not self-evident.

My opponent claims that this is a straw man because "nowhere did I say that experience proved anything." However, I never said that she did. I merely pointed out that by her own reasoning, carbon's sublimation point would be self-evident, and it's not, so her reasoning is incorrect.

My opponent claims, "something is self-evident because it proves itself." However, that does not fit the agreed-upon definition of "self-evident," "known to be true by understanding its meaning without proof." If it proves itself, then it is known to be true with its own proof, and therefore, it cannot be self-evident.

My opponent makes this claim throughout the debate:
1. "These laws are self-evident because they exist to PROVE themselves."
2. "The laws of logic are self-evident. They PROVE themselves."
3. "Something is self-evident because it PROVES itself."
4. "Again - the axioms I mentioned PROVE themselves! Yes, they require PROOF..."
5. "They are still evidence for themselves; they are self-evident."
6. "The law was evidence in and of itself... hence being self-evident!"

Again, I present the definition of "self-evident": "known to be true by understanding its meaning WITHOUT PROOF." No, self-evident does not mean, "evidencing itself," as one would probably assume.

My opponent has contradicted the established definition rather badly. If they prove themselves, then they are understood with proof, and are therefore not self-evident. My opponent seems to be debating under the premise that a self-evident proposition is one that proves itself, but that's far from the established definition. After all, if they prove themselves, then how is that not proof? If she wished for her contentions to actually support the resolution, she should have defined "self-evident" differently.

This was actually my conclusion in Round 3, and my opponent's only opposing response was, "if they can prove themselves, then they are indeed self-evident." However, this is an unsourced, unsupported claim that contradicts the very definition under which we are debating.

My opponent has challenged me to prove that a proof of self-evidence cannot exist. It's rather simple. The definition of "self-evident" requires a lack of proof, so to prove something to be known without proof is contradictory and impossible.

My opponent claims that an axiom is self-evident by definition. I shall repeat the definition of "axiom" that I sourced: "An axiom is a proposition that is not proved or demonstrated but CONSIDERED to be either self-evident, or subject to necessary decision."
This definition does not claim that axioms are self-evident, but rather, points out that they are CONSIDERED to be self-evident. My opponent's attempt at a straw man has been foiled.

All of my opponent's claims about the three basic laws of logic do nothing to demonstrate that they are known without proof.

In conclusion, my opponent has completely missed the mark by establishing a definition that contradicts everything she claims. The laws of logic prove themselves, and are therefore not known without proof. This is rather simple. Something that proves itself is known with proof, and therefore is not self-evident. My opponent admits the laws of logic to prove themselves, and therefore, the laws of logic are not self-evident. The resolution is negated. Vote CON.
Debate Round No. 4
60 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Danielle 3 years ago
Danielle
The concepts of math are begun empirically (apples plus apples...) but quickly move into abstract a priori notions.

"the negation of axioms cannot be [true]."

Indeed
Posted by Dash555 3 years ago
Dash555
justified true beliefs.

The axioms of mathematics and logic are neither justified by something. Nor are they beliefs as the negation of a belief can be true bu the negation of axioms cannot be.
Posted by Dash555 3 years ago
Dash555
Mathematics is not empirically known. Most mathematical structures have no empirical counterparts.What are the empirical counterparts for Cayle numbers, quaternions, or even complex numbers?
Posted by Danielle 3 years ago
Danielle
It's you're*

And no, I can't. I'm at the Northern Illinois University library and I am not a student here, so I can't take out a book.
Posted by gizmo1650 3 years ago
gizmo1650
your at a library and you can't get a book?
Posted by Danielle 3 years ago
Danielle
Out of curiosity, what does the creation argument have to do with the laws of logic being self-evident? Are you saying God is responsbile for logic or what? I don't even remember how we got here. All I know is that you, GS, is saying math is reliable and logic is not even though they're the same thing o.O Anyway... I won't invest in the book (unless I can find it online) but I will watch the video when I get the internet at home (I'm at the library now so I can't).
Posted by GodSands 3 years ago
GodSands
The book goes far more into deph.
Posted by gizmo1650 3 years ago
gizmo1650
if you don't want to get buy the book i found his companion video at http://www.answersingenesis.org...
Posted by GodSands 3 years ago
GodSands
Yeah heard of Jason Lisle? He is a creationist. He has written a book called 'The Ultimate Proof for Creationism' I recomment you read it, he explains what I have been trying to explain far better than I can. So if you want to save time...
Posted by Danielle 3 years ago
Danielle
I really wish you were kidding :/

1) If you agree that logic has the same nature as math, then how can math be empirically known and logic not be? Even if you take a Putnam approch to answering this question (realism), there's no way you can justify 1 being more valuable as a source of knowledge than the other.

2) How can you say that you should "know" math and not just "believe" math? Once again, knowledge is justified true beliefs.

3) If evolution is true, our minds only know subjective knowledge? Wut? What the hell are you talking about? Where are you getting this?! I'm genuinely concerned. You're obviously not learning this in school or a book because it makes no sense whatsoever. Evolution is a justified true belief. Even so, what does that have to do with our understanding of knowledge? Why does knowledge have to be subjective? How do you expect me to respond to this when you're making it up as you go along and none of it follows whatsoever? And what do the objective beliefs you're talking about have to do with the Bible?

Honestly, I have no desire to engage in this discussion any further with you here. I *highly* reccomend that you take an epistimology course as soon as you possibly can. If you wish to debate this further then please send it to me in a debate challenge asap. I'd rather discuss it there because it's more structured and coherent. You should really consider coming up with structured arguments (preferably with bulleted points) if you want to make claims like these... Again, let's just debate this formally because these comments are frying my brain. I feel like my IQ just dropped 10 points after reading that.
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Shakespeare
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