One more time:

You are talking about underlying principles of rationality. To be an underlying prinicple is to UNDERLY A SYSTEM NOT BE DERIVABLE FROM A SYSTEM.

Yes. Do you get how this refutes you yet?

I'll take that as a 'no'

I've already shown you how the law of non contradiction is derivable from the well formed formular of propositional logic. I'll show you again:

On propositional logic:

The point is that there can be no axioms in this logic, the most basic of all modern logics (there are other formulations that do have axioms, though): everything is definitional. And how does one argue with a definition? My point is: the answer to the question "why doesn't everyone accept the axioms of logic?" is that it can be the case that there's nothing to accept. Literally.

This system even allows us to create a proof for the law of non contradiction:

Proof (by reductio):


1) (A & ~A) [Proposition]

2) A [Conjunction elimination from 1]

3) ~A [Conjunction elimination from 1]

4) ~(A & ~A) [Reductio, 1 - 3]

QED

Quote:
How can we create a system of logic without a preexistent rational guiding post?  You are not making any sense. 

You are mixing up two different concepts here.

Your argument declares that there are laws of rational thought that underly all logical systems. I agree with you there.

But your version of the TAG argument goes on to confuse the axioms of syllogistic logic for these axioms of reason. And I am showing you that these axioms are NOT universal.

Funny - you've described yourself here.

If you havent noticed, I've addressed your objection. I've already cited paraconsistent logic for you several times.

http://plato.stanford.edu/entries/logic-paraconsistent/

Now, let me also remind you that I've spoken to you about defense through retortion. You didn't respond because you've likely never seen the term.

What you are using is defense through retortion. Don't get me wrong here, I tend to favor your side. However the law of non  contradiction does not apply in paraconsistent logic.

And, again, it is derivable, and not an underlying principle, in propositional logic.

And to answer your question using paraconsisten logic:

Dialetheias (True Contradictions)

Despite the fact that dialetheism and paraconsistency needs to be distinguished, dialetheism can be a motivation for paraconsistent logic. If there are true contradictions (dialetheias), i.e., there are sentences, A, such that both A and ¬A are true, then some inferences of the form {A , ¬A} ⊨ B must fail. For only true, and not arbitrary, conclusions follow validly from true premises. Hence logic has to be paraconsistent. One candidate for a dialetheia is the liar paradox. Consider the sentence: ‘This sentence is not true’. There are two options: either the sentence is true or it is not. Suppose it is true. Then what it says is the case. Hence the sentence is not true. Suppose, on the other hand, it is not true. This is what it says. Hence the sentence is true. In either case it is both true and not true. (See the entry on dialetheism in this encyclopedia for further details.)

Now, I know you go on to cite A. N. Prior's solution to the paradox (I'll leave aside that it has problems too), but this doesn't change the fact that there are paraconsistent logics that do not use the law of non contradiction. These logics work.

Umm, yes.

actualy, I'm an amateur logician who is helping to correct someone who can't work out the differnce between the laws of reason and aristotle's syllogistic axioms. I've written the logic page I've cited you.

Pretty much, although its more likely that he just formalized it. Now, I'm going to watch you confuse a logical axiom with physics. Common mistake. Without further delay:

No, but that's not an example of the law of non contradiction. The law is an axiom found in logic. Logic has to do with arguments, not things. Things don't avoid contradictions, they simply exist. They simply are.

Any entity has identity. To be one thing is to not be another. To be a square is to have a set of limits that preclude circularity.

To be a contradiction is to be a statement, or set of statements, that conflict.

Do you see the difference?

Oh come on, this looks like a stock reply you pull out when you've got nothing. I'm merely telling you what you'd know if you read the first chapter of a logic textbook! This has nothing to do with atheism! You simply aren't giving the laws of reason.

Yeah, I know.

I'll say it again:

If something underlies every system, it cannot be derived from any system, because it would already be foundational. Right? Its already axiomatic.

You can't build the basement of the building on the third floor, right?

To derive something is to take it from something more basic, i.e. something that underlies it. If you can derive something from a sytem, then it is not an underlying principle.

Well, if the law of non contradiction underlies all rationality, and if propositional logic is rational, then how come

1) the law of non contradiction isn't an axiom in propositional logic?

2) How can we derive it from more basic well formed formular?

You've got to be kidding. Academia is all about taking on sacred cows like the LNC!

Wow, if anything reveals that you don't have much experience, its this claim! 

Trust me, I'm on your side here, but there's a real problem with the LNC and your solution to the problem has problems as well.

 Paraconsistent logic was the rage in logic for the last few years.

You do realize that I've written papers on this, right?  The solutions put forth by A. N. Prior  ( I assume you are basing your response on his work?) have their own problems. Again, I'm on your side here, I've written papers on the subject, but we can't ignore the problems with these solutions.

And at any rate, the point is moot: Paraconsistent logic exists, and the law of non contradiciton is not an axiom in that system. This means the law is not universal to all rationality.

Oh, and I should point out that none of this has to do with why TAG sucks as an argument. We are just quibbling over what is universal and what is not....

Glad a theist sees his problem as well, we can move past the claim that his is just atheistic naysaying.

And yes, none of this has to do with TAG.

She's one of those "I'm a better kind of theist" theists. 

"Hey guys, I believe that God is in my doorknob!  I'm all mystical.  Woooo!"

Do you know any Christian apologists who agree with you?

Actually, it means precisely that! If something is derivable, then it cannot be axiomatic.

Axiom:

In traditional logic, an axiom or postulate 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.

You've just refuted yourself.

It is not true that if something is derivable, then it cannot be axiomatic.  It is possible to both presuppose the validity of logical absolutes AND to demonstrate that they are true using the logical systems which they are used to build.

You are creating a false dichotomy.

Yes, it is true. It's definitional in fact. 

To say that something is derived in a system is to say that it is NOT an axiom. How would you derive something that is already axiomatic?! 

 I Love Irony.

Here you are arguing that the Law of Noncontradiction is universal to all rational thought... yet you are holding that something can be both its own thesis and antithesis. Something can be both foundational to a system, and yet, must be derived from the foundations of the system!

Smile at least. This is funny.

There really is no reason to derive something that is already axiomatic, other than if you are an atheist trying to disprove the universality of the principles themselves.

But just because it COULD be done does not mean that it is not the foundation of the system itself.

I used the word "derive" because that is the word you've been using.   These won't be perfect analogies, but hopefully it will help you see where I am going:

Immanuel Kant prided himself on using reason to demonstrate its own parameters.

Buddhists use desire in order to rid themselves of desire.

Why can't we use logic to prove that its foundations are true?  In fact, ANY logical system will prove its own foundations to be true.  

Duplicate post.

I'll just keep repeating that you cannot derive a foundational statement in any system. That is why they are foundational statements - because you don't need to derive them.

Why can't we use the 17th floor of a building as it's foundation?

In fact, this is not the case. Where are you even getting these assertions from? You're pretty much violating basic knowledge about axioms.

We can't use a logical system to demonstrate the truth of its own axioms, because we'd have to already presupose the axioms in order to use the logic in the first place!

In addition, such a goal as proving logic 'true' is itself rather misguided. Logical systems are not descriptive systems, they are not 'things' that we verify for truth... they are our means for verification in the first place.... (although I'd say logic is not about 'finding truth', it is about assesing arguments for validity)

YOU HAD TO ASSUME THE VALIDITY OF THOSE PRINCIPLES IN THE VERY ARGUMENT THAT YOU USED TO "DERIVE" THEM.

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

In the assumed premise, you've presupposed that A is A and A is not ~A and ~A is ~A and is not A.  You've also presupposed that it is a proposition and is not not a proposition.  You've presupposed that you've used conjunction elimination from the first premise and that what you've used is not DeMorgan's Theorem.

I've only used the word "derive" in a loose sense but apparently you are using it in a precise way.  You did not DERIVE the law of non-contradiction in that sense.  You've DEMONSTRATED it.  There is a fundamental difference.

Now can you show me ANY argument in proposition logic which does not already assume the validity of the three logical principles?

Well, that is the problem, isn't it? TAG really isn't an argument at all. So to put forward a real TAG, you'd have to give a set of connecting premises between "god" and "logic" that demonstrate that the latter relies on the former.

In this sense, NO ONE has ever put forward a TAG.  Which is my hidden point.

The closest you get is the argument that relies on the problem of induction.  And that argument, which also relies on the supposed 'nature of god' suffers frm the very same supposed dilemma found in the problem of induction:

http://www.rationalresponders.com/an_easy_argument_to_refute_van_tillian_calvinist_presuppositionalism

Sleepy,

It seems like you missed my post earlier. I'll post it again so that you can respond to it. Thanks.

Good, that probably means we are using the term the same way.

The logical principles that govern the universe are facts about the universe. The logical principles that govern our rationality are thoughts that correspond to facts about the universe. It might help you understand my position to note the following. It is a fact that my car is my car, but the fact that my car is my car is different from my thought that "my car is my car". Only my thought that "my car is my car" governs my rationality.

No. I hope that the above cleared up these questions for you.

Well, the principles that govern my rationality are certainly "conceptual entities" in the sense that I formulate them in concepts. It is not obvious that the principles that govern the universe are "conceptual entities."

The principles that govern the universe can certainly be described in terms of concepts (for example, we can think truly that "a thing is itself" ), but in that case it is only the proposition used to describe them that is composd of concepts. To understand the distinction I'm trying to make here, think about the fact that the Taj Mahal is white. We can describe the fact that the Taj Mahal is white in terms of concepts (by thinking the proposition "the Taj Mahal is white" ), but the fact that the Taj Mahal is white is true quite apart from that proposition.

These are interesting questions which I would like to debate at some point. However, my online debating experience tells me that if I opened them up, they would likely send the discussion off on a tangent. I want to keep the discussion focused on the issue above (thought vs. fact) for the moment.

I'm sure you are debating these questions with other people at present, and I hope they answer you satisfactorily.

I saw your post.  No offense, I'm just more interested in debating todangst on this issue since he seems to be the resident opponent of TAG.  I'll respond to your post when I get a chance.  I have to go now.

I disagree with 3. Even if 1-4 are true, 5 does not follow.

However let's assume all 5 are true. Then the god that created the universe must have a creator to account for his qualities. Then that god must have a god, and that god must have a god, etc.. to infinity. So ultimately there ends up with no god to account for these qualities.

You're basically setting up a logical argument, then saying there must be an exception(i.e God) to the rules of logic. I'm not buying it.

Basically I'm OK with Goedel proof that any system(including the whole universe) is not both consistent and complete. You are not, so you invent 'God' to be an exception to the rules of logic. Your 'god' in an entitiy immune for the rules of logic that you try to use to prove his existence.

I'm not sure what you mean.  What are some examples of facts about the universe that govern it? 

I'll need examples.  I'm not quite getting what you mean.

What you are doing is trying to separate the behavior of the universe from rationality itself.  This will not work.  You posited a distinction between the FACT that your car is what it is and the THOUGHT that it is what it is.  There is no distinction.  In both cases, you have a TRUTH STATEMENT regarding the behavior of the car, both of which require the application of the mind.  I've addressed this in one of my objections.

Standards of rationality are conceptual entities.  Concepts cannot exist without a mind.  The FACT that you've cited is in accordance with the standards of rationality, which means the fact cannot be separated from thought.

The moment we start discussing truth separate from a mind, we fall into absurdity.  Without a mind, there is no truth.

All principles are conceptual by nature. 

No!

That is a common mistake that atheists make.  The FACT that Taj Mahal is white IS a proposition. 

Do not try to separate rationality from the universe.  You can't do it. 

You're so close to understanding I find myself frustrated for your sake.

Take a moment to reconsider your statement about the implausibility of a universe to which the law of identity does not apply.  You and I both agree (and so should everybody else) that without the law of identity, you can't say anything meaningful about that universe.  Essencially, nothing would exist to say anything about because there would be no way to determine if anything exists at all (due to the lack of identity).

Law of Identity = exist -> minds can exist

Law of Identity = ~exist -> everything can not exist

Thus minds are contengent upon the existence of the law of identity rather than the other way around.

I'm fairly I just demonstrated that the law of identity is not dependent on a mind (if its not true, universe implodes).

Also, the law of identity is a property of the universe much like gravity is.  I'm typing on a small keyboard, so if I don't respond for a while, its because my fingers are too big.

Isn't that precisely the point?  How can anything exist without the law of identity?

How can it not be necessarily true?  How could judge the truth value of anything if the law of identity weren't necessarily true?  Why do we even need a pre-existing standard (if I understand what you're implying)?