Help with logic

[Craig]

An atheist gave me a logical equation that he purports to be a demonstration of his worldview accounting for the axiomatic nature of logic.

I do not want advice on what to say, I'd just like to know what this means.

He says:
a) Given your description of "account" my worldview easily accounts for logic. According to my worldview...

(x)(Logic(x)) & ~(x)(God(x))

It therefore follows...

n(x)(Logic(x)) & ~(x)(God(x)) q.e.d.

Taken from a discussion where I refute a materialist's criticism of Christian theism's "negative" definitions for God's Being: [ame="http://www.youtube.com/watch?v=9gqKr3tioLA"]Ontology & Feces[/ame]

 

[Zenas]

I'd like to know too. I forgot it all and the logic book I held onto is at home. The signs, as I remember, are just short-form for simple words like "and" or "or".

 

[Davidius]

I'm not very advanced in my study of logic, but from the equations it looks like the standard refutation of TAG (which says that it is necessary to postulate God because of the existence of things like logic).

Instead of asserting/presupposing God's existence to account for logic, you just assert/presuppose logic.

In the equations, ~ means "not," so you just replace God in the equation with Logic. "Q.e.d." means "quod erat demonstrandum," i.e. "that which was to be demonstrated," and comes at the end of a logical proof. Here he wants to demonstrate logic as being axiomatic instead of God. Based on the nature of the theistic proof, all one has to do is switch out the terms.

 

[Zenas]

Is the standard refutation then presupposing that logic is eternal and self-sustaining? Are you serious? That defies the terms of logic itself.

 

[Marrow Man]

What does the "n" at the beginning of the last line mean? Other than this, it seems to be a very circular proof, and one that can be easily refuted:

According to my worldview:

I like peanut butter and I do not like cabbage.

Therefore, I like peanut butter and I do not like cabbage. Q.E.D.

or

Barack Obama exists and Harry Potter does not exist.

Therefore, Barack Obama exists and Harry Potter does not exist.

One does not necessarily need to adopt a TAG apologetic to refute the argument, though I believe that argument to be superior in many regards. Plantinga has been good at demonstrating that naturalism (assuming this is the worldview the atheist wishes to adopt, although it is difficult to account for logic in such a worldview) is self-defeating since the thoughts of an organism evolving via random processes is unreliable on the most basic level.

 

[Whitefield]

"n" usually means "necessitation"

 

[Whitefield]

Is the standard refutation then presupposing that logic is eternal and self-sustaining? Are you serious? That defies the terms of logic itself.

Yes, it seems the argument is "logic necessarily is because it is" .. a bit of a truism, but does not answer the question "what is the source of logic?" "The cow necessarily is because there she stands." ... but where did she come from?

 

[Marrow Man]

Is the standard refutation then presupposing that logic is eternal and self-sustaining? Are you serious? That defies the terms of logic itself.

Yes, it seems the argument is "logic necessarily is because it is" .. a bit of a truism, but does not answer the question "what is the source of logic?" "The cow necessarily is because there she stands." ... but where did she come from?

Excellent points. Thanks for pointing out the meaning of "n."

It seems that our atheist friend, in adopting his anti-theistic worldview, is guilty of a subtle form of equivocation, since he seems to posit that belief in logic and lack of belief in God are somehow on par ontologically. God, as a necessary Being, has no "source" and may be presupposed as a foundational belief. The same is not true for logic.

 

[Contra_Mundum]

The problem that I see: "Logic" lacks an axiomatic definition. "Which" logic does the atheist mean? The TAG is not indefinitely applicable, as if there was some generic "god" out there. It requires a systematic, comprehensive defense that makes it internally consistent. This is what the Christian religion claims, and it provides explanatory power for other things--things that are themselves explainable within its parameters, and without contradictions.

The atheist can "claim" that "Logic" or anything he wants (spaghetti, sharpness, a tingle, etc.) is his "self-authenticating" axiom, but the proof is in the pudding. If all he has is an algorithm, he has essentially admitted failure. Because the TAG is proved in the demonstration, not in the formula. If "Logic" is "how the mind works", it still hasn't explained MIND in the first place. One of many deeply troubling lacunae in such a "system."

"Logic" has many forms as "religion" does. There is no "common denominator" among ALL systems of Logic. And, fact is that logic has drawn forth repeated explanations or attempts at explanation. To simply throw up ones hands in the air, and say that logic is "fundamentally basic" is to ascribe a new quality to it that has seldom (if ever) had a philosophical pedigree.

So first there is the fact of multiplicities of incompatible logic-systems, the argument for ONE of which would, when engaged, admits the validity of the presup argument. Second, I would say that the next argument I can think of against the axiom of "Logic" is that in Aristotelian logical syllogism, known FALSEHOODS can be "proven." It is reliant upon undisputed premises, which if untrue nevertheless produce a necessary conclusion. In other words,, Aristotelian logic "works" whether or not the premises are TRUE, which itself demands an explanation, or a justification for using "logic" even if it isn't always "reliable" for pointing to truth.

 

[Craig]

Thanks everyone...that was very helpful.

 

[davidsuggs]

2 Problems

a) Given your description of "account" my worldview easily accounts for logic. According to my worldview...

(x)(Logic(x)) & ~(x)(God(x))

It therefore follows...

n(x)(Logic(x)) & ~(x)(God(x)) q.e.d.

"Given any x, logic is x, and given no x, God is x."

"In any possible world, if logic exists, then logic is x. and in any possible world, if logic does not exist, then God exists."

It seems to me he is trying to predicate existence to both God and logic to show they are incompatible. The problem for them of course, is that in the atheist's attempt to attack the ontological argument for God's existence, he flatly refuses the predication of existence at all, instead claiming that predication presupposes existence. He cannot have it both ways. If he attacks this problem in this way, he has to accept the ontological proof of God's existence. Additionally, he is horribly reifying logic as some entity in and of itself. But it is not. Logic itself is a predication given to God. Thus, the argument misses the point by trying to predicate a predicate. Ultimately, it is self-defeating on two fronts. Which is clear evidence of the Noetic effects of the fall.

 

[Confessor]

Reading this thread made me happy.

 

[Grymir]

All this new fangled symbolic logic. I'd point your friend to some good ole' Aristotelian logic that isn't infected with the Kant/Hume/Modern philosophic junk. Which is where his question is coming from. False Premises to start with.

Sorry, I was going to stay away, but my wife asked me why I hadn't posted to this thread yet, and I replied the above, and voilà. There it is.

 

[Grymir]

BTW, Logic doesn't point to truth, it is a tool used to discover/prove truth (your premises). Hence the premise problem in the OP.