The Roles of Logic and Science in Questions of Theology

[_marg]

Gadianton, you’re either dishonest or stupid.

JAK

This is what we book learnin' folks call a false dichotomy.

I thought of that today, he could be both.

[_Tarski]

With regard to Godel's ontological argument (apparently an attempted clarification of an argument of Leibniz), it is indeed important to realize that the conclusion of such an argument can have no more certainty or clarity than the axioms. Valid logical argumentation about finite sets and about the integers carries force in part because of the clarity and plausibility of the axioms (and our experience in the real world!).
But what if one gets overly ambitious and sets up axioms which rational people disagree about with respect to plausibility and clarity? What do we make of the fact that the axioms have not been part of a long fruitful tradition as has been the Frankel-Zermelo axioms? Without clarity, and without a consistency proof, we are left with little but the speculations and logical toying about of a brilliant man who also indulged in many other mystical and metaphysical speculations. It seems clear that Godel did not think his argument was decisive or clear in the same way that his mathematical work was clear and decisive. It seems to me that he was going out on a speculative limb like we all do late at night after a few drinks (or bong hits?). He was just doing it in the way one would expect of a person train like Godel---in his language.

Notice also that one can consider valid an existential argument such as that given to show the existence of nowhere differentiable continuous functions and yet at the same time question the "reality" of the real numbers!! So it seems that an existence proof in an axiomatic system only establishes existence relative to that system. So it seems that we can be left wondering whether God is "real" even if we accept the formal validity of Godel's ontological argument.

So then what do I mean by real? Well, that is a problem, but not if one wants to talk about a Christian God who can directly interfere with the flow of history. Such a God is a force felt in the physical universe. Surely such a God's reality is empirical since he/she is a being that affects the material and human world.

Does anyone here think that if we can doubt the reality of the real number system that nevertheless Godel has proved that God is real?

Now, although I am a mathematician, I am not a logician as such, and so there are many subtle points I expect to miss in this area (especially with regard to modal logic) but it doesn't take much research to find out that

1. Even Godel didn't think his argument proved the "existence" of God beyond doubt.
2. Godel's notion of God would be totally unlike the Biblical God and at best more like Plato's "The Good".
and
3. Logicians do have big problems with Godel's argument for God even on it's own terms:

see the section "Critique of definitions and axioms" in the Wiki article
http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof

[_Calculus Crusader]

With regard to Godel's ontological argument (apparently an attempted clarification of an argument of Leibniz), it is indeed important to realize that the conclusion of such an argument can have no more certainty or clarity than the axioms. Valid logical argumentation about finite sets and about the integers carries force in part because of the clarity and plausibility of the axioms (and our experience in the real world!).
But what if one gets overly ambitious and sets up axioms which rational people disagree about with respect to plausibility and clarity? What do we make of the fact that the axioms have not been part of a long fruitful tradition as has been the Frankel-Zermelo axioms? Without clarity, and without a consistency proof, we are left with little but the speculations and logical toying about of a brilliant man who also indulged in many other mystical and metaphysical speculations. It seems clear that Godel did not think his argument was decisive or clear in the same way that his mathematical work was clear and decisive. It seems to me that he was going out on a speculative limb like we all do late at night after a few drinks (or bong hits?). He was just doing it in the way one would expect of a person train like Godel---in his language.

Notice also that one can consider valid an existential argument such as that given to show the existence of nowhere differentiable continuous functions and yet at the same time question the "reality" of the real numbers!! So it seems that an existence proof in an axiomatic system only establishes existence relative to that system. So it seems that we can be left wondering whether God is "real" even if we accept the formal validity of Godel's ontological argument.

So then what do I mean by real? Well, that is a problem, but not if one wants to talk about a Christian God who can directly interfere with the flow of history. Such a God is a force felt in the physical universe. Surely such a God's reality is empirical since he/she is a being that affects the material and human world.

Does anyone here think that if we can doubt the reality of the real number system that nevertheless Godel has proved that God is real?

Now, I although I am a mathematician, I am not a logician as such, and so there are many subtle points I expect to miss in this area (especially with regard to modal logic) but it doesn't take much research to find out that

1. Even Godel didn't think his argument proved the "existence" of God beyond doubt.
2. Godel's notion of God would be totally unlike the Biblical God and at best more like Plato's "The Good".
and
3. logicians do have big problem's with Godel's argument for God even on it's own terms:

see the section "Critique of definitions and axioms" in the Wiki article
http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof

Are you the guy who is into differential geometry and stuff like that?

[_marg]

delete

[_marg]

Tarski, I won't copy all your post, but you are a voice of reason. Gad, take note, he makes an argument, it makes sense!

So then what do I mean by real? Well, that is a problem, but not if one wants to talk about a Christian God who can directly interfere with the flow of history. Such a God is a force felt in the physical universe. Surely such a God's reality is empirical since he/she is a being that affects the material and human world.

I've been using the word "actual" God. In otherwords the reality of the God may not be known however it exists as an actuality which potentially could be known scientifically in the future.

[_Tarski]

Are you the guy who is into differential geometry and stuff like that?

I hope you aren't trying to pursue my in real life identity.

Anyway, I think I have already said on these boards that I have done most of my published research in differential geometry.
This semester though, I am going to do a graduate seminar series on quantum physics.

Why do you ask?

[_Calculus Crusader]

Are you the guy who is into differential geometry and stuff like that?

I hope you aren't trying to pursue my in real life identity.

Anyway, I think I have already said on these boards that I have done most of my published research in differential geometry.
This semester though, I am going to do a graduate seminar series on quantum physics.

Why do you ask?

If you are who I think you are then I e-mailed you previously to ask what your specific field is. In any case, I won't be telling anyone who you may or may not be, since you seem to want to keep your identity on the QT.

[_Gadianton]

Tarski, I won't copy all your post, but you are a voice of reason. Gad, take note, he makes an argument, it makes sense!

So then what do I mean by real? Well, that is a problem, but not if one wants to talk about a Christian God who can directly interfere with the flow of history. Such a God is a force felt in the physical universe. Surely such a God's reality is empirical since he/she is a being that affects the material and human world.

I've been using the word "actual" God. In otherwords the reality of the God may not be known however it exists as an actuality which potentially could be known scientifically in the future.

I don't have any problem with what Tarski wrote. In fact, i've tried multiple times to point out Godel's first commitment was platonism. If I wanted your respect marg, or for you to eat out of my hand, all i'd have to do is register a new user and then argue the atheist side.

All either you gor JAK had to do was spend an hour or two carefully reading the wiki entry, you don't have to be a mathemetician like Tarski. But noo. You're both so full of yourselves that you think your common-sense thinking will take down of Godel's stature without either of you previously having any training or even having read a book on logic.

If you and your online remedial learning professor want to call all arguments tautologies because all arguments rest on tautologies, then you're making the same point Pahoran makes when he argues that all knowledge is circular and therefore no argument is ultimately better than any other argument. You'll never find a text on formal logic that labels a deductive argument a tautology unless its conclusion restates a premise. And even if we take your view, and the online professor's view, that doesn't salvage JAK's ridiculous accusation since every argument ever made is a tautology.

I didn't enter this discussion with an interest in what the best arguments for and against Godel (or anyone else on any other thread) are. That doesn't depend on you and JAK or myself. I was interested in the zeal JAK whipped his horse into battle on a topic clearly beyond his grasp. And while Christianity bugs me, ignorant atheism bugs me more.

[_marg]

I don't have any problem with what Tarski wrote.

I don't either. And what he said pretty much coincided with JAK by the way. The difference between you and Tarski is that Tarksi presented an argument. All you did was present ad hominem.

In fact, I've tried multiple times to point out Godel's first commitment was platonism.

What difference does it make if Godel's first commitment was platonism? You say stuff but don't make sense. by the way I haven't spent much time studying philosophy, I'm assuming when you say platonism you are referring to absolute unchanging universal truths/concepts.

If I wanted your respect marg, or for you to eat out of my hand, all I'd have to do is register a new user and then argue the atheist side.

I doubt that would work Gad. You were greyskull weren't you? I didn't agree with you then remember, and yet you were an atheist.

All either you gor JAK had to do was spend an hour or two carefully reading the wiki entry, you don't have to be a mathemetician like Tarski. But noo. You're both so full of yourselves that you think your common-sense thinking will take down of Godel's stature without either of you previously having any training or even having read a book on logic.

First of all Gad I didn't criticize Godel and I asked you to quote me in which I have and you didn't. I said the problem with CC's argument is how he was using Godel's argument for God. It is a closed reasoning system which is not applicable to the actual world and says nothing about an actual God.

If you and your online remedial learning professor want to call all arguments tautologies because all arguments rest on tautologies, then you're making the same point Pahoran makes when he argues that all knowledge is circular and therefore no argument is ultimately better than any other argument. You'll never find a text on formal logic that labels a deductive argument a tautology unless its conclusion restates a premise. And even if we take your view, and the online professor's view, that doesn't salvage JAK's ridiculous accusation since every argument ever made is a tautology.

Sheesh, even after I gave you the extensive credentials of Prof James Hall, books he's written, degrees he has, universities he teaches at ..you are calling him an online professor. Gad not all arguments are tautologies only deductive arguments and he didn't say they were all tautologies he said the circularity of the argument is not what makes an argument a tautology because all deductive arguments are in a sense circular. It is the smallness of the circle, the obviousness that the conclusion states the same as the premises which makes the argument be considered circular or tautological.

I didn't enter this discussion with an interest in what the best arguments for and against Godel (or anyone else on any other thread) are. That doesn't depend on you and JAK or myself. I was interested in the zeal JAK whipped his horse into battle on a topic clearly beyond his grasp. And while Christianity bugs me, ignorant atheism bugs me more.

Well the problem rests with you Gad. You should have entered with an interest in the argument, instead of with the focus on harrassment. It would have reflected better on you. In this thread, you seem to be hostile and small minded.

Just so you know, you have prejudged me. I don't think all atheists are rational or intelligent. I don't think all religious individuals are stupid or irrational. But if there is one thing I do dislike about religion..it is multi billion dollar religious organizations.

[_asbestosman]

As long as we're off topic, I'm just wondering what Gad's thoughts are about my rejection of Penrose's The Emperor's New Mind. Penrose is a brilliant guy--completely out of my league. Even so, I find his argument wholly unconvincing. Despite that, I still think he's a brilliant mathematician and I even enjoy reading The Emperor's New Mind as it contains many interesting aspects of mathematics and logic. I also quite enjoy reading other books of his (one Tarski recommended about mathematics and the universe). He explains some concepts quite well (such as tensors) which had been a bit tricky for me. Even then, I still reject neo-Platonism. Maybe that's why I'm not a mathematician despite being fairly interested in math.

Godel also strikes me as brilliant. I wish I understood his proof. The closest I can get to conceptualizing it is in realizing that computers can represent everything, including mathematical formulas and questoins, with just a bunch of numbers. Still wish I knew how that implied an actul question within a mathematical system. If I'm not mistaken, however, this very thing has parallels to Turing's Halting problem which I do understand fairly well although I don't quite get Church's version yet.


As far as logic and theology goes, I think it has a big tradition behind it since Aquinis and the like. As far as science, not so much. The divide seems to have widened with time. Blame it on God testing our faith or on Him not existing, but there seems to be little open evidence for Him. The best we seem to have are personal experiences we can try to correlate with others, but even those don't always match up depending on a variety of factors.

I also think Logic can be used to help provide insight into implications about God. For example, I tend to enjoy speclating on what things infinity will buy God. Hilbert's Grand Hotel is a fun speculation--maybe God's (countably infinite) children can each rent a room, but then still allow his countably infinite neices and nieces to each have their own room as well by moving to different rooms. I also wonder about a circle of infinite circumference and whether the family tree of God could be like that. I don't see logically why not and I find the idea interesting. In fact, I think a certain course at MIT about infinity and paradoxes would be very interesting (I'm just too cheap to buy the textbooks).