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PostPosted: Thu Aug 30, 2007 8:32 pm 
Gad:
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NO, NO, NO. not all deductive arguments are to some extent "tautologies", why would they be? A deductive argument is either a tautology or it isn't. And Godel is not going to argue a silly tautology. get real.



Really Gad you say "NO, NO, NO" ? Well you better tell that to Professor James Hall. And btw here are his credentials first.

James Hall is the James Thomas Professor of Philosophy, Emeritus, at the University of Richmond, where he taught for 40 years until his retirement in 2005. He received his B.A. from Johns Hopkins University, his Masters of Theology from Southeastern Theological Seminary, and his Ph.D. from The University of North Carolina at Chapel Hill.

At the University of Richmond, Professor Hall was named Omicron Delta Kappa Faculty Member of the Year (2005), Student Government Association Faculty Member of the Year (2005), and he received the University Distinguished Educator Award (2001). He has written many articles and essays and is the author of three books: Knowledge, Belief and Transcendence; Logic Problems; and Practically Profound: Putting Philosophy to Work in Everyday Life. Professor Hall's first course with the Teaching Company was Philosophy of Religion."

Professor Hall specializes in 20th-century analytic philosophy, epistemology, logical empiricism, and the philosophy of religion. At Richmond, he was noted for developing cross-disciplinary courses combining physics, chemistry, economics, psychology, and literature with his own field of philosophy.


For you Gad: In the Teaching Company course called Tools of Thinking, understanding the world through experience and reason Lecture 13 titled "Inferences avoid Equivocation", he says and this is word for word:

" There is a sense in which every deductive argument is circular. If the conclusion you are trying to establish deductively is not in the premises somewhere then how could you argue your way from the premises to the conclusion. The problem with a question begging argument is that the conclusion simply as such, on its face, is just right there. It's not so much that the argument is circular but that the circle is very very small."


Last edited by marg on Thu Aug 30, 2007 8:52 pm, edited 2 times in total.

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 Post subject: non sequitur responder
PostPosted: Thu Aug 30, 2007 8:42 pm 
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Gadianton wrote:
JAK wrote:
Rather than respond to posts, you engage in Argument By Question, Argument From False Authority, Begging The Question (Assuming The Answer, Tautology), Changing The Subject (Digression, Red Herring), Fallacy Of Division, Ad Hominem (attack of persons as substitute for addressing issues), Introduction of the Irrelevant, and Error Of Fact (misquote of JAK). There are likely others which I have omitted.


The main reason you're mad is because you contradicted yourself, you claimed that Godel's argument was circular, then you claimed you never said that and found a way to sidestep the issue because I forgot to put a word in my quotation. I'll be waiting a long time I suppose, for you to look up his formally stated argument on wiki and show me the circularity.

Also, something to keep in mind. I'm no expert on logic, but of the two of us, I am the one who has worked through Godel's incompleteness theorom line by line, along with a few other famous pieces in mathematical logic by Peano, Cantor, Russell, Zermelo, and Kleene. I've also read a couple texts on formal logic, worked problem sets, and modal logic in particular has relevance to areas of interest I have entirely unrelated to religion. So while there are plenty who could kick my *ss in an argument on logic, I know enough to tell when someone has absolutely no clue whatsoever on the subject. And you would be one of those someones.

Tell me I'm wrong. I'll take your word for it. Was yesterday the first day you had ever looked up a definition for "modal logic?" Was today the first day you've ever read a synopsis of Godel's incompleteness theorom? Do you really think that you need to link to definitions of begging the question and so on, as if it would be some kind of revelation for me? The fact that you're completely 'winging' your discussion here is beyond painfully obvious.

At least Marg has read that book by Copi. I mean, God knows that if logic and reason are her passion, she should at least buy one book on formal logic in her life, say, Quine's, "Methods of Logic" and spend a couple months learning something about it. Then amid her repeated lectures to the rest of us on what logical thinking is, she won't all of a sudden get confused on the definition of a tautology. But, Marg has read that one book, and in her strange devotion to your ideas, is able to come up with interpretations of you that you don't deserve, as well she is able to offer some insights that show she kind of gets what's going on and with a little further study and a lot less dogmatism, would probably be decent at philosophy. But you? Dude, I don't even know what to think. All your posts related to logic on this thread have been complete and utter nonsense. Reading a webpage or two on the definitions of some logical fallacies is nowhere near enough to get you through discussions you're trying to have on logic.

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A closed system of argument is an argument having no information flowing into or out of it which is not accounted for in the system.

Closed systems, are self-limiting as they provide for all that is in the system.


Do you have a website to document your definition? (as you tend to have lots of websites to link to)

Gadianton asked:
Can you give an example of a formal proof done in a system that isn't closed?


This begs the question. The issue is the extent to which the process of gathering and assembling information is open to whatever is found in research. The issue is not about “formal proof” exclusively or the construction of a syllogism or syllogistic implication.

JAK

You really don't get what philosophers and logicians do or the reason why they do it. It's going to be hopeless to try and explain these things further.


Gad,

You appear unable to write without engaging in Fallacious Argument.

Those fallacious constructions have obfuscated the claim by CC which was challenged.

It was CC’s position that Godel proved God exists. Your diversionary tactics have not successfully shifted the topic.

Neither you nor CC have produced one scintilla of evidence that Godel proved that God exists. Nor have you established that reason and evidence have relevancy to theology. Truth by assertion unlike application of scientific method does not rely on reason and evidence as does science.

At least two of us here see through your various flawed claims and evasions.

The fallacies of the straw man attack, ad hominem, and shift of topic/issue appear to be primary for you.

JAK


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PostPosted: Thu Aug 30, 2007 8:43 pm 
Gadianton wrote:

Marg,

I'm leaving this thread, if you want to post one or two questions you think are very important in another one, I'll try and respond.


Gad, I asked you questions in this thread to get you to add your input to the issue. All you've done is arrogantly harrass so far. You've given me no reason to respect your knowledge on Godel or on the issue at hand re: logic being essential to theology, so I would have no interest in asking you questions on these topics.


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 Post subject: Re: Stupidity or Dishonesty
PostPosted: Thu Aug 30, 2007 9:11 pm 
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JAK wrote:
Gadianton, you’re either dishonest or stupid.

JAK


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

You know JAK, the only thing worse than an [expletive] moron is a pretentious [expletive] moron like you.

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 Post subject: Re: non sequitur responder
PostPosted: Thu Aug 30, 2007 9:26 pm 
Gadianton wrote:


The main reason you're mad is because you contradicted yourself, you claimed that Godel's argument was circular, then you claimed you never said that and found a way to sidestep the issue because I forgot to put a word in my quotation. I'll be waiting a long time I suppose, for you to look up his formally stated argument on wiki and show me the circularity.

Also, something to keep in mind. I'm no expert on logic, but of the two of us, I am the one who has worked through Godel's incompleteness theorom line by line, along with a few other famous pieces in mathematical logic by Peano, Cantor, Russell, Zermelo, and Kleene.


Well then you are the one who should explain why Godel's ontological argument for God isn't circular, since you claim such understanding. I'm not aware that Godel makes any inductive leaps of reasoning, so if not I assume the argument is deductive. If it is deductive it is circular in reasoning, in that the conclusion contains no new information other than what is already in the premises.


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Tell me I'm wrong. I'll take your word for it. Was yesterday the first day you had ever looked up a definition for "modal logic?"


What difference does that make Gad? You have the opportunity to argue a position but all you keep focusing on is attack. Do you think it a requirement that an individual be a walking encyclopedia, in order to argue a point? What is wrong with research? What is important is whether someone understands the information. You may have read tons Gad on Godel, but if so, it's not apparent, you are not coming across as being able to synthesize that knowledge into a coherent argument related to the issue at hand.

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Do you really think that you need to link to definitions of begging the question and so on, as if it would be some kind of revelation for me? The fact that you're completely 'winging' your discussion here is beyond painfully obvious.


Apparently it is a revelation for you. Apparently you don't appreciate that all deductive arguments are to some extent are circular. If Godel is creating the definitions and axioms how could it not be circular, unless he makes an inductive leap to conclusion, but then it's not a proof, it's no better than a guess or opinion. It offers no useful practical value of understanding of the world.


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 Post subject: Re: Stupidity or Dishonesty
PostPosted: Thu Aug 30, 2007 9:29 pm 
Calculus Crusader wrote:
JAK wrote:
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.


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PostPosted: Thu Aug 30, 2007 9:30 pm 
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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

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Last edited by Tarski on Fri Aug 31, 2007 12:21 am, edited 1 time in total.

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PostPosted: Thu Aug 30, 2007 9:37 pm 
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Tarski wrote:
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?

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PostPosted: Thu Aug 30, 2007 9:39 pm 
delete


Last edited by marg on Thu Aug 30, 2007 9:47 pm, edited 1 time in total.

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PostPosted: Thu Aug 30, 2007 9:46 pm 
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!

Tarski wrote:
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.


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PostPosted: Thu Aug 30, 2007 10:03 pm 
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Calculus Crusader wrote:
Are you the guy who is into differential geometry and stuff like that?

I hope you aren't trying to pursue my IRL 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?

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PostPosted: Thu Aug 30, 2007 11:04 pm 
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Tarski wrote:
Calculus Crusader wrote:
Are you the guy who is into differential geometry and stuff like that?

I hope you aren't trying to pursue my IRL 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.

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PostPosted: Fri Aug 31, 2007 12:42 am 
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marg wrote:
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!

Tarski wrote:
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.


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PostPosted: Fri Aug 31, 2007 1:46 am 
Gad wrote:
I don't have any problem with what Tarski wrote.


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


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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. BTW I haven't spent much time studying philosophy, I'm assuming when you say platonism you are referring to absolute unchanging universal truths/concepts.

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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.

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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.

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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.

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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.


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PostPosted: Fri Aug 31, 2007 1:53 am 
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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).

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I don't either. And what he said pretty much coincided with JAK btw.


No it doesn't. JAK doesn't even have a cursery understanding of the subject matter, it's very obvious. I think we'd better just part ways on JAK's mastery of logic, I won't be responding to apologetics on his behalf anymore in this thread.

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...platonism..


My comments here essentially meant what Tarski said, "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". A platonic God wouldn't be a very big victory and most of us would still be confused over the way in which he actually existed. Also T's point 2 in his summary.

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I'm assuming when you say platonism you are referring to absolute unchanging universal truths/concepts.


Well yeah, "the Good", which is importantly, ontologically distinct from this world. Now think ontological argument...

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It is a closed reasoning system which is not applicable to the actual world and says nothing about an actual God


You might think this parallels something Tarski said, but it doesn't. Your demands on an "actual God" outstrip the supply of Platonism's inventory. In other words, you are wanting to set up the "God" of the ontological argument to be something more than it was meant to be, and then say logic alone or a "closed system" can't demonstrate it. If the ontological argument were true, you'd most likely reject the "God" established as "God".

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..I didn't agree with you then remember


..ah, and i was trying..right?


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PostPosted: Fri Aug 31, 2007 11:45 am 
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asbestosman wrote:
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.


Penrose is weird. Having "read" the first couple hundred pages of "Road to Reality" I would just have to sweep myself under the rug as not worthy. But yeah, I don't think anyone other than Penrose accepts his argument about mind. Consider though, Godel's original proof was meant to argue something similar to what Penrose does. Godel in his paper makes mention of the intellect seeing the truth that the algorithm can't. And this insight has spured a few comments about the mind posessing something over and above what a computer does (Quine and Nagel for instance). But there are too many good reasons to reject the idea. David Chalmers has some online papers where he's debated Penrose and Penrose acknowledges Chalmers as the only one who's taken the time to understand him so maybe you'd find that interesting. One of the biggest problems is, and Penrose even admits it, as he reformulates his arguments into more sophisticated versions, there's far more room for semantic problems and you can see that as he and Chalmers argue over what this or that sentence specifically mean.

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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.


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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.


All I can say is, if you can follow Penrose's "Road to Reality" you should have no trouble with Godel's actual paper which is online (lots of errors though b careful). You'd probably wan't to read something like "Godel's proof" by nagel to get some of the historical context. To see how it means something in math, you'd just have to read up a little on what number theorists were trying to acheive.


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PostPosted: Fri Aug 31, 2007 12:42 pm 
previously: "It is a closed reasoning system which is not applicable to the actual world and says nothing about an actual God"

Gad: "You might think this parallels something Tarski said, but it doesn't. Your demands on an "actual God" outstrip the supply of Platonism's inventory. In other words, you are wanting to set up the "God" of the ontological argument to be something more than it was meant to be, and then say logic alone or a "closed system" can't demonstrate it. If the ontological argument were true, you'd most likely reject the "God" established as "God"."

I'm not wanting to set up the God of the ontological argument to do anything. I've said previously one should appreciate the limitations of what it does say. It is a closed reasoning argument which doesn't link to the actual world. It makes no inductive reasoning leap. Consequently it offers no insight or knowledge in its conclusion regarding any potential God. Any conclusion it makes regarding a God is unreliable. What that boils down to is that the argument that logic is essential to theology has not been successfully argued for. The goal of logic being to reach reliable conclusions. It is CC who tried to use the argument as justification of an actual God, CC tried to link it to the actual world. With regards to your last sentence, and this shows your prejudice, I don't claim there is no God.



previous: "I didn't agree with you then remember"

Gad: "..ah, and I was trying..right?"

Your point Gad was that I only oppose or disagree with believers and that if you came on here using another name but presented yourself as atheist I would be in agreement with anything you said. My point is you already have presented yourself with another name Grayskull, and I didn't agree with you then. As well your admirer EA I didn't agree with either. So you are wrong to think I am prejudiced against believers and support all atheists in whatever they say.

BTW, I'd respond to the rest of your post but I have other things to do first.


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PostPosted: Fri Aug 31, 2007 2:08 pm 
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Gadianton wrote:
All I can say is, if you can follow Penrose's "Road to Reality"

Hahaha. That's quite a joke. I merely deluded myself into thinking I could follow about 1% of it, and most of that was at the very beginning with talk about geometry and thing or two about the implications of the complexity in deceptively simple specifcations such as the Mandlebrott set. For a moment I almost thought I understood the basics of Lie algebra too, but I think I finally overcame that delusion.

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PostPosted: Fri Aug 31, 2007 2:30 pm 
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Quote:
Still wish I knew how that implied an actul question within a mathematical system.


i missed this when i read it the first time. if there's a "question" then i missed it. was it penrose's imaginary conversations which led you to think that?

penrose's examples are really good for getting the intuition down, but they are fast and loose, and I found a review by a mathematician in the right branch of math a long time ago that ripped Penrose apart for all kinds of errors in his presentation.

anyway, it's not a question, but a statement that says, "the formula identified by Godel number 17 is not recursively definable" <---and you can guess the godel number of that statement.

--oh, about Road to Reality, i thought you said Tarski recommended that and you "read" it. now i see that it was another book. yeah, i would read a couple pages, then read about the topic online until i got it well enough, and then read more, until i realized, hey, this is pointless beyond being a topic guide.


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PostPosted: Fri Aug 31, 2007 2:50 pm 
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Gadianton wrote:
Quote:
Still wish I knew how that implied an actul question within a mathematical system.


I missed this when I read it the first time. if there's a "question" then I missed it. was it penrose's imaginary conversations which led you to think that?

Nah, fuzzy memory.
I think I got it as a question in the sense that solving other equations is often seen as a question instead of a statement.

X^2 + x + 1 = 0

is a statement, but usually the question is asked to find all x such that the equation holds true.

Apparently with Godel it's even trickier. Something about Dio-sumthing-or-rather equations and furthermore the fact that the equation is somehow self-referrential in saying that the solution to it--if it exists--cannot be demonstrated from the other axioms or as you said, "the formula identified by Godel number 17 is not recursively definable".

But to be a self-referrential statement, wouldn't it actually need to say, "the formula identified by this Godel number is not recursively definable" <-- and then you guess the Godel number of this statement?

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