The Roles of Logic and Science in Questions of Theology

[_Gadianton]

I don't either. And what he said pretty much coincided with JAK by the way.

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.

...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.

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...

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".

..I didn't agree with you then remember

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

[_Gadianton]

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.

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.

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.

[_marg]

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.

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

[_asbestosman]

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.

[_Gadianton]

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.

[_asbestosman]

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?

[_asbestosman]

--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.

Actually, I'm sure it was Road to Reality although I could be mixing it up with another book. I'm also certain that Tarski recommend that I read it and I tried to do so about a year ago exactly. I think I only made it through about half before I had to return it. While I agree that it isn't as solid as a math textbook, I find it just about as effective at frying my brain. I sometimes think it's like doing drugs, but with more effort required to get a buzz.

[_marg]

previously: I don't either. And what he (Tarski)said pretty much coincided with JAK by the way

Gad: 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.

You are great at cop-outs Gad.

Let's see you back up your personal attack.

Use quotes to show JAK is in disagreement with Tarski's argument.

[_Gadianton]

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?

I probably shouldn't have put the question afterword. That was just a rhetorical question, so, let me try again:

17 = "the formula identified by Godel number 17 is not recursively definable"

he also constructed the formula neg(17 gen r) and showed that if 17 gen r is provable, then so is neg(17 gen r) resulting in a contradiction. So in order for the axioms of basic counting math to be consistent, then necessarily there must be a statement that can't be proven.

[_JAK]

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.

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

question of clarification

marg,

Am I understanding this post correctly?

Did presently “Gadianton” previously posted as “Grayskull” on this same forum?

JAK