Mathematical proof "intelligent design" is meaningless
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29-08-2014, 11:53 AM (This post was last modified: 29-08-2014 02:40 PM by Bucky Ball.)
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 05:00 AM)phil.a Wrote:  The theist transcendent/immanent perspective is that reality consists of (a) God and (b) everything that God created.

So from the big picture, reality is a God/Stuff system.

A real god could make anything work, (ie life or complex systems), no matter whether they are intelligently designed, or not. ID is really an argument AGAINST theism, and omnipotent deities.
The god/stuff system has unexamined silent premises/assumptions. It's incoherent when they are stated.

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29-08-2014, 12:57 PM
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 11:35 AM)Grasshopper Wrote:  
(29-08-2014 07:29 AM)phil.a Wrote:  OK (perhaps this is what you mean but) I am not saying that they disprove ID, but rather that they invalidate ID.

If that is what you mean, can you explain why they aren't applicable?

Phil

Chas can probably give you a more detailed answer (if he hasn't gotten weary of this whole argument), but briefly, Gödel's Theorems make very specific statements about formal systems in logic and mathematics, and they don't apply to anything beyond that. In particular, they don't apply to science, theology, metaphysics, or anything in "real life" -- none of these are formal systems. You keep trying to apply Gödel's Theorems to areas that are way beyond their scope, and you just can't do that. It's like saying arithmetic invalidates Moby-Dick. They have nothing to do with each other.

As to the thread title, mathematical proof also doesn't apply to anything outside of mathematics. Science is basically an inductive process -- it doesn't "prove" things in the same way that mathematicians and logicians do. Mathematical theorems are absolutely true (given the axioms on which they are based), and true for all time. Science is always open to revision.

Well stated. Thumbsup

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29-08-2014, 01:06 PM
RE: Mathematical proof "intelligent design" is meaningless
According to many theists, God is perfect. So applying the word "intelligent" to God would be a bit insulting since it is conceptually far too finite to fit God's perfection. Therefore, God could not have created the universe by intelligent design. There, I just disproved intelligent design from a theist's point of view. Tongue

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29-08-2014, 03:39 PM
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 11:35 AM)Grasshopper Wrote:  
(29-08-2014 07:29 AM)phil.a Wrote:  OK (perhaps this is what you mean but) I am not saying that they disprove ID, but rather that they invalidate ID.

If that is what you mean, can you explain why they aren't applicable?

Phil

Chas can probably give you a more detailed answer (if he hasn't gotten weary of this whole argument), but briefly, Gödel's Theorems make very specific statements about formal systems in logic and mathematics, and they don't apply to anything beyond that. In particular, they don't apply to science, theology, metaphysics, or anything in "real life" -- none of these are formal systems. You keep trying to apply Gödel's Theorems to areas that are way beyond their scope, and you just can't do that. It's like saying arithmetic invalidates Moby-Dick. They have nothing to do with each other.

As to the thread title, mathematical proof also doesn't apply to anything outside of mathematics. Science is basically an inductive process -- it doesn't "prove" things in the same way that mathematicians and logicians do. Mathematical theorems are absolutely true (given the axioms on which they are based), and true for all time. Science is always open to revision.

Ok thanks for that. Basically I intuit quite clearly that any attempt to describe reality purely in terms of itself involves self-reference which leaves holes in what's proven.

Sounds like Godel's theorem to me? I understand that Godel's theorems as laid out applies to formal systems and not necessarily to moby dick. But would you say that maths and reality are radically different domains which don't connect? Or perhaps that the underlying nature of reality isn't logical?

Phil
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29-08-2014, 04:38 PM
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 03:39 PM)phil.a Wrote:  
(29-08-2014 11:35 AM)Grasshopper Wrote:  Chas can probably give you a more detailed answer (if he hasn't gotten weary of this whole argument), but briefly, Gödel's Theorems make very specific statements about formal systems in logic and mathematics, and they don't apply to anything beyond that. In particular, they don't apply to science, theology, metaphysics, or anything in "real life" -- none of these are formal systems. You keep trying to apply Gödel's Theorems to areas that are way beyond their scope, and you just can't do that. It's like saying arithmetic invalidates Moby-Dick. They have nothing to do with each other.

As to the thread title, mathematical proof also doesn't apply to anything outside of mathematics. Science is basically an inductive process -- it doesn't "prove" things in the same way that mathematicians and logicians do. Mathematical theorems are absolutely true (given the axioms on which they are based), and true for all time. Science is always open to revision.

Ok thanks for that. Basically I intuit quite clearly that any attempt to describe reality purely in terms of itself involves self-reference which leaves holes in what's proven.

Sounds like Godel's theorem to me? I understand that Godel's theorems as laid out applies to formal systems and not necessarily to moby dick. But would you say that maths and reality are radically different domains which don't connect? Or perhaps that the underlying nature of reality isn't logical?

Phil

Whole books have been written about how strange it is that mathematics models reality as well as it does. I don't know whether the underlying nature of reality is logical, but I suspect not. Reality at its most basic level (quantum mechanics) seems to be somewhat random, and logic is a human invention. We impose structure on reality to help ourselves understand it. It's unclear to me how much of that structure is inherent in reality itself. Such concepts are deeper than I usually go. Already I feel a headache coming on.

But I am pretty sure that Gödel's Theorems are of little or no use outside the context of formal systems, and Chas seems even more sure of that. Since he is an expert in that field (has degrees in it, even), I will defer to him.

I think part of the problem is illustrated by you using "reality" and "proven" in the same sentence. Basically, I don't think it's possible to "prove" things about physical reality. We can prove, for example, that the Pythagorean Theorem is true in Euclidean space, but we cannot prove that the space we actually live in is Euclidean. Proof has a place in mathematics and logic; it doesn't really have a place in the real physical world. Reality is messier than that. We can model reality, but the model is always approximate.
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29-08-2014, 07:23 PM
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 04:38 PM)Grasshopper Wrote:  
(29-08-2014 03:39 PM)phil.a Wrote:  Ok thanks for that. Basically I intuit quite clearly that any attempt to describe reality purely in terms of itself involves self-reference which leaves holes in what's proven.

Sounds like Godel's theorem to me? I understand that Godel's theorems as laid out applies to formal systems and not necessarily to moby dick. But would you say that maths and reality are radically different domains which don't connect? Or perhaps that the underlying nature of reality isn't logical?

Phil

Whole books have been written about how strange it is that mathematics models reality as well as it does. I don't know whether the underlying nature of reality is logical, but I suspect not. Reality at its most basic level (quantum mechanics) seems to be somewhat random, and logic is a human invention. We impose structure on reality to help ourselves understand it. It's unclear to me how much of that structure is inherent in reality itself. Such concepts are deeper than I usually go. Already I feel a headache coming on.

But I am pretty sure that Gödel's Theorems are of little or no use outside the context of formal systems, and Chas seems even more sure of that. Since he is an expert in that field (has degrees in it, even), I will defer to him.

I think part of the problem is illustrated by you using "reality" and "proven" in the same sentence. Basically, I don't think it's possible to "prove" things about physical reality. We can prove, for example, that the Pythagorean Theorem is true in Euclidean space, but we cannot prove that the space we actually live in is Euclidean. Proof has a place in mathematics and logic; it doesn't really have a place in the real physical world. Reality is messier than that. We can model reality, but the model is always approximate.

Quantum mechanics isn't random; it's probabilistic.

Theorems apply to models, and models are not reality. They're just our best approximations thereof...

Incidentally, we can totally prove our space[time] isn't Euclidean - that's what general relativity states!

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29-08-2014, 07:42 PM (This post was last modified: 29-08-2014 08:34 PM by Revenant77x.)
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 07:23 PM)cjlr Wrote:  
(29-08-2014 04:38 PM)Grasshopper Wrote:  Whole books have been written about how strange it is that mathematics models reality as well as it does. I don't know whether the underlying nature of reality is logical, but I suspect not. Reality at its most basic level (quantum mechanics) seems to be somewhat random, and logic is a human invention. We impose structure on reality to help ourselves understand it. It's unclear to me how much of that structure is inherent in reality itself. Such concepts are deeper than I usually go. Already I feel a headache coming on.

But I am pretty sure that Gödel's Theorems are of little or no use outside the context of formal systems, and Chas seems even more sure of that. Since he is an expert in that field (has degrees in it, even), I will defer to him.

I think part of the problem is illustrated by you using "reality" and "proven" in the same sentence. Basically, I don't think it's possible to "prove" things about physical reality. We can prove, for example, that the Pythagorean Theorem is true in Euclidean space, but we cannot prove that the space we actually live in is Euclidean. Proof has a place in mathematics and logic; it doesn't really have a place in the real physical world. Reality is messier than that. We can model reality, but the model is always approximate.

Quantum mechanics isn't random; it's probabilistic.

Theorems apply to models, and models are not reality. They're just our best approximations thereof...

Incidentally, we can totally prove our space[time] isn't Euclidean - that's what general relativity states!

So what our physicist friends here is saying is math proves Cthulhu.

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29-08-2014, 08:23 PM
RE: Mathematical proof "intelligent design" is meaningless
Just to amplify on my last post: I claimed that we can't really prove things in the real world the way we do in logic and mathematics. I'm anticipating that phil.a will claim that this is due to Gödel's Theorems. I emphatically claim that it has nothing to do with Gödel, and here's why: Proof (formal proof, anyway) is a structure built on definitions, axioms, and rules of inference. Gödel says that even in a formal system, where all that stuff is exactly nailed down, there are limits to what we can prove. In the real world, we don't need Gödel to set limits -- the limits are set much lower right off the bat, because none of that stuff is nailed down. The definitions are fuzzy and inexact, and we don't know exactly what the axioms are. We don't have to worry about the inherent limitations of logic, because we can't even properly do logic -- key pieces of the underlying sturcture are missing. Gödel's Theorems are like the rules of a game, and we're not playing that game. We're playing a different game, with rules that are considerably looser.

Thanks to cjlr for clearing up some of the scientific stuff. Like I said, going too deep gives me a headache, and quantum mechanics is way too deep. Tongue
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29-08-2014, 09:50 PM
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 08:23 PM)Grasshopper Wrote:  Just to amplify on my last post: I claimed that we can't really prove things in the real world the way we do in logic and mathematics. I'm anticipating that phil.a will claim that this is due to Gödel's Theorems. I emphatically claim that it has nothing to do with Gödel, and here's why: Proof (formal proof, anyway) is a structure built on definitions, axioms, and rules of inference. Gödel says that even in a formal system, where all that stuff is exactly nailed down, there are limits to what we can prove. In the real world, we don't need Gödel to set limits -- the limits are set much lower right off the bat, because none of that stuff is nailed down. The definitions are fuzzy and inexact, and we don't know exactly what the axioms are. We don't have to worry about the inherent limitations of logic, because we can't even properly do logic -- key pieces of the underlying sturcture are missing. Gödel's Theorems are like the rules of a game, and we're not playing that game. We're playing a different game, with rules that are considerably looser.

Gödel simply states that a formal logical system cannot be both wholly complete and wholly sound. Or to take some slight liberties of interpretation - a rigourous formal system will inevitably admit of unprovably true statements, and that any given rigourous system cannot prove its own validity (which is... kind of what phil was saying...)

(29-08-2014 08:23 PM)Grasshopper Wrote:  Thanks to cjlr for clearing up some of the scientific stuff. Like I said, going too deep gives me a headache, and quantum mechanics is way too deep. Tongue

Well, you'll certainly not get anywhere with that attitude...
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30-08-2014, 01:20 AM (This post was last modified: 30-08-2014 01:30 AM by phil.a.)
RE: Mathematical proof "intelligent design" is meaningless
(29-08-2014 04:38 PM)Grasshopper Wrote:  Whole books have been written about how strange it is that mathematics models reality as well as it does. I don't know whether the underlying nature of reality is logical, but I suspect not. Reality at its most basic level (quantum mechanics) seems to be somewhat random, and logic is a human invention. We impose structure on reality to help ourselves understand it. It's unclear to me how much of that structure is inherent in reality itself. Such concepts are deeper than I usually go. Already I feel a headache coming on.

But I am pretty sure that Gödel's Theorems are of little or no use outside the context of formal systems, and Chas seems even more sure of that. Since he is an expert in that field (has degrees in it, even), I will defer to him.

I intuit quite clearly that the underlying nature of reality is logical. I'd say the logic fans off to infinite complexity in all directions and also to an infinite degree of abstraction (at it's deepest points it becomes fully abstract, e.g. unrepresentable).

So humans aren't ever going to get to the bottom of it in practical terms, but that's completely different to saying it's not logical, I think it is logical. And if it is, then I think Godel's insights apply.

I don't think logic is a human "invention", I think it's more accurately described similary to the theory of evolution as a human discovery. Yes it is a conceptual structure we ourselves impose, or project on reality, but actually - reality is happy to accept the projection (it fits, so must be truly descriptive of reality in some way)

Quote:I think part of the problem is illustrated by you using "reality" and "proven" in the same sentence. Basically, I don't think it's possible to "prove" things about physical reality. We can prove, for example, that the Pythagorean Theorem is true in Euclidean space, but we cannot prove that the space we actually live in is Euclidean. Proof has a place in mathematics and logic; it doesn't really have a place in the real physical world. Reality is messier than that. We can model reality, but the model is always approximate.

OK well I agree with the above but (in light of what I said earlier) I would frame it slightly differently - I'd say that due to the infinite complexity of actual reality, there will always be practical limits on how well our theories "fit" - and there will always be some error somewhere. Theories tend to overturn previous theories by bringing up the givens and axioms for investigation, I think we could do that for ever and a day without ever getting fully to the bottom of it.

But yes - I agree that in practice, reality can never be practically proven, which is yet another good argument for giving up on ID (not even going there).

My Godel argument is not that it could ever be practically proven, it takes that premise as a given because that's the axiom present in the ID argument. Taking that as an axiom (even though both you and me agree it's not practically possible) I am just saying - even if that were possible, the ID argument by it's self-referential nature cannot prove the existence of god.

I appreciate this is going way deeper than a mathematician might normally go - but please remember - we are having a chat about God here. It's the ultimate question, the deepest possible question, I think we need to expand our imagination until it is the scope of the entire cosmos in the entirety of space-time if we are to even consider doing this question any justice. I think if we are to talk about the Truth of the matter, then math concepts are actually not such a bad conceptual tool to use, since maths is the closest we have to a language of Truth.

In a sense, this discussion itself is indicative of the whole ID debate. I don't think that people engaged in that debate (either for or against) have truly even begun to think about the profundity of what they are actually talking about - how deep and how profound the question is. I find it rather like listening to a reality debate in nursery school, it's just a facile scratching about on the very surface of a problem that extends downwards all the way to infinity.

Phil
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