Scientists prove Goedel's ontological (God) theorem!?

[Kenneth Regan]

Re: Universal Corruption

I don't really understand the bird's eye view vs frog's eye view point. Are they both equally objective 'realities' of our universe, or are they both based on perception making them subjective?

One of the linchpin theorems in computation theory is that a nondeterministic finite automaton (NFA) N can be simulated by a deterministic finite automaton (DFA) M. The NFA N has a set of local states q0,q1,...,q(n-1) it can be in. An NFA's computation starts up in state q0 and thereafter may have choices. Depending on the code of N, it might go q0-to-q1-to-q3-to... or q0-to-q4-to-q2..., and either of these may have further branchings, possibly cycling back to an earlier state. The DFA M has "super-states" that are sets of states of N. Its single state at a given time represents the set of all "possible worlds" N could be in at that time. Continuing the example, M would start up in the state Q0 = {q0}, and deterministically progress to the super-state Q1 = {q1,q4}. The state Q2 after that would be {q2,q3}, and would remain that even if N allowed a direct local branching from q4 back to q3. If N had a branch from q4 back to q1, however, or from q1 to itself (no local change), then the next state would be {q1,q2,q3} instead. And so it goes---deterministically but with up to 2^n total states rather than just the original n. So the analogy is:

N = local = frog's-eye view = what we experience, perceiving randomness.
M = global = bird's-eye view = deterministic, but we don't experience the totality.

The analogy starts becoming concrete when we think of M not as having subsets Q of {q0,...,q(n-1)} but rather distributions D of probabilities p0,p1,...,p(n-1) on these states. Or better, assignments A of amplitudes a0,a1,...,a(n-1), which are complex numbers whose absolute values are the square roots of these probabilities. The D view defines a Markov chain. The A view is what we get in quantum mechanics, and comes with the deterministic evolution defined by Schrödinger's equation. Thus the deterministic evolution at bird's-eye level is managing the sets of possible local worlds q that receive nonzero amplitudes at any given time, while the amplitudes themselves govern the likelihood of experiences by those in q who actually live at frog's-eye level. The "Garden of Forking Paths" slide attempts to picture the interface between the levels geometrically, conveying the spatial "room" of the talk's title.

If our universe if almost fully mechanistic (follows a law of cause-and-effect) at everything besides the quantum level, it is most likely that our own selves being part of nature and the universe are also mechanistic (necessarily following from our genetics and experiences/environment) leaving out free-will entirely. Does quantum indeterminacy have an effect on our free-will? Even if it did if we are not in control of them, how can it be said to have free-will even if we perceive that we do?

My talk "ducks" the scientific line on free will, first posing a different question, then reintroducing free will only in theological modeling. For the latest and best effort I know to preserve a scientific approach to free will (apart from global workspace theory which tends against it), I'll refer you to a post and long paper by my blogging Überpeer, Scott Aaronson.

[Adam Cormier]

Re: Universal Corruption

Thanks, Adam. Your point about multiverse theory is one I also query (can all but finitely many universes be "duds"?) but it's argued by many proponents that nothing possible is excluded, and Brian Greene's book The Hidden Reality takes that aspect as read. My bit about Hawking and creationism is half-joke, half a point about modal necessity. The "why should believers care?" slide is addressed only to believers. I don't have a proof for "universal mind" (I'm contra-pan[en]theism actually) nor for free will, only a suggestion on the latter. Do you grasp how we can have "hard determinism" in the bird's-eye view yet the experience of non-determinism in the frog's-eye view? That's the crux of what I draw from quantum mechanics. What follows it is not meant to be more than "K3: Modeling" as presaged near the beginning.

I have Greene's book I should really get to reading it.
ahh, thanks for clarifying on those issues.

I don't really understand the bird's eye view vs frog's eye view point. Are they both equally objective 'realities' of our universe, or are they both based on perception making them subjective?

If our universe if almost fully mechanistic (follows a law of cause-and-effect) at everything besides the quantum level, it is most likely that our own selves being part of nature and the universe are also mechanistic (necessarily following from our genetics and experiences/environment) leaving out free-will entirely. Does quantum indeterminacy have an effect on our free-will? Even if it did if we are not in control of them, how can it be said to have free-will even if we perceive that we do?

[Kenneth Regan]

Re: Universal Corruption

Thanks, Adam. Your point about multiverse theory is one I also query (can all but finitely many universes be "duds"?) but it's argued by many proponents that nothing possible is excluded, and Brian Greene's book The Hidden Reality takes that aspect as read. My bit about Hawking and creationism is half-joke, half a point about modal necessity. The "why should believers care?" slide is addressed only to believers. I don't have a proof for "universal mind" (I'm contra-pan[en]theism actually) nor for free will, only a suggestion on the latter. Do you grasp how we can have "hard determinism" in the bird's-eye view yet the experience of non-determinism in the frog's-eye view? That's the crux of what I draw from quantum mechanics. What follows it is not meant to be more than "K3: Modeling" as presaged near the beginning.

[Adam Cormier]

Re: Universal Corruption

Embarrassing to relate, an outdated version of my cosmology-and-religion talk got onto my webpage; it is fixed now.

I enjoyed reading over the slides from your talk. Having Hawking's Many World's theory imply creationism's plausibility I'm not sure if I buy though, even if there are an infinite many worlds, creationism being correct in one doesn't necessarily follow from this. Number Analogy: 1,3,5,7 to infinity would be an infinite set of numbers but exclude an entire other infinite amount of numbers 2,4,6,8...etc. We know that the facts in our world have to correspond to at least one real world, but because we have no evidence for creationism it is only possibly found in the infinite amount of worlds, therefore the mainstream evolutionary view is more realistic to follow even giving Hawking's Many World's Theory is correct.

I think my number analogy is also good for responding to the multiverse theorists who say that in a multiverse every possible event happens, where even if there are an infinite number of universes it is possible an entire other infinite of possible events is excluded from the multiverse.

On the points on why should believer's care, I feel that one can get many of those benefits from studying philosophy and not necessarily having to be a believer to think and contemplate the why questions and the bigger questions behind life and the universe.

Is it still possible that even though religion and science don't fight (I disagree because I'd say at its core the scientific approach to truth is based on axioms that don't allow God to exist [or at least has no reason to interfere with humanity], metaphysical naturalism for example), philosophy and religion do. They both view a lot of the same questions on morality, knowledge and metaphysics.

Also when you say that many scientists and believers/non-believers believe the universe to have a 'mind' is more of an argument from popularity. Is there any actual proof of this mind of the universe?

Would you mind going over your proof for free-will, as I can't make it out just from the power-point slides, I'm divided on that issue, but I'm probably closer to hard determinism now than anything else. Also you make a pretty big jump at the end there, the possibility of a god/deity does not make it automatically possible the judeo-christian God does, which I would argue has many more logical problems to face than a simple pantheist or even deistic god.

[Kenneth Regan]

Re: Universal Corruption

Embarrassing to relate, an outdated version of my cosmology-and-religion talk got onto my webpage; it is fixed now.

[Kenneth Regan]

Re: Universal Corruption

I have the beginnings of an attempt to address Bob Armstrong's question, together with some unfinished notes. For the "problem of evil" specifically I have nothing better than this answer.

[Kenneth Regan]

Scientists prove Goedel's ontological (God) theorem!?

I co-manage a blog in my field that is actually named for Gödel. My sources for a mock-interview of Gödel which I co-wrote have links on Gödel's argument, including a rebuttal by my former Oxford chess team captain Peter Millican (who also verified that J.K. Rowling wrote The Cuckoo's Calling).

I paraphrase Anselm's original version as follows: God can be defined as the sum of all improvements. If it is possible for this sum to exist, then its existence is an improvement, so it does.

Gottfried Leibniz---he of the calculus and Germany's answer to Fig Newtons---introduced the "possible" qualifier, and this is integral to the modal logic used by Gödel and Plantinga. Modal logic has qualifiers "Diamond" for "possible" and "Box" for "necessary". Call a proposition G of modal logic a "Diamond Box" if you can prove that Diamond-G implies Box-G. Upon showing that the G interpreted as the existence of God has this property, you obtain the conclusion "if the existence of God is possible, then it is necessary." The deduction itself is ironclad---the Standord Encyclopedia article notes people in my field verified it by hand long before the article cited in this thread---so the interpretation becomes the issue. Gödel was (IMHO) able to overcome mathematical objections akin to Russell's paradox to the kind of "maximal sum" or "positivity metric" needed (along lines of a long post I recently wrote), but that goes only yea-far for interpretation.

A more-mundane analogy from probability theory is that some events E follow a zero-one law: If E has non-zero probability---that is if E is possible---then its probability must be 1, analogous to necessary. Mathematical models of gas diffusion and epidemics have this feature, which tends to apply especially for eventualities that are definable in basic logic. The one popular book that endeavors to define a scientific probability framework for G is Richard Dawkins' The God Delusion. His pivotal Chapter 2 assigns God---not just "G" but the flesh-and-blood being---a nonzero probability. This in the context of this thread, plus his strong support for children reading the Bible expressed last year, have me currently rather happy with him, actually.

[Kevin Pacey]

Re: Universal Corruption

...
P.S. The problem that I opened with is difficult. It is the question of whether, after creation, God shepherds his flock to some extent. Does God actually intervene in human (or other) history, and alter the course of what should have been? Many believers say "Yes" and refer to this as "miracle". Unfortunately, this leads to the extremely difficult question - why does he see fit to intervene in some situations and not others...

Hi Bob

The part I quoted in bold is sometimes answered by priests, spiritual advisers and such by something like "I'm in sales, I'm not in management". :)

Fwiw, I think prayer, or being prayed for, might at least sometimes make a huge difference, as far as your quiery goes. This in turn also may depend hugely on the strength of the belief in the existence of God that the person praying has. A prayer from someone having (or close to having) 100% certainty in belief that God exists can move a mountain,etc., if that is God's will also (usually assuming, I suppose, that the person(s) praying is/are reasonably good-hearted person(s)).

Sometimes there are good reasons, perhaps only ever known to God, why a given prayer goes unanswered. Who knows, sometimes a good person is a badly needed addition to heaven, I might hazard to guess. On the other hand, many interventions may occur everyday and go unnoticed, such as favourable 'coincidences' such as a traffic light happening to turn at the right moment to prevent an accident. Or the supposedly fluke luck that allowed the underdog Americans to win a critical victory at the Battle of Midway, when just when all the Japanese planes were about to be launched from carriers, three seperate groups of dive bombers stumbled upon the Japanese ships simultaniously ('divine intervention' was how one veteran of the battle decided to explain it).

[Kevin Pacey]

Re: Universal Corruption

Hi Bob

There is a basic 'plot' in most (all!?) versions of the Christian Bible, as far as the fate of creation goes.

First, there came 'the Fall' (in the Book of Genesis), as I mentioned in my last post. At that point, after Adam and Eve disobeyed God by eating forbidden fruit (perhaps a metaphor for sex!?), evil and sin were introduced, as I understand it (unless one considers the Serpent as one already existing form of evil, perhaps[?]). Reproduction of living creatures, including mankind, began after Adam and Eve were expelled from the Garden of Eden.

Fast forward to the end of the Bible, to the Book of Revelation. After a few (seven) years of great evil, suffering and tribulation on earth (which at least some people say could happen at about our time in history, in fact), through which some fortunate Christians may be evacuated (according to some interpretations), this book of the Bible predicts that Jesus will return to rule the Earth, and and eventually there will be no more death or suffering etc. At least that's my understanding.

Fwiw, I have issues with this last Book of the Bible, if not other parts of the Bible too, which I think may possibly have suffered due to translation(s) over time. Puts me in the awkward position of having to cherrypick what parts/principles I trust in. As I mentioned in another thread, I certainly believe in the Golden Rule (Do unto others as you would have them do unto you). Other principles may follow from that.

Of course, all of these stories and arguments are irrelevant (along with this whole thread) if one is a committed aetheist.

[Kevin Pacey]

Re: Universal Corruption

On the point about compassion, I suppose compassion may need only be felt, if not immediately (or ever) delivered to the victim(s) of some misfortune caused by evil, in order to still be of value in the face of evil(s). Such compassion could be felt by God Himself, or posssibly existing [guardian] angels, who may need to learn/have increased compassion, along with deceased persons possibly, or merely living persons who learn of the misfortunes of others, say in a distant place. Regarding evils caused by 'nature' (as I put it), I thought it to be understood to include landslides etc., or even diseases. That's besides any allowed interventions by a devil or demons, if such are supposed to exist. Similar arguments could conceivably apply if animals were the victims of evil rather than people.

I didn't seem to have trouble rejecting Hegel's views re: Free Will, whatever they were, and so these views did not affect me when Hegel included them in his arguments on his so-called 'problem of evil'.

One trap I almost fell into as a student was to think that as another defence to 'the problem of evil' there was the apparent necessity for death (usually considered an evil) since a presumably finite universe (or at least finite planets like Earth) would be unsuitable for unrestrained population growth (in the absence of death), assuming reproduction is desirable - already perhaps not a given, in that if one believes in the Adam and Eve story, reproduction by living things apparently did not occur until after 'the Fall', which was the result of an apparently bad choice of disobedience.

The biggest problem with this 'defence' (besides the Adam and Eve story, if believed) is that God might have created an infinite universe with an infinite flat plane Earth, where an ever expanding population of living organisms would always have room to live, even if death never occured.

[Bob Armstrong]

Universal Corruption

While the Free Will Defense might be a strong theodicy to the problem of evil focusing on human caused evils (Most philosophers consider Alvin Platinga's version of it to successfully refute the logical form of the problem, which I disagree with but it shows the strength of it above many other attempts to justify evil), it only looks at a portion of the actual problem.

The Problem from Natural Evil against the existence of God is unanswered by this and your compassion point doesn't seem sufficient to justify all suffering (as many times compassion does not come to those that are suffering). If an all-loving God created this universe, he created our Earth. Specifically on Earth there are multiple different types of natural disasters that bring massive suffering and damage to life both human and non-human. Why a God would create a planet that kills his beloved creation is a significant problem for those believing in the Judeo-Christian God.

Hi Adam & Kevin:

For those who believe in a God-creator, a significant issue is whether he has then abandoned his creation, to let it evolve naturally, however much suffering may result. Does Life trump Suffering?

God created matter. Matter corrupts. Thus suffering is the result on a material level. Is this acceptable to those who are God-believing?

For believers of more modern stripe, God endowed his inanimate matter with the potential to combine, under the right circumstances, to create an animate being. This animate being had within it the potential of intelligence. But is the intelligence determinative - that is, driven only by its inherent material thrust to survive? Or did God allow for the potential that intelligence would be accompanied by free will? That is, it could decide among different drives within it. If intelligent species (man is not alone on earth in this) can make decisions, then they are capable of causing suffering in other animates. This we refer to as the problem of human evil.

So, is it the case, that a God-creation must be free of all corruption - material and intelligent?

Bob A

P.S. The problem that I opened with is difficult. It is the question of whether, after creation, God shepherds his flock to some extent. Does God actually intervene in human (or other) history, and alter the course of what should have been? Many believers say "Yes" and refer to this as "miracle". Unfortunately, this leads to the extremely difficult question - why does he see fit to intervene in some situations and not others. But this discussion would somewhat hijack the thread, so I will just leave it here.

[Adam Cormier]

Re: Scientists prove Goedel's ontological (God) theorem!?

It's been a long time since I studied philosophy, but I seem to recall 'the problem of evil' was, in the end, not a problem for me personally, as far as reaching any sort of limiting conclusion about God was concerned (not that I was at all sure of His existence at the time).

If my vague recollection is at all right, I persuaded myself that the following counter-arguments were valid (I don't know how many people have made them over time):
(1) there needs to be real consequences for any bad decisions resulting from free will (if one argues that people have it, and that it is compatible with determinism - though after a whole course on that issue my rather trite conclusion was that resolving that issue all depended on how one chose to define free will :D - fwiw, I think they are compatible);
(2) there is a need for compassion (in the face of the consequences of evils caused by man or nature) - as far as God might be concerned, even, how can one truly love something (e.g. an individual person) if it is (at least physically) indestructible or undamagable, in whole or in part.

While the Free Will Defense might be a strong theodicy to the problem of evil focusing on human caused evils (Most philosophers consider Alvin Platinga's version of it to successfully refute the logical form of the problem, which I disagree with but it shows the strength of it above many other attempts to justify evil), it only looks at a portion of the actual problem.

The Problem from Natural Evil against the existence of God is unanswered by this and your compassion point doesn't seem sufficient to justify all suffering (as many times compassion does not come to those that are suffering). If an all-loving God created this universe, he created our Earth. Specifically on Earth there are multiple different types of natural disasters that bring massive suffering and damage to life both human and non-human. Why a God would create a planet that kills his beloved creation is a significant problem for those believing in the Judeo-Christian God.

[Kevin Pacey]

Re: Scientists prove Goedel's ontological (God) theorem!?

I agree with Berkeley when he states that the ontological argument fails because we cannot have an idea (conception, whatever) of God. My personal philosophical position is that ONLY God exists. I believe in nothing else. But the problem of evil is convincing. Evil does exist, therefore an all-knowing, all-loving and all-powerful God cannot exist. God, then, cannot be all of the above. As Hegel would suggest, God must therefore be an evolving Being, coming to greater self-knowledge over historical time. God, then, cannot exist outside of Time. God has a past, present and future, and is an eternally changing Being.

I do not know whether Hegel was a 1.d4 or a 1.e4 player.

It's been a long time since I studied philosophy, but I seem to recall 'the problem of evil' was, in the end, not a problem for me personally, as far as reaching any sort of limiting conclusion about God was concerned (not that I was at all sure of His existence at the time).

If my vague recollection is at all right, I persuaded myself that the following counter-arguments were valid (I don't know how many people have made them over time):
(1) there needs to be real consequences for any bad decisions resulting from free will (if one argues that people have it, and that it is compatible with determinism - though after a whole course on that issue my rather trite conclusion was that resolving that issue all depended on how one chose to define free will :D - fwiw, I think they are compatible);
(2) there is a need for compassion (in the face of the consequences of evils caused by man or nature) - as far as God might be concerned, even, how can one truly love something (e.g. an individual person) if it is (at least physically) indestructible or undamagable, in whole or in part.

[Mario Moran-Venegas]

Re: Scientists prove Goedel's ontological (God) theorem!?

He He,

"Just ran the code on my Mac. Says God's name is Steve.
Checked on PC to confirm, but it tells me God's name is Bill.
Tried a couple of Linux boxes. Each one went and created its own universe. Several, in fact."

love this post to Spiegel's article

1. The "work" done by these "scientists" using computers imho is not more serious than the above quote.

2. Platinga simply reformulated older statements more rigorously. But what is the use of an improved tautology?

3 .Tautology to the nth power = tautology

4. I have therefore proven that 1. Nf3 exists...

[Mario Moran-Venegas]

Re: Scientists prove Goedel's ontological (God) theorem!?

He He,

"Just ran the code on my Mac. Says God's name is Steve.
Checked on PC to confirm, but it tells me God's name is Bill.
Tried a couple of Linux boxes. Each one went and created its own universe. Several, in fact."

love this post to Spiegel's article