6 ms·

Gödel's Proof of God's Existence

39 points by netrus 13y ago

netrus 13y ago
As an atheist, I have mixed feelings about it. I like it as a training in logic, yet I feel it is of no theological value...
- pmelendez 13y ago
  From the paper: "Gödel defines God as a being who possesses all positive properties. He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy" I'm not an atheist, but for truth's sake you would notice that Gödel definition of God is very wide and not necessarily aligned with any mainstream religion.
- Shorel 13y ago
  Reading the Wikipedia version of that, it is full of HUGE assumptions: > Axiom 5: Necessary existence is a positive property That's in total disagreement with evolution. No being is really necessary. > Corollary 1: The property of being God-like is consistent. Now that's in huge disagreement with any religious book, as all of them are full of inconsistencies. Any proof lacks any value if the starting axioms lack value by themselves. Newton wasted years of his life studying the bible. We shall simply view all this as the waste of time it was and simply expect future genius to not do the same.
- bsullivan01 13y ago
  "God" doesn't necessarily mean one that cares what you ate on Friday.....or if you pushed the elevator buttons on Shabbat.
  - astrodust 13y ago
    Replace "God" with "burrito" and it's the same thing.
- dragonwriter 13y ago
  I am a Christian, and I think this argument (and more simple ones of the same general form -- notably St. Anselm's) are good examples of the limitations and abuses of logic; they are superficially attractive in isolation, but if you accept the basic form (and, particularly -- as pointed out Kant's critique of Anselm's argument, which is equally applicable to Godel's -- accept the erroneous idea that existence can be treated as a predicate) you can "prove" the existence of pretty much anything.
- ianstallings 13y ago
  I wouldn't worry, Gödel himself was only trying to prove that mathematics could be used to determine if God existed and he himself did not publish it until he was near death because people would think he believed in God. If anything it was a more formal approach to the Ontological Argument put forward by Anselm of Canterbury, and he was trying to show how modal logic can be used as language in proof theory, and "the study of what can and cannot be proved in mathematical systems of deduction. Issues of completeness of mathematical systems, the independence of axioms from other axioms, and issue of the consistency of formal mathematical systems are all part of proof theory." http://sas.uwaterloo.ca/~cgsmall/ontology.html http://sas.uwaterloo.ca/~cgsmall/ontology.html http://en.wikipedia.org/wiki/Anselm_of_Canterbury http://en.wikipedia.org/wiki/Anselm_of_Canterbury
cliveowen 13y ago
I didn't know there was software to verify mathematical proofs. Heck, I didn't even know there was a formal syntax for writing them.
- netrus 13y ago
  A prominent example for proofs by computer algorithms is the 4 color theorem: http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
  - aardvark179 13y ago
    That's not quite the same thing. The 4 colour theorem was proved by boiling it down to several thousand test cases and using a computer program to test those by colouring them. This paper is about using theorem provers to check axioms for consistency and proofs derived from those.
- dylandrop 13y ago
  See http://en.wikipedia.org/wiki/Automated_theorem_proving#Decidability_of_the_problem http://en.wikipedia.org/wiki/Automated_theorem_proving#Decid... Important to note Gödel's completeness theorem here! You might be even more interested in Prolog, a language which has a close relationship with this stuff: "Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is declarative: the program logic is expressed in terms of relations, represented as facts and rules. A computation is initiated by running a query over these relations." (http://en.wikipedia.org/wiki/Prolog http://en.wikipedia.org/wiki/Prolog) This is why everyone should take an AI class.
  - lutusp 13y ago
    > Important to note Gödel's completeness [sic] theorem [sic] here! ITYM incompleteness theorems. http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the...
pohl 13y ago
A God-like being possesses all positive properties A5 Necessary existence is a positive property Oh, yeah, that's not circular at all...
- zamalek 13y ago
  > He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy. Various slightly diﬀerent versions of axioms and deﬁnitions have been considered by Godel and by several philosophers who commented on his proof. Such is the world of philosophy. Remember that some of the greatest scientists and mathematicians lived when all of it was just philosophy. Philosophy is a training exercise to think imaginatively and some of our best science stems from an imaginative spark. It's like saying that people professional athletes running around a field (philosophy) is pointless because they are not running in a race for gold (science) at that specific point in time. This is by all means not scientific, precisely because you can't address that specific subject matter scientifically: 1. God exists if he makes himself/herself visibly and measurably known and is observed and measured by a human being and the observations are confirmed by peers within the scientific community. 2. God does not exist if a human is present to see the end of the universe (or variant there-of) and he has not been yet observed (assuming he/she is tied to the existence of the universe) and the lack of observation is confirmed by peers within the scientific community. We simply don't know until either (1) or (2) is satisfied, therefore this is exactly the type of stuff philosophy is good at. It's not saying "can we prove it" it's saying "let's think about creative ways to prove it if we can get a little lax about the scientific method." Were "getting lax about the scientific method" means that "proof" can be derived from either common sense or logical arguments.
  - deleted 13y ago
    [deleted]
    - zamalek 13y ago
      You mis-interpreted my statement :) > you can't address [the existence of God] scientifically Maybe one day science and philosophy will meld to the point where this might be possible in a peer reviewed in the Nature journal kind-of possible way, God cannot be addressed by the current scientific method. What's valuable about Paul Graham's line-of-thinking is that he can distinguish between science and religion - something that very few can do (and is likely going to make this HN post explode into a pointless evolution vs. creation argument - which is missing the point of the experiment entirely).
jamesbritt 13y ago
This feels like begging the question. Start with a selective, loaded definition of "god" that seems to amount to "A god is a being who must exist." God is all that is good; not existing is not good, therefore god must exist. QED.
- alanctgardner2 13y ago
  > selective, loaded definition of "god" Well, you can't really win here. It's either a hand-wavey definition you could never formally prove, or a rigid, 'loaded' definition. That said, the basis of the proof does seem to be that 'if god exists, then he must exist', which is not really groundbreaking.
  - dragonwriter 13y ago
    > That said, the basis of the proof does seem to be that 'if god exists, then he must exist', which is not really groundbreaking. Actually, its "if god must exist, he exists".
  - simonh 13y ago
    IMHO what Godel's 'proof' boils down to is that if it is possible for God to exist, then God must exist. The discussion of possible worlds is an attempt to strictly formalize and make consistent the argument that it's possible for God to exist.
- deleted 13y ago
  [deleted]
JonnieCache 13y ago
– The basic modal logic K is suﬃcient for proving T1, C and T2. – Modal logic S5 is not needed for proving T3; the logic KB is suﬃcient. – Without the ﬁrst conjunct φ(x) in D2 the set of axioms and deﬁnitions would be inconsistent. – For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2. So, does god exist or not? Can anyone proficient in symbolic logic translate this for us? As someone who's read the first 2/3 of GEB at least twice, I'm planning to reorganise my entire worldview around this.
- MichaelAza 13y ago
  Yeah, seriously, what's the verdict? And where's the formalization itself? Show me the code, I have a whole worldview I need to re-evaluate here. Edit: Seems like this is the code - https://github.com/FormalTheology/GoedelGod https://github.com/FormalTheology/GoedelGod
- deleted 13y ago
  [deleted]
  - jameskilton 13y ago
    >> Does an omnipotent being exist in a heaven above? Not literally, no. Can you prove that an omnipotent being doesn't exist? You make a statement of fact without any backup evidence. I wouldn't be surprised if it is impossible to prove or disprove, using the material world we're a member of, the existence of an omnipotent being who lives outside of this material world.
    - deleted 13y ago
      [deleted]
    - mseebach 13y ago
      Metaphysical God is metaphysical.
- driverdan 13y ago
losethos 13y ago
LOL God says... Virtual-Notary.Org hereby notes that on Date: Monday September 09, 2013 10:48.22 EDT (UTC-0400) a random drawing in the range [1, 100000], inclusive, based on a hardware source of true randomness, yielded the following decision. Random Value: 47226 ------ 25:21 Let integrity and uprightness preserve me; for I wait on thee. 25:22 Redeem Israel, O God, out of all his troubles. 26:1 Judge me, O LORD; for I have walked in mine integrity: I have trusted also in the LORD; therefore I shall not slide. 26:2 Examine me, O LORD, and prove me; try my reins and my heart. 26:3 For thy lovingkindness is before mine eyes: and I have walked in thy truth. 26:4 I have not sat with vain persons, neither will I go in with dissemblers. 26:5 I have hated the congregation of evil doers; and will not sit with the wicked. 26:6 I will wash mine hands in innocency: so will I compass thine altar, O LORD: 26:7 That I may publish with the voice of thanksgiving, and tell of all thy wondrous works.
ebbv 13y ago
It's not really a logical proof, it's completely masturbatory. I can set a definition of money that all money belongs to me, and your money is money, and therefore your money is mine. That doesn't mean that all your money is my money. Following a false premise through to its logical conclusion doesn't mean the premise is true.
bachback 13y ago
Gödel is so overrated. How is this actually science? "This work has been supported by the German Research Foundation under grant BE2501/9-1."
- pmelendez 13y ago
  I believe that a "Formalization, Mechanization and Automation" of any logic proof would enter in the definition of science
agentultra 13y ago
This was paid for by tax-payer money? Wow Germany. Awesome. I've only just begun studying Gödel's proof of incompleteness and so I'm not qualified in any way to verify this paper. However it seems to me, as a layman, to be a very large stretch and mostly a tongue-in-cheek exercise of various logic proof verification software. Or possibly a troll. Hard to tell. :)
samatman 13y ago
This would appear to be a more formal version of Thomas Aquinas' Argument from Gradation of Being, borrowing some elements of the Argument from Possibility and Necessity. Logically proving the existence of God is a very old game. Modern atheists tend to ignore these proofs in favor of attacking superstition and the more obvious theological nonsense. Which is a shame, because they can be refuted, with interesting consequences for one's worldview. The stance that most powerfully refutes any Ultimate argument for God (of which there are a few good ones) is, imho, Madhyamaka Buddhism, which holds that everything is empty because all phenomena dependently co-arise.
deleted 13y ago
[deleted]
deleted 13y ago
[deleted]
- keiferski 13y ago
  This is an exercise in high-level logic performed by philosophy/mathematics professors, not a simpleminded /r/atheism debate about religion.
  - deleted 13y ago
    [deleted]
    - okamiueru 13y ago
      Pardon my presumptuousness in answering for someone else. But, it seems that by talking about apatheism, it was suggested that one should not waste time with such inquiries, as they give little to no value. However, a different view on this, is that it's an exercise in logic. That whether god exists or not, is irrelevant to the actual discussion. tl;dr: It could seem as the top post was "I don't care about this, because I don't care about religion. I'm an apathist.", which was met with "this can still be valuable, and interesting, from an intellectual point of view".
      - keiferski 13y ago
        Yes, well put, thank you for answering for me.
- Swizec 13y ago
  But it's simple. God does exist. She is a cultural phenomena and his effects can be felt in all our lives very obviously. If nothing else, then because our ancestors used it as an excuse to "civilise" the rest of the world so we can all live now as one big dysfunctional civilisation. But if you can experience the effects of something it is very likely that it does in fact exist.
  - DougBTX 13y ago
mej10 13y ago
http://en.wikipedia.org/wiki/Ontological_argument http://en.wikipedia.org/wiki/Ontological_argument There are obvious (and not so obvious) problems with such an argument even when formalized, some of which are discussed on the Wikipedia page.
msluyter 13y ago
This is one version of the ontological proof, which has a long history. For an overview: http://en.wikipedia.org/wiki/Ontological_argument http://en.wikipedia.org/wiki/Ontological_argument
mbubb 13y ago
How cool. Made me think of a Uni course on Thomas Aquinas from eons ago. I'll have to go back and check but I think: "An essence of an individual is a property possessed by it and necessarily implying any of its properties" could have come from Aquinas' "Being and Essence". And - forgive me it has been eons - didn't Wittgenstein deal with this time of formulation showing you could in parallel construct its opposite.
joshdance 13y ago
If there were a God and he was all powerful, and he wanted you to believe before you knew He existed, it makes sense that you would be unable to prove or disprove His existence.
- MrBra 13y ago
  now that is interesting.
- benjohnson 13y ago
  Indeed! if God mad His existence easily knowable, it would take away your free will to have faith.
jballanc 13y ago
Now what would be really interesting is some form of comparison between this proof and the conjecture by Brian Greene (and others) that it is highly likely that we are all bit players in a massive computer simulation of a Universe...
- lutusp 13y ago
  Yes, but those ideas aren't comparable -- proof or disproof of one doesn't influence the other. They're orthogonal ideas.
icpmacdo 13y ago
Everything in this thread is going way over my head. Would someone be kind enough to explain it to me like I'm 5?
- lutusp 13y ago
  It's an argument that, if certain logical conditions are met, then the principle of the existence of God is inescapable. Note that I said the principle, not the fact -- the fact was not the matter under discussion. It's like discussing the concept of an honest politician -- such a thing can obviously be proven to exist in principle, but that doesn't require that it exist in fact, in everyday reality. A good thing, too.
chrislipa 13y ago
The proof's axioms deal with what kinds of things have the property of being 'positive' (A1-A5). But lacking a separate definition of what positive means, we really have no choice but to view these 5 axioms as an implicit description of 'positivity' and wonder what mathematical models realize these axioms. One thing to note from the axioms is that for every property either that property or the negation of that property (but not both) has the label of 'positive'. This is already pretty strong, because it's making claims the about the 'positivity' of properties that are completely unrelated to the rest of the argument. It's almost just a labeling game: given p and -p, you must label exactly one as 'positive'. Is the property of being red positive? Saying no is equivalent (according to these axioms) to saying that the property of not being red is positive. You can pick one model for the axioms where being red is 'positive', and then the God that's shown to exist will be red. You can pick another where being not red is 'positive', and then the proof implies that God will not be red. It's not a logical contradiction because they're different models, but it certainly makes one wonder what the proof is talking about when it mentions 'positivity'. I have a suspicion that the axioms themselves generate an inconsistency and hence they could generate proofs for any statement. Anyways, this paper is about formal theorem provers, not theology, so hats off to the researchers implementing higher-order logic.
lutusp 13y ago
People who read these tracts need to understand that the goal is not to literally prove that God exists (all superficial appearances to the contrary), only to show that the argument can be made and is logically consistent. The same argument can be made with equal justification about Bigfoot, the Loch Ness monster, or an honest politician. All other issues aside, the Holocaust proves that either (a) God doesn't exist, or (b) he's Spinoza's God, the one who can't be bothered about humans and their problems.

39 points by netrus 13y ago

As an atheist, I have mixed feelings about it. I like it as a training in logic, yet I feel it is of no theological value...

pmelendez 13y ago
From the paper: "Gödel defines God as a being who possesses all positive properties. He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy" I'm not an atheist, but for truth's sake you would notice that Gödel definition of God is very wide and not necessarily aligned with any mainstream religion.
Shorel 13y ago
Reading the Wikipedia version of that, it is full of HUGE assumptions: > Axiom 5: Necessary existence is a positive property That's in total disagreement with evolution. No being is really necessary. > Corollary 1: The property of being God-like is consistent. Now that's in huge disagreement with any religious book, as all of them are full of inconsistencies. Any proof lacks any value if the starting axioms lack value by themselves. Newton wasted years of his life studying the bible. We shall simply view all this as the waste of time it was and simply expect future genius to not do the same.
bsullivan01 13y ago
"God" doesn't necessarily mean one that cares what you ate on Friday.....or if you pushed the elevator buttons on Shabbat.
- astrodust 13y ago
  Replace "God" with "burrito" and it's the same thing.
dragonwriter 13y ago
I am a Christian, and I think this argument (and more simple ones of the same general form -- notably St. Anselm's) are good examples of the limitations and abuses of logic; they are superficially attractive in isolation, but if you accept the basic form (and, particularly -- as pointed out Kant's critique of Anselm's argument, which is equally applicable to Godel's -- accept the erroneous idea that existence can be treated as a predicate) you can "prove" the existence of pretty much anything.
ianstallings 13y ago
I wouldn't worry, Gödel himself was only trying to prove that mathematics could be used to determine if God existed and he himself did not publish it until he was near death because people would think he believed in God. If anything it was a more formal approach to the Ontological Argument put forward by Anselm of Canterbury, and he was trying to show how modal logic can be used as language in proof theory, and "the study of what can and cannot be proved in mathematical systems of deduction. Issues of completeness of mathematical systems, the independence of axioms from other axioms, and issue of the consistency of formal mathematical systems are all part of proof theory." http://sas.uwaterloo.ca/~cgsmall/ontology.html http://sas.uwaterloo.ca/~cgsmall/ontology.html http://en.wikipedia.org/wiki/Anselm_of_Canterbury http://en.wikipedia.org/wiki/Anselm_of_Canterbury

cliveowen 13y ago

I didn't know there was software to verify mathematical proofs. Heck, I didn't even know there was a formal syntax for writing them.

netrus 13y ago
A prominent example for proofs by computer algorithms is the 4 color theorem: http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
- aardvark179 13y ago
  That's not quite the same thing. The 4 colour theorem was proved by boiling it down to several thousand test cases and using a computer program to test those by colouring them. This paper is about using theorem provers to check axioms for consistency and proofs derived from those.
dylandrop 13y ago
See http://en.wikipedia.org/wiki/Automated_theorem_proving#Decidability_of_the_problem http://en.wikipedia.org/wiki/Automated_theorem_proving#Decid... Important to note Gödel's completeness theorem here! You might be even more interested in Prolog, a language which has a close relationship with this stuff: "Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is declarative: the program logic is expressed in terms of relations, represented as facts and rules. A computation is initiated by running a query over these relations." (http://en.wikipedia.org/wiki/Prolog http://en.wikipedia.org/wiki/Prolog) This is why everyone should take an AI class.
- lutusp 13y ago
  > Important to note Gödel's completeness [sic] theorem [sic] here! ITYM incompleteness theorems. http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the...

pohl 13y ago

A God-like being possesses all positive properties A5 Necessary existence is a positive property Oh, yeah, that's not circular at all...

zamalek 13y ago
> He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy. Various slightly diﬀerent versions of axioms and deﬁnitions have been considered by Godel and by several philosophers who commented on his proof. Such is the world of philosophy. Remember that some of the greatest scientists and mathematicians lived when all of it was just philosophy. Philosophy is a training exercise to think imaginatively and some of our best science stems from an imaginative spark. It's like saying that people professional athletes running around a field (philosophy) is pointless because they are not running in a race for gold (science) at that specific point in time. This is by all means not scientific, precisely because you can't address that specific subject matter scientifically: 1. God exists if he makes himself/herself visibly and measurably known and is observed and measured by a human being and the observations are confirmed by peers within the scientific community. 2. God does not exist if a human is present to see the end of the universe (or variant there-of) and he has not been yet observed (assuming he/she is tied to the existence of the universe) and the lack of observation is confirmed by peers within the scientific community. We simply don't know until either (1) or (2) is satisfied, therefore this is exactly the type of stuff philosophy is good at. It's not saying "can we prove it" it's saying "let's think about creative ways to prove it if we can get a little lax about the scientific method." Were "getting lax about the scientific method" means that "proof" can be derived from either common sense or logical arguments.
- deleted 13y ago
  [deleted]
  - zamalek 13y ago
    You mis-interpreted my statement :) > you can't address [the existence of God] scientifically Maybe one day science and philosophy will meld to the point where this might be possible in a peer reviewed in the Nature journal kind-of possible way, God cannot be addressed by the current scientific method. What's valuable about Paul Graham's line-of-thinking is that he can distinguish between science and religion - something that very few can do (and is likely going to make this HN post explode into a pointless evolution vs. creation argument - which is missing the point of the experiment entirely).

jamesbritt 13y ago

This feels like begging the question. Start with a selective, loaded definition of "god" that seems to amount to "A god is a being who must exist." God is all that is good; not existing is not good, therefore god must exist. QED.

alanctgardner2 13y ago
> selective, loaded definition of "god" Well, you can't really win here. It's either a hand-wavey definition you could never formally prove, or a rigid, 'loaded' definition. That said, the basis of the proof does seem to be that 'if god exists, then he must exist', which is not really groundbreaking.
- dragonwriter 13y ago
  > That said, the basis of the proof does seem to be that 'if god exists, then he must exist', which is not really groundbreaking. Actually, its "if god must exist, he exists".
- simonh 13y ago
  IMHO what Godel's 'proof' boils down to is that if it is possible for God to exist, then God must exist. The discussion of possible worlds is an attempt to strictly formalize and make consistent the argument that it's possible for God to exist.
deleted 13y ago
[deleted]

JonnieCache 13y ago

– The basic modal logic K is suﬃcient for proving T1, C and T2. – Modal logic S5 is not needed for proving T3; the logic KB is suﬃcient. – Without the ﬁrst conjunct φ(x) in D2 the set of axioms and deﬁnitions would be inconsistent. – For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2. So, does god exist or not? Can anyone proficient in symbolic logic translate this for us? As someone who's read the first 2/3 of GEB at least twice, I'm planning to reorganise my entire worldview around this.

MichaelAza 13y ago
Yeah, seriously, what's the verdict? And where's the formalization itself? Show me the code, I have a whole worldview I need to re-evaluate here. Edit: Seems like this is the code - https://github.com/FormalTheology/GoedelGod https://github.com/FormalTheology/GoedelGod
deleted 13y ago
[deleted]
- jameskilton 13y ago
  >> Does an omnipotent being exist in a heaven above? Not literally, no. Can you prove that an omnipotent being doesn't exist? You make a statement of fact without any backup evidence. I wouldn't be surprised if it is impossible to prove or disprove, using the material world we're a member of, the existence of an omnipotent being who lives outside of this material world.
  - deleted 13y ago
    [deleted]
  - mseebach 13y ago
    Metaphysical God is metaphysical.
driverdan 13y ago

losethos 13y ago

LOL God says... Virtual-Notary.Org hereby notes that on Date: Monday September 09, 2013 10:48.22 EDT (UTC-0400) a random drawing in the range [1, 100000], inclusive, based on a hardware source of true randomness, yielded the following decision. Random Value: 47226 ------ 25:21 Let integrity and uprightness preserve me; for I wait on thee. 25:22 Redeem Israel, O God, out of all his troubles. 26:1 Judge me, O LORD; for I have walked in mine integrity: I have trusted also in the LORD; therefore I shall not slide. 26:2 Examine me, O LORD, and prove me; try my reins and my heart. 26:3 For thy lovingkindness is before mine eyes: and I have walked in thy truth. 26:4 I have not sat with vain persons, neither will I go in with dissemblers. 26:5 I have hated the congregation of evil doers; and will not sit with the wicked. 26:6 I will wash mine hands in innocency: so will I compass thine altar, O LORD: 26:7 That I may publish with the voice of thanksgiving, and tell of all thy wondrous works.

ebbv 13y ago

It's not really a logical proof, it's completely masturbatory. I can set a definition of money that all money belongs to me, and your money is money, and therefore your money is mine. That doesn't mean that all your money is my money. Following a false premise through to its logical conclusion doesn't mean the premise is true.

bachback 13y ago

Gödel is so overrated. How is this actually science? "This work has been supported by the German Research Foundation under grant BE2501/9-1."

pmelendez 13y ago
I believe that a "Formalization, Mechanization and Automation" of any logic proof would enter in the definition of science

agentultra 13y ago

This was paid for by tax-payer money? Wow Germany. Awesome. I've only just begun studying Gödel's proof of incompleteness and so I'm not qualified in any way to verify this paper. However it seems to me, as a layman, to be a very large stretch and mostly a tongue-in-cheek exercise of various logic proof verification software. Or possibly a troll. Hard to tell. :)

samatman 13y ago

This would appear to be a more formal version of Thomas Aquinas' Argument from Gradation of Being, borrowing some elements of the Argument from Possibility and Necessity. Logically proving the existence of God is a very old game. Modern atheists tend to ignore these proofs in favor of attacking superstition and the more obvious theological nonsense. Which is a shame, because they can be refuted, with interesting consequences for one's worldview. The stance that most powerfully refutes any Ultimate argument for God (of which there are a few good ones) is, imho, Madhyamaka Buddhism, which holds that everything is empty because all phenomena dependently co-arise.

deleted 13y ago

[deleted]

deleted 13y ago

[deleted]

keiferski 13y ago
This is an exercise in high-level logic performed by philosophy/mathematics professors, not a simpleminded /r/atheism debate about religion.
- deleted 13y ago
  [deleted]
  - okamiueru 13y ago
    Pardon my presumptuousness in answering for someone else. But, it seems that by talking about apatheism, it was suggested that one should not waste time with such inquiries, as they give little to no value. However, a different view on this, is that it's an exercise in logic. That whether god exists or not, is irrelevant to the actual discussion. tl;dr: It could seem as the top post was "I don't care about this, because I don't care about religion. I'm an apathist.", which was met with "this can still be valuable, and interesting, from an intellectual point of view".
    - keiferski 13y ago
      Yes, well put, thank you for answering for me.
Swizec 13y ago
But it's simple. God does exist. She is a cultural phenomena and his effects can be felt in all our lives very obviously. If nothing else, then because our ancestors used it as an excuse to "civilise" the rest of the world so we can all live now as one big dysfunctional civilisation. But if you can experience the effects of something it is very likely that it does in fact exist.
- DougBTX 13y ago

mej10 13y ago

http://en.wikipedia.org/wiki/Ontological_argument http://en.wikipedia.org/wiki/Ontological_argument There are obvious (and not so obvious) problems with such an argument even when formalized, some of which are discussed on the Wikipedia page.

msluyter 13y ago

This is one version of the ontological proof, which has a long history. For an overview: http://en.wikipedia.org/wiki/Ontological_argument http://en.wikipedia.org/wiki/Ontological_argument

mbubb 13y ago

How cool. Made me think of a Uni course on Thomas Aquinas from eons ago. I'll have to go back and check but I think: "An essence of an individual is a property possessed by it and necessarily implying any of its properties" could have come from Aquinas' "Being and Essence". And - forgive me it has been eons - didn't Wittgenstein deal with this time of formulation showing you could in parallel construct its opposite.

joshdance 13y ago

If there were a God and he was all powerful, and he wanted you to believe before you knew He existed, it makes sense that you would be unable to prove or disprove His existence.

MrBra 13y ago
now that is interesting.
benjohnson 13y ago
Indeed! if God mad His existence easily knowable, it would take away your free will to have faith.

jballanc 13y ago

Now what would be really interesting is some form of comparison between this proof and the conjecture by Brian Greene (and others) that it is highly likely that we are all bit players in a massive computer simulation of a Universe...

lutusp 13y ago
Yes, but those ideas aren't comparable -- proof or disproof of one doesn't influence the other. They're orthogonal ideas.

icpmacdo 13y ago

Everything in this thread is going way over my head. Would someone be kind enough to explain it to me like I'm 5?

lutusp 13y ago
It's an argument that, if certain logical conditions are met, then the principle of the existence of God is inescapable. Note that I said the principle, not the fact -- the fact was not the matter under discussion. It's like discussing the concept of an honest politician -- such a thing can obviously be proven to exist in principle, but that doesn't require that it exist in fact, in everyday reality. A good thing, too.

chrislipa 13y ago

The proof's axioms deal with what kinds of things have the property of being 'positive' (A1-A5). But lacking a separate definition of what positive means, we really have no choice but to view these 5 axioms as an implicit description of 'positivity' and wonder what mathematical models realize these axioms. One thing to note from the axioms is that for every property either that property or the negation of that property (but not both) has the label of 'positive'. This is already pretty strong, because it's making claims the about the 'positivity' of properties that are completely unrelated to the rest of the argument. It's almost just a labeling game: given p and -p, you must label exactly one as 'positive'. Is the property of being red positive? Saying no is equivalent (according to these axioms) to saying that the property of not being red is positive. You can pick one model for the axioms where being red is 'positive', and then the God that's shown to exist will be red. You can pick another where being not red is 'positive', and then the proof implies that God will not be red. It's not a logical contradiction because they're different models, but it certainly makes one wonder what the proof is talking about when it mentions 'positivity'. I have a suspicion that the axioms themselves generate an inconsistency and hence they could generate proofs for any statement. Anyways, this paper is about formal theorem provers, not theology, so hats off to the researchers implementing higher-order logic.

lutusp 13y ago

People who read these tracts need to understand that the goal is not to literally prove that God exists (all superficial appearances to the contrary), only to show that the argument can be made and is logically consistent. The same argument can be made with equal justification about Bigfoot, the Loch Ness monster, or an honest politician. All other issues aside, the Holocaust proves that either (a) God doesn't exist, or (b) he's Spinoza's God, the one who can't be bothered about humans and their problems.