The "Greatest" proof (pun intended) for the existence of God - Anselm

[dostoyevskyfan]

Since the ontological proof has been recently “resurrected” via Norman Malcolm (Harvard) and Plantinga (ND), I thought it was be interesting to discuss it. Most Catholics now don’t find recourse to it, and many still believe that Kant “killed” it with his semantical “predicate” nonsense.

Malcolm found another version of Anselm’s proof (in anselm’s writings) which has remained dormant over the years and is apparently immune to these “verbal gymnastics” lines of critique. Anselm “believed in order to understand rather than seeking understanding in order to believe”. I maintain that he discovered via prayer, an irrefutable argument for the existence of God. On the other hand, even if we as Catholics, can prove the existence of God, there will never be a proof for “faith”. People believe whatever they want irrespective of truth.

Anyway I’d be interested in hearing some commentary from believers and non-believers. Here’s the syllogism. You can find the argument in Malcolms writings but I think you need to pay money to actually get the article.

1. If God exists, then his existence is logically necessary. (timeless, eternal, uncreated, etc)
2. An impossible non-existence is greater than a possible non-existence. (eg. a unicorn)
3. If God does not exist, then his existence is logically impossible since He is that “than which nothing greater can be conceived”. (He cannot come into existence, or come out of existence)
4. Either God’s existence is logically impossible or logically necessary.
5. If God’s existence is logically impossible, then the concept of God is self contradictory.
6. The concept of God is not self-contradictory.
7. Therefore God is logically necessary.
8. Therefore God exists.

Discuss.

 

[JohnDamian]

I shall address this, but first I shall say I never found use for his proof, it was too short and very blunt.

1. If God exists, then his existence is logically necessary. (timeless, eternal, uncreated, etc)

True

1. An impossible non-existence is greater than a possible non-existence. (eg. a unicorn)

True

1. If God does not exist, then his existence is logically impossible since He is that “than which nothing greater can be conceived”. (He cannot come into existence, or come out of existence)

False - there is no causal predication of nessecity for the greatest conceivable to be the greatest in reality; furthermore; it may suffice for another entity that is not the greatest conceivable to fulfill the essential characteristics predicated upon the essence of a nessecary being (hypothetical).

1. Either God’s existence is logically impossible or logically necessary.

False It is positable that a thing generating the universe may expend itself (that it’s fruit may be the greatest of its powers), and as the principle that the greatest conceived is not nessecarily the greatest in material reality there is no causal nessecity for this to be so.

1. If God’s existence is logically impossible, then the concept of God is self contradictory.

True

1. The concept of God is not self-contradictory.

True

1. Therefore God is logically necessary.

False - This jumps the gun by presuming the greatest and not the least, one should only presume the least nessecary for the ends. Imagine a brick had been lifted off the floor, it would be wise to say that “whatsoever picked that up must be at least strong enough to do so” and NOT "whatsoever picked that up must be the strongest conceivable thing that could have picked it up.

1. Therefore God exists.

True; but not for aforegiven reasons.

 

[rvilbig]

Another interesting version of Anselm’s argument was put forth by Kurt Gödel (of Incompleteness Theorem fame). He uses modal logic: here’s a link to it.

There’s also an interesting proof of the golden rule using formal logic. This was developed by the Jesuit priest and logician Harry Gensler (link).

-Ryan Vilbig
ryan.vilbig@gmail.com

 

[inocente]

1. If God exists, then his existence is logically necessary. (timeless, eternal, uncreated, etc)
2. An impossible non-existence is greater than a possible non-existence. (eg. a unicorn)
3. If God does not exist, then his existence is logically impossible since He is that “than which nothing greater can be conceived”. (He cannot come into existence, or come out of existence)

If, in (3), God is “that than which nothing greater can be conceived”, then (1) is false. We can conceive of a greater God, who’s existence does not have to be logically necessary.

 

[hatsoff]

Since the ontological proof has been recently “resurrected” via Norman Malcolm (Harvard) and Plantinga (ND), I thought it was be interesting to discuss it. Most Catholics now don’t find recourse to it, and many still believe that Kant “killed” it with his semantical “predicate” nonsense.

Malcolm found another version of Anselm’s proof (in anselm’s writings) which has remained dormant over the years and is apparently immune to these “verbal gymnastics” lines of critique. Anselm “believed in order to understand rather than seeking understanding in order to believe”. I maintain that he discovered via prayer, an irrefutable argument for the existence of God. On the other hand, even if we as Catholics, can prove the existence of God, there will never be a proof for “faith”. People believe whatever they want irrespective of truth.

Anyway I’d be interested in hearing some commentary from believers and non-believers. Here’s the syllogism. You can find the argument in Malcolms writings but I think you need to pay money to actually get the article.

Just to be clear, the argument in question is surely Malcolm’s. I very much doubt St. Anselm constructed a formally valid deductive argument. Anselm was at most the principal inspiration for the argument.

1. If God exists, then his existence is logically necessary. (timeless, eternal, uncreated, etc)
2. An impossible non-existence is greater than a possible non-existence. (eg. a unicorn)

These premises may perhaps provide rhetorical support for other premises (though none I can fathom), but they are not themselves part of the deductive argument(s). In fact, I see two valid deductive arguments which have for some strange reason been fused together. They are as follows:

1. Either God’s existence is logically impossible or logically necessary.
2. If God’s existence is logically impossible, then the concept of God is self contradictory.
3. The concept of God is not self-contradictory.
4. Therefore God is logically necessary.

In the statement calculus, we may express this:

(4) M or N
(5) M only if S (equivalent to not-S only if not-M)
(6) not-S
(6’) therefore, not-M (from 5,6)
(7) therefore, N (from 4,6’)

Alternatively, we have the following argument:

1. If God does not exist, then his existence is logically impossible -]since He is that “than which nothing greater can be conceived”. (He cannot come into existence, or come out of existence)/-]
2. If God’s existence is logically impossible, then the concept of God is self contradictory.
3. The concept of God is not self-contradictory.
4. Therefore God exists.

The strikethrough indicates rhetoric, which although often valuable for understanding an argument, is superfluous with respect to deductive validity. The statement calculus formulation:

(3) not-G only if M (equivalent to not-M only if G)
(5) M only if S (equivalent to not-S only if not-M)
(6) not-S
(6’) therefore, not-M (from 5,6)
(8) therefore, G (from 3,6’)

This is the same kind of reasoning given by acolytes of Plantinga, and perhaps also Plantinga himself. The problem, however, is that phrases like “logically necessary” and “logically impossible” are deceptively ambiguous. What do they mean, exactly? Well, here is one possible interpretation: We may take the phrase “God is logically necessary” to mean that, given sufficient information, we could affirm the truth of a proposition P, which, along with propositions Q1, Q2, …, Qm, already known to be true, entails G, the proposition that God exists. In contrast, a statement like “God is logically impossible” we take to mean that, given sufficient information, we could affirm the truth of some proposition P*, which, along with Q1*, Q2*, …, Qn*, already known to be true, entails not-G. Given this interpretation, the statement “either God is logically necessary or else God is logically impossible” communicates nothing more than that we can know whether or not God exists, given sufficient information. Furthermore, the statement that “God is not logically impossible” indicates only that, if God does not exist, then we will never know that God does not exist, no matter how much information we accumulate.

Clearly that kind of interpretation is unhelpful for proving that God exists, since no one in their right mind would affirm any of the argument’s key premises, taken as such. So, what interpretation shall we provide instead? Plantinga’s formulation uses possible-worlds semantics, but that approach is plagued with its own problems. Namely, in order to make the argument work, we must restrict in advance our possible worlds set of such a way only a theist would approve.

If you have another interpretation in mind, feel free to provide it.

 

[Betterave]

Very interesting. Here’s my attempt to understand the argument:

1. If God exists, then his existence is logically necessary. (timeless, eternal, uncreated, etc)
   …i.e., it pertains to the concept of God to exist necessarily
2. An impossible non-existence is greater than a possible non-existence. (eg. a unicorn)
   …“greater” as in ontologically ‘thicker,’ closer to being in the full sense of the word, and farther removed from ‘nothing(ness)’
3. If God does not exist, then his existence is logically impossible since He is that “than which nothing greater can be conceived”. (He cannot come into existence, or come out of existence)
   …self-evidently true given the meanings of the terms
4. Either God’s existence is logically impossible or logically necessary.
   …follows from: (Eg v ~Eg) (God exists or not), together with 1 and 3
5. If God’s existence is logically impossible, then the concept of God is self contradictory.
   …explication of terms
6. The concept of God is not self-contradictory.
   …self-evident
7. Therefore God is logically necessary.
   …follows from 4, 5, 6
8. Therefore God exists.
   …as logical beings we cannot but affirm that which is logically necessary, therefore we must affirm God (see 7), and existence is part of the concept of God (see 1)

 

[Betterave]

Just to be clear, the argument in question is surely Malcolm’s. I very much doubt St. Anselm constructed a formally valid deductive argument. Anselm was at most the principal inspiration for the argument.

I remember reading Anselm’s argument years ago and being surprised at how subtle it was compared to the usual presentations of it. I’m curious, what is the basis for your remark here?

 

[hatsoff]

I remember reading Anselm’s argument years ago and being surprised at how subtle it was compared to the usual presentations of it. I’m curious, what is the basis for your remark here?

“Subtle” isn’t what concerns me. If you read the OP, it sounds like (non-professional) modern philosophy, and not medieval philosophy. While I admit I haven’t much experience in the latter, I would be very surprised indeed if Anselm’s text reads much like the OP.

Now that I think of it again, however, it doesn’t sound like professional modern philosophy, either. So perhaps it isn’t Malcolm’s argument after all, but rather dostoyevskyfan’s.

 

[coolduude]

What about Plantinga’s argument?
(By the way, if you guys want me out of this thread let me know and I’ll make my own )

Now in his version of the argument, Plantinga conceives of God as a being which is “maximally excellent” in every possible world. Plantinga takes maximal excellence to include such properties as omniscience, omnipotence, and moral perfection. A being which has maximal excellence in every possible world would have what Plantinga calls “maximal greatness.” So Plantinga argues:

1. It is possible that a maximally great being exists.

1. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

1. If a maximally great being exists in some possible world, then it exists in every possible world.

1. If a maximally great being exists in every possible world, then it exists in the actual world.

1. If a maximally great being exists in the actual world, then a maximally great being exists.

1. Therefore, a maximally great being exists.

 

[Betterave]

“Subtle” isn’t what concerns me. If you read the OP, it sounds like (non-professional) modern philosophy, and not medieval philosophy. While I admit I haven’t much experience in the latter, I would be very surprised indeed if Anselm’s text reads much like the OP.

Now that I think of it again, however, it doesn’t sound like professional modern philosophy, either. So perhaps it isn’t Malcolm’s argument after all, but rather dostoyevskyfan’s.

Well obviously it’s a schematization of the original argument. If you ever do spend some time reading medieval philosophy, I think you’ll discover it’s not difficult to find easily formalized arguments that can be easily enough expressed in the “modern professional” way. Another question, just curious again: do you think (you seem to imply) that all “professional modern philosophy” (whatever you mean by that) sounds the same? What does it sound like??

 

[hatsoff]

Another question, just curious again: do you think (you seem to imply) that all “professional modern philosophy” (whatever you mean by that) sounds the same?

No.

 

[JohnDamian]

1. It is possible that a maximally great being exists.

True

1. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

False - it is not nessecarily true, by virtue of it’s potentiality, that such a being would have to exist even if the replications of possible worlds occured ad infinitum; one could flip a coin eternally and never get heads.

1. If a maximally great being exists in some possible world, then it exists in every possible world.

False - This again makes a presumption that the world is contingent upon this being (which is a seperate, better argument). There is no causal link between there being a maximally great being in one (possible) world, and there being one in this world by nessecity; especially since it has not been apodeictically demonstrated that one nessecarily exists in a singly potential world.

1. If a maximally great being exists in every possible world, then it exists in the actual world.

True - but it has not been demonstrated that one exists in every possible world, so this (true) conclusion is unfounded.

1. If a maximally great being exists in the actual world, then a maximally great being exists.

True - but the premises are false, see above.

1. Therefore, a maximally great being exists.

True - but not for aforegiven reasoning.

 

[wanstronian]

It fails in precisely the same way as all other variations of the ontological argument.

 

[dostoyevskyfan]

“Subtle” isn’t what concerns me. If you read the OP, it sounds like (non-professional) modern philosophy, and not medieval philosophy. While I admit I haven’t much experience in the latter, I would be very surprised indeed if Anselm’s text reads much like the OP.

Now that I think of it again, however, it doesn’t sound like professional modern philosophy, either. So perhaps it isn’t Malcolm’s argument after all, but rather dostoyevskyfan’s.

Although I would love to take credit for it as it appears to me both valid (follows from deduction) and sound (all premises are true), it would be intellectually dishonest. It is the proof that has remained at the center of western philosophy (from medieval times all the way to "professional modern philosophy) for a thousand years. Anselm created it but other endorsers include spinoza, descartes, liebnez, Hegel, Godel, all the way up to Malcolm and Plantinga, who are/were “professional modern philosophers”. Even the atheist Sartre incorporated a modern version of the ontological proof to demonstrate the existence of a “god” who was not conscious of himself in his work being and nothingness. The proof has influence over both theistic and secular existentialism.

If you are in doubt that the argument existed in a similar way to how I have presented it, then why don’t you read the fordham.edu/halsall/basis/anselm-proslogium.html proslogium for yourself?

Malcolm didn’t create the argument nor did he attempt to take credit for it; he merely put it into the format of a logical syllogism.

Kant’s objection to the argument was that “being isn’t a real predicate” or that “a hundred possible dollars are indistinguishable from a hundred actual dollars in the mind”. Hegel corrected him in his lectures on the philosophy of religion amazon.com/Lectures-Philosophy-Religion-One-1827/dp/0520060202 by basically stating that “necessary existence”* is* a real predicate and can be, even though “being” isn’t.

You are discovering some heavy stuff. I can understand that it may seem intellectually daunting to the average atheist. At one point Bertrand Russell (philosophical atheist) was actually convinced of the proofs veracity.

As to the above poster, saying that “the proof fails like all other versions of the proof” doesn’t not make it invalid or unsound. In order to formally refute it in the context of logic, you have to attack a premise or the logical structure of the argument,…or just reject logic and reason all together like many secular thinkers have in the past.

 

[RobNY]

dostoevskyfan,

(6) is the problem premise.

It is true, of course, but the question is whether it can be known to be true by reason.

Do you have any proofs of (6)? Leibniz tried, but see if his axioms are acceptable to an atheist.

God bless,
Rob

 

[ddarko]

Another interesting version of Anselm’s argument was put forth by Kurt Gödel (of Incompleteness Theorem fame). He uses modal logic: here’s a link to it.

There’s also an interesting proof of the golden rule using formal logic. This was developed by the Jesuit priest and logician Harry Gensler (link).

-Ryan Vilbig
ryan.vilbig@gmail.com

This is not related to the debate but the problem with the ‘‘Golden Rule’’ is that for it to work, you first have to assume
1) you know how to treat yourself right
2) that there is a objective right way to treat yourself

Otherwise you are still screwed lol.

So I think argument from objective moral values is the strongest argument for God!

God Bless

 

[coolduude]

Here’s another formulation of the argument I posted earlier:

1. God exists in the understanding but not in reality. (Assumption for reductio)
2. Existence in reality is greater than existence in the understanding alone. (Premise)
3. A being having all of God’s properties plus existence in reality can be conceived. (Premise)
4. A being having all of God’s properties plus existence in reality is greater than God. (From (1) and (2).)
5. A being greater than God can be conceived. (From (3) and (4).)
6. It is false that a being greater than God can be conceived. (From definition of “God”.)
7. Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)
8. God exists in the understanding. (Premise, to which even the Fool agrees.)
9. Hence God exists in reality. (From (7), (8).)

 

[hatsoff]

You are discovering some heavy stuff. I can understand that it may seem intellectually daunting to the average atheist. At one point Bertrand Russell (philosophical atheist) was actually convinced of the proofs veracity.

First of all, this is nothing new. I’m familiar with various ontological arguments, and, as is the case for most philosophers (of which I am not), I remain thoroughly unconvinced by it. Second, there is nothing “intellectually daunting” about it. Every ontological argument I’ve encountered amounts to little more than a semantic game, and this version is no different in that regard, as I have pointed out. That’s probably why wanstronian gave his offhanded comment.

 

[wanstronian]

First of all, this is nothing new. I’m familiar with various ontological arguments, and, as is the case for most philosophers (of which I am not), I remain thoroughly unconvinced by it. Second, there is nothing “intellectually daunting” about it. Every ontological argument I’ve encountered amounts to little more than a semantic game, and this version is no different in that regard, as I have pointed out. That’s probably why wanstronian gave his offhanded comment.

That, plus a lack of time to post and the fact that I was using a mobile device!

Basically, the Ontological Argument and all variations thereof, hinge on the intention to ‘imagine’ God into existence by giving him the quality of ‘necessary existence.’ The logic, such as it is, is held together loosely by dodgy semantics and a desire for the conclusion to be true.

As I pointed out to WSP on a thread a few weeks back, arbitrarily giving something the characteristic of ‘necessary existence’ doesn’t make it exist; if it did I’d be off spending the ‘necessary pile of money in my bank vault.’

All the ‘proofs’ for God are so easily debunked, yet people keep posting new minor variations as if they think they’ve cracked it! I’d be really pleased if someone came up with a juicy new one that we can all get stuck into!

 

[wanstronian]

What about Plantinga’s argument?

1. It is possible that a maximally great being exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. If a maximally great being exists in the actual world, then a maximally great being exists.
6. Therefore, a maximally great being exists.

It’s embarassing, isn’t it!