The Ontological Argument for God

I’ve never understood the supposed difficulty in refuting the ontological argument for god’s existence.  Apart from the fact that it’s an argument from logic and reason alone, rather than from any actual verifiable evidence – which should rule it out as an argument to be considered seriously anyway in my view – it never seemed to make any sense.  Still, some people apparently believe it, including one recent commenter who listed it among the numerous “proofs” that god exists, so I thought it was time I deconstructed it.  As you’ll see, it didn’t take long to locate the logical fallacy that’s at its heart.

The ontological argument was originally put forward by Anselm of Canterbury in the 11th century.  Wikipedia has two versions of it, but I’m going to refer to what I think is a better version at The Internet Dictionary of Philosophy: “The Classic Version of the Ontological Argument” as they call it, which they say can accurately be summarized thus:

1) It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (i.e., the greatest possible being that can be imagined).

2) God exists as an idea in the mind.

3) A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.

4) Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (i.e., a greatest possible being that does exist).

No.  Correction - if God exists only as an idea in the mind, then all this means is that we can imagine something that is greater than the idea of God in the mind – not greater than a God who actually exists.  Anselm’s argument relies entirely on equivocation - the misleading use of a term that has more than one meaning, while glossing over which meaning is intended at a particular time.  Specifically, Anselm relies on there being two meanings of the word “God,” and he slips between these definitions as it suits him.  What are these two meanings of the word “God”?  They are (1) a god who exists in reality and (2) a god who exists only in the mind.  In point 4 above he uses the “god who exists only in the mind” version, but in point 5 he tries to make you think he was talking about the “god who exists in reality,” because point 5 is:

5) But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

Yes, but “the greatest possible being that can be imagined” is not God who exists only as an idea in the mind – so there is no contradiction.  It only seems to be a contradiction because Anselm is equivocating between the different meanings of the word “God” and has glossed over which meaning he is using at different points in his argument.

6) Therefore, God exists.

No.  Epic FAIL.  Therefore nothing.  All this shows is that we can imagine something greater than a God who exists only in the mind. But “God who exists only in the mind” is not “a being than which none greater can be imagined.”  In fact, premise 3 specifically states there can be something greater than this – a God who exists in reality - and so the argument is contradicted by its own premises.  “God who exists only in the mind” is not God, as defined in premise 1, and so it is possible to imagine something greater, without violating premise 1.

Anselm’s mistake will become clearer if we define his terms in a less ambiguous way.  I will rename Anselm’s different versions of God, as God-1 and God-2:

God-1 = God who exists in reality (the thing whose existence we are trying to prove).

God-2 = a God who exists only as an idea in the mind.

Now we can rephrase the argument:

1. Nothing greater than God-1 can be imagined
2. God-2 exists. 
3. God-1 is greater than God-2
4. If God-1 does not exist then we can imagine something greater than God-2 (i.e., God-1)
5. But we cannot imagine something that is greater than God-1
6. Therefore God-1 exists

You can see quite clearly now that the argument is bogus.  Point 4 is where it goes wrong.  It only appears to work because Anselm equivocates about the definitions of God-1 and God-2.  This is what he is doing.  He is trying to make point 4 sound like, “If God-1 does not exist then we can imagine something greater than God-1” (which would be a contradiction to point 1).  But point 4 only makes sense as “…we can imagine something greater than God-2 (i.e., God-1),” as in my version.  (Otherwise he is actually saying “If God-1 does not exist then we can imagine something greater than God-1 (i.e., God-1),” which is gibberish.)  He hopes you won’t notice he changed God-2 to God-1 in point 5, setting up the contradiction to point 1.  But he wasn’t talking about God-1 in point 4, so there is no contradiction.  Consequently, point 6 “Therefore God-1 exists,” just doesn’t follow.

Not only that, but now we’ve deconstructed it, we can see it doesn’t even make sense.  Consider this.  Point 5 is just a restatement of point 1.  So if you leave out this repeated point (you don’t need it here since it’s already been stated), the last two points (4 and 6) are:

• If God-1 does not exist then we can imagine something greater than God-2 (i.e., God-1)
• Therefore God-1 exists

To simplify even further, we can cut out what this allows us to imagine, which leaves:

• If God-1 does not exist then …
• … God-1 exists

To go back to the phrasing of the original argument, he is saying, if God exists only as an idea in the mind, then God exists in reality. Or, put it even more simply, if God doesn’t exist then he exists.

I have read several versions of Anselm’s argument, and they all fall apart for exactly the same reason - the logical fallacy of equivocation.  The only surprising thing about this argument, in my view, is that anyone thinks it should be taken seriously.

Comments

[Mike]

This is the most straight-forward, clear-cut dissection of the ontological argument I have ever read.

[Deen]

That's an interesting way to take the ontological argument apart, I hadn't seen this one before. Thanks for enlightening me :).

What's most interesting about the ontological argument to me is in how many different ways it can fail. Is existence really a property? Is existence really necessarily a positive property? Is there really such a thing as a greatest being, or would this be more like saying there is a greatest prime number? And is it possible for any logically consistent being to have all possible positive properties? For instance, can anything be both absolutely merciful and absolutely just at the same time?

Sure, some of those objections have counter-arguments, but they aren't nearly as persuasive as the ontological argument is often presented to be. In a wider perspective, it all looks like trying to fix a house of cards while it's already collapsing. As a whole, the ontological argument is not terribly convincing.

[Kallan]

I was going to suggest the equivocation is in the term "exists", but now that I've looked over the logic again it's pretty clear that using "god" is a far more elegant way of defining the fallacy. Brilliant post mate.

[AndyD]

I would have thought it fell apart when he assumed the conclusion in point one.

If I say "we can imagine nothing greener than the the greenest of green unicorns" (and that statement, by its nature, must be true) then continue point-by-point as above, would I prove not only that unicorns exist but they are greener than the greenest green?

[Rimantas]

I think it would be easier to track if you were using God-Idea and God-Reality instead of God-1 and God-2 :)

[WScott]

Good analysis. AndyD also makes a great point: substitute Bigfoot or Little Green Men From Mars and the argument works just as “well.” The universe really doesn’t give a damn what human imagination is or isn’t capable of.

I do have to quibble with this part of your post:

…it’s an argument from logic and reason alone, rather than from any actual verifiable evidence – which should rule it out as an argument to be considered seriously anyway in my view

I would agree that an argument from logic or reason generally carries less weight than an argument based on actual evidence. But logical arguments still have their place – in philosophy, if not in experimental science – and as long as there is no contradicting evidence, I don’t think it’s fair to dismiss all such arguments out of hand. That is, you’re welcome to say “In the absence of supporting evidence, I personally don’t find that argument compelling.” But don’t be so quick to throw out reason & logic, if only because they’re in such short supply these days.

[Jer]

Whoa - I'm not sure that I follow with your dropping of point 5 altogether. Point 5 is what makes it an argument by contradiction - yes it's just a restatement of the initial premise, but that's because that restatement needs to be there to show that it's a contradiction of your initial argument.

But your point is quite clearly proven if you leave the statement in place:

4. If God-1 does not exist then we can imagine something greater than God-2 (i.e., God-1)
5. But we cannot imagine something that is greater than God-1
6. Therefore God-1 exists

This clear delineation between God-1 and God-2 shows that there actually IS no contradiction between point 4 and the initial premise restated as point 5. It's all based on the assumption that G1==G2 which was never stated in the "proof" and is what the arguer was trying to prove in the first place.

(The whole argument is silly anyway because the very premise of the whole argument is refutable. That particular "definition" of God is built on sand and can be refuted by imagining a God-3 who created God-1 - as many Gnostics did back in the first century or so. The argument only works if it's a heresy to consider the existence of something superior to God in the first place, and it falls apart if you're able to refute that. Much like Pascal's wager is dependent on there only being a single definition of God that you're allowed to contemplate, and not the multitude of interpretations of God - let alone the multitude of gods - that exist in the real world.)

[AndyD]

On re-reading I can only see two significantly positive (worthwhile) points in the whole original argument.

1. God is conceptual, imagined.

2. God exists as an idea.

The rest is gibberish and at best proves that God exists in the mind as an imagined concept or idea which, as best I can tell, are the same thing.

Noddy is also imagined and exists as an idea and concept. Whoopie do.

[Dude]

Demolish this next please http://www.answersingenesis.org/articles/2009/08/10/logical-fallacies-equivocation

[Jimmy_Blue]

Dude:

Not much point in demolishing it.

Since the author already redefines terms to mean whatever they want them to in order to seem to make an argument, they would just as likely do the same to escape any criticism.

[PaulJ]

I've never really understood the ontological argument. I'm not a philosopher, but what it seems to be saying is "I can imagine that God exists, therefore God exists."

All the stuff about greater or lesser beings seems irrelevant. I don't see why our capacity to imagine something existing in reality should have any repercussions at all for whether it actually does exist in reality.

I can imagine little green men in a spaceship existing in reality. Doesn't mean they do.

[Karl Witahaky]

"1) It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (i.e., the greatest possible being that can be imagined)."

FAIL: Imagination is not part of a logical argument. Imagination is not bounded by scope or logic. You can always imagine something bigger or more powerful, even if it is not a logical concept.

"2) God exists as an idea in the mind. "

FAIL: Something's existence or non-existence is unrelated to whether any sentient being has a concept or understanding of that thing in their mind.

"3) A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind."

FAIL: This again confuses and equates the concept of an understanding of a thing with the actuality of a thing. It also presumes a universal standard of "greatness" (either qualified or quantified).

"4) Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (i.e., a greatest possible being that does exist)."

FAIL: This conclusion is dependent on three faulty statements of (poor) logic. (Conclusion only follows if we accept the 3 previous statements

5) But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

FAIL: See my notes from #1 above.

6) Therefore, God exists.

FAIL: see notes on #4

Try this on for size:
-If god exists, nothing greater than god can be imagined.
-Imagination is unbounded and unlimited
-Therefore god cannot exist because you can always imagine something greater.

Frankly the whole thing dies on statement #1, and there's really no point in following it any further except as a useful exercise in logical deconstruction.

[Helena]

The strange part is that you seem to think it hadn't been refuted before. It was refuted by the first scholastics (Abelard and his crowd), and then again by Aquinas. No serious person has advanced this argument since then. In fact it was used in my undergraduate course work as an index of the abysmal level to which logic had fallen in the early middle ages. But then I suppose some creationists do still try to use it.

I will also mention to some of the other respondents that Abelard is not using 'imagination' the way you think he is, but as a technical term with a special meaning. So the comments about imagination above make as much sense as when creationists say 'Evolution is just a theory.' The Stanford Encyclopedia would be a good place to go on-line to find out what he means.

[Tom Foss]

Skeptico: I like this article; it's a very different take on the Ontological Argument than the ones I've usually encountered (and used).

No. Correction - if God exists only as an idea in the mind, then all this means is that we can imagine something that is greater than the idea of God in the mind – not greater than a God who actually exists.

I first heard the Ontological Arguments in a class I took on Philosophical Theology a few years back. There was another part of the argument when I heard it that made it no less problematic, but harder for an undergrad to argue against. The introduction argued that anything you can imagine has some basis in the real world--either it actually exists, or it is a combination of things which actually exist. So while I can imagine blue apples, even though blue apples don't exist, it's because apples exist and blue things exist, and I'm just combining the two. Then it launched into the "I can imagine the greatest thing ever," and so forth.

That bit seems to be pure assertion to me, and something like reverse-Platonism besides. Even if it were true, power exists and the concept of perfection exists, and agents exist, so it doesn't seem like it'd be hard to combine those extant concepts into the concept of a God which does not necessarily exist.

But that addition gave the argument's flaws an additional layer of obfuscation, and I'm fully convinced that the only reason the Ontological Argument seems convincing to anyone is because it's usually dressed up in the most obfuscatory language possible. See also the Transcendental Argument and most Cosmological Arguments.

AndyD:

I would have thought it fell apart when he assumed the conclusion in point one.

Yeah, the argument is circular (but again, tries to cover up the fact that it makes the conclusion part of the definition in the initial premise.

WScott:

I would agree that an argument from logic or reason generally carries less weight than an argument based on actual evidence. But logical arguments still have their place – in philosophy, if not in experimental science – and as long as there is no contradicting evidence, I don’t think it’s fair to dismiss all such arguments out of hand.

I think it's perfectly fair to dismiss any purely philosophical argument that purports to describe anything real. Pure philosophy may have its place in mathematics and such, but outside of those limited domains, it's utterly useless. I can draw up a perfectly valid logical argument that proves that fairy elephants in purple leotards dance through Trafalgar Square each day at noon, but no one should be using that to plan their travel arrangements. Philosophical arguments only have utility in the real world if they are sound, which requires their premises to be justified in reality. The only reliable way to determine the soundness of premises is by using scientific observations.

So, the more specific version of what Skeptico said might be: in discussions of reality, logical arguments deserve serious consideration if and only if grounded in sound premises as established through empirical observation.

PaulJ:

I've never really understood the ontological argument. I'm not a philosopher, but what it seems to be saying is "I can imagine that God exists, therefore God exists."

Actually, I think it's even worse than that. It's "I define God as a being who exists. Therefore, God exists."

Karl:

Try this on for size:
-If god exists, nothing greater than god can be imagined.
-Imagination is unbounded and unlimited
-Therefore god cannot exist because you can always imagine something greater.

A couple of people made similar points, and I think that they are missing an aspect of the argument. What the argument says, as I interpret it, is that God is the greatest thing you can imagine, so if you imagine something that is even greater, then it must be that the greater thing is God, and the previous thing wasn't. God is defined as whatever greatest being you can possibly imagine--in terms of this argument. As usual, the argument at most would get you up to a deist God; it's very easy to imagine a greater God than the Judeo-Christian one.

Helena:

No serious person has advanced this argument since then.

No serious person has advanced a No True Scotsman argument, either.

I think you'll find an awful lot (literally and figuratively) of serious theologians do continue to use the ontological argument in various forms, the most prominent being Alvin Plantinga.

[Big Al]

I quite like the "handicap argument", i.e. something like

The creation of the Universe is the greatese real achievement, because it encompasses all other real achievements.

An achievement is greater, the greater the handicap of the achiever.

The greatest possible handicap is not to exist.

Therefore a God who created the Universe and does not exist is greater than one which created the Universe and which does exist.

Therefore God does not exist.

[Deen]

@Tom Foss:

What the argument says, as I interpret it, is that God is the greatest thing you can imagine, so if you imagine something that is even greater, then it must be that the greater thing is God, and the previous thing wasn't.

But that makes the definition of "greatest thing you can imagine" meaningless, just like the "largest number you can imagine" is meaningless: no matter how big a number you imagine, you can always add one to it and get a larger number. But this doesn't make this larger number the largest number imaginable either, since you can add one to that one as well. So there can be no "largest number imaginable" at all. Similarly, it's quite reasonable to say that there can't be a "greatest being imaginable".

Like I said, it's amazing in how many ways the ontological argument can be attacked. It's fun to see more and more of these ways appearing on this thread. And yet, as you say, some still advocate it.

[TechSkeptic]

holy crap al, that is hilarious

[Karl Witahaky]

I was going to post a reply to Tom Foss, but Deen pretty much covered it.

I'll just add that since imagination is not bound by scope or logic, you can even imagine a number bigger than infinity, even if logically and mathematically, it is an invalid concept and there can be no such thing. In my imagination infinity +1 is bigger than infinity

I can always imagine a god greater than the next one, therefore I am god!

[WScott]

I can draw up a perfectly valid logical argument that proves that fairy elephants in purple leotards dance through Trafalgar Square each day at noon, but no one should be using that to plan their travel arrangements.

And here I thought I was the only one who saw those… ;)

Well put. However, the fairy elephant argument is easily refuted by verifiable evidence. I'm talking about logical arguments for which there is no evidence pro or con, or at least insufficient evidence. I agree you still don't make travel plans around them, but they can be a useful place to start looking for evidence. Put another way: treat it as a hypothesis, not a conclusion.

[AvalonXQ]

The informal ontological proof certainly seems flawed. I would be very interested in seeing what you do with Godel's formal proof:
http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof

[dsmith77]

The Ontological Argument is, IMO, the most useless of all the historical arguments for God. Quite frankly, it's practically a strawman. Have you visited the other arguments in other posts?

Also, why do you state that arguments derived purely from logic and reason should be excluded? I realize that scientific proof is preferred, but there are areas of scientific inquiry that cannot be seen or measured and (so far) can only be understood indirectly or perhaps mathematically.

Most of the time in science, the mathematical basis for a theory is formulated first. Later observations verify the theory and further investigation follow. As an interesting opposite, fields of force in gravity actually developed the other way around with the mathematical basis coming later.

[Deen]

AvalonXQ: many of the objections against the ontological argument also apply to Gödel's version: is existence a property? Can an entity have all possible positive traits, or will some of those traits be contradictory? If so, axiom 3 fails.

But there are other objections in the wiki article you cite. For instance, it turns out that the the proof is so generic, that you can prove anything is necessarily true.

But really, when it comes down to it, Gödel's version also pretty much asserts that God exists by definition: a God-like entity is defined to have all positive traits, and (necessary) existence is defined as a positive trait. You'd almost wonder what the rest of the argument is needed for. Unless it's for obfuscation, of course.

[Tom Foss]

Big Al: I like that argument too, mainly since it exposes the argument's arbitrariness. Since the same argument can be used to establish contradictory claims, it really doesn't serve as proof of anything.

Deen:

But that makes the definition of "greatest thing you can imagine" meaningless, just like the "largest number you can imagine" is meaningless:

I think the "greatest thing" definition starts out meaningless. The term "greatest" is overly vague, as is the term "imagination." I think this is why people like Plantinga use terms like "maximally perfect"--i.e., a God who is perfect in every possible way (or something)--because the word "perfect" is less ambiguous.

WScott:

Well put. However, the fairy elephant argument is easily refuted by verifiable evidence. I'm talking about logical arguments for which there is no evidence pro or con, or at least insufficient evidence. I agree you still don't make travel plans around them, but they can be a useful place to start looking for evidence. Put another way: treat it as a hypothesis, not a conclusion.

Then we switch "Trafalgar Square" to "Gliese 581c," a planet which we know very little about. The claim still tells us nothing useful, even if it is logically valid. A hypothesis is really only useful if it works from what we already know--most hypotheses start with observations or anomalies in current understanding. Without some grounding in evidence, I really can't think of what utility a purely logical argument would have with regard to determining reality.

[Michael Dickens]

1. The creation of the universe is the most marvelous achievement imaginable.
2. The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
3. The greater the disability (or handicap) of the creator, the more impressive the achievement.
4. The most formidable handicap for a creator would be non-existence.
5. Therefore if we suppose that the universe is the product of an existent creator we can conceive a greater being — namely, one who created everything while not existing.
6. Therefore, God does not exist.

[TechSkeptic]

That was funnier the first time it was presented.

[dilip]

Last i recalled ontological means the study of existence, and your opening sentence was redundant.

[Deen]

@dsmith77: it's true that sometimes purely logical or mathematical reasoning puts science on the path of a new discovery. However, in all of those cases, the arguments will have empirical elements in the premises and conclusions, tying the argument to the real world. If not, it wouldn't be science, as there would be nothing to test and observe. The ontological argument, and other "purely logical" arguments, don't connect to the empirical world in any way, and therefore can't tell us anything about the empirical world.

[Deen]

@Tom Foss: "Perfect" isn't very well defined either. Perfect in what way? In normal usage, "perfect" always refers to some other criterion. A "perfect sphere" refers to a body that is an exact representation of a particular mathematical equation; a "perfect conductor" is a material that conducts electrical current with exactly zero losses; etc etc.

It already gets a lot harder to define what a "perfect car" is - what is a car supposed to do, and when can you say it does so perfectly?

And whatever a "perfect being" is supposed to be (let alone a "maximally perfect being"), is anyone's guess.

[WScott]

A hypothesis is really only useful if it works from what we already know--most hypotheses start with observations or anomalies in current understanding.

Fair point.

[Big Al]

1) The most irritating being conceivable is Jar-Jar Binks.

2) A Jar-Jar Binks who really existed, and whom you could not dimiss by simply walking out of a cinema or pressing fast-forward on a remote would be far more irritating than a Jar-Jar Binks who was just a collection of ones and zeroes inside a computer.

3) Therefore, Jar-Jar Binks exists.

4) I'm just glad he doesn't live on this planet.

5) Yet.

6) And should he ever come here, I'd steal his spaceship and get the hell out of here.

[Big Al]

It already gets a lot harder to define what a "perfect car" is - what is a car supposed to do, and when can you say it does so perfectly?

A vehicle is intended to carry a person from one place to another, ideally with minimal discomfort, maximal speed and maximal coolness.

It's gotta be a toss-up between KITT and the Star Trek transporter.

[AvalonXQ]

Reminds me of a quote from Stephen Wright: "I got a new camera. It's really advanced; you don't even need it."

Clearly the perfect camera has the positive property of nonexistence.

[Chayanov]

What's funny is that, for many theists, their imagined god really isn't the greatest thing ever, because they place so many limits on what their god can and can't do.

"Imagine God."
"Now imagine God wearing a cape."
"Now imagine God wearing a cape and riding a T rex."
"Now imagine the T rex has lasers..."

[Big Al]

Imagine God as omnipotent, onmiscient and all the rest, but in the character of Jar Jar Binks...

And the LORD said, "Meesa makee all sparkly shiny shine!"

And there was light.

Omigawd, this meme just won't go away!

[Cyberguy]

If someone comes up to you and says:

"It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (i.e., the greatest possible being that can be imagined)."

The answer at this point is to say "I am just imagining two of those right now!".

[Tom S. Fox]

I don't get this argument. You can't imagine anything greater than god, therefore god exists? Looks like a non sequitur to me.

[TechSkeptic]

Tom,

that is exactly the way I have always thought about it.

[efrique]

Excellent analysis.

I have sometimes pointed out that even if it worked (which I argue it doesn't for other reasons) its an argument for any imaginable god with the attributes under discussion... which is no help if you're talking about a particular god of a particular book; indeed, all I have to do is imagine a god better in some trivial way, and clearly the specified god isn't the one that might be proved by Anselm's argument.

[Skeptico]

Mike:

This is the most straight-forward, clear-cut dissection of the ontological argument I have ever read.

Thanks.  That’s what I was going for.

Andy, Karl Witahaky:

I realize there are other ways to tackle the argument. My purpose was to show that even if you were to accept all the premises of the argument, it still fails due to a basic error of logic.

Helena:

The strange part is that you seem to think it hadn't been refuted before.

I was prompted by Colin McGinn interviewed in the atheism tapes saying that no one had been able to pinpoint where the argument was wrong.

AvalonXQ:

The informal ontological proof certainly seems flawed. I would be very interested in seeing what you do with Godel's formal proof:
http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof

I found that to be incomprehensible.  Perhaps someone with a better knowledge of math could have a go.

dsmith77:

Also, why do you state that arguments derived purely from logic and reason should be excluded? I realize that scientific proof is preferred, but there are areas of scientific inquiry that cannot be seen or measured and (so far) can only be understood indirectly or perhaps mathematically.

It’s only since we started testing things that we really began to learn how the world works.  Logic and reason alone hasn’t given us much of value that I can think of. And we don’t have to see see things directly. If things can be seen indirectly, then they are based on evidence not just logic and reason. Math proofs are more than just logic, but ultimately even scientific theories based just on math will have to be confirmed by experiment, if they are to be taken seriously.

[Citizen Z]

AvalonXQ:

The informal ontological proof certainly seems flawed. I would be very interested in seeing what you do with Godel's formal proof:
http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_

Putting an argument in formal notation doesn't correct faulty logic. In this case it's the same faulty logic, it's sleight of hand "begging the question".

As far as I can see, the problem with Godel's formal proof is the axioms. You can, technically have zero problems with logic, but that's no guarantee of correctness. For example, this works logically:

1) All shirts are blue.
2) I'm wearing a shirt.
3) The shirt I'm wearing is blue.

But it's obviously not correct, but the starting axiom is faulty. Axioms should be self-evident and uncontroversial. In Godel's case there's a disconnect between Axiom 3, Axiom 5, and his "God" property.

Axiom 5: Necessary existence is a positive property (Pos(NE)).

Sure, ok.

Axiom 3: If P1, P2, P3, ..., Pn are positive properties, then the property (P1 AND P2 AND P3 ... AND Pn) is positive as well.

I'll buy that, too, but note the emphasis I added.

property G: if x is an object in some possible world, then G(x) is true if and only if P(x) is true in that same world for all positive properties P.

Ok... so where's the proof that G(x) is true? We've got all these "if"s, but where are any shown to be true? Godel (and Plantinga) essentially misuse the "plenitude principle" - everything that can happen will happen - (http://en.wikipedia.org/wiki/Plenitude_principle) to "prove" G(x) is true. The problem is you have to agree that something "can happen" (existence of God), which the exact thing they're trying to prove. Another wrinkle is that many sensible people would agree that God "can happen", in that it's possible, as opposed to the plenitude principle, which would really only be appropriate for something that currently doesn't defy physics or logic or would otherwise be controversial. I don't know if that's the way it's viewed in philosophical circles, that's just the way I see it.

Put another way, infinite monkeys on typewriters will eventually type out Shakespeare, but would they ever type out an oil painting? A log cabin? A supernova? Or, heck, even type out a bonafide perfect supernatural being called God? I don't know anyone who would buy that.

[rx7ward]

Existence is not a predicate.

http://www.philosophyofreligion.info/theistic-proofs/the-ontological-argument/st-anselms-ontological-argument/existence-is-not-a-predicate/

[yakaru]

Citizen Z, Thank you.

[Big Al]

infinite monkeys on typewriters will eventually type out Shakespeare

Never quite got this. Won't an infinite number of monkeys come up with Shakespeare in an infinite number of ways immediately?

[Martin]

Yeah, except I think Shakespeare is used here as an ordered sequence of finite length (e.g. every character he ever wrote in chronological order), and thus there's only one way of coming up with Shakespeare.

In math terms, the probability, P, of not reproducing a given sequence of length k in n trials on a (special monkey-style) keyboard with 27 keys is

P = [1 - (1/27)^k]^n

A long as k is finite you can make P zero by letting n --> infinity, so one of those god damn monkeys should get it right on the first attempt as far as I can tell.

[Big Al]

Well, I was imagining a string of k monkeys, each typing a single character simultaneously with the other k-1, so that, in sequence, one could read the entire works of the Bard.

Maybe not instant, but within the time frame of a single keypress.

Mind you, finding them would be tricky... you'd need to wade through an infinite number of every possible combination of k letters from "AAAAAAA...A" to "ZZZZZZ...Z" and everything in between.

And at the same time, the same work translated into every single language in the world that ever was or ever will be, so it would help if you were multi-lingual.

And an infinite number of non-k sequences, and blank pages.

And the complete works of Edgar Allen Poe, Virgil and the Marquis de Sade.

Tintin.

The New York Yellow Pages, 1962, '63, '64, '67 and '92 in reverse alphabetical order.

I just hope you're patient.

[Marcus Ranum]

It reminds me of another of my favorites:
1) Bread crumbs are better than nothing
2) Nothing is better than a good steak!
3) Therefore breadcrumbs are better than a good steak.

If someone tells this one at the dinner-table you are allowed stick your fork into the back of their hand.

Seriously, though, what passes for theological reasoning is laughable except for where they take it seriously enough to kill over.

[Bronze Dog]

And everything's better with breading.

[Big Al]

Remember next time you have a headache: nothing works faster than Anadin.

Pretty versatile stuff, that old nothing.

[BK]

It seems to me that the ontological argument for God poses a bit of a dilemma for theists:

1. If God is the greatest being that can be imagined, then "he" can can produce an exact replicate of "himself"

2. A God that did produce an exact replicate is greater than one who did not.

3. Therefore, if one God exists, multiple (actually infinitely many) Gods exist.

The only alternatives to this argument are:

1. God is NOT the greatest being that can be imagined.

2. God does not exist

For those who believe in the ontological "proof," which one is it?

[imarriedaxtian]

This is a great and educational post. Can you do a similar post on the Kalam Cosmological Argument for god? I have read many refutations but its am still unclear to me.

On another note, I have always thought it was Godel Incompleteness theorem that put paid to these sort of logical proofs for god's existence.

That is, if you describe a set of axioms (self evident truths or propositions) and construct a set of theorems around these axioms, you cannot disprove any of the original axioms using the results.

Most of these logical arguments always sneak in some form of the proposition that there is a god. Hence ~god becomes a contradiction.

[Tom Foss]

If you haven't been there yet, you might make a trip to the Iron Chariots counter-apologetics wiki. I haven't looked at their Kalam page recently, but they're generally a good place to start.

[Skeptico]

From Wikipedia, the Kalam cosmological argument starts:

Premise 1: Everything that begins to exist has a cause.

Premise 2: The universe began to exist.

Conclusion 1: Therefore, the universe must have a cause.

The flaw is premise #1 – we simply don’t know enough to be able to say that. Strictly speaking, we know it’s false since according to quantum physics, subatomic particles do spontaneously appear out of nowhere, without a cause. The error is in thinking that what we observe in our everyday lives applies universally, including at the quantum level and including at the big bang.

[Big Al]

Why is it necessary that the greatest being which can possibly be imagined be omnipotent and eternal?

I don't think our finite, short-lived minds are capable of imagining such a being. Of course, many people say they can, but it's easy to say you can imagine drinking the Atlantic dry, eating Mount Everest or living as an amoeba, but I for one can't actually encompass the reality of doing so beyond the statement that I can.

As far as I can tell, the greatest being possibly imaginable seems to be a petty, egotistical, vindictive, narrow-minded dasher of hopes and dreams.

Therefore Simon Cowell exists, but that's about as far as I can go.

[Ryan Michael Whitmore]

A hypothesis is really only useful if it works from what we already know--most hypotheses start with observations or anomalies in current understanding. Without some grounding in evidence, I really can't think of what utility a purely logical argument would have with regard to determining reality.

Tom, thanks for saying what I was thinking the whole time. I know, I'm late. Sue me; the interwebs are just making their way to my part of The Mid.

[Ned]

God can only be known by faith, which is to say that God's existence is self-evident.

In following the link you provide, I noticed that several people have dismantled this same argument, including other theists.

I really don't care whether you believe in God, but perhaps you could attempt something like intellectual honesty.

[Skeptico]

Ned:

What on earth are you babbling about?

[Bronze Dog]

Faith is the act of assuming one's conclusion. In other words, circular reasoning. Why don't you try being honest with yourself, Ned: You are fallible just like we are.

Science was invented to counteract our flaws, and will humbly change its mind if new ideas are better supported by the universe in the form of evidence.

Faith blindly asserts that the believer is the perfect in his proclamations, and arrogantly assumes that if the universe's evidence contradicts the believer, it's the universe that's wrong. Faith is a straight road to solipsism.

[Martin]

Faith is the act of assuming one's conclusion.

Because it's faith, right??

[Big Al]

God can only be known by faith, which is to say that God's existence is self-evident.

Yet we are told certain, fortunate people, conveniently a couple of thousand years ago and a couple of thousand miles away were routinely shown all sorts of slam-dumk proofs like parting the Red Sea and turning water into wine and feeding the 5000 and bringing Lazarus back to life.

Yet these fortunate people, who might not have believed without witnessing these flashy miracles, are all called saints and you can supposedly ask them to ask God to to favours for you.

As for self-evident, it was once self-evident that the world was flat, that blood stayed where it was, that maggots spontaneously generated from rotting meat and that heavy objects fall faster than light ones.

This is what you get when evidence is eschewed as irrelevant. Why does God demand this of us? Why is ignorance such a hallowed state?

[aaronp]

Try this ontological argument on for size:

A God that does not exist (but otherwise has all the powers of a God that does exist) cannot be destroyed by an existent God because the non-existent God is already non-existent. Therefore a non-existent God is more powerful than an existent God. Therefore the existent God is not actually God (having been superceded by a non-existent God).

[Big Al]

Sounds like a rehash of the "handicap" argument, aaronp - a being that can create a universe without actually existing is greater than one which does exist.

[aaronp]

Ah shucks, your right BigAl, thats exactly what it was. I thought I had come up with the 'handicap' argument :-).

[Joseph]

The main flaw of the argument is clearly in the word "God" in #4: "if God exists only as an idea in the mind, then we can imagine something that is greater than God (i.e., a greatest possible being that does exist)."

Classic equivocation fallacy. That's not the same "God" as defined at the beginning of the argument.

Or to put it another way, replace "God" with "the idea of God," and the argument no longer makes any sense.

Two can play at that game, though. Let me try an ontological argument for the non-existence of God.

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can exist.

2. It is a conceptual truth that God is omnipotent, able to do everything and anything.

3. Let us assume God exists.

4. From #2, God must be able to create a being greater than himself.

5. We arrive at a contradiction, since #4 contradicts #1. Therefore, assumption at #3 must be false.

Where's the flaw?

[Bronze Dog]

The main flaw of the argument...

By now, I think we can just say there's no "main flaw" and we're dealing with fractal wrongness. ;)

[Big Al]

Joseph, I believe the usual statement along those lines goes soething like, "Can Almighty God make a rock so heavy that He can't lift it?"

If He can't make such a rock, He's not omnipotent. And if He can can't lift the rock he's made... He's not omnipotent.

[C Man]

Bronze Dog -

"Faith is the act of assuming one's conclusion. In other words, circular reasoning. Why don't you try being honest with yourself, Ned: You are fallible just like we are."

So "we" all fallible? Doen't this mean any scientific conclusions "we" make are fallible?

"Science was invented to counteract our flaws, and will humbly change its mind if new ideas are better supported by the universe in the form of evidence."

Please cite reference for your assertion as to why science was invented. Please cite example when science "humbly" changed its mind. You may want to reread Kuhn's analysis showing science clings to theories flying in the face of evidence, until they become so untennable that a paradigm shift is necessary.

"Faith blindly asserts that the believer is the perfect in his proclamations, and arrogantly assumes that if the universe's evidence contradicts the believer, it's the universe that's wrong. Faith is a straight road to solipsism."

So, you have "faith" in nothing? Does it not take faith to believe scientic theories espoused by fallible people?

[TechSkeptic]

CMan,

So "we" all fallible? Doen't this mean any scientific conclusions "we" make are fallible?

Yes. It is well accepted that new verified observations about a phenomenon will lead to modification of the theories surrounding it. Modern synthesis describes far more than Darwin ever imagined his theory of evolution would encompass.

Please cite example when science "humbly" changed its mind.

Oh please this list is endless.

Aether being the substance space was made out of
Helocibacter Pylori being the main culprit of stomach ulcers rather than stress or spicy food
Earth being an Oblate Spheroid rather than a sphere
Newtonian Physics
Blood Letting

I could go forever. Sometimes our understanding is dead wrong (bloodletting) and sometimes it is simply innaccurate (newtonian physics). In either case, the understanding gets modified when strong evidence becomes available.

science clings to theories flying in the face of evidence, until they become so untennable that a paradigm shift is necessary

Yes that is exactly right. this is as opposed to keeping the same dogma for centuries without change. When evidence is strong enough, the conclusions of science changes. What do you propose as a better model? Shall we modify our understanding of the universe every time some quack does a financially motivated study on 12 kids and starts claiming that vaccines causes autism?

I can't speak for BD, but I try hard to have faith in nothing. I use, at every opportunity, evidence and systematic understanding of processes to shape my decisions and actions. I wish more people did that.

[Big Al]

So "we" all fallible? Doen't this mean any scientific conclusions "we" make are fallible?

Yes, but science is falsifiable, whereas religion is not. Scientific theories make specific, verifiable predictions that would disprove them if found to be incorrect. There is nothing in religion that says, "If X, then God cannot exist".

Please cite reference for your assertion as to why science was invented. Please cite example when science "humbly" changed its mind.

To add to TechSkeptic's admirable job:

The "billiard ball" atom
The "plum pudding" atom
The "planetary" atom

Science is like sculpture, making ever finer trims and chips to get ever closer to the beauty within.

Relgion shows us a lump of stone and says, "That's all you get."

You may want to reread Kuhn's analysis showing science clings to theories flying in the face of evidence, until they become so untennable that a paradigm shift is necessary.

When was the last time religion bowed to a paradigm shift, or even acknowledged that one was necessary? No amount of evidence changes any religion. Ever.

So, you have "faith" in nothing? Does it not take faith to believe scientic theories espoused by fallible people?

Individual scientists may have faith in their own theories, but it is nothing compared to the weight of experimental evidence.

Blondlot had faith in his n-rays.
Fred Hoyle (incidentally, a great throretician who was ripped off by the Nobel Prize committee) had faith in the Steady State universe.
Newton had faith that light was made up of particles.
Huygens had faith that light was made up of waves.

However, EVIDENCE had the final word.

[Bronze Dog]

Doen't this mean any scientific conclusions "we" make are fallible?

Of course, but which is more reliable: Something that's been repeatedly evaluated and double-checked, or something someone just randomly threw together and assumed it would work.

We know we're fallible, which is why scientists constantly question themselves and each other.

Please cite reference for your assertion as to why science was invented.

Funny, it's one of those things that seems obvious, just from looking at how it functions.

Please cite example when science "humbly" changed its mind.

It's funny that you're utterly unaware of any of those things my friends cited. Unlike religion, when scientific consensus changes its mind, there's no bloodshed involved.

You may want to reread Kuhn's analysis showing science clings to theories flying in the face of evidence, until they become so untennable that a paradigm shift is necessary.

You mean the guy who couldn't clearly define what he meant by "paradigm"? And aren't those "paradigm shifts" the sort of thing science makes possible?

So, you have "faith" in nothing? Does it not take faith to believe scientic theories espoused by fallible people?

Ah, the scent of equivocation in the morning. I have trust in the results of people rigorously double-checking themselves. That's how scientific consensus is achieved.

And just because the process isn't perfect doesn't mean you can sour grape your way into inaction and solipsism. Ever heard of the Perfect Solution Fallacy?

[C Man]

OK Bronze Dog, do you expect me to believe that your threshold for believing something is that it is rigorously double-checked? I'm thinking you are also meaning observable, empirical, measurable, and repeatable.

If an historian tells you that Nero played the fiddle while Rome burned, how is this conclusion to be double-checked, observed, measured, and repeated? How is any historical event, for that matter? Yes, you can look at evidence such as pot shards dug out of the ground, what contemporaries in the historical time period have written. But the evidence cannot be tested, repeated, witnesses cannot interrogated or cross-examined.

Are not you, in fact, yourself using the Perfect Solution Fallacy to refute other persons beliefs about historical events by saying there is no scientific evidence of them, when, there cannot be scientific evidence of any historical event?

[Tom Foss]

Just to add my two cents:

So "we" all fallible? Doen't this mean any scientific conclusions "we" make are fallible?

Certainly, which is why science never claims absolute certainty and has a method of self-correction built in.

Please cite reference for your assertion as to why science was invented.

This is just asinine. Here's a reference: any book on the philosophy of science. Hell, even most high school science textbooks will touch on this matter. Humans are prone to a number of errors in thought and observation--mistaking correlation for causation, assuming agency where none exists, finding patterns in random noise, making hasty generalizations, etc.--the methods of science specifically work to cut down on these sorts of errors by controlling for unwanted factors, making careful repeated observations, and requiring multiple verifications before any result or conclusion is generally accepted, among other things.

Please cite example when science "humbly" changed its mind. You may want to reread Kuhn's analysis showing science clings to theories flying in the face of evidence, until they become so untennable that a paradigm shift is necessary.

First, Kuhn is not the be-all, end-all of the philosophy of science. If nothing else, there's Karl Popper's work on falsificationism, which stands rather at odds with Kuhn's paradigmatic model, though I suspect that the truth is somewhere in-between. You're basically latching onto the term "humbly" here as though it has particular significance. It's more poetic license and personification than anything else. Science is a set of methods and a body of knowledge; it is not capable of humility or egotism, and it can neither change its mind nor cling to anything.

Scientists, on the other hand, can do all those things. Science marches forward, whether the scientists involved cling to older theories or humbly alter their conclusions in light of new evidence--and I'd wager that both happen with any significant findings. Einstein led the paradigm shift that came out of general relativity, then staunchly resisted the following shift brought by quantum mechanics and dynamic models of the universe. Once again, scientists are humans, prone to human faults.

So, you have "faith" in nothing? Does it not take faith to believe scientic theories espoused by fallible people?

No, it doesn't. In addition to all the reasons proffered by others above, we don't need to have "faith" in scientific theories because we have the practical evidence that science works. The very same methods, standards, and understandings which produce those theories are what allow us to apply those theories to practical problems and develop technological solutions. Atomic theory, quantum theory, general relativity, heliocentrism, gravity, electromagnetism, and a host of other scientific theories are used to allow me to communicate with you via the Internet. The theory of evolution, the germ theory of disease, the theories underlying immunology and epidemiology, all work together to produce the flu vaccine I'm getting later in the week. I don't need to have faith in science; its efficacy is consistently demonstrated in my regular observations.

OK Bronze Dog, do you expect me to believe that your threshold for believing something is that it is rigorously double-checked? I'm thinking you are also meaning observable, empirical, measurable, and repeatable.

Perhaps for some things more than others. Don't assume that one metric or standard fits all claims or situations.

If an historian tells you that Nero played the fiddle while Rome burned, how is this conclusion to be double-checked, observed, measured, and repeated?

C Man, you begin by inserting words into Bronze Dog's mouth, then try to insinuate hypocrisy by offering a situation which fails to meet the standards you assumed? Your strawman is showing, C Man.

But let's say that someone does claim that Nero fiddled while Rome burned. We do have ways of verifying that, or at least, of determining whether or not there's any good reason to believe it. We can ask certain questions: is this consistent with what else we know about historical events of the time? On what basis is the historian making that claim? There are basic questions that can knock the teeth out of this claim right away: did Rome burn? Was Nero alive at the time? Did fiddles exist? Was Nero known to play the fiddle? Are there contemporary accounts of these events?

The claim ultimately fails, as the answer to a number of these questions falsifies it. The first, and perhaps most trivial, is that the Great Fire of Rome occurred in 64 CE, while nothing that we'd call a fiddle existed for another thousand years.

Suetonius, the likely source for modern iterations of the claim, actually says that Nero sang while Rome burned. We may be inclined to believe this, except that Suetonius was not alive at the time of the fire, and was thus working from secondhand sources. Tacitus provides us with a contemporary account--if a youthful one--which not only gives an alternate account of where Nero was during the fire (Antium), but also mentions that the claim of his singing over the fire spread as a rumor around the city.

See, it's not difficult to establish the likelihood of a historical claim, and the methods are much the same as in experimental sciences. We start with a hypothesis, we reason what we would expect to find if the hypothesis were true, and we look for evidence that would support or refute that hypothesis. If someone claims that Nero fiddled while Rome burned, we would expect to find generally agreeing accounts of precisely that happening. Moreover, we should be able to find the source of the historian's claim and evaluate the veracity and likelihood of that source with similar methods.

The evidence we would require to believe a claim largely depends on the nature of the claim. Claiming that the Emperor of Rome sang while Rome burned is not particularly extraordinary; we already have overwhelming evidence that people are capable of singing, and that people respond to traumatic experiences in different ways. It would not require much more evidence to cause us to believe this claim; it is pretty low on the extraordinariness scale. And yet, it does not meet those low standards, since we have conflicting accounts, and since our only contemporary source which mentions the claim also says that it is a baseless rumor.

Claiming that Nero fiddled while Rome burned is more extraordinary; it would require fiddles to exist long before we believe them to have been first invented. In order to believe this, we would require a higher quality of evidence. At the very least, we would expect to find people writing about this instrument around the time Nero lived; at best we would expect to find evidence of fiddles that could be reliably dated back to the first century CE.

If the claim were that Nero flew around Rome, igniting the fires with his heat vision, we would require a much higher standard of evidence. While the other claims were already supported by the evidence of humans' capabilities, this claim contradicts what we know about human abilities, and so would require more specific and higher quality evidence than the more mundane claims.

This is the basis for the general maxim that extraordinary claims require extraordinary evidence, a basic principle in scientific investigations.

You misunderstand what "scientific evidence" (and for that matter, double-checking) is, and try to attribute that misunderstanding to Bronze Dog, when you're the one who brought up that laundry list of terms in the first place. That you do not understand what constitutes scientific evidence or how different claims require different standards of evidence is not Bronze Dog's mistake.

[Big Al]

I'm thinking you are also meaning observable, empirical, measurable, and repeatable.

CMan, you make it sound as if these are useless rituals below intellectual consideration.

If an historian tells you that Nero played the fiddle while Rome burned, how is this conclusion to be double-checked, observed, measured, and repeated? How is any historical event, for that matter? Yes, you can look at evidence such as pot shards dug out of the ground, what contemporaries in the historical time period have written.

Straw man. Historical research, no matter how rigorous and exhaustive it may be, is not science. As far as I know, no scientific theory is based on the concept of Nero fiddling while Rome burned - although what I know of musical history tells me he was as likely to be playing a Fender Stratocaster.

But the evidence cannot be tested, repeated,

See above. History is not science.

witnesses cannot interrogated or cross-examined.

Anecdotal evidence - also not acceptable as scientific evidence. Witnesses may be biased, lying or mistaken.

Are not you, in fact, yourself using the Perfect Solution Fallacy to refute other persons beliefs about historical events by saying there is no scientific evidence of them, when, there cannot be scientific evidence of any historical event?

There are many historical events that have scientific evidence to back them up (consider the now-ubiquitous forensic evidence in crime trials or document analysis).

There are many others which have been disproven in the same way.

There are countless others which never will be proven or disproven.

However, this is still a straw man. Nobody here has tried to opine that every historical event must have scientific evidence for it.

History and science are two different disciplines, as are science and mathemtatics. Many historians will feel validated by scientific research, and many scientists use copious amounts of mathematics in their work.

But a historian does not need to understand science to do history, and a scientist does not necessarily require to fully understand maths to do science.

Nonetheless all of the disciplines require at least some sort of proof (mathematics the strongest, history the least and science in the middle). All of these are therefore reasonable intellectual disciplines.

Religion doesn't ask for any evidence at all, and seems to regard anyone who asks for it as a feeble-minded infant in need of amused patronisation. Evidence is anathema to religion.

Regard that as a virtue if you wish, but don't expect everyone else to agree.

Personally, I regard religion's promises as on a par with the Nigerian 419 scam emails that amuse me for a while before I delete them: "And you expect me to believe this... why?"

[Tom Foss]

Thanks, Big Al. After I posted, I realized I should have done more to delineate the difference between historical questions and scientific ones.

[Big Al]

Don't worry, Tom. You left plenty of food for thought in any case.

That is, to someone whose critical faculties are not on a crash diet.

[Bronze Dog]

Excellent comment above, Tom. I approve this message on my behalf.

As for my standards of evidence, to make it explicit, vary on circumstance. If I'm playing a videogame, and read that rapidly pushing a button can influence the probability of a common event, I don't need much reason to examine the evidence in great detail: It's just a game, and rapid fire doesn't cost much. Low risk, low liability.

If we're talking about something with higher stakes, like my health, I'll perform a greater amount of research and hold higher standards: I won't take an herbal pill because of an anecdote. I'd look at the scientific consensus and possibly ask for double-blind control studies or something like that.

Nitpick that'd be better for another thread: I do think of history as a form of science, just one that usually has to work with lower quality evidence and has to sift through all the noise to find the best answers it can. The underlying philosophy looks the same to me. Of course, because of lower quality evidence, when new, higher-quality forms of evidence show up, historians need to put a little extra effort into considering that old answers might be wrong.

[Igor]

"When was the last time religion bowed to a paradigm shift, or even acknowledged that one was necessary? No amount of evidence changes any religion. Ever."

They acknowledged that it may be wrong to stone people to death. Notwithstanding same, no revision to the guidebook were made to acknowledge said paradigm shift

[Big Al]

All the marvellous rape, torture and death punishments detailed in Leviticus, Colossians and Deuteronomy are still present: I'm not aware of any Pope in history repealing them.

They just seem to have dropped out of favour as common Anglican and Catholic sermon material.

A paradigm shift, perhaps, but of tectonic speed.

[yakaru]

And it's not really a paradigm shift, strictly speaking. More like a policy change. For it to be a paradigm shift, pretty much the entire system has to have been revised at the most fundamental level. And it doesn't happen all that often in science either.

Personally, I'm not even all that sure that the Copernican revolution can really be called that either, because "science" at that time was very different from what we understand by it today.

Excellent comments above, Tom & Al.

[Big Al]

The real paradigm shift, on the order of impact of the acceptance of quantum mechanics and general relativity, would be for a popular pope to publicly resign his office, declaring the notion of an all-powerful, all-knowing, personal deity to be incompatible with logic and reason.

I'm not holding my breath.

[Amanda Siegel]

I'm afraid I cannot accept the counter argument you have present against St. Anselm's ontological argument (OA). I understand that the OA is a very complex argument that requires a definite kind of abstract thinking to fully comprehend, and thus is frequently misinterpreted. And indeed, you have misinterpreted it.
Looking at the actual transcript of the argument will show that Anselm does not use the term "god" in his argument itself. He asks us to consider the greatest conceivable being (GCB). One can argue whether you ought to call the GCB God (although I don't think the definition would be unwarranted). But, the point is that we must simply consider a being that is ontologically superior in every way, that cannot conceivably be improved upon. And then the argument from a contradiction follows: 1) It is apparent that a GCB can exist at least in the imagination, 2) We will grant that it is an ontologically superior trait to exist in reality than it is to exist only in the imagination, 3) We will assume that the GCB exists only in the imagination, but we then find ourselves facing an absurdity. For it is now possible for us to imagine a being greater than the GCB, which has the quality of existing in reality. This is absurd because we cannot by definition conceive of a being greater than the GCB. 4) Thus, because our assumption leads to an absurdity, we must reject our assumption and assume that the GCB must have the quality of existing in reality. As you can see, the use of the concept and term "greatest conceivable being" makes any equivocation of the term impossible. The idea of a GCB is completely unambiguous, there can only be one GCB, the greatest. (And by this I mean ontologically greatest, you can speculate that some people differ on what they call "great", but ontological greatness deals with traits that are universally and inarguably superior) So because you have misinterpreted the argument to the extent that your counter argument of equivocation doesn't even address the utilized term, I'm afraid that I cannot see any reason to reject the Ontological Argument.

Side Note: I would also like to critique your assumption that an argument by reason and logic alone should be considered inferior to one based on evidence. Philosophers make a distinction between what is called "a priori" reasoning:conclusions that are founded on reason and logic, and "a posteriori" reasoning: conclusions that are founded on evidence and experience. In the field of philosophy, it is widely agreed upon that arguments reasoned a priori (as the OA is), are much stronger than arguments reasoned a posteriori. This is because even our senses and experience can not be trusted as absolute truth (further exploration of this would require a discussion of Descartes' Epistemological musings). And so even a very convincing argument reasoned from evidence is not concrete while a validly constructed a priori argument with true premises is undeniably true. An example of this is that the discoveries made in science are conducted through a posteriori reasoning and the theories of mathematics are made through a priori reasoning.
I hope this critique can further the discussion of this famous argument which I find incredibly stimulating intellectually. I can only hope that my explanation and defense of Anselm's argument will further shed light on why he so staunchly believed the assertion that "The fool says in his heart, there is no God".

[Akusai]

Dear undergraduate philosophy major:

Whether it is "God" or the "GCB," it remains that the argument defines a being into existence. The label is irrelevant. You cannot simply say "This thing exists by definition" and prove it to exist.

Your condescending breakdown of a priori and a posteriori reasoning, something the majority of us here know quite well already, thank you, serves only to highlight your own ignorance of the topic at hand. We are well aware that science is a posteriori and mathematical proofs are a priori. The interesting thing about math, to use your example, is that mathematical proofs are not true in the traditional sense of the word; they are only "true" in the sense that their conclusions are consistent with their premises, which are consistent with the axioms on which the particular system of mathematics being used is based. A mathematical truth is "true" only in the context of the system from which it is derived; it may also accord with physical reality, e.g. the ratio of the circumference of a circle really is pi as far as we can tell, but that's a different kind of truth, and the geometrical proof has to be verified by measuring actual circles to see if the conclusion accords with reality.

Mathematical systems and logical systems (of which there are many more than just basic philosophical formal logic) are simply formal systems and have no special grasp on capital-T "Truth." They need not even accord with reality to be consistent or useful. Google "formalism" if you want more information. You come off as a bit of a Platonist, and the world has come a long way in the last 2400 years.

To speak more at your apparent level, where formal philosophical logic is the only logic, and a priori proofs in the absence of actual observations about the world are somehow more reliable indicators of truth than actual observations about the world, I will simply say this: even if we assume that we can know truths about the physical world in the absence of physical observations, and that formal philosophical logic is a system that allows us to discover those truths through the construction of arguments, an argument must be both valid and sound for its conclusion to be true, a trivial point with which I'm sure you're familiar. Validity, as I'm sure you also know, means that the structure of the argument is proper; it is free from structural fallacies and non-sequiturs, and its conclusion derives logically from its premises. Simple validity, however, does not make an argument true. It must be sound, and soundness requires that every single premise is also true. To know if those premises are true, you have a couple of options: you can verify them against physical reality by rigorous a posteriori observation (i.e. science), or you can construct a new syllogism to justify every single premise in your original argument.

Your second option leaves you either crafting an infinite series of arguments to back up each new set of premises, or reduces you, in the end, to relying upon the bedrock axioms upon which the system is built, axioms that are assumed to be true but can never be proven true within the system, only by reference to another, outside system, as Ernst Godel showed last century.

Crafting a valid deduction does not lead one to truth about the physical world; it can generate hypotheses that can be tested against the physical world and verified or falsified, but until you actually look at reality, you have no reason to suppose that anything you say about it is true.

I can say, for example:

p1. All men are mortal.
p2. Socrates is a man.
c. Socrates is mortal

But that basic deduction wasn't verified until the man drank the hemlock and perished. If Socrates was still alive, the evidence of reality would give us reason to question the syllogism, and we'd have to either redefine the word "man" to either include the concept of "mortal" or disinclude the concept of "Socrates" to make any proof similar to the above a priori and semantic (as it stands, "all men are mortal" is a tentative, though exceedingly likely to be true, statement based on exhaustive data from millennia of dying men and thus an a posteriori claim), redefine "mortal," or we'd have to change p1 to reflect the new knowledge that not all men are mortal.

Given that such a simple and classic syllogism could, in principle, be falsified through reference to empirical reality, tell me again how you can know that God (or the GCB) exists without looking, or, in fact, even attempting to look.

As you can see, your freshman-level analysis ignores multifarious complexities; not only do you show a lack of understanding of formal theories of logic, but you seem to think that because a logical argument is attempting to posit an a priori truth that all parts of the argument are therefore demonstrative of an a priori process. Here you are unwittingly committing the fallacy of division in addition to displaying only a surface-level understanding of how logic actually functions.

Finally, "The fool says in his heart that there is no God" is something people like us here tend to get quite often. It's insulting, it demonstrates nothing whatsoever about the existence of God, and everyone who tosses it about seems to think that they're the first person to do so. Well, you're not. It's old hat. Get a new line.

[Larian LeQuella]

I say the whole argument falls apart at argument one. Theitards are notorious for having horrible imaginations, and only being able to imagine that which they have been told. ;)

[Larian LeQuella]

@ Amanda Siegel. Read your own bible, I suggest Matthew 5:22. ]:)

[Ryan]

LOL Akusai, I could smell that underclassman lecture from here. Give her a break - it's her first year and they probably haven't gotten past Aristotle.

It'd be interesting to talk to her in four years.

[Akusai]

Give her a break - it's her first year and they probably haven't gotten past Aristotle.

I'd be more inclined to give her a break if she wasn't so condescending and puffed up about the "depths" of her knowledge. Part of intellectual advancement is getting taken down a peg or two now and then. It's how we learn not to assume we know everything just because we suddenly know a lot more stuff than we did a few months ago.

But I think you have to admit I was a lot nicer to her than I am to lots of other people on the internets.

[Amanda Siegel]

Akusai, I would first like to thank you for your elaboration (and certainly expansion) of my very brief and basic description of arguments from reason and arguments from experience. I must, of course, grant that my note didn't actually have anything to do with my critisism of the counter-argument to the OA, but was meant as a quick defence of the value of a priori arguments. I would be curious to know if it is my defence, and not simply my explanation that you disagree with; but that would be more useful in perhaps a different venue.

I will also apologise if my critique also managed to attack your intellect as well as the counter-argument. (It was not my intention) But I will assure you that if I had depths of knowledge I would have certainly included that fact in my response (it would have added considerable credence to my argument, at least in the rhetorical sense).

That aside, I would like to respond to your brief concern with how the conclusion of the OA follows the argument's premises. I ask that we consider that the OA is an argument by contradiction. Anselm never makes the assertion that 1) We can imagine and define a GCB, Thus 2) This GCB exists. He does propose the concept of a GCB and ask that we grant the existence of this GCB at least in the imagination. Then he makes the assumption that the GCB does NOT exist in reality. This assumtion appears to lead us to a logical absurdidty (which I tried to properly explain in my description). Thus, the assumtion must be rejected, and we should then assume that the GCB DOES in fact exist in reality. If you have a concern with the contradiction or absurdity that Anselm finds when he supposes the GCB's non-existence, then I request that you propose it and hopefully I can find a way to respond to it.

I will also quickly assure you that my allusion to Anselm's famous use of the "fool says in his heart..." quote was not meant as an insult. And while I will agree that its misuse can be debilitating for theists and atheists alike, the heart of it (In Anselm's use, perhaps not the biblical one) can be taken to mean that anyone who dismisses (or accepts for that matter) a belief without reasonable justification (or in the face of reasonable justification to the contrary) is a fool. Arguments like the OA are frequently used to defend that theists do discuss and consider reasonable justification for their beliefs, and hopefully that will continue to be evidenced in this discussion.

[Nico]

) We can imagine and define a GCB.

No, Anselm imagines and defines a GCB and assumes it must be God. The problem is the Gods in Greek, Egyptian, Aztec and Nordic cultures were never omnipotent or ominpresent (if this was his definition of greatness). In order for the argument to hold, Anselm must first explain why the "Gods" I listed are not really Gods.

[Nico]

Another flaw with Anselm's argument, is that he conceives existence as a trait for greatness. However, existance adds nothing to the "identity" being described.

Imagine an object (give it a weight, shape and color). If the object exists or not, it would still have the same weight, shape and color.

Similarly, Anselm's God is omnipotent and omnipresent. Well, weather real or imaginary, this God is still omnipotent and omnipresent.

Since existance adds nothing to the identity being described, rejecting its existance is not a logical absurdity.

Unless Anselm (or anybody else) can prove that assumption, the argument fails.

Btw. This is the rebuttal by Kant Existance is not a predicate

[Ryan]

the heart of it (In Anselm's use, perhaps not the biblical one) can be taken to mean that anyone who dismisses (or accepts for that matter) a belief without reasonable justification (or in the face of reasonable justification to the contrary) is a fool.

Honey-hon, equating the statement The fool says in his heart that there is no God to dismissing extraordinary claims that lack extraordinary evidence tells me you really need to pay attention to your next several years of undergrad philosophy (or whatever they call it in the UK). It's insulting to us grown-ups.

Let me steal from the best:

When you have millions of observations leading to the same consistent understanding of the universe — millions of paths that follow this same route from start to finish, and all seem to dovetail so wonderfully — that understanding provides a lot of confidence. That confidence equates to a lot of certainty. Is it the absolute certainty of mathematics? Of course not...such certainty doesn't exist outside of mathematics. But it's an incredible amount of justified certainty, because it's backed by all of that confidence...which is backed by true understanding...which is backed by real examination, brought about by skeptical questioning of our concepts.

Given the fact that I have no evidence or even a convincing argument to suggest that gnomes live in my ass, are you a fool to believe they don't? Or are you a bigger fool to believe they do?

Your 101 textbook explanation of "the value of a priori arguments" is not needed here. Go impress your friends still in twelfth year.

Trust me, you'll find this comment funny when you're in your mid to late twenties. Most of us are guilty of what Akusai O-so-rightly called "underclassmen lectures".

[Akusai]

Most of us are guilty of what Akusai O-so-rightly called "underclassmen lectures".

And I might add that my initial comment will seem an underclassman lecture to someone who knows far more about formal systems than I do and understands those issues far better. But I know enough to know that I know very little.

Also, I take issues with:

Arguments like the OA are frequently used to defend that theists do discuss and consider reasonable justification for their beliefs, and hopefully that will continue to be evidenced in this discussion.

Nobody believes on the basis of the OA, TAG, Kalam, or any other "argument" in favor of a deity. Those are only ever dreamed up after the fact in the presence of prior belief. They are frequently used to pretend that theists consider reasonable justification for their beliefs; in actuality, they serve as nothing more than rationalizations for something that theists believed without any justification or evidence before.

St. Anselm believed before he cooked up the OA. Anthony Plantinga believed before he birthed the philosophical abortion that is his modal logic version of the OA. And you, Amanda, believed before you were ever aware of the existence of the OA, just like every other theist who, at some point in their lives, stumbled upon some overwrought theology and used it to rationalize something they believed beforehand, anyway.

[Akusai]

To further respond to a couple of specific claims:

I must, of course, grant that my note didn't actually have anything to do with my critisism of the counter-argument to the OA, but was meant as a quick defence of the value of a priori arguments.

It had everything to do with your counter-argument, because your counter, and indeed the OA (and any purely logical "proof" of God's existence) is based on this strange idea that a priori arguments can discover facts about reality in the absence of observations of reality. Logic is "infallible," but only in a very strict sense: it is infallible within the limited context of the logical system being used. The axioms and laws of logic and mathematics are not, as Plato would have us believe, writ large in the fabric of the cosmos; they are ideas that we came up with. Some are useful in describing reality, and some are not.

. If you have a concern with the contradiction or absurdity that Anselm finds when he supposes the GCB's non-existence, then I request that you propose it and hopefully I can find a way to respond to it.

You apparently didn't read anything I said previously, or at least didn't understand it. Perhaps I wasn't terribly clear; that's entirely possible, as I always have a hard time gathering my thoughts when talking about formal systems.

The problem here is that a contradiction in a logical argument has no bearing on what is or must be in reality. This is the crux of the oldest rebuttal to the OA, that of the "Greatest Possible Island," which I'm sure you've heard, but I'll reproduce it here to help elucidate my subsequent comments.

Simply put, imagine the greatest possible island. It has everything that makes an island perfect (we'll be leaving aside the issue of Anselm's "Great-making qualities," all of which are arguable and drawn from the canon of laudatory characteristics in his specific cultural context). Whether it is real or imaginary, it is the most perfect possible island. But, as you said, if we assume it doesn't exist, then we're left with a contradiction; it cannot be the most perfect island if it doesn't exist in reality. Therefore, the Greatest Possible Island does exist in reality.

Except you can't just say "There's an island out there because logic dictates that there has to be." You have to find the island. The "proof by contradiction" hasn't given you any new knowledge at all because all you've done is craft a consistent logical structure with no necessary ties to actual reality.

As an aside, the standard counter to the GPI rebuttal is basically "Yeah, well God is different to an island." If you were going to say that, stop, because it's special pleading at its most pathetic.

Back to logical contradictions: the law of non-contradiction (an axiom of most systems of logic, but by no means all) is violated regularly at the subatomic level of physical reality. Electrons, for example, exist as probability waves that are, in a very real sense, both spin-up and spin-down states at the exact same time. Light acts as both a wave and a particle at the same time. These are brute facts about the universe that demonstrate that an apparent contradiction, as considered by our logical and linguistic structures, has nothing to do with what actually exists in the universe. The universe does what it does, and repeating "A is A, A is not not A" over and over again doesn't change the fact that, in reality, sometimes A just is not A. Sometimes contradictory propositions are true simultaneously. Reality is a bitch, and she has the ability to slap logic around like a redheaded stepchild.

[Bronze Dog]

The reason we need actual observations of the universe: The universe is not bound by the limits of your imagination.

People who rely on thought experiments and "pure logic" like the OA are pretty much saying otherwise. Like faith, it's the act of declaring yourself to be the supreme arbiter of the universe.

[Rob Gilham]

One particular assumption of the OA, the idea that there must be something that is the greatest (or least) of some quality, doesn't actually hold consistently over all systems.

For instance, what is the largest real number that is less than 1? There isn't one.

If you take the complex plane and remove the origin, what is the shortest line between 1 and -1? There isn't one.

Even in a purely a priori system like mathematics the notion of greatest or least (however you want to quantify or qualify it) doesn't always exist. Therefore the central argument of OA (i.e. the idea that there must be an entity that is the superlative) falls apart before it even gets started.

[BKsea]

Does the greatest conceivable building exist? If we abbreviate this "GCB" and follow Amanda's "proof," the answer is yes. That may come as a bit of a disappointment for a lot of architects

[Darth Cynic]

What about the most powerful and evil of all beings?