Saturday, December 15, 2007

A simple Ontological argument

Today I will be considering a simple Ontological proof of God. Ontological arguments are basically attempts to prove God through concepts alone, without any real-world evidence. This particular variant has been fully discredited in modern times (and this is not just my atheist bias talking). This isn't so much an attempt to argue about God as it is an exercise in reasoning.

The Ontological proof is in three steps.
  1. Definition: "God" is the greatest being imaginable.
  2. Premise: It is greater to necessarily exist than to not necessarily exist.
  3. Conclusion: God necessarily exists.
There is a very simple counterargument using what's called reductio ad absurdum. We show that if ontological argument works, various absurd results must also follow. Take the following example:
  1. Definition: "Drod" is the greatest video game imaginable.
  2. Premise: It is greater to necessarily exist than to not necessarily exist.
  3. Conclusion: Drod necessarily exists.
Similarly, I could argue that the greatest sandwich exists, the greatest dad exists, and the greatest island exists. I do not even need to confine myself to objects of the form of "the greatest [blank] imaginable", nor do I have to assume any premises. Take the following:
  1. Definition: The "IPU" is an invisible pink unicorn that necessarily exists.
  2. Conclusion: the IPU necessarily exists.
I could continue to use this argument to prove the existence of anything, as long as I define it to necessarily exist. That is absurd. Unfortunately, while the reductio ad absurdum tells us that the ontological argument cannot possibly work, it does not tell us exactly where it goes wrong.

In my opinion, the central question of this argument is this: what sort of control do you have over objects when you define them? Normally, when I define something, I have full control over its properties. If I define a triangle to be a polygon with three sides, these properties must be true. There is no triangle with more than three sides, because if an object has more than three sides, it cannot be a triangle.

Why can't I do the same with the property "necessarily existing"? Let's try the same argument I tried with the triangle. "There is no God that doesn't necessarily exist, because if an object doesn't necessarily exist, it cannot be God." Aha! The argument with the triangle only proves that if there is a triangle, then it has three sides. Similarly, this argument only shows that if God exists, then God must necessarily exist. The Ontological Argument basically assumes what it is trying to prove. We fully control the properties of an object that we define, but we cannot control whether there is an instance of the object in the real world. (Some philosophers go on to say that existence cannot be a property of an object, but that distinction is irrelevant for now.)

In the spirit of critical-thinking fun, I shall attempt a similar argument going in the other direction. This isn't a serious argument, just what passes for humor in my mind. Any refutations?
  1. Definition: "God" is the greatest being imaginable.
  2. Premise: A being would be greater if its existence could be proven with the Ontological Argument.
  3. Premise: The Ontological Argument is impossible.
  4. Conclusion: God is impossible.

32 comments:

cf said...

This is very simple and easy to understand - well done and thank you!

Hugo said...

I take some issues with this post or line of argument, but they're somewhat on the emotional/intuitive level. Maybe I can concretise them into words at some point, but for now I'm too lazy. (Until they're concretised, I wouldn't know if there's much logical substance to my issues, might be on a more philosophical level. Actually, it might just be that I "dislike" your argument/post as much as I dislike the ontological argument, which would confirm the value of your post.)

That said, I really just wanted to note that a triangle doesn't really exist either... it is a mathematical and abstract concept. It is a 2D shape. It is represented on a piece of paper, but it isn't actually real. Is God not maybe as real as a triangle then? (If you see where I'm going with this, it probably connects to the issues I'm touching on in the previous paragraph.) Noting that the triangle doesn't exist...

Logical/intellectual noodling... both of these. Yea, to me, the ontological argument is indeed argument-by-definition: "picture the greatest". There, you've just created a concept and it now exists. ;-)

miller said...

I believe the abstractness of the triangle is irrelevant, as I could have simply chosen a different example. I only chose triangles for their cleanness of definition.

For example, we may define a book as a bunch of binded pages with words. Given that books exist, we can say that there exist binded pages with words. However, we cannot prove, solely from definitions, that books really exist.

Personally, I rather like the ontological arguments (there are others). They're like the philosophical versions of those proofs that 1=0. I believe that what they try to prove is impossible. It's not the God part in particular that is impossible, but the bridging from mere concept to reality. (Of course, it's easy for me to just say it's impossible.)

Anonymous said...

You are wrong, yuo are saying that the ontological argument could work for anything but it doesn't. The reason for this is that God is non-contingent, whereas the likes of a unicorn/island etc are contingent

miller said...

Would it work for the "NCI", which is defined as the greatest non-contingent island imaginable?

Chuck said...

Your reducio ad absurdum did not work against Anselm and it is not going to work today.

Islands, ice cream cones, video games, etc. are all imperfect by their very nature, which makes it a non-sequitur to predicate any one of them as "greatest conceivable".

Any material thing is a particular conglomeration of matter which requires an external account for why it is one particular form and not some other. Thus, you cannot simply define a material thing as non-contingent. Furthermore, no matter how great you conceive these things to be, I can always conceive of them to be greater.
Can you conceive of a god that is more intelligent than an omnipresent God?

If you want to take away materiality and continue to apply this objection, you may do that but you'll find that as you continually chip away, you'll be left with something which shares the same attributes as God which you happen to refer to as something else. According to Leibniz's law, these would be the same thing.

The problem with Anselm's argument is that it does not quite have the rigor of the more modernized versions of this proof, which leaves it open to certain objections. Of course, Anselm did not have a system of modal logic to work with. He simply had his skill for rhetoric.

chuck said...

"Can you conceive of a god that is more intelligent than an omnipresent God?"

This should read "Can you conceive of a god that is more intelligent than an OMNISCIENT God?"

miller said...

Trackback: my analysis of a more sophisticated ontological argument

Jo said...

well described, but when you were talking about
'the greatest sandwhich, greatest dad, etc.' you gotta remember that all of these things are contingent. whereas God is non contingent

The Barefoot Bum said...

Contingency is not a well-defined concept in philosophy. Philosophers don't really understand causality. (Which is no particular shame: causality is an extremely subtle concept.)

miller said...

I can see the relevance of contingency to the modal ontological arguments, but not to the one shown here. Would you care to demonstrate it?

Anonymous said...

The 'greatest possible non-contingent island that is is conceivable' is a concept that makes no sense because:

a) the properties that make an island great have no conceivable end. For example, if the number of palm trees is what determines how great an island is, an island can always have more palm trees. Hence, there is no conceivable end to how great an island can be and thus the term 'greatest conceivable island' is meaningless. You could argue that the same is true of the concept of 'God' but most philosophers believe that there are logical limitations to God (for example, God's omnipotence means that he can do anything that is *logically* possible). If that is true, then 'God' is a conceivable concept.

b) an island is by definition a contingent entity, as the concept of an island relies upon other concepts such as land and water, which themselves are contingent upon earth, which itself is contingent upon the universe and so on. In contrast 'that than which no greater can be conceived' is something which would not contingent upon anything else. And because only 'that than which no greater can be conceived' would be expected to have this property, the ontological argument works only for the concept of God.

You're overall conclusion that this simple ontological argument is wrong is correct. But overload arguments are not the reason for why this is. The traditional Kantian criticism is much more damning.

The Barefoot Bum said...

I will repeat my comment: We do not yet have a precise and unequivocal definition of "contingent".

Note that if contingency means "having a definitional relationship to other definitions" (in the sense that the definition of "island" is indeed contingent on the definition of "land" and "sea"), then definition "that which nothing greater can be conceived" is equally contingent on all the other things that the definiendum is greater than.

"Nothing" would seem to refer to, well, nothing, but it doesn't: In this context, it means (more or less) everything but, and therefore is contingent (in the above sense) on everything else.

But I don't know that the kind of definitional contingency is a trivial concept: every definition is "contingent" because it sets the definiendum apart from everything else. If you try to make "God" non-contingent in this sense, it is not at all clear that the concept can be defined.

Of course, in philosophy, that's not a bad thing: I've met very few philosophers who consider clarity and precision as anything but evils to be abhorred.

The Barefoot Bum said...

Er... I don't know that the kind of definitional contingency is not a trivial concept...

Anonymous said...

When I said that an island is by definition contingent, what I meant was that an island by definition is made of land surrounded by water and hence is contingent upon land and water for its existence, just as any physical object in the universe is contingent upon the universe for its existence. If we define a non-contingent entity as 'that which exists through itself' then no physical entity could be non-contingent because all physical entities are composite entities and, as Avicenna argued, something which exists through itself would necessarily need to be non-composite for otherwise, it would not exist through itself but through the constituent parts that make it up.

The point that I was just trying to make is that a 'non-contingent island' is a concept as contradictory as a 'square circle.' Even if 'contingency' is a concept that is still quite mysterious, I think we can agree on that much.

The Barefoot Bum said...

If we define a non-contingent entity as 'that which exists through itself'

Once you start permitting self-referential definitions, you get into all sorts of trouble.

Besides, the definition at hand is "a being such that no greater being can be conceived." I'm at a loss to detect your definition of contingency in this definition.

If your intention is simply to keep adding vague post hoc qualifications to confuse us until we give up in disgust and you can declare victory by default, you're well on your way.

Anonymous said...

I was simply noting Avicenna's take on the concept of non-contingency. If you can't handle that, then that's your problem, not mine.

If you honestly think that there could ever exist an actual physical island that is non-contingent, then you are hopeless.

The Barefoot Bum said...

I was simply noting Avicenna's take on the concept of non-contingency.

And here I thought we were discussing Anselm's take on the ontological argument.

If you honestly think that there could ever exist an actual physical island that is non-contingent, then you are hopeless.

You continue with your profound and forceful logical argumentation. If you use the
"Neener Neener Neener" attack my position becomes precarious unless I can successfully adapt the "I'm rubber and you're glue" defense.

Anonymous said...

Nor am I remotely impressed with your attempts to retreat back into the position that we simply do not understand the concept of contingency very well, especially when you swat down my attempt to supply just such an operational definition of the term 'non-contingency' by appealing to a well-respected philosopher whose works are obviously pertinent to this discussion. Anselm's definition of God is 'that than which no greater can be conceived,' which implies that God is non-contingent for it is greater to be non-contingent than contingent. To work with this concept of 'non-contingency' with any hope of fully understanding it, it is necessary to provide it with a more precise definition, one which Avicenna supplied, precisely so that we can avoid the ambiguities that you use as a shield to prevent any meaningful dialogue.

I have strove to show why the concept of a non-contingent island is self-contradictory. My reasoning comes from another influential philosopher, John Hick, who perhaps more succinctly describes what I have been trying to:

More importantly, ‘that than which no greater can be conceived’ exists necessarily, whilst an island, or any finite object that Gaunilo might have chosen instead, can exist only contingently. Anselm’s argument in its second form, and it is this second form that is developed in the ‘Reply’ to Gaunilo, is that it is more perfect to exist necessarily than to exist contingently, and that therefore that than which no more perfect can be conceived exists necessarily, and therefore exists. But this argument cannot be applied to ‘that island than which no more perfect can be conceived.’ An island, being by definition a part of the physical world and thus dependent for its formation and character upon other aspects of the world, as well as sharing the contingent nature of the world as a whole, cannot be the subject of the Anselmian argument. That reasoning only applies to the unique case of the being than which no more perfect can be conceived.

(John Hick. Arguments for the existence of God, 1971)

You have utterly failed to show how I am wrong and if your best response is that you're made of glue, then the best I can do is wish you luck in not getting all stuck up to your ignorance.

miller said...

Anonymous, you might be more interested in my discussions of the modal ontological argument. This is only supposed to be a basic introduction to ontological arguments without getting into modalities. Contingency really has nothing to do with it, so it doesn't matter how specific or vague you are about the concept.

I agree with you that we can't simply define a "non-contingent island" into being. But why can't we do it? Is it because the concept is internally inconsistent? Perhaps. But more to the point, it's because you can't assign the property of non-contingency until after you find an instance of a non-contingent island.

This is generally true of any property in any definition. For example, I can define a "sandy island" to be an island that is sandy. I can prove that all sandy islands are sandy. But I can't prove that there is any instance of a sandy island without, you know, looking for one.

Seriously, if you need to appeal to ancient philosophers to understand this one, then you're overthinking it (or underthinking it).

Anonymous said...

Good summary thanks - i dont really see why people are arguing about it, this summary of the argument never said this is true ..blahblahblah , therefore people should argue about its substance somewhere else really.

albeenocookie said...

That's THE Ontological argument. Ontology is to do with your perception of reality, being and existence. Sorry, pet hate. awesome blog though

miller said...

It's an ontological argument because there are multiple other ontological arguments which I have written about elsewhere.

miller said...

Kant's refutation actually refers mostly to the second premise, but in my opinion the weakness of the ontological arguments lays actually in the first premise. "God" is the greatest being imaginable.
Actually "imaginable" is what it makes it unpalatable. You can very well say "the cosmic egg", or "Parmenides what-is", or Demiurge, or eternal fire...(all of them are non contingent, or can be seen like that, although you can discuss about the relation between the Demiurge and maths...basically we are assuming the possibility of a superior existence, and in this way we can assume anything, but, as the saying goes, "a posse ad esse non valet consequentia"...

miller said...

My understanding is that Kant has multiple distinct refutations.

miller said...

That's true, but as I understand it, Kant's main argument centers on the fact that we shouldn't treat existence as a real predicate, etc...my point is that you can start by imagining any non contingent entity as "the greatest source of everything that exists", even "water" or "fire", etc...the ontological argument would provide the same false conclusion.

miller said...

Okay, I wasn't sure which Kantian argument you were referring to.



Here you're making a reductio ad absurdum argument, which points to the existence of a problem with the ontological argument, but does not specify what the problem is. Kant's argument, on the other hand, specifies a particular problem (although it's a problem that I think is solved in other ontological arguments).

miller said...

Look at it this way: the ontological argument is circular, an invalid syllogism based on an obvious tautology. You state that God is the greatest being(by saying this you already formulated the conclusion), and then in the end you restate the same thing...it's like running alone around a pole and proclaiming yourself winner...

miller said...

I don't think it's possible for an obvious tautology to also be an invalid syllogism.

miller said...

What I wanted to say is that is a patched-up syllogism, built on sand...

miller said...

I don't think colorful metaphors have a place in this discussion. You want to say that there is an incorrect syllogism. I don't know which syllogism you are referring to or why you think it's incorrect. I don't even know whether you agreed or disagreed with my point about reductio ad absurdum not specifying the problem.

miller said...

Really sorry for the delay…

Look, one can make many points here, and anyway it’s the
sort of discussion which can go on for ever…

1)no, it’s not a demonstration Reductio ad absurdum, like in maths, and
I don’t think that extrapolating from one domain to another is always helpful. You
can easily demonstrate, using this method, that the mediators in a triangle are
concurrent in a single and one point only, but this kind of demonstration
presents many more difficulties in philosophy…

My point was to show that by using this so called syllogism(patched-up,
invalid, having the appearance of…, you name it), you can “demonstrate”
anything, exactly because it’s not a proper logical construction.

If you say “fire is the greatest imaginable source of everything”, you
might even pretend to demonstrate it, using the template provided by the
ontological argument. You cannot even say that is absurd…how do I know that
behind the quarks isn’t really a sort of fire, hidden, a very subtle plasma continuum, which gives the lie
to the “quantum view” of the universe…

2)in my opinion, the main weakness of the ontological arguments lies in
the premise.

2.1When you talk of “God”, you implicitly invalidate the rest of the
argument…simply because you are already stating what you purport to
demonstrate(and the so-called final conclusion restates the premise, albeit in
a slightly different form).

When you say “God is…” you mean several things, but the subtext which
is the most important is that implicitly you admit not only the possibility of
its existence but actually its reality itself(when I say “iron is…”, I state
its existence as an ore, or as part of the group of metals in the Mendeleev table, etc). for an atheist, the word God in a
phrase is nothing more than a noun, surrounded by other nouns and verbs, devoid
of any real term of reference…so it’s just grammar and nothing more…

2.2 I have many issues with the word “imaginable”. What is
imaginable for us, all very smart, or half smart, or whatever, may not be imaginable for a poor man, who has to toil
day and night all his life for a meagre subsistence on a piece of barren land…

Faraday didn’t imagine that energy can move in quanta,
neither Maxwell that space and time can be looked at as one…up there, or down, can
be many more imaginable things we don’t know anything about…what about “an
infinite number of gods is the greatest thing imaginable”…

We couldstart another line of argument if you use the
word “possible”. I cannot imagine neither 10-11 dimensions of the strings(and I
don’t think that anyone can, intuitively), as I cannot imagine the existence of
wormholes(you might say they can be described ONLY mathematically)…that doesn’t
mean that they are not possible…

So, probably the word “possible” might give a wider scope to
the premise, but still, it doesn’t clarify it. It’s not a real premise, it’s a
conclusion.

The ontological argument doesn’t demonstrate anything. It’s
just a pretentious tautology.