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Ontological Argument

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Parvinder

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« on: July 08, 2008, 03:00:46 pm »
Is this a good ontological argument?

Premise 1): A necessary and maximally great being “B” possibily exist.

Premise 2): Therefore “B” exists in some possible worlds.

Premise 3): If “B” exists in some possible worlds, then “B” must exist in all possible worlds.

Premise 3a): If “B” exist only some possible worlds, and not all possible worlds then “B’s” existence is contingent.

Premise 3b): “B” however can not be necessary and contingent (law of non-contradiction)

Premise 4): Since “B” exists in all possible worlds then “B” would exist in the actual world (since the actual world is a sub-set of the set of possible worlds)

Premise 5): Therefore “B” exists in the actual world.

Premise 6) Therefore “B” (which is a necessary and maximally great Being) exist.


:)

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Harvey

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« Reply #1 on: July 08, 2008, 03:40:37 pm »
Parvinder wrote: Is this a good ontological argument?

Premise 1): A necessary and maximally great being “B” possible exist.

Premise 2): Therefore “B” exists in some possible worlds (from premise 1).

Let's suppose that "B" means a "round square being." Would you agree that "B" in this case is possible?


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Parvinder

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« Reply #2 on: July 08, 2008, 04:21:32 pm »
harvey1 wrote:
Quote from: Parvinder
Is this a good ontological argument?

Premise 1): A necessary and maximally great being “B” possible exist.

Premise 2): Therefore “B” exists in some possible worlds (from premise 1).

Let's suppose that "B" means a "round square being." Would you agree that "B" in this case is possible?

No.  I don't see how something that is self-contradictory can be possible, and hence doesn't apply to "B."


:)

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Harvey

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« Reply #3 on: July 08, 2008, 05:00:08 pm »

Parvinder wrote: I don't see how something that is self-contradictory can be possible, and hence doesn't apply to "B."

In that case, can I recommend the following change to your premises?:


Premise 1): A necessary and maximally great being “B” conceivably exists.

Premise 2): Therefore, if "B" is possible, then “B” exists in some possible worlds

Would you agree to that change?


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Craig

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« Reply #4 on: July 08, 2008, 05:10:50 pm »

Premise 2): Therefore, if "B" is possible, then “B” exists in some possible worlds



Wouldnt it need to exist in ALL possible worlds?
"You'll never stop at one. Ill take you all on!" - Optimus Prime

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Parvinder

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« Reply #5 on: July 08, 2008, 05:32:32 pm »
harvey1 wrote:

Quote from: Parvinder
I don't see how something that is self-contradictory can be possible, and hence doesn't apply to "B."

In that case, can I recommend the following change to your premises?:


Premise 1): A necessary and maximally great being “B” conceivably exists.

Premise 2): Therefore, if "B" is possible, then “B” exists in some possible worlds

Would you agree to that change?

Perhaps, but wouldn't something that is possible be conceivable?

Here's the way I see it, illogical things are not possible so they can't be a canidate for "B."

Hope that makes sense.

Thanks!
:)

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Parvinder

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« Reply #6 on: July 08, 2008, 05:33:36 pm »
Craig wrote:

Premise 2): Therefore, if "B" is possible, then “B” exists in some possible worlds



Wouldnt it need to exist in ALL possible worlds?

I take care of that, as the argument proceeds.

Thanks!
:)

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Harvey

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« Reply #7 on: July 08, 2008, 05:43:06 pm »

Parvinder wrote: Perhaps, but wouldn't something that is possible be conceivable?

Everything that is possible is conceivable, but not everything conceivable is possible. For example, I can conceive of there always being a universe no matter how far back that I can imagine, but that doesn't mean that this is possible.

Parvinder wrote: Here's the way I see it, illogical things are not possible so they can't be a canidate for "B."


The problem is that a necessary and maximally great being might be illogical given a world where the most fundamental entities are brute facts (contingent). So, "B" remains conceivable but it's possibility is contentious.

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Chris

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« Reply #8 on: July 09, 2008, 09:52:28 am »

Harvey1: "Everything that is possible is conceivable, but not everything conceivable is possible..."

Let's break this statement up into its component parts.

(1) For any/all objects x, if x is possible then x is conceivable.

Or in predicate logic: [P = x is possible; C = x is conceivable]

(1') (x)(Px implies Cx).

(2) It is not the case that for any object x, if x is conceivable then x is possible.

Or in predicate logic:  [P = x is possible; C = x is conceivable]

(2') ~(x)(Cx implies Px)

Now, in order to properly assess the truth value of (1') and (2'), I need to no more about the predicate "possibly." Or, in order for me to assess the truth value of (1), and (2), I need to know more about what is meant by your use of the term "possibly" in both sentential sentences.

The various types of possibility I'm aware of include the following:

(a) epistemic possibility

(b) nomic possibility

(c) metaphysical possibility

(d) logical possibility

(e) broadly logical possibility

(f) deontic possibility [1]

I'm pretty sure that you had in mind either (a), (c), (d), or (e). Broadly logical possibility has been  subject to some interpretive debate (interpretive in the sense that some have misunderstood Plantinga's musings on this). [2]

Clear Counter-Examples to (1) and (1'):

Counter-Example #1: If by "possibility" you meant (a), (c), (d), or (e), then (1) and (1') is clearly false. Fermat's last theorem has either an affirmation or a denial. That theorem's denial or affirmation is possible, but no one has been able to conceive of either the denial or the affirmation of this theorem. There are many corollaries to this counter-example. I could simply suggest that there are a great many complex necessary truths (which given S5 are also possible truths), which have not been conceived by human persons, and yet they are perfectly possible. There are even possible truths about the future (say contingent truths about the nature of heaven) which have not been conceived by humanity, and yet they are obviously perfectly possible in the sense of (a), (c), (d), and (e).

I stand corrected. Fermat's last theorem was proven, and cannot therefore be viewed as something which has not been conceived. Thank you Harvey1.

_______________________________________

[1] There are a few others.

[2] Plantinga says, "...truths of propositional logic and first order quantification theory, let us say-are necessary in the narrow sense...But the sense of necessity in quesiton--call it 'broadly logical necessity' is wider than this. Truths of set theory, arithmetic and mathematics generally are necessary in this sense..." The Nature of Necessity (Oxford: Clarendon Press, reprint 1982), 1-2. It's unclear though, if Plantinga is equating "broadly logical necessity/possibility" with metaphysical necessity/possibility. The examples of "broadly logically necessary" propositions he gives would today be classified as metaphysically necessary, however some (me included) would argue that mathematical propositions when true are logically necessary. I think part of the reason for some of this confusion is that Kripke was the first to introduce the expression "metaphysical possibility/necessity", and prior to that many philosophers (I think at times even Plantinga) used "logical necessity/possibility" and/or "broadly logical necessity/possibility" for what is now called "metaphysical necessity/possibility". See Saul Kripke, Naming and Necessity (Cambridge, MA: Harvard University Press, 1980); George Bealer, "Modal Epistemology and the Rationalist Renaissance," in John Hawthorne and Tamar Gendler (eds.), Conceivability and Possibility (Oxford: Clarendon Press, 2002), 71-125.

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Chris

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« Reply #9 on: July 09, 2008, 12:43:27 pm »

Premise 1): A necessary and maximally great being “B” possibly exist.

Every atheist I’m aware of will reject this premise. Many of them, who think theism is coherent, will still reject this premise. The reason why is directly due to the confused modal nature of the premise itself.

           When you stipulate that a being is a necessary one, you are by consequence also stipulating that that being possibly exists. Let us translate this into talk about propositions (pace modality de dicto instead of modality de re). [1] One particular system of modal logic is called the Brouwer system. That system has a characteristic axiom. The axiom is: [L = the necessity operator; M = the possibility operator; p = a maximally great being exists]

(1) If p, then necessarily, possibly, p. [2]

(1’) If p, then LMp.

It’s clear from (1) and (1’) that when one says that p is true in a, then it is necessarily the case that p is possibly true. In other words, as soon as a proposition is true in the actual world, due to the nature of modal accessibility, that same proposition is possibly true in all other possible worlds. Your first premise is like (1) but you’ve chosen to stick the necessity operator in the antecedent, and put erase the necessity operator in the consequent.

Your first premise when understood in terms of modality de dicto, is saying:

(Premise 1) If necessarily p, then possibly p. [3]

           Well, this premise is an obvious truism. If p is true in all possible worlds, then of course p is possible, since it’s true in all possible worlds. If it were impossible it couldn’t even be true in one possible world. Interestingly, because you have the necessity operator governing p in the antecedant, your argument (and premise 1) begs the question. As soon as someone admits that p is necessary, by virtue of that admission you have the existence of that maximally great being you’re trying to prove. So in order for me to accept the soundness of your argument I have to accept premise one, but premise one has as its antecedent the claim that this maximally great being exists necessarily, thus one of your premises contains the conclusion you’re arguing for. This is a fallacy in logic known as petitio principii. [4] Your argument is therefore invalid.

Premise 2): Therefore “B” exists in some possible worlds.

According to your first premise, B would actually exist in all possible worlds, not just “some” possible worlds. Why? Because you stipulate in the antecedent of premise one that this being is a necessary being.

Premise 3): If “B” exists in some possible worlds, then “B” must exist in all possible worlds.

This already follows from premise one.

Premise 3a): If “B” exist only some possible worlds, and not all possible worlds then “B’s” existence is contingent.

Yes.

Premise 3b): “B” however can not be necessary and contingent (law of non-contradiction)

The proposition p is necessarily true, and the proposition p is contingent do not contradict each other. The law of non-contradiction (LNC) is ~(p &~p). The proposition p is necessarily true may entail p is not contingent, but it itself does not contradict the statement p is contingent, it only entails the truth of a proposition which contradicts the statement about p’s contingent truth.

Premise 4): Since “B” exists in all possible worlds then “B” would exist in the actual world (since the actual world is a sub-set of the set of possible worlds)

There is nothing wrong with this statement. I am curious about your use of the word “since.”

Premise 5): Therefore “B” exists in the actual world.

Again this follows from premise one alone.

Premise 6) Therefore “B” (which is a necessary and maximally great Being) exist.

Edit your argument, and make grammatical changes as well please. I’d love to see how you change it in light of the aforementioned criticisms.

________________________________________

[1] Modality de dicto is modal talk about propositions, where as modality de re is modal talk about the exemplification of properties and their complements. Modality de re is also concerned with the mode of existence certain beings enjoy, i.e., whether the beings in view are contingent, or necessary. See Alvin Plantinga, The Nature of Necessity (Oxford: Clarendon Press, reprint 1982), 9-13; Alvin Plantinga, “De Re et De Dicto,” in Matthew Davidson (ed.), Essays in the Metaphysics of Modality (New York, NY: Oxford University Press, 2003), 25-45.

Recall that a being exists by necessity, or is a necessary being iff (this means “if and only if” by abbreviation) that being exists in all possible worlds. Recall that a being exists contingently, if it exists in the a (this represents the actual world), and does not exist in all other possible worlds. See Alvin Plantinga, The Nature of Necessity (Oxford: Clarendon Press, reprint 1982), 55-62.

[2] Michael J. Loux, “Introduction,” in Michael J. Loux (ed.), The Possible and the Actual: Readings in the Metaphysics of Modality (Ithaca, NY: Cornell University Press, 1979), 23.

[3] If Lp, then Mp.

[4] Irving M. Copi and Carl Cohen, Introduction to Logic (Upper Saddle River, NJ: Pearson Prentice Hall, twelfth edition 2005), 151.

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Harvey

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« Reply #10 on: July 09, 2008, 01:56:05 pm »

CGWeaver wrote: Now, in order to properly assess the truth value of (1') and (2'), I need to no more about the predicate "possibly." Or, in order for me to assess the truth value of (1), and (2), I need to know more about what is meant by your use of the term "possibly" in both sentential sentences.

(c) metaphysical possibility

CGWeaver wrote: Counter-Example #1: If by "possibility" you meant (a), (c), (d), or (e), then (1) and (1') is clearly false. Fermat's last theorem has either an affirmation or a denial. That theorem's denial or affirmation is possible, but no one has been able to conceive of either the denial or the affirmation of this theorem.


Fermat's last theorem was proved a few years ago in 1994. However, even prior to this time there was "conceivable" proofs that, at first, were prima facie conceivable and then later secunda facie conceivable (e.g., in 1993 Wiles thought he had a proof but a few months later realized that he was mistaken).

CGWeaver wrote: I could simply suggest that there are a great many complex necessary truths (which given S5 are also possible truths), which have not been conceived by human persons, and yet they are perfectly possible.


When I say something is conceivable that does not mean something is predictable. Rather, I mean that there are elements shared by a possible-thing and a conceivable-thing. These elements include the rough criteria of possibility (e.g., there is an imagined scenario where the overall description is correct in/as some possible world, this "something" is describable to some degree to identify it from some other closely resembling object, etc.). However, conceivability lacks some criteria of possibility that make it a superset of possibility (e.g., there is an imagined scenario where the detailed description is correct in/as some possible world, this "something" is describable in exact degree to identify it from some other closely resembling object, etc.)

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Chris

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« Reply #11 on: July 09, 2008, 02:05:35 pm »

I stand corrected. Fermat's last theorem was proven, and cannot therefore be viewed as something which has not been conceived. Thank you Harvey1

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Chris

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« Reply #12 on: July 09, 2008, 02:43:19 pm »

Harvey…what do you mean by “conceivable”? Do you mean “able to form a mental image about”? Or, do you mean “able to stipulate i.e., think about?” Or do you mean something else? If what you mean by “conceivable” is “able to think about”, or “able to stipulate” then (a) your understanding of conceivability is such that (1) and (1’) are trivially true (b) your understanding of conceivability is way outside of the literature’s understanding of what it means for something to be conceivable.[1]

From your last pericope it seems to me that your suggesting something a bit softer than (1) or (1’). You seem to be claiming: [P = x is possible; C = x is conceivable]

(1’’) (x)(Px implies possibly Cx)

My counter-example (although now falsified) has corollaries. Those corollaries were not trying to specify an idea of prediction, but rather the fact that there are propositions whose contents entail their possible truth, but no one has conceived (and by conceive I mean “able to form a mental image of” or something like that) of them at all. If what you said in (1) and (1’) is really true, then I’d dare say that there are propositions which are possibly true, but no human person will ever conceive of them. Obviously, intricate super-complex solutions to infinite set theory, or infinite binary logic are so complex that only God can conceive of their solutions. What this means is that, whether or not a proposition is metaphysically possible, does not depend at all, upon the cognitive abilities of human persons viz. their ability to conceive of the relevant state of affairs, or propositions about that state of affairs.



[1] See for example David Chalmers, “Does Conceivability Entail Possibility?,” in Tamar Gendler and John Hawthorne (eds.), Conceivability and Possibility (Oxford: Clarendon Press, 2002), 145-200.

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Harvey

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« Reply #13 on: July 09, 2008, 03:51:34 pm »

CGWeaver wrote: Harvey…what do you mean by “conceivable”? Do you mean “able to form a mental image about”? Or, do you mean “able to stipulate i.e., think about?” Or do you mean something else? If what you mean by “conceivable” is “able to think about”, or “able to stipulate” then (a) your understanding of conceivability is such that (1) and (1’) are trivially true (b) your understanding of conceivability is way outside of the literature’s understanding of what it means for something to be conceivable.[1]

Chalmers I think provides a number of allowable definitions of conceivability (e.g., negative conceivability, positive conceivability, primary conceivability, secondary conceivability, prima facie conceivability, ideal conceivability, perceptual imagination conceivability, coherent modal imagination conceivability, etc.). I'm not so much trying to define conceivability as to distinguish it from possibility.

In other words, possibility contains a few criterions that if those properties are present, then something is indeed possible. For example, the overall description must make sense, the detailed description must make sense, it must be logically coherent, etc. Conceivability is a category that shares some criteria of possibility, but lacks some of the essential features of possibility.

This is not a trivial approach since conceivability has criteria that must be met. For example, it is not conceivable that mathematics to be equivalent to paper since it does not share any criteria of possibility (for example, we cannot identify the body of mathematics with paper whatsoever, not even in a prima facie manner).

CGWeaver wrote: My counter-example (although now falsified) has corollaries. Those corollaries were not trying to specify an idea of prediction, but rather the fact that there are propositions whose contents entail their possible truth, but no one has conceived (and be conceive I mean “able to form a mental image of” or something like that) of them at all.


That particular definition of conceivability is weak. That's not to say it's not usable in certain contexts. For example, Chalmers in that paper you referenced gives a mental picture of a grim reaper paradox that obviously is not possible, but is conceivable. We could either work on a definition of conceivability that meets your objection (while allowing us to think of conceivability as a property of a statement), or we can just accept that conceivability and possibility are context-laden. Therefore, if we go that route, we need to be very cautious when moving outside of the appropriate conceivability-possibility context.

I prefer the latter approach. Some conceivable-contexts do not require mental images. My central point, however, is to avoid contexts and talk in terms of generalities. That is, there exists a conceivable-context to talk about all possible propositions (e.g., as mentioned by Chalmers).

CGWeaver wrote: If what you said in (1) and (1’) is really true, then In fact, I’d dare say that there are propositions which are possibly true, but no human person will ever conceive of them. Obviously, intricate super-complex solutions to infinite set theory, or infinite binary logic are so complex that only God can conceive of their solutions. What this means is that, whether or not a proposition is metaphysically possible, does not depend at all, upon the cognitive abilities of human persons viz. their ability to conceive of the relevant state of affairs, or propositions about that state of affairs.


I would accept that there are conceivable-contexts which only God can conceive of and which are not possible. This is not equivalent to "mathematics is paper" example since from God's point of view a conceivable object might share a number of properties shared by a possible object, but because the conceivable object lacks one property (e.g., God's will to allow it), it is not possible--even though it is conceivable.