Analyses and Critiques of Ontological Arguments
Damion Reinhardt

Introduction

The ontological argument

Statement of the argument
Anselmic Absurdities
Analysis of the Argument
The ontological argument from necessary existence
Statement of the argument
Cartesian Absurdities
Analysis of the Argument
Modal reformulation of the argument
Statement of the argument
Hartshornean Absurdities
Analysis of the Argument
Possible worlds reformulation of the argument
Statement of the argument
Plantingan Absurdities
Analysis of the Argument
Conclusion
 


 

Introduction

The various ontological arguments for the existence of God may seem utterly absurd to most persons upon first reading, indeed, it is doubtful that it has convinced many unbelievers of the truth of its conclusion.  Paradoxically, the ontological argument has generated a notable and long-standing stir among students of philosophy and has since its inception been addressed by several so-called greats of western philosophical thought.  Even today philosophers of a apologetic bent continue to formulate new variations on the argument.

This widespread interest may not be due to the argument's inherent soundness but rather because its analysis involves some of the more interesting and uncertain problems of philosophy; a thorough examination of the various forms of the argument reveals that it is precisely in the weakness of each formulation that said problems arise, giving the argument a deceptive appearance of soundness. Let us look first at the original formulation of the argument.
 

The ontological argument

The English Platonist St. Anselm of Canterbury (c. 1033-1109) first proposed his ontological argument in his Proslogion, and he elaborated on it further in his reply to the skeptical monk Gaunilo.

Statement of the argument

Anselm states the argument in the second chapter of Proslogion:

Therefore, Lord, you who give knowledge of the faith, give me as much knowledge as you know to be fitting for me, because you are as we believe and that which we believe. And indeed we believe you are something greater than which cannot be thought. Or is there no such kind of thing, for "the fool said in his heart, 'there is no God'" (Ps. 13:1, 52:1)? But certainly that same fool, having heard what I just said, "something greater than which cannot be thought," understands what he heard, and what he understands is in his thought, even if he does not think it exists. For it is one thing for something to exist in a person's thought and quite another for the person to think that thing exists. For when a painter thinks ahead to what he will paint, he has that picture in his thought, but he does not yet think it exists, because he has not done it yet. Once he has painted it he has it in his thought and thinks it exists because he has done it. Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought.1 And certainly that greater than which cannot be thought cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater.2 If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible.3 Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality. 4 Anselm's original formulation of the ontological argument may then be formulated thus:
(A1) That than which no greater may be thought (God) exists in thought.
(A2) Existence in reality is greater than existence in thought alone.
(A3) If God were to exist in thought alone, then a God who exists in reality would be greater than the greatest conceivable being, which would be a contradiction, hence
(AC) God exists in reality
Anselmic Absurdities

To the skeptical reader this argument has the feel of a cheap parlor trick, but it may yet be quite unclear at which point Anselm pulls his logical sleight of hand.  Many people respond to such seemingly deceptive argumentation by attempting to modify some of the terms of the argument to achieve absurdities without changing the essence of the argumentation.  Let us consider a few such instructive exercises in Anselmian sleight of hand.

A monk in the abbey of Marmoutie by the name of Gaunilo formulated a variation on the argument was based on the idea that we could replace "a being than which nothing greater may be conceived" with some other greatest thing.  He used the example of a greatest island, which Anselm objected to on the grounds that a greatest actual island does not fit his argument's concept of greatest conceivable.  So, what of a greatest conceivable island?  Plantinga attempts to refute such a modification of Gaunilo's objection on the grounds that the idea of a greatest conceivable island is inherently contradictory, those things which make an island great such as the number of Nubian maidens or coconuts have no inherent upper limit.  Of course, such a problem could easily be avoided by theorizing a "Heavenly Isle" which is unlimited by finitude in its perfections.  Alternatively, if we are careful in our enumeration of specific properties of greatness we may avoid such problems of finitude when positing the greatest of earthly things.  The greatest conceivable size 6 gold ring could be defined as a ring which is greatest in but a few attributes: size 6-ness, roundness, gold purity, and existence.  By Anselm's line of reasoning, then, there must exist a perfect size 6 gold ring somewhere.

  • The ring than which no greater may be thought exists in thought.
  • Existence in reality is greater than existence in thought alone.
  • If the ring were to exist in thought alone, then a ring which exists in reality would be greater than the greatest conceivable ring, which would be a contradiction, hence
  • The ring exists in reality
    • In the more general case may be constructed by replacing greatest being (God) with any carefully defined category of Greatest Conceivable Something, such as the "greatest conceivable heavenly isle" or the "greatest conceivable size-6 gold ring" or the "greatest cherubim"  So long as we carefully enumerate the properties which may make something great such that they may all be maximizable and we implicitly include existence among those properties, then the argument may be applied to speak many such Greatest Conceivable Somethings (GCS's) into existence. So, the ontological argument may well be applied to anything with a given set of maximizable properties of greatness in order to define Greatest Conceivables into existence.  Categorical nitpicking aside, Gaunilo's objection is barking up the right tree.

    Now consider a more drastic variation upon the Anselmian argument.

    Hence, God must ensure that at all times there is a human about to a comprehend Him, or He risks disappearing altogether -- we have thus uncovered why human faith is said to be so crucial to God.  Brushing aside such sarcasm, the disciple of Anselm would no doubt object that existence in human understanding does not add anything to the greatness of a being.  Such an admission, however, puts her in a particularly nasty bind.  Having admitted that understanding is worth precisely nothing in terms of greatness, she implies that for God to have any greatness at all, He must first exist in reality.  The original Anselmian argument would reduce thusly:
    (A1) That than which no greater may be thought (God) exists in thought.
    (A2') Existence in reality conveys greatness, existence in thought conveys none.
    (A3') If God were to exist in thought alone, then a God he would have no greatness, hence
    (AC) God exists in reality
    God is defined as 'the greatest' which is taken to include greatness in existence and hence he must therefore exist by definition.  Now the argument seems seems like a flagrant attempt to define God into existence.  The original formulation of the argument may also be such an attempt but it if so it is somewhat more subtle.

    Analysis of the Argument

    The above examples give us some sense of the illogic of Anselm's ontological argument, but to determine precisely where and how the original argument goes awry we must turn to a through examination of the argument itself.

    (A1) That than which no greater may be thought (God) exists in thought.
    (A2) Existence in reality is greater than existence in thought alone.
    (A3) If God were to exist in thought alone, then a God who exists in reality would be greater than the greatest conceivable being, which would be a contradiction, hence
    (AC) God exists in reality
    The argument is sound, if premises A1, A2, and A3 are sound the conclusion AC follows.  Let us then examine these premises.

    Premise A1 seems reasonable enough, we may indeed form the concept of a greatest conceivable being.  However, it should be noted here that such a concept is merely an idea, nothing more.  It cannot be said to exist except as an idea in the mind.  The concept of a greatest conceivable may exist in someone's understanding with or without the attendant belief that such a concept really exists within the universe as we know it, as Anselm himself points out in reference to his proverbial fool.

    Moving on to A2, we have the claim that "Existence in reality is greater than existence in thought alone."  Is this self-evident or necessarily true?  Firstly, there some ambiguity in this usage of the term greater.  It is relatively easy to consider such things as greater degrees of power, knowledge, and morality.  However, can existence rightly be called one of those things which makes something great?  If I asked one to describe a great fireman, sports car or interstellar spaceship, would existence be listed as one of the things which makes something great?  The Batmobile is superior to nearly any real sports car in nearly every relevant way, and most anyone asked to compare the two would say it is thus the greater without regard for the fact that it does not in fact exist.  This brings us to the (closely related) second problem, the validity of comparing a concept to a being.  Are not concepts and beings far more different than apples and oranges?  Is the idea of an Armageddon virus somehow inferior to the real thing?  Is the idea of a greatest conceivable being somehow lesser than the being itself?

    If we accept the validity of step A2, then the reasoning in step A3 is flawless and the conclusion inevitable.  But is a contradiction truly present?  The conception of a God who exists in thought alone cannot contradict an objectively real God who truly exists, ideas do not contradict reality, they are merely reflective of it (or else inaccurate).  The contradiction is truly between two competing conceptions of God, that of him as great in every way and yet completely imaginary and that of God as great in every way and also existent.  To illustrate this idea of God as an idea, let us paraphrase Anselm's argument to rightly emphasize that we are dealing not with the reality of God but rather the conception thereof:

    (A1'') We may form the conception of God.
    (A2'') Existence in reality is greater than existence in thought alone.
    (A3'') If the conception of God were to include existence in thought alone, then a conception of God who exists in reality would be greater than the former conception, which would be a contradiction, hence
    (AC'') A rational conception of God must include the idea of existence in reality
    Truly, then, these conceptions of God do contradict one another, and Anselm's argumentation may well be used to demonstrate the logical implausibility of the former idea in favor of the latter.  Thus it may rightfully said that the ontological argument demonstrates that a rational conception of a greatest being must include the idea that the being exists (necessarily and non-contingently, but we'll get to that later), but that is quite irrelevant to the question of whether of not such a being truly does exist.  A correct conception of the idea of God should include existence, but this does not imply belief that such a conception reflects reality.

    These considerations of the conceptual nature of the argument naturally beg the question of validity of defining God as "something greater than which cannot be thought" and attempting to deduce existence from such a definition.  Given that we allow existence as a property indicative of greatness and that we believe that God is the greatest conceivable being, it is clear that we must conclude that there exists a God, but how reasonable is it to argue from such a definition?  Have we not then slipped in existence into our given definition of God, thereby flagrantly begging the question?  To better elucidate the problems in the ontological argument, forego the convoluted ontological argumentation and enumerate the properties of God as given in Anselm's definition: God is defined as that being which is perfectly great in power, knowledge, morality, and existence.  But this is clearly an attempt to define God into existence, completely unacceptable for purposes of argumentation.  One could as easily define anything so as to include existence, and thus demonstrate the existence thereof.

    The ontological argument from necessary existence

    It may rightly be said that the above argument is not the only ontological argument proposed by Anselm in Proslogion.  He goes on to state in chapter three a distinct argument grounded in the idea of necessary existence (something necessarily exists if it cannot not exist), which is later elaborated upon by Descartes.

    Statement of the argument

    From Proslogion:

    In fact, it so undoubtedly exists that it cannot be thought of as not existing. For one can think there exists something that cannot be thought of as not existing, and that would be greater than something which can be thought of as not existing. For if that greater than which cannot be thought can be thought of as not existing, then that greater than which cannot be thought is not that greater than which cannot be thought, which does not make sense. Thus that than which nothing can be thought so undoubtedly exists that it cannot even be thought of as not existing.
    René Descartes also formulated the ontological argument in terms of necessary existence in his Meditations:
    ...For being accustomed in all other things to make a distinction between existence and essence, I easily persuade myself that the existence can be separated from the essence of God, and that we can thus conceive God as not actually existing. But, nevertheless, when I think of it with more attention, I clearly see that existence can no more be separated from the essence of God than can its having its three angles equal to two right angles be separated from the essence of a [rectilinear] triangle, or the idea of a mountain from the idea of a valley; and so there is not any less repugnance to our conceiving a God (that is, a Being supremely perfect) to whom existence is lacking (that is to say, to whom a certain perfection is lacking), than to conceive of a mountain which has no valley...

    While from the fact that I cannot conceive God without existence, it follows that existence is inseparable from Him, and hence that He really exists; not that my thought can bring this to pass, or impose any necessity on things, but, on the contrary, because the necessity which lies in the thing itself, i.e. the necessity of the existence of God determines me to think in this way. For it is not within my power to think of God without existence (that is of a supremely perfect Being devoid of a supreme perfection) though it is in my power to imagine a horse either with wings or without wings.

    The ontological argument from necessary existence was revived in this century by one Norman Malcolm, who wrote of it in an article entitled Anselm's Ontological Arguments.

    Bearing in mind that something exits contingently if it may possibly not exist, whereas something exists necessarily if it cannot possibly not exist; the ontological argument from necessary existence runs something like this:

    (C1) The greatest conceivable being may exist contingently or necessarily
    (C2) Necessary existence is greater than contingent existence
    (C3) If God were to exist contingently, then a God who exists necessarily would be greater, which would be a contradiction, hence
    (CC) God exists in reality
    Cartesian Absurdities

    The most obvious problem with such an argument is that we could easily tag necessary existence onto any concept and thus define it into existence.  I may formulate the concept of the necessarily existent $100 bill in my left pocket, and conclude that such an object must therefore verily exist, and I am surprised and disappointed when I try to pick up the tab at the local bistro and discover to my chagrin that the money is not there.

    Many object that such a bill does not and cannot contain necessary existence within itself as a concept, only God may do that.  Certainly, the idea of God as greatest conceivable being is a concept which must be ascribed with necessary existence, but cannot other concepts also be defined so as to include necessarily existence?  Perhaps, perhaps not.  The objection is duly noted, but the point remains  that necessary existence was included within our definition of God and it is from that which we are attempting to argue.

    Analysis of the Argument

    A noteworthy problem with the ontological argument from necessity is that a greatest conceivable being would theoretically have the property of omnipotence, that is, that ability to do anything logically possible, including the ability to annihilate itself.  This of course conflicts with the idea of necessary existence, and perhaps indicates an inherent incoherence in the concept of a greatest conceivable being.

    The various arguments from necessary existence ultimately suffer from the same fatal flaw as the original, it is quite invalid to deduce existence from our definition of a given concept.  Stating that a supreme being as defined must be conceived as necessarily existent is merely stating that the definition of God given includes the concept of necessary existence, which tells us nothing of its existence in actuality.  Should the concept of necessary existence may be demonstrably applicable to only one specific concept, that of the prime mover (here we tread into the domain of the cosmological arguments), even then we cannot rightly argue from this concept to assert that it must correspond to reality.

    This may be made more evident by once again elucidating the conceptual nature of the ontological argument:

    (C1') The greatest concievable being may be conceived as existing contingently or necessarily
    (C2') Necessary existence is greater than contingent existence
    (C3') If God were to be conceived as existing contingently, then a God who is conceived as existing necessarily would be greater, which would be a contradiction, hence
    (CC') God must be conceived as existing in reality
    Again, the ontological argument has demonstrated something of the proper conception of a greatest conceivable being, but nothing of the nature of reality.

    Modal reformulation of the argument

    Following Norman Malcom's renewal of interest in the ontological argument, particularly the arguments from necessity, Charles Hartshorne took the argument from necessary existence a step further by reformulating it in terms of modal logic.

    Statement of the argument

    Hartshorne's version of the ontological argument may be summarized thusly:

    (H1) If God exists, then God's existence must be necessary.
    (H2) If God does not exist, then God's non-existence must be necessary (i.e., God's existence is impossible.)
    (H3) Either God exists or God does not exist. (excluded middle)
    (H4) God's existence is either necessary or impossible. (from 1,2,3)
    (H5) God's existence is not impossible (i.e., it is possible).
    (HC) Therefore God's existence is necessary.
    Hartshornian Absurdities

    Just as the earlier versions of the argument, so this final reformulation of the argument is also subject to immediate and intuitive modification so as to demonstrate its absurdity.  Hartshorne's fifth premise may be changed so as to read

    (H5') God's non-existence is not impossible (i.e., it is possible that God does not exist).
    from which we must then conclude that God's existence is in fact impossible.

    We then have a situation such that assuming that there may be a God leads one to the inescapable conclusion that there must be a God, whereas assuming that there may not be a God leads one to the inescapable conclusion that there must not be a God.  This is a direct consequence of the modal assertion that God is either impossible or necessary.  This premise is not beyond question, as we shall see.

    This ontological argument is also subject to parody.  Consider the necessary law of inverse gravity (NLIG), defined as an ontologically necessary law of physics, identical to the law of gravity as we know it, but reversed in direction.  Objects are repelled rather than attracted.  Now, replace God in Hartshorne's modal argument with the NLIG.

    (H1') If NLIG exists, then NLIG's existence must be necessary.
    (H2') If NLIG does not exist, then NLIG's non-existence must be necessary (i.e., God's existence is impossible.)
    (H3') Either NLIG exists or NLIG does not exist. (excluded middle)
    (H4') NLIG's existence is either necessary or impossible. (from 1,2,3)
    (H5') NLIG's existence is not impossible (i.e., it is possible).
    (HC') Therefore the NLIG's existence is necessary.
    So, we must live in a universe in which gravity works backwards, which is evidently not the case.

    Analysis of the Argument

    H1 is to be considered sound if we accept the above argumentation that the greatest conceivable being must exist necessarily if indeed it does exist.

    The truth of premise H2 is quite questionable.  It seems that if the concept of god does not correspond to reality, it is not therefore true that the concept must therefore be considered logically impossible.  This seems to be an unsound premise in the argument.

    The fundamental problem of an invalid inference from concept to reality is evident in this argument as well, we cannot derive from the necessarily existence inherent in a given concept that the concept truly exists.  Taking into account that we are still arguing from a concept, the argument is truly:

    (H1'') If the concept of God corresponds to reality, then God's existence must be necessary.
    (H2'') If the concept of God does not correspond to reality, then the concept of God must be logically contradictory.
    (H3'') Either God exists or God does not exist. (excluded middle)
    (H4'') The concept of God's existence must therefore be thought of as either necessary or impossible. (from 1,2,3)
    (H5'') The concept of God existence is not logically impossible (i.e., it is possible).
    (HC'') Therefore the concept of God's must include necessary existence.
    This parallels the original Anselmian argument in that it demonstrates that a rational concept of greatest conceivable being must necessarily include existence, but fails to tell us anything of actual existence.

    Plantinga's possible worlds argument

    Modern American apologist-philosopher Alvin Plantinga radically reformulated the modal argument in terms of possible worlds theory to avoid what he sees as a few methodological problems.

    Statement of the argument

    Plantinga's argument is as follows:

    (P1) A thing has maximal greatness if and only if it has maximal excellence in every possible world.
    (P2) Whatever has maximal excellence is omniscient, omnipotent and morally perfect.
    (P3) There is a possible world in which the property of possessing maximal greatness is exemplified.
    (P4) The property of possessing maximal greatness is exemplified in every possible world.
    (P5) If maximal greatness is exemplified in every world, then it is exemplified in this world.
    (PC) There exists (in this world) a being who is omniscient, omnipotent, and morally perfect (i.e., God).
    Plantingan Absurdities

    Plantinga's final version of the ontological "argument triumphant" suffers from effectively the same interesting defect as the modal argument above.  Consider a modified version of premise (P3):

    (P3') There is a possible world in which maximal greatness is not instantiated.
    Following Plantinga's logic, if maximal greatness is instantiated in some possible world then it must be instantiated in all possible worlds, and hence if it is not instantiated in some possible world then it cannot have been instantiated in any possible world.

    Analysis of the Argument

    Again, we have an argument from the conception of a being with maximal greatness to the reality of such a being.  In premise P3, Plantinga is effectively claiming that God's existence is indeed logically conceivable, and therefore must be actually realized.

    It is difficult but perhaps not entirely futile to recast Plantinga's argument back into terms of modality and conception:

    (P1'') The concept of maximally great being necessarily includes the idea of maximal excellence.
    (P2'') The concept of maximal excellence includes omniscience, omnipotence and moral perfection.
    (P3'') The concept of maximal greatness is logically possible.
    (P4'') The concept of maximal greatness is logically necessary.
    (P5'') The logical necessity of this concept implies the actuality of this concept.
    (PC'') There exists (in this world) a being instantiating the concept of maximal greatness.
    It seems that Plantinga has made the crucial false step from conception to reality in premise five, his 'new' argument fails in precisely the same way as its predecessors.

    Conclusion

    All of the ontological arguments are fundamentally flawed in that they attempt to argue from definition to reality.  Kant perhaps put it best when he wrote, "There is already a contradiction in introducing the concept of existence -- no matter under what title it may be disguised -- into the concept of a thing which we profess to be thinking of solely in reference to its possibility.  If that be allowed as legitimate, a seeming victory has been won; but in actual fact nothing at all had been said: the assertion is a mere tautology."