Greater than which nothing can be conceived




















It might be the case that, other things being equal, a set of dishes that is indestructible in this world is greater than a set of dishes that is not indestructible in this world. But it is very hard to see how transworld indestructibility adds anything to the greatness of a set of dishes that is indestructible in this world.

From our perspective, there is simply nothing to be gained by adding transworld indestructibility to a set of dishes that is actually indestructible. And the same seems to be true of God. Suppose that an omniscient, omnipotent, omnibenevolent, eternal and hence, so to speak, indestructible , personal God exists in this world but not in some other worlds.

It is very hard to make sense of the claim that such a God is deficient in some relevant respect. It is simply unclear how existence in these other worlds that bear no resemblance to this one would make God greater and hence more worthy of worship.

From our perspective, necessary existence adds nothing in value to eternal existence. There have been several attempts to render the persuasive force of the ontological argument more transparent by recasting it using the logical structures of contemporary modal logic. One influential attempts to ground the ontological argument in the notion of God as an unlimited being. As Malcolm describes this idea:. God is usually conceived of as an unlimited being.

He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing. Lack of moisture can prevent trees from existing in a certain region of the earth. But it would be contrary to the concept of God as an unlimited being to suppose that anything … could prevent Him from existing.

The unlimited character of God, then, entails that his existence is different from ours in this respect: while our existence depends causally on the existence of other beings e. Here is his argument for this important claim. A very similar argument can be given for the claim that an unlimited being exists in every logically possible world if it exists in some possible world W ; the details are left for the interested reader.

Since there are only two possibilities with respect to W and one entails the impossibility of an unlimited being and the other entails the necessity of an unlimited being, it follows that the existence of an unlimited being is either logically necessary or logically impossible. The existence of an unlimited being is logically impossible only if the concept of an unlimited being is self-contradictory.

Rather, as we saw above, Malcolm attempts to argue that there are only two possibilities with respect to the existence of an unlimited being: either it is necessary or it is impossible. And notice that his argument does not turn in any way on characterizing the property necessary existence as making something that instantiates that property better than it would be without it.

In particular, Premise 2 is not obviously correct. To defend this further claim, one needs to give an argument that the notion of a contingent eternal being is self-contradictory. Indeed, there are plenty of beings that will probably never exist in this world that exist in other logically possible worlds, like unicorns.

Plantinga begins by defining two properties, the property of maximal greatness and the property of maximal excellence, as follows:. Accordingly, the trick is to show that a maximally great being exists in some world W because it immediately follows from this claim that such a being exists in every world, including our own. There is no logically possible world in which a square circle exists given the relevant concepts because the property of being square is inconsistent with the property of being circular.

Here is a schematic representation of the argument:. The S5 system of modal logic includes an axiom that looks suspiciously similar to Premise To see that this criticism is unfounded, it suffices to make two observations. First, notice that the following propositions are not logically equivalent:.

Second, notice that the argument for Premise 4 does not make any reference to the claim that all propositions bear their modal status necessarily. Plantinga simply builds necessary existence into the very notion of maximal greatness.

Since the notion of maximal greatness, in contrast to the notion of an unlimited being as Malcolm defines it, is conceived in terms that straightforwardly entail existence in every logically possible world and hence eternal existence in every logically possible world , there are no worries about whether maximal greatness, in contrast to unlimitedness, entails something stronger than eternal existence. As is readily evident, each version of the ontological argument rests on the assumption that the concept of God, as it is described in the argument, is self-consistent.

Broad expresses it:. Let us suppose, e. Then there would be three possible beings, namely, one which combines X and Y , one which combines Y and Z , and one which combines Z and X , each of which would be such that nothing … superior to it is logically possible.

For the only kind of being which would be … superior to any of these would be one which had all three properties, X , Y , and Z ; and, by hypothesis, this combination is logically impossible. Thus, if there are two great-making characteristics essential to the classically theistic notion of an all-perfect God that are logically incompatible, it follows that this notion is incoherent. Here it is important to note that all versions of the ontological argument assume that God is simultaneously omnipotent, omniscient, and morally perfect.

As we have seen, Plantinga expressly defines maximal excellence in such terms. There are a number of plausible arguments for thinking that even this restricted set of properties is logically inconsistent.

For example, moral perfection is thought to entail being both perfectly merciful and perfectly just. But these two properties seem to contradict each other. To be perfectly just is always to give every person exactly what she deserves. But to be perfectly merciful is to give at least some persons less punishment than they deserve.

If so, then a being cannot be perfectly just and perfectly merciful. Thus, if moral perfection entails, as seems reasonable, being perfectly just and merciful, then the concept of moral perfection is inconsistent. The problem of divine foreknowledge can also be seen as denying that omniscience, omnipotence, and moral perfection constitute a coherent set.

Roughly put, the problem of divine foreknowledge is as follows. If God is omniscient, then God knows what every person will do at every moment t. To say that a person p has free will is to say that there is at least one moment t at which p does A but could have done other than A. But if a person p who does A at t has the ability to do other than A at t , then it follows that p has the ability to bring it about that an omniscient God has a false belief — and this is clearly impossible.

On this line of analysis, then, it follows that it is logically impossible for a being to simultaneously instantiate omniscience and omnipotence. Omnipotence entails the power to create free beings, but omniscience rules out the possibility that such beings exist. Thus, a being that is omniscient lacks the ability to create free beings and is hence not omnipotent.

Conversely, a being that is omnipotent has the power to create free beings and hence does not know what such beings would do if they existed. Thus, the argument concludes that omniscience and omnipotence are logically incompatible.

If this is correct, then all versions of the ontological argument fail. Kenneth Einar Himma Email: himma spu. Introduction: The Non-Empirical Nature of the Ontological Arguments It is worth reflecting for a moment on what a remarkable and beautiful! The Classic Version of the Ontological Argument a. The Argument Described St. Anselm , Archbishop of Canterbury , is the originator of the ontological argument, which he describes in the Proslogium as follows: [Even a] fool, when he hears of … a being than which nothing greater can be conceived … understands what he hears, and what he understands is in his understanding.

The argument in this difficult passage can accurately be summarized in standard form: It is a conceptual truth or, so to speak, true by definition that God is a being than which none greater can be imagined that is, the greatest possible being that can be imagined.

God exists as an idea in the mind. 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.

It is conceivable that God exists in reality. It is conceivable that there is a being greater than God. Follows from 2, 3, and 4 C. It is conceivable that there is a being greater than that than which nothing greater can be conceived. Follows from 1 and 5. It is conceivable that Bob be taller than he is.

Premise to be reduced to absurdity. Follows from 1. Follows from 2. Follows from 2, 3, and 4. Focus on the case of ontological arguments for the conclusion that God exists. Theists and non-theists alike can agree that there is spatio-temporal, or causal, or nomic, or modal structure to the world the basis for cosmological arguments ; and that there are certain kinds of complexity of organisation, structure and function in the world the basis for teleological arguments ; and so on.

But theists and non-theists are in dispute about whether there are perfect beings, or beings than which no greater can be conceived, or … ; thus, theists and non-theists are in dispute about the indirect subject matter of the premises of ontological arguments.

Of course, the premises of ontological arguments often do not deal directly with perfect beings, beings than which no greater can be conceived, etc. However, the basic point remains: ontological arguments require the use of vocabulary which non-theists should certainly find problematic when it is used in ontologically committing contexts i. Note that this characterisation does not beg the question against the possibility of the construction of a successful ontological argument—i.

For it may be that the vocabulary in question only gets used in premises under the protection of prophylactic operators which ward off the unwanted commitments. Of course, there will then be questions about whether the resulting arguments can possibly be valid—how could the commitments turn up in the conclusion if they are not there in the premises?

Before we turn to assessment of ontological arguments, we need to get clear about what the proper intended goals of ontological arguments can be. Suppose we think of arguments as having advocates and targets: when an advocate presents an argument to a target, the goal of the advocate is to bring about some change in the target. What might be the targets of ontological arguments, and what might be the changes that advocates of these arguments aim to bring about in those targets?

In the coming discussion, it will be supposed that the targets are atheists and agnostics, and that the goal is to turn them into theists. Suppose that an advocate presents an ontological argument to a target.

What conditions must that arguments satisfy if it is fit for its intended purpose? A plausible suggestion is that, minimally, it should make the targets recognise that they have good reason to accept the conclusion of the argument that they did not recognise that they have prior to the presentation of the argument. Adopting this plausible suggestion provides the following criterion: a successful ontological argument is one that should make atheists and agnostics recognise that they have good reason to believe that God exists that they did not recognise that they have prior to the presentation of the argument.

Note that this criterion has a normative dimension: it adverts to what atheists and agnostics should do when presented with the argument. There is an important discussion to be had about whether we should suppose that the targets of ontological arguments are atheists and agnostics, and that the goal is to turn them into theists.

However, it is simply beyond the scope of this entry to pursue that discussion here. Objections to ontological arguments take many forms. Some objections are intended to apply only to particular ontological arguments, or particular forms of ontological arguments; other objections are intended to apply to all ontological arguments.

It is a controversial question whether there are any successful general objections to ontological arguments. One general criticism of ontological arguments which have appeared hitherto is this: none of them is persuasive , i.

Any reading of any ontological argument which has been produced so far which is sufficiently clearly stated to admit of evaluation yields a result which is invalid, or possesses a set of premises which it is clear in advance that no reasonable, reflective, well-informed, etc.

For each of the families of arguments introduced in the earlier taxonomy, we can give general reasons why arguments of that family fall under the general criticism. In what follows, we shall apply these general considerations to the exemplar arguments introduced in section 2. An obvious problem is that claims involving that vocabulary cannot then be non-question-beggingly detached from the scope of that definition. In the example given earlier, the premises license the claim that, as a matter of definition, God possesses the perfection of existence.

But, as just noted, there is no valid inference from this claim to the further claim that God exists. Often, these operators have two readings, one of which can cancel ontological commitment, and the other of which cannot. In our sample argument, the claim, that I conceive of an existent being than which no greater being can be conceived, admits of the two kinds of readings just distinguished.

On the one hand, on the reading which gives cancellation, the inference to the conclusion that there is a being than which no greater can be conceived is plainly invalid.

On the other hand, on the reading in which there is no cancellation, it is clear that this claim is one which no reasonable, etc. Suppose that we agree to think about possibility and necessity in terms of possible worlds: a claim is possibly true just in case it is true in at least one possible world; a claim is necessarily true just in case it is true in every possible world; and a claim is contingent just in case it is true in some possible worlds and false in others. Some theists hold that God is a necessarily existent being, i.

The sample argument consists, in effect, of two premises:. A minimally rational non-theist cannot accept both of these premises — they entail that God exists in every possible world whereas a minimally rational non-theist maintains that there is at least one possible world in which God does not exist.

Given that a minimally rational non-theist says that there is at least one possible world in which God does not exist, such a non-theist can offer a parallel counterargument with the following two premises:. These premises entail that God exists in no possible world, and hence that God does not exist in the actual world.

Considered together, the argument and the counterargument just mentioned plainly do not give anyone a reason to prefer theism to non-theism, and nor do they give anyone a reason to prefer non-theism to theism. Naive Meinongians will suppose that if F is instantiated with any property, then the result is true and, quite likely, necessary, analytic and a priori.

So, for example, the round square is round; the bald current King of France is bald; and so on. Choice of vocabulary here is controversial: Let us suppose for the sake of example that the right thing to say is that the former things exist and the latter do not. The point is that non-theists are not prepared to include god s in the former group of objects—and hence will be unpersuaded by any argument which tries to use whatever vocabulary is used to discriminate between the two classes as the basis for an argument that god s belong to the former group.

Cognoscenti will recognise that the crucial point is that Meinongian ontological arguments fail to respect the distinction between nuclear assumptible, characterising properties and non-nuclear non-assumptible, non-characterising properties. It should, of course, be noted that neither Meinong, nor any of his well-known modern supporters—e. Terence Parsons, Richard Sylvan—ever endorses a Meinongian ontological argument; and it should also be noted that most motivate the distinction between nuclear and non-nuclear properties in part by a need to avoid Meinongian ontological arguments.

It should not be surprising that they fail. But, however the account goes, non-theists will insist that expressions which purport to refer to god s should be given exactly the same kind of treatment. However, even those who accept principles of unrestricted composition—i. If it is impossible that God exists — as all who deny that God exists suppose, on the further assumption that, were God to exist, God would exist of necessity — then it cannot be true both that the God-properties are closed under entailment and that there are properties that are not God-properties.

Those who take themselves to have good independent reason to deny that there are any gods will take themselves to have good independent reason to deny that there are God-properties that form a non-trivial collection that is closed under entailment.

Even if the forgoing analyses are correct, it is important to note that no argument has been given for the conclusion that no ontological argument can be successful. Even if all of the kinds of arguments produced to date are pretty clearly unsuccessful—i. Perhaps it is worth adding here that there is fairly widespread consensus, even amongst theists, that no known ontological arguments for the existence of God are persuasive. Most categories of ontological argument have some actual defenders; but none has a large following.

Many other objections to some ontological arguments have been proposed. All of the following have been alleged to be the key to the explanation of the failure of at least some ontological arguments: 1 existence is not a predicate see, e. There are many things to say about these objections: the most important point is that almost all of them require far more controversial assumptions than non-theists require in order to be able to reject ontological arguments with good conscience.

Trying to support most of these claims merely in order to beat up on ontological arguments is like using a steamroller to crack a nut in circumstances in which one is unsure that one can get the steamroller to move! Of course, all of the above discussion is directed merely to the claim that ontological arguments are not dialectically efficacious—i.

It might be wondered whether there is some other use which ontological arguments have—e. This seems unlikely. After all, at best these arguments show that certain sets of sentences beliefs, etc.

But the arguments themselves say nothing about the reasonableness of accepting the premisses. So the arguments themselves say nothing about the unconditional reasonableness of accepting the conclusions of these arguments.

Those who are disposed to think that theism is irrational need find nothing in ontological arguments to make them change their minds and those who are disposed to think that theism is true should take no comfort from them either. Positive ontological arguments—i.

For many positive ontological arguments, there are parodies which purport to establish the non-existence of god s ; and for many positive ontological arguments there are lots usually a large infinity! Here are some modest examples:. Hence God does not exist. If such a being does not exist, then we can conceive of a greater being—namely, one exactly like it which does exist.

But I cannot conceive of a being which is greater in this way. Hence, a being than which no greater can be conceived except that it only ever creates n universes exists. Hence it is not possible that God exists. Hence, the existent perfect being who creates exactly n universes is existent.

Hence the perfect being who creates exactly n universes exists. There are many kinds of parodies of Ontological Arguments. The aim is to construct arguments which non-theists can reasonably claim to have no more reason to accept than the original Ontological Arguments themselves. Of course, theists may well be able to hold that the originals are sound, and the parodies not—but that is an entirely unrelated issue. There are many parodic discussions of Ontological Arguments in the literature.

A relatively recent addition to the genre is described in Grey , though the date of its construction is uncertain.

This parody—at least in its current state—is inferior to other parodies in the literature, including the early parodies of Gaunilo and Caterus. Surely it is quite easy to imagine even more marvellous achievements—e.

These arguments have been discussed, annotated and amended by various leading logicians: the upshot is a family of arguments with impeccable logical credentials. Interested readers are referred to Sobel , Anderson , Adams b, and Hazen for the history of these arguments, and for the scholarly annotations and emendations.

Here, we give a brief presentation of the version of the argument which is developed by Anderson, and then make some comments on that version. This discussion follows the presentation and discussion in Oppy , Definition 2: A is an essence of x if and only if for every property B , x has B necessarily if and only if A entails B.

Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified. Axiom 2: Any property entailed by—i. Axiom 6: For any property P , if P is positive, then being necessarily P is positive. Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.

Given a sufficiently generous conception of properties, and granted the acceptability of the underlying modal logic, the listed theorems do follow from the axioms. This point was argued in detail by Dana Scott, in lecture notes which circulated for many years and which were transcribed in Sobel and published in Sobel It is also made by Sobel, Anderson, and Adams.

So, criticisms of the argument are bound to focus on the axioms, or on the other assumptions which are required in order to construct the proof. Some philosophers have denied the acceptability of the underlying modal logic. And some philosophers have rejected generous conceptions of properties in favour of sparse conceptions according to which only some predicates express properties. But suppose that we adopt neither of these avenues of potential criticism of the proof.

What else might we say against it? At most, the various axioms which involve this concept can be taken to provide a partial implicit definition. I is the property of having as essential properties just those properties which are in the set. G 1 , G 2 , … are further properties, of which we require at least two. The creatures are distinct because each has a different set of essential properties.

Then consider the following argument:. Under suitable assumptions about the nature of accessibility relations between possible worlds, this argument is valid: from it is possible that it is necessary that p , one can infer that it is necessary that p. Setting aside the possibility that one might challenge this widely accepted modal principle, it seems that opponents of the argument are bound to challenge the acceptability of the premise.

They cannot, perhaps, be said to prove or establish their conclusion. So God exists. So God does not exist. While there is room for dispute about exactly why all of this is so, it is plausible to say that, in each case, any even minimally rational person who has doubts about the claimed status of the conclusion of the argument will have exactly the same doubts about the claimed status of the premise.

Some commentators deny that St. Anselm tried to put forward any proofs of the existence of God. Even among commentators who agree that St. Anselm intended to prove the existence of God, there is disagreement about where the proof is located. Some commentators claim that the main proof is in Proslogion II , and that the rest of the work draws out corollaries of that proof see, e. Other commentators claim that the main proof is in Prologion III , and that the proof in Proslogion II is merely an inferior first attempt see, e.

In what follows, we ignore this aspect of the controversy about the Proslogion. Instead, we focus just on the question of the analysis of the material in Proslogion II on the assumption that there is an independent argument for the existence of God which is given therein. Here is one translation of the crucial part of Proslogion II due to William Mann , —1 ; alternative translations can be found in Barnes , Campbell , Charlesworth , and elsewhere :.

There have been many ingenious attempts to find an argument which can be expressed in modern logical formalism, which is logically valid, and which might plausibly be claimed to be the argument which is expressed in this passage.

To take a few prime examples, Adams , Barnes and Oppenheimer and Zalta have all produced formally valid analyses of the argument in this passage. We begin with a brief presentation of each of these analyses, preceded by a presentation of the formulation of the argument given by Plantinga , and including a presentation of some of the formulations of Lewis Chambers works with the analysis of Adams From 1 and 2.

It is false that a being greater than God can be conceived. Hence, it is false that God exists in the understanding but not in reality.

Each thing which exists in reality is greater than any thing which exists only in the understanding. If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. Hence the being than which no greater can be conceived exists in reality. From 1 - 6 , by a complex series of steps here omitted.

From 1, 2, 3. For any understandable being x , there is a world w such that x exists in w. For any understandable being x , and for any worlds w and v , if x exists in w , but x does not exist in v , then the greatness of x in w exceeds the greatness of x in v. There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.

Hence There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. From 1 - 3. Hence There is in the understanding a unique thing than which there is no greater. Hence There is in the understanding something which is the thing than which there is no greater. From 2 , by a theorem about descriptions.

Hence There is in the understanding nothing which is greater than the thing than which there is no greater. From 3 , by another theorem about descriptions. If that thing than which there is no greater does not exist in reality , then there is in the understanding something which is greater than that thing than which there is no greater.

Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, it won't be considered further here. Considered as interpretations of the argument presented in the Proslogion , these formulations are subject to various kinds of criticisms. And that is surely a bad result. Second , the Meinongian interpretations of Barnes , Adams and Oppenheimer and Zalta produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.

Consider, for example, the case of Oppenheimer and Zalta. It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases?

But, then, mark the consequences. So, by the first claim, there is at least one existent perfect being in the understanding. And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being. This argument gives Anselm everything that he wants, and very much more briefly. The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived.



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