Necessary Existence

 

A necessary being is defined as something whose nonexistence is impossible. You and I are contingent beings, meaning that it is possible for us to exist, but also possible for us not to exist. But a necessary being was never born, and will never die. There is never a time or place in which it does not exist. No external force caused its existence, and no external force can cause its destruction; it is self-causing. Many theologians believe that God would be a necessary being.

During the Middle Ages, beliefs about God were greatly influenced by Plato and Aristotle, and one of the results of this is the belief that God is a being of pure form. It was thought that the potential for change came from being composed of matter, because it is always possible for matter that is currently in one form to become corrupted, and to take on a new form. Since God is thought to be incorruptible and unchanging, they reasoned that this meant that God must be a being of pure form with no material substance at all. This would mean that God has no potentiality for change, and is fully actualized in all ways. A contingent being composed of matter may have accidental properties (a property is an attribute, quality, or characteristic) that it has merely by chance, such as the fact that I was born an American citizen, but all properties of a fully actualized being would be necessary, essential, and permanent. So, if God has the property of existence at all, it is thought to be necessary rather than contingent existence.

Another argument for this view is that a necessary being would seem to be greater than a contingent being. It would have greater permanence, existing eternally, and its existence would not be dependent upon anything else. Charles Hartshorne and Norman Malcolm have argued that there are actually two distinct versions of Anselm’s ontological argument. The more well-known one relies upon the idea that something which exists is greater than something that does not. But another formulation indicates that Anselm meant that something which has necessary existence would be greater than something with contingent existence:

And it so truly exists that it cannot be conceived not to exist. For it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if ‘that than which nothing greater can be conceived’ can be conceived not to exist, it is not that than which nothing greater can be conceived. But this is a contradiction. So truly, therefore, is there something than which nothing greater can be conceived, that it cannot even be conceived not to exist. And this being thou art, O Lord, our God.[1]

Anselm first says that it is possible to conceive of something with necessary existence. A being whose nonexistence is impossible would be greater than one whose nonexistence is possible; thus, if God is ‘that than which nothing greater can be conceived’ then God must be a necessary being. Anselm believes that it is impossible to even coherently conceive of a necessary being as not existing because it would be self-contradictory to say that something whose nonexistence is impossible does not exist. Norman Malcolm believes this as well, and defends this version of the argument. But is this really a self-contradictory position? To answer that, some background information is needed concerning analytic and synthetic propositions.

Analytic and Synthetic Propositions

An analytic proposition is one that can be known a priori, which means prior to, or without experience. Definitions are a good example. You know that the proposition ‘A bachelor is an unmarried man’ is true merely by knowing what the term ‘bachelor’ means. You do not need any personal experience with bachelors, nor do you need your five senses in order to verify that the claim is true. Now it could be true that we have acquired our understanding of the term at least partially from experience, but nevertheless, it can still be considered a priori if, once you have acquired a knowledge of the concept, you can know the truth or falsity of the claim merely from the concept.

Synthetic propositions are those that are not true or false by definition. There is nothing about them that would tell us, simply from an analysis of the concept, whether the claim is true or false, so a posteriori knowledge, or experience gained through the senses, is required. Sometimes the testimony of others can also be used as evidence for a synthetic claim, based upon what their senses have told them. ‘It is raining outside’ is a good example of a synthetic proposition. If eight people enter the room and say that it is raining outside, and all of them were soaking wet when they came in, that is pretty good evidence that the claim is true. An a posteriori claim is never known with one hundred percent certainty, because our senses could always be mistaken. Yet most of our knowledge is based upon experience. In most cases, we simply have to settle for a high degree of probability.

An existential claim for any contingent thing would obviously have to be synthetic. Some think, however, that since a necessary being exists by definition, the claim that it exists would be an analytic proposition. This is a key feature of ontological arguments: each one seeks, in various ways, to prove that God exists merely through a careful analysis of the concept of God. The idea is that just as one knows that ‘A bachelor is an unmarried man’ simply by knowing what a bachelor is, one could also know that ‘A necessary being exists’ simply by understanding what a necessary being is.

If all of this were true, that would mean that the proposition ‘God exists’ is true by definition, and cannot possibly be false. Most of us would not have the intuition that this is so. However, those who defend this position would tell you that this is simply because we do not understand the concept of God very well. Everyone understands what the term ‘bachelor’ means, so they have no trouble understanding why a bachelor cannot be married. But few truly understand God, so they do not fully comprehend the logical implications of what kind of being God would have to be; if they did, they would understand that the definition itself entails existence. This would mean that the atheist’s position is similar to that of a person who thinks that a triangle can have four angles because they do not understand that ‘tri’ means three. It was my understanding that Eleonore Stump took a position roughly similar to this (though she did not explain it in this way) in a class lecture during a course I took from her some years ago. She claimed that God’s ‘essence is existence’, so to say that God does not exist is self-contradictory.

Objections

I have three main objections to these arguments for a necessary being: 1) It is not correct to consider any claim of actual existence an analytic proposition. 2) These arguments rely upon circular reasoning. And 3) such arguments make an unwarranted existential assumption. The last two are essentially the same objection, just explained in a different way.

It is wrong to think that God’s existence can be known a priori. One can use analytic reasoning to show that something does not exist, such as a ‘square-circle’, because all that is required for that is to show that the definitions are contradictory. But a claim that something does exist is a different matter. The supposed self-contradiction in saying that a necessary being does not exist is only true in the trivial sense that it contradicts the concept of necessary existence. This means nothing unless that theoretical concept corresponds to an actual object in real life, and there is no way to verify that part of the claim a priori. Analytic reasoning only tells us about the relations of ideas to one another. All that could ever be demonstrated a priori is a hypothetical proof based upon definitions that may or may not correspond with reality. Any claim which asserts that an object exists is a synthetic proposition that requires verification.

The fact that there is even a debate about whether God exists implies that it is not an analytic claim. There are no grand philosophical treatises on whether a bachelor is an unmarried man; the truth of the claim is so immediately obvious that there is no need. A true analytic proof would be self-evident. Now I realize that the claim is that it would be self-evident if everybody just understood the subject of God well enough to understand the implications, but this is just not true. Nearly everyone understands the concept of necessary existence, it is just that many of them do not believe that there is anything that has necessary existence. This confusion of a synthetic claim for an analytic one leads to pseudo-contradictions that masquerade as real ones. For example, here is a quote from Norman Malcolm:

So if God exists His existence is necessary. Thus, God’s existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists.[2]

This is a false dilemma. Malcolm recognizes only two available options when in reality there are more. You do not need to prove that the concept of God is self-contradictory or logically impossible in order to reject the conclusion, all that you have to say is that the claim that there is a God is false, or at least that this argument does not provide enough evidence to prove that there is one. I assume that he thinks this is not a viable option because he believes it would be like saying ‘a necessary existent does not exist’ which is clearly self-contradictory. But the definition is not the part of the claim that is being rejected. In saying that the claim is false, I am not misunderstanding or contradicting the concept of necessary existence, I am asserting that nothing fits into that category, or, in other words, there is not a real object whose type of existence is necessary existence. It should be understood as a truth-functional claim like, ‘It is false that there is such a thing as a necessary existent’ which, of course, is not self-contradictory. It does not follow from the definition of a necessary being that there is a necessary being.

The problem with trying to prove that something exists only from its definition is that we cannot confirm whether that definition refers to a real object or merely to a fictional concept. It is tautological that a bachelor is unmarried, that a unicorn has one horn, and that a necessary being exists, but a tautology does not have to refer to any real object. Nothing about stating a theoretical exposition of the kind of properties an entity would have, if it existed, commits one to saying that it does, in fact, exist. A fictional entity does not have any actual properties, necessary or otherwise. One cannot reason from the entity’s proposed, potentially hypothetical properties to prove that the entity exists without begging the question.[3] It is not necessarily circular to make the claim that there could be something with necessary existence, the problem is reasoning from the purported necessary existence of the being, a claim that has not yet been verified, to prove that there is a being.

Since there is some uncertainty as to whether the term ‘necessary being’ refers to a real object, with actual properties, or to a fictional concept with only hypothetical properties, all that we can really say is ‘If there is such a thing as a necessary being, then one of its essential properties would be existence’. Stating the claim as a conditional keeps us from making an unwarranted existential assumption. We must be careful not conflate the definition of necessary existence with the claim that there is something which actually has that property.

Kant’s Argument

When I worked out these objections, I thought that they were entirely original with me. But then, while working on an essay about Anselm’s more well-known ontological argument, I was looking up Immanuel Kant’s famous ‘existence is not a predicate’ objection, and came across a section in which he discusses necessary existence in more general terms. I was amazed at how similar his objections were to my own. It just goes to show that whenever you think that you have come up with a really unique, original idea, you just have to do a little reading and you will usually find that somebody has beaten you to it by a few hundred years or so. Oh well. I can at least explain the point more clearly so that it is better understood.

Kant uses the terms ‘subject’ and ‘predicate’ extensively. Finding the subject and predicate of a proposition is kind of like finding the subject and verb of a sentence in English grammar, except even easier. The subject term comes first, and is what the proposition is about. The predicate is what is said about the subject. For example, in ‘Some cats are quick’, ‘cats’ is the subject term, ‘quick’ is the predicate term. Or, if you said ‘A necessary being exists’, ‘necessary being’ is the subject term, and ‘exists’ (or things that exist) would be the predicate term. Now see if you can spot the similarities between what I argued for above and what Kant says here:

Every geometrical proposition-a triangle has three angles-it was said, is absolutely necessary; and thus people talked of an object which lay out of the sphere of our understanding as if it were perfectly plain what the conception of such a being meant.

All the examples adduced have been drawn, without exception, from judgments and not from things. But the unconditioned necessity of a judgment does not form the absolute necessity of a thing. On the contrary, the absolute necessity of a judgment is only a conditioned necessity of a thing, or of the predicate in a judgment. The proposition above-mentioned, does not enounce that three angles necessarily exist, but, upon condition that a triangle exists, three angles must necessarily exist-in it. And thus this logical necessity has been the source of the greatest delusions. Having formed an a priori conception of a thing, the content of which was made to embrace existence, we believed ourselves safe in concluding that, because existence belongs necessarily to the object of the conception (that is, under the condition of my positing this thing as given), the existence of the thing is also posited necessarily, and that it is therefore absolutely necessary-merely because its existence has been cogitated in the conception.

If, in an identical judgment, I annihilate the predicate in thought, and retain the subject, a contradiction is the result; and hence I say, the former belongs necessarily to the latter. But if I suppress both subject and predicate in thought, no contradiction arises; for there is nothing at all, and therefore no means of forming a contradiction. To suppose the existence of a triangle and not that of its three angles, is self-contradictory; but to suppose the nonexistence of both triangle and angles is perfectly admissible. And so it is with the conception of an absolutely necessary being. Annihilate its existence in thought, and you annihilate the thing itself with all its predicates; how then can there be any room for contradiction? Externally, there is nothing to give rise to a contradiction, for a thing cannot be necessary externally; nor internally, for, by the annihilation or suppression of the thing itself, its internal properties are also annihilated. God is omnipotent-that is a necessary judgment. His omnipotence cannot be denied, if the existence of a Deity is posited-the existence, that is, of an infinite being, the two conceptions being identical. But when you say, God does not exist, neither omnipotence nor any other predicate is affirmed; they must all disappear with the subject, and in this judgment there cannot exist the least self-contradiction.

You have thus seen, that when the predicate of a judgment is annihilated in thought along with the subject, no internal contradiction can arise, be the predicate what it may. There is no possibility of evading the conclusion-you find yourself compelled to declare: There are certain subjects which cannot be annihilated in thought. But this is nothing more than saying: There exist subjects which are absolutely necessary-the very hypothesis which you are called upon to establish. For I find myself unable to form the slightest conception of a thing which, when annihilated in thought with all its predicates, leaves behind a contradiction; and contradiction is the only criterion of impossibility, in the sphere of pure a priori conceptions.

Against these general considerations, the justice of which no one can dispute, one argument is adduced, which is regarded as furnishing a satisfactory demonstration from the fact. It is affirmed, that there is one and only one conception, in which the nonbeing or annihilation of the object is self- contradictory, and this is the conception of an ens realissimum [Latin for ‘most real being’]. It possesses, you say, all reality, and you feel yourselves justified in admitting the possibility of such a thing. (This I am willing to grant for the present, although the existence of a conception which is not self-contradictory, is far from being sufficient to prove the possibility of an object.) Now the notion of all reality embraces in it that of existence; the notion of existence lies, therefore, in the conception of this possible thing. If this thing is annihilated in thought, the internal possibility of the thing is also annihilated, which is self-contradictory.

I answer: It is absurd to introduce-under whatever term disguised-into the conception of a thing, which is to be cogitated solely in reference to its possibility, the conception of its existence. If this is admitted, you will have apparently gained the day, but in reality have enounced nothing but a mere tautology. I ask, is the proposition, this or that thing (which I am admitting to be possible) exists, an analytical or a synthetical proposition? If the former, there is no addition made to the subject of your thought by the affirmation of its existence; but then the conception in your minds is identical with the thing itself, or you have supposed the existence of a thing to be possible, and then inferred its existence from its internal possibility-which is but a miserable tautology. The word reality in the conception of the thing, and the word existence in the conception of the predicate, will not help you out of the difficulty. For, supposing you were to term all positing of a thing, reality, you have thereby posited the thing with all its predicates in the conception of the subject and assumed its actual existence, and this you merely repeat in the predicate. But if you confess, as every reasonable person must, that every existential proposition is synthetical, how can it be maintained that the predicate of existence cannot be denied without contradiction-a property which is the characteristic of analytical propositions, alone.

Kant’s point is that necessity is derived from propositions rather than things, and is internal, between subject and predicate. If there is a subject that entails a certain predicate, the predicate is necessary, and the two must be in agreement or there is a contradiction. However, there is no external necessity that would require a subject to be present. He uses a triangle to demonstrate. ‘A triangle has three angles’ will be our proposition. ‘Triangle’ is the subject, ‘having three angles’ is the predicate. If I ‘annihilate’ the predicate in thought but retain the subject, or in other words, if I say that the subject exists, but the predicate does not, this would be contradictory. I cannot coherently do that because the predicate is entailed by the subject necessarily according to how the subject is defined. It would be self-contradictory to say that a ‘triangle’ does not have three angles (or that it has any number other than three). However, if I ‘annihilate’ the subject in thought, then our proposition would say, ‘ A [no subject] has three angles’. It is odd to say that having three angles would be predicated of nothing, and even more so to say that it would necessarily be predicated of nothing. The lesson to be learned from this is that all of the necessity in a proposition disappears if the subject disappears. So rejecting the claim that there is a subject does not result in a contradiction because there would simply be nothing; no subject, no predicate, no proposition, just nothing, because nothing is predicated of nothing. This is true even if ‘exists’ was the necessary predicate before the subject was annihilated.

This argument is similar to my point that the subject could be fictitious, and that if it is, it would only have hypothetical rather than actual properties. However, I think that it works better to say that the entity could be fictitious because it makes the objection more clear, and avoids the pseudo-contradiction that one is often accused of if he says that a necessary being does not exist. Malcolm objects to Kant’s argument in that very way:

I think that Caterus, Kant, and numerous other philosophers have been mistaken in supposing that the proposition “God is a necessary being” (or “God necessarily exists”) is equivalent to the conditional proposition “If God exists then He necessarily exists.” For how do they want the antecedent clause, “If God exists,” to be understood? Clearly they want it to imply that it is possible that God does not exist. The whole point of Kant’s analysis is to try to show that it is possible to “reject the subject.” Let us make this implication explicit in the conditional proposition, so that it reads: “If God exists (and it is possible that He does not) then he necessarily exists.” But now it is apparent, I think, that these philosophers have arrived at a self-contradictory position. I do not mean that this conditional proposition, taken alone is self- contradictory. Their position is self-contradictory in the following way. On the one hand, they agree that the proposition “God necessarily exists” is an a priori truth; Kant implies that it is “absolutely necessary,” and Caterus says that God’s existence is implied by His very name. On the other hand, they think that it is correct to analyze this proposition in such a way that it will entail the proposition “It is possible that God does not exist.” But so far from its being the case that the proposition “God necessarily exists” entails the proposition “It is possible that God does not exist,” it is rather the case that they are incompatible with one another! Can anything be clearer than that the conjunction “God necessarily exists but it is possible that He does not exist” is self-contradictory? . . .

I do not think that Malcolm really understood Kant’s argument for why it is not self-contradictory to reject the subject, as he never really even addressed it. Of course, misunderstanding Kant is no great fault. Anyone who has entire philosophy journals dedicated just to trying to understand what the hell he was saying is not exactly easy to interpret. But Kant’s whole point was that denying the subject is much different than retaining the subject and denying the predicate, which is what Malcolm is doing. Saying that the claim should be a conditional should not be interpreted as ‘If God exists (and it is possible that a necessary existent does not exist) then He necessarily exists’. Rather, it should be thought of as expressing doubt as to whether the claim that there is a subject is factually true, more like this, ‘If there is a necessary being (and it is possible that it is simply a made-up fictional idea) then it would necessarily exist’. This does not reject the subject outright, but it expresses some doubt concerning it, and reminds us that the predicate is only necessary if there is a subject. Malcolm continues:

One conclusion we may draw from our examination of this criticism is (contrary to Kant) there is a lack of symmetry, in an important respect, between the propositions “A triangle has three angles” and “God has necessary existence,” although both are a priori. The former can be expressed in the conditional assertion “If a triangle exists (and it is possible that none does) it has three angles.” The latter cannot be expressed in the corresponding conditional assertion without contradiction.

You can easily express the corresponding conditional assertion without contradiction! Here it is: ‘If there is a God (and it is possible that there is not) then such a being would be a necessary existent’. The only reason that there appears to be a ‘lack of symmetry’ between the two propositions is because Malcolm is conflating the assertion of what kind of properties a necessary being would have, if there is such a thing, with the assertion that there is such a thing.

The Modal Argument

Alvin Plantinga has an interesting ontological argument that he calls ‘the victorious modal version’. The argument makes use of what are called ‘possible worlds’, which can be thought of as alternative states of affairs. The concept is similar to counterfactual history. Historians sometimes imagine what might have happened with the war in Vietnam if Kennedy had not been assassinated, or how things would be different today if the Nazis had gotten the atomic bomb before the United States did, etc. Anything that is not self-contradictory is logically possible, and would be a state of affairs that is represented in at least one possible world.

There is much debate whether possible worlds are 1) real concrete objects, just like the actual world, 2) abstract entities, or 3) fictions. Plantinga believes they are abstract entities. He does not necessarily think that they could be perceived by the senses, but they are real nonetheless. They would exist independently of humans, so they would not be merely an idea. Perhaps they would be similar to how some think of geometric figures, such as a line, or a perfect circle. I think of possible worlds as fictions, similar to the setting of a novel. This is only a very brief, basic introduction to the concept of possible worlds, but it should be enough to make Plantinga’s argument comprehensible. Here it is:

1) There is a possible world in which unsurpassable greatness is exemplified.

2) The proposition a thing has unsurpassable greatness if and only if it has maximal
excellence in every possible world is necessarily true.

3) The proposition whatever has maximal excellence is omnipotent, omniscient, and
morally perfect is necessarily true.

4) Hence, the entity possessing unsurpassable greatness is instantiated in every world, including the actual one.[4]

The first thing I would like to point out is that this argument is not very convincing if you think of possible worlds as fictions. Imagining a fictional possible world, in which there is an imaginary entity of unsurpassable greatness, even considering all of the wonderful hypothetical predicates of excellence that it would have, does nothing to prove that there really is such a thing in the actual world. The argument thus relies heavily upon Plantinga’s interpretation of possible worlds, or upon viewing them as concrete objects just like the actual world.

Imagine that the argument was expressed in normal everyday language rather than possible worlds. It would be saying basically this:

1. It is logically possible that there is something which is unsurpassably great.
2. By definition, if something is unsurpassably great it always exists.
3. Therefore, there must be something which is unsurpassably great.

Formulated in this way, the argument is obviously invalid, and, in fact, quite weak. There are really two questions of possibility and necessity contained in the premises, and the argument conflates them and tries to pass one off for the other. The first premise is about the possibility that there is a subject. The second refers to the necessity of subject and predicate agreement, because the predicate is entailed by the definition of the subject. But this second premise does not provide any support for the claim that there is a subject; the conclusion does not become necessary simply because the predicate would be necessary, if, in fact, there is a subject. Only the first premise supports the conclusion, and all that follows from it is that it is logically possible that the conclusion is true, not necessary that it is.

Plantinga’s argument is more subtle in its shift from one sense of possibility and necessity to another, but it has the same basic structure. Premises 2 and 3 say that ‘unsurpassable greatness’ is a subject that entails maximal excellence in every possible world, which in turn entails instantiation (meaning that there is an actual instance of it) in every world. So the claim that ‘unsurpassable greatness is exemplified’ in premise 1 is really saying that there is a possible world in which something is instantiated in all possible worlds.

The argument could be simplified to say:

1. There is a possible world in which something is instantiated in all possible worlds.
2. Therefore, there must be something which is instantiated in all possible worlds.

Is it possible for this premise to be true? If we say no, then we would need to be able to demonstrate why. It is not self-contradictory, so no matter how remote you think the odds of it being true are, it would have to be true in at least one world. If we acknowledge that the world is possible, that would seem to necessarily lead to this conclusion because it would be self-contradictory for there to be a possible world like this unless there is something which is instantiated in all worlds. The interesting thing, though, is that it is also not self-contradictory to say that there is no such thing as ‘something which is instantiated in all possible worlds’. Defenders of the modal argument will try to claim that it is, but it is not a contradiction in terms, it simply contradicts the claim that there is something that is in all worlds. This creates a paradox. Neither claim is self-contradictory, so there is a world in which each is true, but either there is something that is instantiated in all worlds, or there is not, it cannot be both at the same time. That means that one of those worlds has to contradict the true state of affairs in all worlds (including that one).

The problem is not limited only to this particular claim either. There would be many such results with this form of argument. For instance:

1. There is a possible world in which everything is blue in all possible worlds.
2. Therefore everything is blue in all possible worlds.

It is a known fact that there are things in the actual world that are not blue, so we know that the conclusion is false. Yet there is nothing self-contradictory about claiming that everything is blue in all worlds, so I think one would have to admit that it is logically possible. Thus, the argument has a true premise, which would appear to entail the conclusion, and yet somehow, the conclusion is false.

To complicate matters even further, there are similar claims that would contradict this one, but are equally possible, such as:

1. There is a possible world in which everything is orange[5] in all possible worlds.
2. Therefore everything is orange in all possible worlds.

If it is logically possible for everything to be blue in all worlds, then it is logically possible for everything to be any other color as well. But of course this leads to contrary conclusions. If everything is identified as blue in all worlds, then it cannot at the same time be true that everything (or even one thing) is identified as orange in all (or any) worlds, and vice versa. One way to escape the problem would be to simply reject the notion that premises like these really are possible, but I do not see any reason why they would not be. What is needed is a different interpretation of such premises.

A proposition such as ‘There is a possible world in which x is true in all possible worlds’ is really a claim of metapossibility. I call it that because it seems to be a second-order, or higher level type of possibility and necessity. Instead of interpreting the claim as the assertion that x is true within one world of the set, it should be understood as a claim about the entire set that could possibly be true; which means that the claim itself is outside of the set to which it refers. When a proposition about all worlds is necessary or impossible, there is no need to even refer to the meta-level, we just say that the claim is true or false. However, there are instances in which a proposition about all worlds is not true by definition, nor a contradiction in terms, and this results in a complex claim of higher level, or second-order modality.

It may appear that this solution does not fully eliminate the contrary (or contradictory) results of prior examples because there would still be a meta-level world in which everything is blue in all standard worlds, another in which everything is orange in all standard worlds, another for green, and red, etc. This is not problematic, though, because each result only represents the state of affairs in one metapossible world rather than all of them. What made the prior interpretation untenable is that it resulted in everything being blue in all worlds and everything being orange in all worlds at the same time. It is absurd to say that an object is both actually round and actually square at the same time, and this is equivalent to that. However, it is not absurd to say that something is actually square, and possibly (or potentially) round, or vice versa, nor that an object has some other actual shape now, but it is possible that it could be round, and possible that it could be square. Furthermore, there is a possible world within the standard set in which everything is blue, and another in which everything is orange, etc., even though that is not the true state of affairs in the actual world. At the meta-level, the actual state of affairs in the set of standard worlds is equivalent to the actual world within the standard set of possible worlds. The necessity that everything is blue in all standard worlds would only be actual if that particular possibility was actualized. But of course, the claim is only that this state of affairs is possible, not that it has been, or ever would be actualized.

The first premise of Plantinga’s argument is a claim of metapossibility because it is clear from the other two premises that the term ‘unsurpassable greatness’ is meant to entail instantiation in every world. ‘There is a possible world in which unsurpassable greatness is exemplified’ is equivalent to ‘It is possible that “something which would be instantiated in all possible worlds” is instantiated’. If Plantinga meant for the premise to refer to a world within the set, one might well ask why the claim is restricted to only one world. It seems as though his purpose in doing this is to make the premise appear more plausible. But this is misleading. Is the implication supposed to be that unsurpassable greatness is exemplified in some, but not necessarily all worlds? Surely he could not mean that, because that would make the claim self-contradictory based upon the definition provided of ‘unsurpassable greatness’. The only truly coherent interpretation of the premise, if meant to refer to worlds within the same set, would be ‘unsurpassable greatness is exemplified in all possible worlds’ which is essentially tautological, according to the definition, but there is no reason that one must accept that definition as corresponding with reality.

Now perhaps Plantinga would argue that if something has unsurpassable greatness it would have to be instantiated in all meta-level worlds as well, if it is in one. But this would bring us back to the same objection. If the premise is supposed to be understood as ‘unsurpassable greatness is exemplified in all metapossible worlds’ that would indicate that the claim is necessarily true, rather than possibly true. But no one can truthfully say that they know that claim to be true with absolute necessity. How could you? If it was known with certainty, there would be no need to make an argument for it. So, the premise would instead have to be ‘It is possible that there is “something which would be instantiated in all metapossible worlds”’, which is a claim of tertiary-level modality. This could continue on and on to further levels, but little would be accomplished by it, because such claims are always merely possible.

If the claim that there is such a thing is not necessary, that means that it is logically possible for there to be a meta-level world in which it is not the case that unsurpassable greatness is exemplified. This must be understood correctly. A claim that retains the subject but rejects its necessary predicate is self-contradictory, and thus would not be the state of affairs in a possible world, or a metapossible world. But a claim that rejects the subject outright, as in ‘It is not the case that “something which would be instantiated in all possible worlds” is instantiated’ is possible, and would be represented. Of course, it must be the case that either there is something that is instantiated in all possible worlds or there is not. But this does not mean that one of the claims has to be impossible. Both can be possible, or one can be possible and the other actual, without contradiction. In this case, since the two claims are contradictories, one of them would be actual, and the other possible. The one that is actual is the true state of affairs in the set of standard worlds, and the other represents how things could be in the set of standard worlds.

This same general point applies within the standard set of worlds as well. According to Kripke semantics, a proposition is said to be necessarily true when it holds in all possible worlds and possibly true when it holds in at least one world. Holding in all possible worlds is interpreted by many to mean that a necessary being would be instantiated in all possible worlds. If one defines it that way then there would be no difference between a necessary being and how Plantinga defined unsurpassable greatness. However, holding across all possible worlds (which is a slight modification I would make) is not necessarily the same thing as instantiation in all possible worlds. The fact that a bachelor is unmarried could be said to hold across all possible worlds because in every world in which there is a bachelor, he is unmarried; however, it is not the case that a bachelor is instantiated in every world.

To say that a property is necessary just means that it must be a predicate of the subject in all cases in which there is a subject. In contrast, a contingent or accidental property could, and would be a predicate of the subject in at least one, but not necessarily all cases in which there is a subject. A unicorn could be brown in one possible world, and gray in another, or, there could be a world in which some are brown, and others gray, because color is a contingent property of that subject. There could even be a possible world in which a unicorn changes colors, as happened with a horse that I once owned who went from a blue roan when he was young to almost completely white when he was older. But in any world in which there is a unicorn, it must always have exactly one horn, because that is a property entailed by the subject.[6] So whenever and wherever a subject is instantiated, it has a necessary property, but there is no necessity that a subject is instantiated in every world. This ought to be obvious, since a unicorn has a necessary property, but is not instantiated in the actual world.

Necessary existence is no different than any other necessary property. If you were to say otherwise, you would be guilty of something akin to Malcolm’s pseudo-contradiction. Something has necessary existence in a possible world if it always exists according to that state of affairs. I grant that such a state of affairs is possible. But the opposing claim, that no such subject is instantiated (in which case there are no predicates either, necessary or otherwise) is also possible, and this would be the state of affairs in at least one world, according to which, there would be nothing that always exists, or rather, no subject that does. The real question in all of this is whether the subject is instantiated in the actual world. Since it could be instantiated in some worlds but not others, it is unknown which way it would be in the actual world. Thus, the claim that there is a necessary being in the actual world, or that a being of unsurpassable greatness is in all possible worlds, including the actual one, is a synthetic claim that would require verification through experience (i.e. revelation, religious experience) to confirm. Without confirmation, such a being could only be considered hypothetical.

6/4/2015

[1] Proslogion 3

[2] All quotes from Norman Malcolm come from the essay, ‘Anselm’s Ontological Arguments’ found in the anthology God Matters: Readings in the Philosophy of Religion. The quoted material from Immanuel Kant is taken from this anthology as well.

[3] I would like to differentiate this objection of circularity from others. Some contend that the more well-known version of Anselm’s ontological argument is circular. That criticism would be true of the version given above, but not of his more well-known version. The alleged problem is that the definition of God that Anselm uses, ‘that than which nothing greater can be conceived’ already implies existence, so using this definition in a proof for God’s existence is circular. However, the whole point of the argument is supposed to be that God’s existence is tautological, and that merely understanding the concept correctly reveals the truthfulness of the claim. I think Anselm could reply to this criticism that the term ‘God’ itself implies existence, if properly understood, and that his definition simply elucidates the true meaning already contained in the concept to make it more obvious to the rest of us. The argument is no more circular than any other valid argument. All valid arguments actually beg the question, by definition, because in order to be valid, there cannot be anything in the conclusion that was not already contained in the premises. Thus, one would always be assuming in the premises what one is attempting to prove in the conclusion. Because of this, the charge of circular reasoning is a pretty weak objection unless you can also show why at least one of those premises is, or at least could be false. You cannot just reject Anselm’s definition of God simply because it leads to a conclusion that you do not like. To really disprove it, one would have to show what is wrong with it, and if there is nothing wrong with it, then the fact that it implies existence just shows that the argument is valid. I have argued elsewhere, though, that the problem is not the definition, it is that Anselm equivocates with it, using it to apply both to God and to the theoretical concept of God. I accept that God could be referred to as ‘that than which nothing greater can be conceived’, but reject the claim that the concept of God is that. The concept only represents something that would be that, if it was an object. It is just wrong to refer to something that exists in one’s understanding alone (or as merely a concept or an idea) as ‘that than which nothing greater can be conceived’. If the atheist simply rejects the claim that the mere concept of God in his mind is that, then his position is not self-contradictory (as he never says that there could be something greater than ‘that than which nothing greater can be conceived’, only that there could be something greater than the fictional concept of God) there is no reductio ad absurdum, and the argument does not necessarily imply that God exists.

[4] Plantinga, Alvin. The Nature of Necessity, Oxford University Press, 1974 p. 216.

[5] If one wanted to make the two claims contradictory, ‘non-blue’ could be substituted for ‘orange’.

[6] Assuming that the term ‘unicorn’ is meant to be taken literally. If instead it was meant to refer to the name of a species, or was used as a proper name, then it could still apply even if the animal had somehow lost its horn, and there would be no necessary entailment from the term. Even so-called ‘necessary properties’ largely depend upon context and how terms are used, as necessity is derived merely from how things are defined. Kripke argues that once something has a given name, it is a ‘rigid designator’ and necessarily refers to that thing throughout the possible worlds. For example water must always be H2O, and vice versa. This is true to an extent, because if terms can have different referents and definitions in some worlds than they do in others then there is equivocation in how those terms are being used. For the sake of consistency, we have to stipulate that there is relative necessity in how terms like ‘bachelor’ are used across all possible worlds. But there is no absolute, or external necessity that something must have a given name or definition, that is just how we use the term. We could always pick a different word to stand for the same thing, or define that one differently, if we wanted to. If ‘bachelor’ was instead defined as ‘married man’, and everyone understood it and used it that way, then it would be a necessary entailment from the subject that a bachelor is married. Though this is ‘possible’ in the sense that the term could be used differently than it is, it would be wrong to say that a bachelor is married in a possible world because that is not how the term is used, and it would violate the rules of the system to use it differently than how everyone else does, as that would cause mass confusion.