Proofs for God’s existence are supposed to be concerned with establishing that God exists in reality. In what follows I am going to argue that one of the most important lessons we can draw from Anselm’s famous argument in the Proslogion is that these proofs should at least as much be concerned with making sure that God exists in the understanding of those to whom such proofs are addressed.
In order to make this point, in the next section I will present a very simple, intuitive reconstruction of Anselm’s argument. Then, in the third section, I will show that since the argument thus reconstructed is obviously valid, and it would be foolish to challenge any other of its premises except the assumption that God does not exist in reality, it is a sound proof of God’s existence. Nevertheless, in the fourth section, I will argue further that despite its soundness, this proof can rationally be rejected by anyone who refuses to think seriously of anything as that than which nothing greater can be thought, that is, by anyone who does not really have God in his mind. Obviously, this last claim, with the rather vague adverbs “seriously” and “really”, is begging for clarification. Providing that clarification will be the task of the fifth, concluding section of the paper.
The following is what I take to be a simple and intuitive reconstruction of the reasoning in c. 2 of the Proslogion. The letter ‘d’ in this reconstruction simply serves as an abbreviation of the description ‘that than which nothing greater can be thought’.
In fact, if we let
our variables x and y range over anything that is thinkable, then we may
reconstruct this argument using standard quantificational notation as follows:
1. g=d
2. U(d)
3. ~R(d)
4. "x(U(x) & ~R(x)) ® $y(G(y)(x)
5. (U(d) & ~R(d)) ® $y(G(y)(d) [4,
UI]
6.
$y(G(y)(d)) [2,
3, MP]
Here, ‘U( )’ = df. ‘( ) is in the understanding’; ‘R( )’ = df. ‘( ) is in reality’; ‘G( )( )’ = df. ‘( ) can be thought to be greater than ( )’.
But 6, claiming that
something greater can be thought than that than which nothing greater can be
thought, is contradictory, so at least one of the premises from which it
followed has to be false. But none of the self-evident premises can be false,
so the false premise has to be the assumption, namely, 3. So, its denial,
namely, that d is in reality is true; therefore, by 1, God is in reality, that
is to say, God really exists.
That there really is a formal contradiction in the
conclusion can easily be brought out by means of the following simple
formalization: d =df. ix.~$y(G(y)(x)); ‘P( )’ =df. ‘$y(G(y)( ))’;
$y(G(y)(ix.~$y(G(y)(x))))
Û
P(ix.~Px)
Û
$z("x(~Px
®
x=z) & ~Pz & Pz) Þ $z(~Pz & Pz); where ‘$y(G(y)( ))’ =df.
‘some y can be thought to be greater than ( )’ =df. ‘something
greater can be thought than ( )’
The previous reconstruction contains only two deductive steps, a universal instantiation concluding 5, and a modus ponens, concluding 6, the validity of which is unquestionable. The conclusion, given that the letter ‘d’ was introduced as a mere abbreviation of Anselm’s description, is clearly self-contradictory. For that than which nothing greater can be thought is something (whether merely in the mind or in reality) than which nothing greater can be thought, and of this the conclusion states that something greater than it can be thought, so the conclusion entails that something is such that nothing greater than it can be thought and something greater than it can be thought, which is an explicit contradiction.
But then, the reductive step, claiming that at least one of the premises has to be false, is clearly valid. Therefore, if all the other premises are indeed unquestionably true, then the argument constitutes a sound proof of the denial of premise 3, which is the ultimately intended conclusion.
In view of these considerations, then, the only possible way to attack this proof is by challenging the acceptability of its other premises.
Now it would clearly be foolish to challenge the first
premise, which simply stipulates what we should understand by the name ‘God’,
just as I stipulated that in the context of the argument we should understand
the same by the letter ‘d’ as by the English phrase, translating Anselm’s Latin
phrase: id quo nihil maius cogitari potest. To be sure, it is
questionable whether one really understands what is meant by this phrase
itself, but this would still not undermine the validity of the stipulation,
namely, that whatever one understands by this phrase, they should understand
the same by the name ‘God’. So the first premise has to be accepted simply on
account of its being a stipulation of linguistic usage. Of course, this need
not, and does not, mean that this is an arbitrary stipulation. In fact,
this stipulation on Anselm’s part is merely a succinct formulation of established
usage, as is clear from the more detailed, and at the same time authoritative,
explanation of this usage Anselm could gather from
To be sure, a more sophisticated opponent at this point might object that even if the first premise is meant to be stipulative, the stipulation cannot be accepted by anyone who does not believe in God’s existence. For the premise in itself entails that there is something, indeed, one and the same thing, corresponding to the name ‘God’ and to Anselm’s description, but this is precisely what is denied by those who deny the existence of God. Therefore, assuming the first premise renders the argument question-begging.
To this objection Anselm could immediately respond that his example of the painter who can be said to have a picture in his mind before actually painting it was designed to show that there being something corresponding to a name or a description, as long as it is only in the mind, does not entail that the object corresponding to the name or description actually exists in reality. However, those who deny God’s existence only deny that there is an object in reality corresponding to the name ‘God’ and to Anselm’s description. They certainly do not deny that believers have such an object in their mind. So, having an object in mind, corresponding to the name and the description, does not in itself entail that the object exists in reality, which can and should be realized even by those who do not accept that God exists in reality, whence the premise can be assumed without begging the question.
Of course, at this point, the mere mention of objects in the mind, or objects of the mind, apparently treated as constituting a distinct realm of entities over and above ordinary objects may give rise to a swarm of objections.
Nevertheless, without trying to list and address those objections one by one, while always risking that we miss the next person’s favorite, we may show why it is ontologically as well as logically entirely harmless to talk about mere objects of the mind, without thereby committing ourselves to a distinct realm of mysterious entities, indeed, to any sort of entities over and above the ordinary ones, and without any logical inconsistency whatsoever.
In the first place, we should make clear that the phrase “x is an object of the mind” means nothing more nor less than the phase “x is or can be thought of”. But then, since we can think of ordinary objects of our environment, we certainly should not worry about those objects of our minds. What philosophers would rather worry about are alleged objects of the mind other than ordinary objects, which are supposedly indicated by the phrase “x is a mere object of the mind”.
So, next we should make clear that the phrase “x is a mere object of the mind” is not to be construed as indicating a special sort of object, indeed, in the same way as the phrase “fake diamond” is not to be construed as indicating a special sort of diamond, or the phrase “fictitious detective” as a special kind of detective. Just as fake diamonds are not diamonds, and fictitious detectives are not detectives, so too, mere objects of the mind are not objects. But then, what are they?
Now questions of this kind can be understood in two ways. When we ask: “What is an X?”, then we may either mean “I wonder what you mean by ‘an X’ when you are talking about an X?” or we may mean “I know what you mean by ‘an X’ when you are talking about an X, but I wonder what sort of thing such an X is”. For example, the question “What is a fake diamond?” in the first sense can appropriately be answered by saying: “By ‘a fake diamond’ I mean something that looks exactly like a diamond but is not a diamond”. In the second sense, however, it can be answered by saying “A fake diamond is a cubic zirconia crystal”.
In the first sense, I have already answered the question of what an object of the mind or an object of thought is: an object of thought is whatever we can think of. Therefore, what we mean by “a mere object of thought” is whatever we can think of that is not a real object, a real entity. But from this it should be clear that whoever understands this intended meaning of the phrase cannot sensibly ask the question “What is a mere object of the mind?” in the sense of asking what sort of object or entity a mere object of thought is, indeed, not any more than someone who understands what we mean by the phrase “fake diamond” can sensibly ask what sort of diamond a fake diamond is. For given the intended meaning of the phrase, a mere object of thought is no more an object or an entity than a fake diamond is a diamond.
To be sure, at this point one may object that this intended meaning of the phrase itself cannot be coherent, and that is why it causes so much trouble. For, according to this understanding of the phrase, a mere object of thought would have to be something that is not any object, any entity at all, that is, something that is not any single thing, whence the phrase cannot possibly apply to anything; therefore, since only those claims can be true that are about something, no claims intended to be about mere objects of thought can be true, indeed, not even the claim that they are thought of, but do not exist.
In response to this objection we may point out in the first place that it is generally not true that only those claims can be true that are about something. For if an affirmation is true only if it is true about something, then the contradictory negation may be true precisely because the affirmation is not true about anything. For example, the affirmation “The present King of France is bald” fails to be true not because the present King of France has hair, but because France presently has no king. But then, the contradictory negation of the affirmative claim, interpreted with a wide-scope negation has to be true. That is to say, “The present King of France is not bald”, taken in the sense “It is not the case that the present King of France is bald” and not in the sense “The present King of France is a person who is non-bald”, has to be true. Therefore, by parity of reasoning, if the phrase “mere object of thought” in the sentence “A mere object of thought is not an object” cannot apply to anything, then the sentence taken in the sense “It is not the case that a mere object of thought is an object”, and not in the sense “A mere object of thought is something that is a non-object”, has to be true.
But, furthermore, it is simply not true that the phrase “a mere object of thought” cannot apply to anything in any context whatsoever. After all, we have just agreed that what we mean by the phrase “a mere object of thought” is whatever that can be thought of but is not a really existing object. But then in the context of the proposition “A mere object of thought is thought of but does not exist” the phrase clearly applies to something that is thought of but does not exist.
However, can anything be thought of that does not exist? For, apparently, the affirmative answer would entail the absurdity that there is something that is thought of and does not exist, that is, there exists something that is thought of and does not exist, that is to say, there exists something that does not exist, which is plain contradiction.
In response to this objection, it is easy to show that whoever would deny his ability to think of something that does not exist would thereby disqualify himself from intelligent discourse. For intelligent discourse requires the use of memory, namely, remembering the things previously uttered in the discourse. But whatever was previously uttered no longer exists; therefore, unless someone is able to think of something that no longer exists, he is simply unable to participate in intelligent discourse.
To be sure, if someone were to say that what was once uttered still exists, we should point out that in the way we (including Anselm) are using the verb ‘exists’ (or its equivalents), its tense is to be taken seriously. According to this usage, what once was present, but is no longer present does not exist. In the same way, what will be, could be, or merely imagined or thought to be present, but is not actually present does not exist. Of course, we grant our opponent’s right to use the word differently, but then he should also grant our right to use it this way; and since the opponent is attacking Anselm’s argument, which follows this usage, the opponent has to follow the same usage, unless he wants to talk past Anselm. Therefore, according to this usage, what was uttered, and is no longer uttered, no longer exists, yet, to maintain intelligent discourse it has to be thought of. Hence, intelligent discourse is possible only if something that does not exist can be thought of.
But then, since intelligent discourse is possible (let’s hope!), thinking of something that does not exist should also be possible. Therefore, since thinking of something that does not exist is possible, something can be thought of that does not exist, and so, in the context of the proposition “A mere object of thought is thought of but does not exist” the phrase “a mere object of thought” can refer to something that is thought of but does not exist.
Furthermore, the claim that something is thought of but does not exist certainly does not entail the contradiction that there exists something that does not exist, unless the word “Something” in “Something is thought of that does not exist” is understood to be restricted to existents. But clearly, there is nothing to warrant that interpretation; indeed, as we have seen, assuming it would disqualify its upholders from intelligent discourse.[2]
All in all, Anselm’s possible defense against the alleged question-begging resulting from accepting the first premise is clearly vindicated: since it is possible to think of things that do not exist, we can certainly think of that than which nothing greater can be thought without thereby committing ourselves to its existence in reality. So with this understanding of the premise, it should be acceptable even by atheists as merely specifying the intended meaning of the term ‘God’, without thereby assuming what needs to be proved, namely, that the name ‘God’ or the corresponding description refers to any really existing thing.
But then the second premise can only be attacked by saying that for some particular reason it is not possible for that than which nothing greater can be thought to be in the understanding, that is, for some particular reason it is not thinkable. Therefore, unless there is some objective reason why that than which nothing greater can be thought cannot be thought of, this object of thought has to be in the mind of those who can and do think of it, whereas only those would not have it in their minds who either on account of some personal inability cannot think of it, or because of some stubborn unwillingness would not want to think of it. But since the premise merely states that this object of thought is at least in some mind, in particular in the mind of those who wish to deny that it exists, the premise has to be accepted, unless it can be shown that that than which nothing greater can be thought is objectively unthinkable. But this can only be the case if it can be shown that Anselm’s description is inconsistent.
However, besides the fact that the description is certainly not explicitly, formally inconsistent, showing its implied inconsistency would probably be a rather difficult task. In any case, as long as one does not have such a proof at their disposal they may consistently think of something of which they (perhaps mistakenly) think that it is that than which nothing greater can be thought. So they would still have to accept premise 2.
Now, since anybody who would want to reject Anselm’s conclusion would accept premise 3, we can move on to the last premise, namely, premise 4.
In connection with this premise one may immediately raise the question: why would it be self-evident that if something that is thought of does not exist in reality then something greater can be thought? After all, we always can think of things that do not exist but are greater than whatever we can find in reality. We may happen to find the biggest elephant in the world, but even then we certainly can think of one that is bigger. So, it seems that it is simply not true that just because the elephant in our thought does not exist, the real elephant is greater. On the contrary, it is the elephant in our thought that is greater.
Now the clue to the proper understanding of this premise, which, to be sure, is not spelled out in the Proslogion, can be found in the Monologion, where Anselm tells us how we should understand the term ‘greater’ in connection with the supreme being:
I do not mean great in terms of size, like some sort of body; but something which, the greater it is, the better or more valuable it is, like wisdom. And since only that which is supremely good can be supremely great, it is necessary that there is something that is best and greatest, -- i.e., of everything that exists, the supreme.[3]
However, being and goodness are convertible. As Anselm puts it:
Since the highest good is the highest being, it follows that every good is being and every being is good.[4]
Therefore, the greater a thing is in Anselm’s sense, the better it is, and the better it is the more it is a being. But then, regardless of whether at this point one can make sense of the idea of several degrees of being, it is clear that what does not exist at all, is not good at all, and so it is not great at all. And so, if a thing does not exist, anything that exists is greater than it, and thus anything that is thought to exist is thought to be greater than it; therefore, when something does not exist, a greater certainly can be thought, namely something that is thought to exist.
But then, if anything that exists is greater than anything that is merely thought to exist, but does not, how can we think of something greater than what exists? Didn’t we just agree that we can think of an elephant that is greater than the biggest elephant in the world?
Now, when think of an elephant greater than the biggest elephant in the world, we think of something that is thought to be a greater elephant than the biggest elephant in the world, but it is not an elephant that is greater than the biggest elephant in the world. But then, clearly, what we think of is not greater, but is merely thought to be greater, just as it is not an elephant, but is merely thought to be an elephant.
However, given these considerations it is quite understandable that Anselm’s confrere, Gaunilo, thought there was still something wrong with this argument, even if perhaps we may not quite be able to pinpoint exactly what. After all, if we think not just of an elephant that is greater than any real elephant, but we think of some elephant than which no greater can be thought, or lest we should think of greatness only in terms of size, we think of an island so perfect that no more perfect than it can be thought, then it seems that by the force of Anselm’s reasoning we would have to conclude that the elephant than which no greater can be thought, or the island than which no more perfect can be thought, exists. But this is absurd, for, apparently, in this way we should be able to prove, for all kinds of things, that there is a thing of that kind than which nothing greater can be thought, however, this is obviously false. Indeed, this is also impossible, for then we would have to have, despite Euclid’s proof in the Elements, a prime number than which no greater is thinkable, but that is precisely what Euclid’s proof showed to be impossible.
In response to this objection, it should be clear in the first place that Gaunilo’s objection can work only if his analogy is correct, that is, Anselm’s description of what we are supposed to understand by the name ‘God’ can indeed be replaced without further ado with the description of the lost island, or any other kind of thing than which no greater can be conceived.
However, obviously not any kind of thing can be conceived to
be such that a greater than it cannot be conceived. This is precisely the case
with the greatest prime number. Since
But then, if we realize that the concept of Gaunilo’s
However, it is easy to show that the concept of Gaunilo’s
To be sure, on the other possible reading of the description “the island than which no more perfect is thinkable”, it should indicate the island than which no greater island is thinkable. And then, of course, even if there may be a more perfect being than the most perfect island thinkable, one certainly cannot think of an island that would be more perfect than that than which no more perfect island is thinkable.
But this move cannot save Gaunilo’s objection either, for replacing Anselm’s description by this description in Anselm’s argument would only yield the conclusion that something greater than the island than which no greater island is thinkable can be thought, which is not contradictory, so the final, reductive step of the argument would have to fail.
In fact, the failure of Gaunilo’s
Therefore, it holds only for that than which nothing
greater can be thought that absolutely speaking no greater being than it
can be thought. But then no
Yet, this last remark should already highlight why, despite the soundness of Anselm’s proof, one may rationally reject its conclusion. For although it is true that whoever forms in their mind the concept of that than which nothing greater can be thought is thereby committed to thinking that it exists, there is nothing in Anselm’s argument that would force anyone to think of anything as that than which nothing greater can be thought in the first place.
For the second premise of the argument, stating that that than which nothing greater can be thought is in the understanding, is true either because that than which nothing greater can be thought is in some understanding, or because it is in every understanding. But, then, even if the argument is sound, for the second premise is true when it is verified only for some understanding, it will not be compelling for anyone who does not have this object in their understanding. Therefore, unless it can be shown that this object has to be in every understanding, it will not be a universally compelling proof.
To be sure, Anselm intended to establish that whoever understands his description has to have the object it describes in their understanding. However, the mere linguistic understanding of a description simply never entails commitment to thinking of something as that to which the description applies, whether in reality, or at least in one’s own mind. We can always accept other people’s descriptions of objects they think of with the tacit proviso that whatever they think of as such may not in fact be such, for they may be mistaken, or deliberately misleading, or just simply making something up for entertainment, without the intent to be “taken seriously”, that is, without the intent to have us believe that their descriptions applied to anything.
In fact, this is precisely how we understand fiction: we understand that the author’s descriptions are meant to describe some characters the author had in mind, but we need not believe that those descriptions in fact apply to some characters (concerning which the author’s descriptions might even possibly be false); indeed, we need not even think that the author himself ever believed his descriptions applied to anything at all.
On the other hand, when we know that we are not dealing with a piece of fiction, then we may still perfectly understand the author’s descriptions as ones which the author believes to apply to the characters he is describing (assuming we do not think the author is deliberately deceptive in his description), yet we need not think that those descriptions truly apply to the characters the author intended to describe.
Therefore, if someone has this type of understanding of Anselm’s description, namely, understanding that when believers think of God, then they think of what they truly believe is something than which nothing greater can be thought, then this person can have a genuine understanding of the believer’s description, but without any commitment to thinking that this description applies to anything in his own mind. On the contrary, the non-believer, when he thinks of what believers think of as that than which nothing greater can be thought, does not think of it as that than which nothing greater can be thought. He does think of the same object of thought alright, but he does not think of it as being greater than anything at all, for he thinks it is just a mere figment of the believers’ mind.
But then it should be obvious why Anselm’s argument cannot be persuasive for those who for some reason are unable or unwilling to entertain “seriously” the idea of God as that than which nothing greater can be thought. For a person who thinks of God as possibly just a figment of the believer’s mind will certainly not think of that figment as that than which nothing greater can be thought, and even though he understands that whoever thinks of God in the way the believer does is thereby committed to the real existence of that figment, still, he will not be forced into the same commitment by Anselm’s argument, for he does not think of God in the same way in the first place.
Therefore, it should be clear that the persuasive force of Anselm’s argument — to be sure, not its soundness — hinges on whether the person considering the argument is both willing and able to entertain seriously the idea of God, that is, not as possibly a mere figment of the believer’s mind, but as representing the real source of all perfection, all goodness, and all being, and which therefore cannot possibly lack being. But it is precisely this consideration that cannot be replaced by a “snappy” description, which itself is but the summary of a long, and complex meditative process that simply nobody can “skip”, if they really want to see what it takes to have id quo nihil maius cogitari potest in the mind.
Gyula
Klima
E-mail:
klima@fordham.edu
US: http://www.fordham.edu/gsas/phil/klima/
EU: http://193.225.239.10/~gyula/
Presented at
the 2000 Annual Meeting of the
American Catholic Philosophical Association
in Dallas, TX, November 4, 2000
[1]
Cf. “
[2] Note that in view of this result, we need not bother much about the slogan that existence is not a predicate. For although on one possible reading this slogan is obviously true, on that reading it is irrelevant, whereas on the reading on which it is relevant, it is false. On the reading on which this slogan is obviously true, it says that the word ‘exists’ and its equivalents, according to the usage regulated by modern analytic philosophy inspired by Fregean logic, express a second-order Fregean concept. This is obviously true, but irrelevant because that Fregean (Kantian) concept is not the concept that Anselm is working with. On the other hand, the other, relevant reading of the slogan should express the claim that there cannot be a first order concept conveyed by the word ‘exists’, for that assumption would lead to the contradiction that something that exists does not exist. However, we could just see that this contradiction simply does not follow.
[3] Monologion, c. 2. p. 13.
[4] On the Fall of the Devil, c. 1, p. 196.