SAINT ANSELM’S PROOF:
A Problem of Reference, Intentional Identity and Mutual Understanding
0. Introduction: a problem of existence or of reference?
Saint Anselm’s proof for God’s existence in his Proslogion, as the label “ontological” retrospectively hung on it indicates, is usually treated as involving some sophisticated problem of, or a much less sophisticated tampering with, the concept of existence. In this paper I intend to approach Saint Anselm’s reasoning from a somewhat different angle.
First, I will point out that what makes many of our contemporaries think it involves a problem with the concept of existence is our modern conception of reference, intimately tied up with the concept of existence. On the other hand, I also wish to show that the conception of reference that is at work in Saint Anselm’s argument, indeed, that is generally at work in medieval thought, is radically different, not so tied up with the concept of existence, while it is at least as justifiable as the modern conception.
Secondly, I intend to show that with this understanding of Saint Anselm’s argument we can see that it is a valid proof of God’s existence. But then we shall immediately face the problem of the rationality of atheism: does the Fool deny God only because he is truly a fool (as Anselm himself and many medieval defenders of his proof held)?
In the third section of the paper, therefore, I show how, despite the validity of Saint Anselm’s proof, an atheist can consistently maintain his position, even within the medieval conception of reference. But this will immediately raise the problem whether in thinking of God the Saint and the Fool can ever think of the same object, i.e., all the thorny problems of intentional identity.
In the ensuing discussion, I consider how the conception of reference presented in the first section handles these problems, and how it is related to contemporary discussions of the “causal”, or “historical explanation theory” of reference.
In the concluding section of the paper I remark on the value of these considerations for understanding Saint Thomas Aquinas’ rejection of Saint Anselm’s proof, and the significance of this rejection in his alternative program of natural theology. I will also briefly reflect on the possibility of mutual understanding between people of radically different worldviews.
1. The modern vs. the medieval conception of reference
On the paradigmatic account of reference in contemporary philosophical semantics, owing in large part to Russell’s Theory of Descriptions, the burden of reference is taken to be carried basically by the bound variables of quantification theory, which supposedly reflects all there is to the universal logical features, or “deep structure” of natural languages.1 This account, coupled with the Kantian-Fregean idea of existence as a second-order predicate, i.e., a quantifier, quite naturally leads to Quine’s slogan: “to be is to be a value of a bound variable”.2
Within this framework, Saint Anselm’s reasoning is either bound to be regarded as sheer nonsense, falling prey to a simple category-mistake3, or, on a more charitable account, allowing some sense of existence as a (first-order) predicate, it may be interpreted as presupposing a referent for his key-description (“that than which nothing greater can be thought of”), and hence, though proving that this referent is existent and cannot be thought to be nonexistent (in the first-order sense), failing to provide a proof that there really is such a referent (in the second-order sense).4
Leaving the former, and cruder, form of criticism aside,5 I think it is worth noticing in the second one the smooth transition from “the description has/does not have a referent” to “the referent of the description does/does not exist”, or (giving the word “exist” to Quine’s Wyman6), “there is an object/there is no object referred to by the description”. What is interesting in the smoothness of this transition is how easy it is nowadays to have an unreflected, and accordingly deep conviction that whatever more restricted meanings existence may have, the full scope of being is that of the possible range of reference of the expressions of our language.7
In medieval thought, this certainly was not the prevailing idea. According to the medieval view, inspired originally by Aristotle’s Perihermeneias, reference, following meaning, is a property of linguistic expressions only insofar as they express thoughts, i.e., mental acts of users of the language. Accordingly, linguistic expressions refer to what their users intend by them to refer to in a given context, that is, what they think of while using the expression either properly, or improperly.8 So referring was held to be a context-dependent property of terms: according to this view, the same expression in different propositional contexts may refer to different things, or refer to something in one context, while refer to nothing in another. As it was spelled out systematically already in the freshly booming logical literature of the 12th century in the theory of ampliation9, terms that are actually not true of anything may have referents, or in the current terminology, supposita, in the context of intentional verbs, such as “think”, “want”, “imagine” and the like. But, to be sure, these referents are not to be construed as beings (entia), or objects, simpliciter, but as objects of thought — according to 13th century terminology, beings of reason, entia rationis.10
At this point, however, anyone having qualms about “multiplying entities”, indeed, “obscure entities”, should be reminded that the distinction between objects, or beings (entia) simpliciter, and objects of thought, or beings of reason (entia rationis) is not a division of a given class (say the class of objects, or beings, or entities) into two mutually exclusive subclasses. The class of beings or objects is just the class of beings or objects simpliciter, that is, beings without any qualification, of which beings of reason or objects of thought do not form a subclass. Mere beings of reason, therefore, are not beings, and mere objects of thought are not a kind of objects, indeed, not any more than fictitious detectives are a kind of detectives, or fake diamonds are a kind of diamonds.
Qualifications of this kind are what medieval logicians called determinatio diminuens, which cannot be removed from their determinabile on pain of fallacia secundum quid et simpliciter.11 Accordingly, admitting objects of thought, or beings of reason, as possible objects of reference, does not imply admitting any new objects, or any new kind of beings, so this does not enlarge our ontology.
So on this conception Quine’s answer to “the ontological problem”: “What is there?”, namely, “Everything” is true. For on this conception the claim: “Everything exists” (or its stylistic variants: “Everything is” or “Everything is a being” or “Everything is an existent” or “There is/exists everything”) is true.12 Still, “Something that does not exist can be thought of” is also true, where, the subject being ampliated in the context of the intentional predicate, “Something” binds a variable that ranges over mere objects of thought that do not exist.13
According to this conception, in an appropriate ampliative context we can successfully refer to what we can think of according to the proper meaning of the terms involved. But thinking of something does not imply the existence of what is thought of. Thus, in the same way, referring to something does not imply the existence of what is referred to, or, as the medievals put it, significare (‘to signify’) and supponere (‘to refer’) ampliate their object-terms to nonexistents in the same way as intelligere (‘to think’, ‘to understand’) and other verbs signifying mental acts do.14
Of course, Saint Anselm did not yet possess all the sophisticated distinctions of the logical theory of the following three centuries. But that it was essentially the same conception of reference that was at work in his mind when he formulated his arguments in the Proslogion is clearly shown by his insistence against Gaunilo that his crucial description “that than which nothing greater can be thought of” is in no way to be equated with “greater than everything”. It is precisely the ampliative force, recognized as such by 12th-century logicians, that is missing from the latter, and is missed from it, though not described as such, by Saint Anselm in his response to Gaunilo’s objection.
As he says: “what if someone were to say that there is something greater than everything there is [...] and [that] something greater than it, although does not exist, can still be thought of?”15 Evidently, we can think of something greater than the thing greater than everything, unless the thing that is greater than everything is the same as that than which nothing greater can be thought of. But Anselm’s point here is precisely that although, of course, there is nothing greater than the thing greater than everything, which is supposed to exist, something greater than what is greater than everything still can be thought of, if the thing greater than everything is not the same as that than which nothing greater can be thought of. So if the thing greater than everything is not the same as that than which nothing greater can be thought of, then something greater still can be thought of; therefore, that than which nothing greater can be thought of can be thought of, even if it is not supposed to exist.
Accordingly, Saint Anselm conceives of this description as referring at least to what can be thought of, an object of thought, which, as such, may be, but need not be an object, a being simpliciter. All he requires for his proof is that anyone who claims to understand his description should concede that he thinks of something to which the description is thought by him to apply, whether there is something to which the description in fact applies or not, and it will be the task of the proof to show that what is so thought of has to be not only a mere object of thought, but also an object simpliciter, i.e., that it has to exist.
2. The proof
With this understanding of Anselm’s conception of the relationship between existence and reference we can see that his argument constitutes a valid proof of God’s existence without committing him either to an ontology overpopulated with entities of dubious status or to the question-begging assumption that the referent of his description exists. In fact, we can see this even within the framework of standard quantification theory, provided we keep in mind that in the context of Anselm’s argument, this context being an ampliative context, we should interpret our variables as ranging over objects of thought, only some of which are objects simpliciter.
To render this interpretation explicit, let me reformulate Anselm’s description “that than which nothing greater can be thought of” as “the thought object than which no thought object can be thought to be greater”. Accordingly, let me propose the following reformulation of Anselm’s argument:
By the meaning of the term,
(1) God is the thought object than which no thought object can be thought to be greater
Now suppose that
(2) God is only in the intellect (i.e. God is thought of, but does not exist)
(3) any thought object that can be thought to exist in reality can be thought to be greater than any thought object that is only in the intellect
And it cannot be doubted that
(4) God can be thought to exist in reality
(5) Some thought object can be thought to be greater than the thought object than which no thought object can be thought to be greater [1,2,3,4]
which is a contradiction, whence we have to abandon our supposition that God is only in the intellect, so he has to exist in reality, too.
Translating “thought object” in its different occurrences by ‘x’ and ‘y’, “God” by ‘g’, “... can be thought to be greater than...” by ‘M( )( )’, “... is only in the intellect” by ‘I( )’, and “... can be thought to exist in reality” by ‘R( )’, and using ‘i’ as the descriptor, and ‘$’ as the existential quantifier, the following is a valid formalization of the above reasoning in quantification theory (the intermediate steps (a) and (b) are inserted here only to facilitate recognizing how an actual derivation might proceed):
(a) M(g)(g) [2,3,4, UI, &I, MP]
(b) ($y)(M(y)(g)) [a, EG]
(5) ($y)(M(y)(ix.~($y)(M(y)(x))) [1,b, SI]
(Where UI is Universal Instantiation, &I is Conjunction Introduction, MP is Modus Ponens, EG is Existential Generalization and SI is Substitutivity of Identicals.)
Abbreviating ‘($y)(M(y)( ))’ as ‘P( )’, (5) will look like ‘P(ix.~P(x))’, i.e., ‘($x)(~Px & ("y)(~Py®x=y) & Px)’, which implies ‘($x)(~Px & Px)’, an explicit contradiction. But then, since (1), (3) and (4) have to be accepted as true, (2) has to be rejected as false. So it is not true that God exists only in the intellect. But since to exist only in the intellect means to exist in the intellect but not in reality, not to exist only in the intellect means either not to exist in the intellect, or to exist in the intellect and also in reality. Therefore, since God, being thought of, does exist in the intellect, he has to exist also in reality.
Evidently, this piece of reasoning cannot be torpedoed on the basis that it presupposes that there is something than which nothing greater can be thought of, as it only requires that something is thought of than which nothing greater can be thought of. But Anselm makes it clear that anyone who claims to understand the phrase “that than which nothing greater can be thought of” has to think of something than which nothing greater can be thought of, which, therefore, being thought of, is in the intellect, as its object. By the above argument we can see, however, that it cannot be only in the intellect, whence we concluded that it has to be in reality, too.
3. The atheist, who is not a fool
It seems, therefore, that all that Anselm’s proof requires is that modicum of rationality which is needed to understand a simple descriptive phrase, to reflect on what the description implies, and to conclude to these implications concerning the thought object one has in mind as a result of understanding the description.
Indeed, the next argument requires no more either. If you understand the phrase “something which cannot be thought not to exist”, you have to think of something which cannot be thought not to exist. But what cannot be thought not to exist is certainly greater than anything that can be thought not to exist. So, if that than which nothing greater can be thought of were something that can be thought not to exist, then something greater than that than which nothing greater can be thought of could be thought of, which is impossible. Therefore, that than which something greater cannot be thought of cannot be thought not to exist.
But already Anselm himself, as well as later on Gaunilo, had to realize at once that such a simple proof is not necessarily “foolproof”. For the recalcitrant Fool can immediately turn Anselm’s second argument around, pointing out that Anselm’s second conclusion denies the obvious, namely that God can be thought not to exist, as his (the Fool’s) own example shows.
Anselm’s retort, that the Fool’s denial was possible in the first place only because he is truly a fool, thoughtlessly mumbling words he himself does not understand, leads us directly to the crux of the very possibility of a dialogue between the Saint and the Fool, or put in less biased terms, between the theist and the atheist. For, evidently, to avoid a complete breakdown of communication, some basic requirements of rationality should be met equally on both sides. So clarifying these basic requirements is in the best interest of both parties. Let us see, therefore, which are those basic requirements of rationality that the Fool seems to fail to meet.
Anselm claims that when the Fool said in his heart: “There is no God”, he could do so only because he did not know correctly what he was speaking about (no matter whether aloud or just to himself)16, as he simply did not understand the word “God” properly. Thus far, the Fool is not guilty of irrationality, only of ignorance of the proper meaning of an expression. If I say “An isosceles has four sides”, of course I am talking nonsense, but I may think that the word “isosceles” in English refers to squares, in which case what I mean by this sentence makes perfect sense, although what the sentence means is nonsense. If, however, someone tells me that the word “isosceles” in English refers to plane figures having just three sides, two of which are equal, the situation is different. If I claim to understand this explanation, I cannot stick any longer with my previous assertion, and be not guilty of irrationality, as I assent to what I know to be impossible, which is at least a sure sign of irrationality.
But Anselm’s charge is precisely that once the atheist is told what the word “God” means, the first argument shows him that he cannot assent to his original claim on pain of contradiction. So he cannot assent to it, except irrationally, and therefore, if he insists on his denial, he deserves to be called a fool.
Consequently, in view of the validity of Anselm’s reasoning, the only way the atheist can rationally maintain his position is by denying one of Anselm’s premises. Of course, it would be foolish of him to challenge the theist’s “meaning-postulates”, since this would at once disqualify him as an intelligent interlocutor. So this leaves him with denying either that God can be thought to exist in reality, or denying that God, that than which nothing greater can be thought of, is even in the intellect.
Choosing the first alternative would amount to claiming that God’s concept is contradictory. Establishing this claim might require from the atheist a specification of his concept of God, which may very well be contradictory, but can easily be dismissed by the theist as inadequate. In any case, in Anselm’s argument the concept of God to be employed is adequately specified by the first premise, and the atheist would probably be hard pressed to show that the description “that than which nothing greater can be thought of” is self-contradictory.
At this point, however, the atheist may shift the burden of proof by saying that even if this description does not seem to contain any prima facie contradiction, it may well be contradictory. By way of analogy, he may bring up the description: “the greatest prime number”, which, on the face of it, does not appear to be contradictory, so it seems to refer to the greatest prime number. But, as we know from Euclid, the assumption that there is a greatest prime number leads to contradiction, so the description cannot refer to anything.
In response, the theist first of all can point to the whole tradition of rational (as opposed to mystical) theology showing how apparent contradictions concerning God’s nature are resolved.17 Second, he can say that a contradiction, if derivable at all, could be derived from this description only with the help of other assumptions, just as in the case of the greatest prime. But, unlike the case of the greatest prime, these auxiliary assumptions probably need not be accepted as true. Finally, concerning Anselm’s argument one can also say that the premise attacked by the atheist does not even require that Anselm’s description should be free from such implied contradictions. For the premise requires only that one can think that God (under Anselm’s description) exists, which one can do even with the greatest prime, until one actually realizes the implied contradiction. So the burden of proof falls back upon the atheist, if he wishes to challenge this premise. Therefore, he has to turn to the other premise anyway, asking whether he has to admit God as at least a possible object of thought.
In response to this question the atheist now may claim that the way Anselm wishes to force him to think of God will not make him admit that God is even in the intellect, at least, in his intellect, despite the fact that he understands very well what Anselm means by his description, which may not be contradictory after all. For understanding this description does not require him to believe that it applies to anything, so understanding this description will not make him think of anything that he thinks to be such that nothing greater than it can be thought of. So, since he denies that the description applies to any thought object he can think of, he just does not have such a thought object in his mind, while he perfectly understands what is meant by this description.
But here the theist swoops down: of course, the atheist is just a fool! Indeed, a wicked fool, who, only because of his insistent denial, admits to be simply unable to think of the same thought object that I think of, that is, God. With this last move the atheist just revealed himself for the miserable fool he is, for in order to maintain his untenable position he simply gives up his otherwise natural human ability to think of God, that than which nothing greater can be thought of. As Saint Bonaventure put it: “the intellect has in itself [...] sufficient light to repel this doubt and to extricate itself from its folly. Whence the foolish mind voluntarily rather than by constraint considers the matter in a deficient manner, so that the defect is on the part of the intellect itself and not because of any deficiency on the part of the thing known.”18
But even without these moral implications, it seems that the theist now may justifiably claim that, as a result of his denial, the atheist just rendered himself unable to think of a humanly otherwise thinkable thought object. By denying the existence of God the atheist will never be able to think of the same God as the theist, whose conception of God logically implies the existence of God, as Anselm’s proof shows.
4. Intentional identity and parasitic vs. constitutive reference
At this point, however, we have to notice that precisely the theory of reference outlined earlier as being implicit in Anselm’s argument offers the atheist a way out of his predicament. According to this theory, we should recall, what determines reference is primarily the intention of the speaker, whence it may be called the intentional theory of reference. This theory agrees with the recent “historical explanation”19—as opposed to the Russellian—theory of reference on the fundamental insight that speakers may successfully refer to objects by descriptions that do not apply to these objects. For Saul Kripke this indicates that speaker’s reference may diverge from semantic reference. In the Kripkean framework, however, it is also assumed that the speaker’s reference is to that which the speaker at least believes satisfies his description.20 On the intentional theory not even this is always required. I may successfully refer to what you think of without ever believing what you think or believe of your thought object, or even knowing under what description you would identify this thought object, by merely intending to refer to what you intend to refer to. Adapting Kripke’s example, if you say “her husband is kind to her”, referring to a man whom you mistakenly believe to be her husband, I may correct you by saying: “the man you refer to is not her husband”; but I may also pick up your referent sarcastically by the same description, which I know does not apply, and say: “‘her husband’ happens to be her kind boss”, or, simply preying on your false belief, I can tell you some other things about “her husband”, that is, about the man whom you mistakenly believe to be her husband. Furthermore, writers of fiction certainly do not believe their descriptions to be true of their characters. They simply make up their characters, conceiving of them as satisfying their descriptions, but without ever believing the truth of these descriptions. Accordingly, their readers who know that what they read is a piece of fiction, do not believe these descriptions to be true either. They can, nevertheless, successfully refer to the same characters, and can e.g. correct one another’s memories concerning these characters, taking as the standard of their correctness the way the author conceived of these characters. Again, in guessing games, in which one has to find out what another person has in mind, though not allowed to ask directly, one asks for and receives information concerning the thought object the other person has in mind, trying to find out under what description the person identifies this thought object. But throughout this process, the questioner thinks of the same thought object as the answerer, without knowing under what description or name the answerer identifies this thought object.21
As can be seen, on this account one simply sidesteps the problem of trying to find criteria of intentional identity in terms of the properties thought objects have. Indeed, on this account a mere thought object is not an object at all, and has no properties at all.22 A mere thought object is endowed with properties by the mind whose thought object it is, in the sense that the mind conceives of this thought object as having some properties. But then, the same thought object may be intended also by another mind, which may not endow the same thought object with the same properties, i.e. it may conceive of the same thought object, but not as having the same properties. Accordingly, if one mind entertains a thought object under some particular description, another mind may make what I would call parasitic reference to the same thought object, by merely intending to refer to the same thought object that the first conceives of, but not conceiving it under the same description, indeed, sometimes even denying that the description in question in fact applies to this thought object.
Now, when one thinks of a thought object under some description and thinks the description applies to that thought object (or just conceives of this thought object as one satisfying this description, not necessarily believing that the description in fact applies to this thought object), in which case we can say he makes constitutive reference to that thought object, he is obliged to conclude to all implications he realizes his description has concerning that thought object, to avoid inconsistency. On the other hand, if someone else picks up this referent, though for some reason not thinking that the description applies to the thought object in question, making parasitic reference to this thought object, he is not obliged to conclude to the same implications concerning this thought object.
Along these lines, then, the atheist may consistently maintain his position even despite the validity of Anselm’s argument, and still claim that he is able to think of the same thought object as the theist, so the theist has no reason to doubt his mental capabilities. In particular, he can say that when Anselm thinks of that than which nothing greater can be thought of, Anselm has a thought object in mind that he thinks satisfies his description, along with all its implications. The atheist, however, can then think of the same thought object, but not think that the description applies to it, whence he is not forced to conclude to whatever valid implications the description may have concerning that thought object.
So the atheist can claim that he perfectly understands Anselm’s description, and still deny that he has in mind something of which he thinks satisfies Anselm’s description. At the same time he can also point out that this does not prevent him from thinking of Anselm’s thought object, by making parasitic reference to it. So Anselm’s proof will not convert the atheist, who does not share Anselm’s belief that his description applies to something, though he understands that many people have this belief, and he is even able to identify the object of this belief, as that fiction, the God of the religious.
So the atheist, when speaking about God, is constantly making parasitic reference to the theist’s object of thought, using the theist’s beliefs to refer to this thought object, but without ever sharing them. Accordingly, he will be willing to admit that whoever thinks of something as that than which nothing greater can be thought of also has to think that this thing exists in reality, and that it cannot even be thought not to exist in reality. Being a consistent atheist, however, he himself will think of nothing as that than which nothing greater can be thought of (whence that than which nothing greater can be thought of as such will not be in his mind). But he still will be able to think of what theists think of as that than which nothing greater can be thought of.
5. Conclusion: parasitic reference, natural theology and mutual understanding
Parasitic reference to each other’s thought objects between people not sharing each other’s beliefs seems to be a ubiquitous phenomenon. The most sensitive cases are, of course, those that involve people’s most basic beliefs, such as religious belief. Accordingly, parasitic reference is a phenomenon to be seriously reckoned with not only in dialogues between theists and atheists, but also between people of different religious faith.
Saint Thomas Aquinas was evidently aware of this problem, as is clear from his discussion of a certain aspect of the dialogue between Christians and pagans:
“... the Catholic who says that the idol is not God contradicts the pagan who claims that it is, for both of them use the name ‘God’ to signify the true God. For when the pagan says that the idol is God, he does not use this name insofar as it signifies something that people only believe to be God, <but which is not God>, for in this way he would be telling the truth, as sometimes even Catholics use this name in this signification, as when it is said that all the gods of the heathen are demons.”23
Aquinas’ principal point here is that both the pagan and the Christian can use the same word, “God”, in the same sense, meaning the true God, whence the affirmation and negation of the same term of the same object, namely of the pagan’s idol, by the two parties yields a real contradiction. On the other hand, he also remarks on a possible parasitic usage of the same term by the Christian in such a dialogue. According to the Christian, the term “God” in its proper meaning cannot refer to the idol, which is why he denies that the idol is God. Still, he can use the same term in an improper sense, not meaning the true God, but meaning what the pagan believes to be the true God, thereby referring to the pagan’s god, namely the idol. So here Aquinas is evidently aware of the possibility of the type of reference I called parasitic, when a person not sharing someone else’s belief may use the other’s belief to make reference to the thing thought by the other person to satisfy this belief.
Given the awareness of this possibility on Aquinas’ part and the possibility to evade by its help the force of Anselm’s argument, we may risk the assumption that this awareness played some role in Aquinas’ rejection of Anselm’s argument.
Indeed, in the Summa contra Gentiles St. Thomas writes as follows:
“... granted that by the name ‘God’ everyone understands that than which a greater cannot be thought of, it does not follow that there is something than which a greater cannot be thought of in the nature of things. For we have to posit the name and its interpretation in the same way. Now from the fact that it is conceived by the mind what is indicated by the name ‘God’, it does not follow that God exists, except in the intellect. Whence it is not necessary either that that than which a greater cannot be thought of exists, except in the intellect. And from this it does not follow that there is something than which a greater cannot be thought of in the nature of things. And so no inconsistency is involved in the position of those who think that God does not exist: for no inconsistency is involved in being able, for any given thing either in the intellect or in reality, to think something greater, except for those who concede that there is something than which a greater cannot be thought of in the nature of things.”24
In this passage, Aquinas explicitly refers to the asymmetry in the positions of the theist and the atheist with respect to Anselm’s argument. Those who think of God as that than which nothing greater can be thought of, making constitutive reference to God by this description, cannot think that he does not exist, save inconsistently. For those, however, who think that for any thought object a greater is thinkable, no inconsistency arises when they make parasitic reference to what in their view is mistakenly believed by the theists to satisfy this description, which, in their view, exists only in the theists’ intellect.
Anselm’s argument, therefore, can be compelling only for those who are willing to make by his description constitutive reference to God, that is, whose “universe” of thought objects already contains a thought object than which, they think, nothing greater is thinkable. This willingness, however, cannot be enforced by Anselm’s argument on anyone whose “universe” of thought objects does not contain such a thought object. Such a person, therefore, has to be persuaded first to be willing to think of something as that than which no greater is thinkable. But this, in view of the possibility of parasitic reference, cannot be achieved by simply telling him to think of what the description applies to, as he simply does not think the description applies to anything, although, of course, he believes that others think it applies to something.
As can be seen, what helps the atheist maintain the consistency of his position is his isolating the theist’s thought objects from his own: when it comes to giving a consistent account of the world as he sees it, the beliefs concerning God, though may be known to him, are simply irrelevant to the atheist (except insofar as belief in God influences the thinking and behavior of religious people), as these beliefs do not concern his own thought objects, those that he is committed to, by making constitutive reference to them. So to prove for the atheist that there is a God requires to show him that given the domain of thought objects he is already committed to, he is also committed to making constitutive reference to something that the theist can justifiably identify for him as God.
Now this seems to be precisely Aquinas’ program of natural theology in the Summa Theologiae. Given our normal everyday commitment to objects of the empirical, physical world, Aquinas’ proofs for God’s existence intend to show us that by this commitment we are also committed to make constitutive reference to a Prime Mover, a First Cause, a First Necessary Being, etc., which, he says, are all what a theist would identify as God (“et hoc dicimus Deum”). Then he goes on to show us that God, to whom we are thus committed to make constitutive reference by all these descriptions, is simple, perfect, good, infinite, ubiquitous, immutable, eternal and one. In this way the atheist is not allowed to keep God, as an object of sheer parasitic reference, in isolation from his own beliefs. Indeed, throughout Aquinas’ argumentation no single description is given which would presumably give the full meaning of the term “God” for the atheist, in the possession of which he could claim to have a full grasp of the meaning of this term, and then use it parasitically to refer to what the theist believes satisfies this term. Instead, the term is given a gradually growing content with every conclusion concerning the thing to which we are already committed to make constitutive reference by five different descriptions, in virtue of the existence proofs. So, no wonder that the two questions in the Summa Theologiae following these considerations are precisely Aquinas’ systematic reflections on how we analogically “stretch” our mundane concepts to have a contentful concept of God, and how this concept enables us to speak about God.
In fact, it is precisely this type of conceptual build-up that is missed from Anselm’s proof by Gaunilo on behalf of the Fool:
“Suppose I heard something said of a man I never knew and of whose existence I was unaware. By reason of the special or general knowledge I have of what a man is or what men are, I could think of this individual as that real thing itself which a man is. And still it might be that the man I thought of was nonexistent, for example, if the man who spoke of him was lying, nevertheless, I was thinking of him as a real thing, not as that which would be that particular man, but any man whatsoever. But when I hear “God” or “something greater than all else”, I do not have this in my understanding in the same way that I had this nonexistent man, since I can think of the latter in terms of some real and familiar thing, whereas I can only think of the former in terms of mere words and one can never or scarcely ever think of anything real in this way. For although when something is thought of in this way, it is not so much the word itself (i.e. the sounds and syllables, which are real enough) that we think of, as the signification of the word heard; still, it is not thought of in the same way as by someone who knows what the word is wont to signify, namely, by whom this is thought of as a thing that is real at least in thought, but rather like by one who does not know this, who thinks of it merely by the affections of his mind produced by hearing this word, trying to imagine what is signified by it. And it would be a surprise if he ever truly attained to [that which is signified] in this fashion. And yet it is just in this way and no other that the object is in my understanding when I hear and understand a person who says there is a being greater than anything that can be thought of. So much for the claim that this supreme nature exists already in my understanding.”25
In view of the foregoing discussion, Gaunilo seems to be perfectly justified in saying that the atheist, despite the fact that he understands Anselm’s description, will not have that than which nothing greater can be thought of in his mind in the required manner, i.e., making constitutive reference to it. His own beliefs and commitments being logically isolated from the intended referent of Anselm’s description, his understanding of this description will be restricted to a mere verbal understanding, without any commitment to, or any proper concept of, its intended referent. So Anselm’s description will not provide the atheist with a logical shortcut to a proper concept of God. The lesson we can learn from Aquinas’ natural theology is that this concept has to be built up in a human mind gradually, on the basis of one’s already existing concepts and existing commitments, for otherwise its proper object will never get integrated into the “universe” of proper thought objects of this mind, but will be acknowledged only by way of parasitic reference, as belonging to the “universe” of others.
So what seems to be required from the theist to understand the atheist in the first place is to realize how the atheist can look at the world without a God and still be able to conceive of God in a non-committed, parasitic manner, as being an object of the theist’s beliefs, but bearing no relevance to his own beliefs. On the other hand, to understand perfectly the theist, the atheist has to be able to think of God as the theist does, as bearing utmost relevance to everything thinkable. But for this, he would have to go through the same long meditative process that the theist did in building up his own concept of God.
Indeed, in general, this kind of concept-acquisition seems to be essential for mutual understanding between people conceptualizing the world (and what is beyond) differently, thereby being committed to radically different “universes” of thought objects. Unless one is able to learn to think and live with the concepts of another person and the thought objects constituted by them, one will always fail to have a real grasp on the meaning of the other person. This, however, need not mean that people can understand only those persons all of whose beliefs they share. What is required for proper understanding is rather the ability to let the other person’s beliefs constitute one’s own “universe” of thought objects, trying to achieve a “fusion of their horizons”.26 This can be done, however, only in a long dialectical process, which may take adjusting the beliefs of either party, who should not seek sheer “winning” in a debate (for that is the concern of sophists), but to win over the other to one’s belief and/or to be won over to the other’s belief, for the sake of what is true and good. But this, of course, requires openness, patience and respect from both parties. Indeed, this requires that attitude which defines our profession, the Love of Wisdom.27
Albert of Saxony 1974 Perutilis Logica, Georg Olms Verlag, Hildesheim-New York, 1974
Anonymous author 1967 “Tractatus de Proprietatibus Sermonum”, in: de Rijk, L.M. (ed.) 1967, pp.728-730
Boolos, G. 1984 “To Be Is To Be a Value of a Variable (or To Be Some Values of Some Variables)”, The Journal of Philosophy, 8(1984), pp.430-431.
Buridan, J. 1957 Tractatus de Suppositionibus, (ed. M. E. Reina), Rivista Critica di Storia della Filosofia, 1957, pp.175-208, pp.323-352.
Buridan, J. 1977 Sophismata, (ed. T.K. Scott) Stuttgart-Bad Cannstatt, 1977
de Rijk, L.M. (ed.) 1967 Logica Modernorum (I-II), Assen: Van Gorcum, 1967
Gadamer, H. G. 1989 Truth and Method, New York: Crossroad, 1989
Garfield, J. L. – Kiteley, M. (eds.) 1991 Meaning and Truth: The Essential Readings in Modern Semantics, Paragon Issues in Philosophy, New York: Paragon House, 1991
Geach P.T. 1969 God and The Soul, Routledge and Kegan Paul: London, 1969
Haaparanta, L. 1985 Frege’s Doctrine of Being, Acta Philosophica Fennica, 39(1985), Societas Philosophica Fennica: Helsinki, 1985
Klima G. 1983 “Szent Anzelm és az ontológiai istenérv” (“Saint Anselm and The Ontological Argument”), Világosság, 24(1983), supplement, pp. 3-9
Klima, G 1988 Ars Artium: Essays in Philosophical Semantics, Medieval and Modern, Doxa Library 1, Budapest: Institute of Philosophy of the Hungarian Academy, 1988
Klima, G. 1984 “Libellus pro Sapiente: A Criticism of Allan Bäck’s Argument Against Saint Thomas Aquinas’ Doctrine of the Incarnation”, The New Scholasticism, 58(1984), pp. 298-312.
Klima, G. 1993 “The Changing Role of Entia Rationis in Medieval Philosophy: A Comparative Analysis with a Reconstruction”, Synthese, 96(1993), pp. 25-59.
Kneale, W. 1949 “Is Existence A Predicate?”, in: Feigl, H. – Sellars, W.: Readings in Philosophical Analysis, New York: Appleton-Century-Crofts, Inc., 1949
Knuuttila-J. Hintikka (eds.) 1986 The Logic of Being, Dordrecht, Holland, 1986
Kripke, S. 1991 “Speaker’s Reference and Semantic Reference”, in: Garfield, J. L.- Kiteley, M. (eds.) 1991
Lambert of Auxerre 1988 “Properties of Terms”, (ch. VIII. of his Logica, ed. Franco Alessio, Florence: La Nuova Italia, 1971) translated in: Kretzmann, N. – Stump, E. (eds.): The Cambridge Translations of Medieval Philosophical Texts, Cambridge: Cambridge University Press, 1988
Lycan, W. 1991 “The Trouble with Possible Worlds”, in: J. L. Garfield-M.Kiteley (eds.): Meaning and Truth: The Essential Readings in Modern Semantics, Paragon Issues in Philosophy, New York: Paragon House
Parsons, T. 1980 Nonexistent Objects, New Haven: Yale University Press, 1980
Quine, W.V.O. 1971 “On What There Is”, in: From a Logical Point of View, Harvard University Press: Cambridge, MA, 1971
Schwartz, P. 1990 Naming, Necessity and Natural Kinds, Ithaca: Cornell University Press, 1990
St. Anselm of Canterbury 1968 Sancti Anselmi Opera Omnia, ed. F.S. Schmitt, Stuttgart-Bad Canstatt: F. Frommann Verlag, 1968
St. Bonaventure 1891 Quaestiones Disputatae de Mysterio Trinitatis, in: Opera Omnia, tom. V, Quaracchi: 1891
St. Thomas Aquinas 1980 Opera Omnia, Frommann-Holzboog, Stuttgart-Bad Cannstatt
Wippel, J.F. – Wolter, A.B. 1969 Medieval Philosophy: from St. Augustine to Nicholas of Cusa, New York: The Free Press, 1969
1 This idea was most aptly characterized, just in order to be refuted, by George Boolos in the opening section of Boolos, G. 1984.
2 For the Kantian origins of Frege’s ideas on existence, connecting his views to Kant’s criticism of the Ontological Argument, see Haaparanta, L. 1985
3 “Because existence is a property of concepts the ontological argument for the existence of God breaks down.” Frege (GLA, #53.) as quoted by Haaparanta, L. 1985, p.54.
4 I provided this type of criticism in a paper I wrote ten years ago in Hungarian. See Klima, G. 1983. I think most of the more recent criticisms can be reduced to this type, but showing this in detail would take another paper (or even a book that is not worth writing, for it would not be worth reading). I am grateful to my friend and colleague, Sándor Ferencz, for having made me rethink this type of criticism.
5 After all, people may have various conceptions attached to the same words, so as long as they make their meaning clear they are not to be chastised for a different usage. Indeed, this is all the more so when the different usage is not just some capricious idiosyncrasy, but regular in a wider community. But even Frege, the father of the quantifier-analysis of the concept of existence, conceded some sense of existence (Wirklichkeit) in which it is a first-order concept. That the antique and medieval notion of existence (as actuality) is such a first-order concept, was argued for quite early by P.T. Geach in his “Form and Existence”, and “What Actually Exists” in: Geach P. T. 1969. But nowadays this is already pretty much a commonplace among medievalists. For extremely useful studies concerning the concept of being in a historical context, see Knuuttila, S. – Hintikka, J. (eds.), 1986.
6 W.V.O. Quine: “On What There Is”, in: Quine, W.V.O. 1971. p. 3. By the way, it is interesting that Quine apparently never asked himself: to whom does the name “Wyman” refer? — nobody? — then how do I know that Wyman is not the same as McX? For despite the fact that nothing in the world “wymanizes”, let alone “mcxizes”, Wyman and McX are quite distinguishable imaginary characters in Quine’s paper: Wyman, e.g., is introduced to us as a “subtler mind”, than McX. As we shall see, these questions are easily answerable on the basis of the theory of reference advanced in this paper. Not so on the basis of Quine’s.
7 “The fundamental thesis of those who believe existence to be a predicate is that there is a sense of ‘being’ logically prior to existence and applicable to the possible as well as to the actual.” Kneale, W. 1949. p. 40. Cf. also the Introduction of Parsons, T. 1980. We shall immediately see why this characterization does not apply to the medieval conception of existence and reference.
8 Cf. e.g. Buridan on suppositio impropria, in Buridan, J. 1957, pp.175-208, pp.323-352. (see ch.3.1. p.200.), also, his discussion of whether in ‘homo est species’ the term ‘homo’ suppposits for a concept properly (ch.3.2. pp.203-204.), or, in general, the common medieval distinction between what is said de virtute/secundum proprietatem sermonis and what is not, or indeed the very divisions of the kinds of supposition, reflecting the insight that the same term may refer to different things depending on what the speaker or the author intends to refer to in the given context.
9 See the anonymous treatises in de Rijk, L. M. (ed.) 1967.
10 For more on the role entia rationis played in medieval semantics and ontology see Klima, G. 1993.
11 For more on the 13th-century theory of this fallacy see Klima, G. 1984. For a formal treatment of the theory of ampliation and the semantics of such “diminishing” determinations see “Existence, Quantification and the Medieval Theory of Ampliation” in: Klima, G. 1988.
12 This is one of the essential points on which this theory differs from a Meinongian theory of objects. See Parsons, op. cit., Introduction; W. Lycan: “The Trouble with Possible Worlds”, in: Garfield, J. L. and Kiteley, M. (eds.) 1991. The other is the different principle of individuation for thought objects. See below n. 22.
13 Cf. Buridan’s treatment of Non ens intelligitur in Buridan, J. 1977. c.5. 7um sophisma
14 E.g. Buridan in Buridan, J. 1957, pp.175-208, pp.323-352: “... terminus ampliatur ad praeterita, futura et possibilia si construatur cum verbo significante actum animae intellectivae...” (p.349.), “... verba significantia actus animae cognoscitivae, sicut sunt ista verba ‘cognoscere’, ‘intelligere’, ‘significare’, ‘supponere’, ‘permittere’ et huiusmodi...” (p.345.). Or, as his pupil, Albert of Saxony put it: “All verbs, even in the present tense, which of their very nature can concern future, past and possible things as well as present ones (habent naturam transeundi rem ita futuram vel praeteritam vel possibilem sicut et praesentem) ampliate their terms to all times, future, past and present, like these: think, know, mean and the like. And what accounts for this is that a thing can be thought of without any difference of time (sine differentia aliqua temporis), sc. abstracted from any place and time. And so, when a thing is thought of in this way, then a thing which was, or will be, or can be may be thought of as well as a thing which is. Therefore, if I have the common concept from which we take (a quo sumitur) this name ‘man’, then I can think indifferently of all men, past, present and future. And this is why these verbs can concern past or future things as well as present ones.” Albert of Saxony 1974, Tr.2. c.10. 8a regula. But already in the 13th century Lambert of Auxerre provided a good general criterion for distinguishing ampliative from non-ampliative verbs, which also gives a plausible explanation for the phenomenon: “... it is important to know that an action can be related to substance in two different ways: in one way as regards that in which it is and of which it is stated - as when one says ‘Socrates is running’ ... - in the other way as regards that of which it is stated although it is not in it - as when one says ‘Caesar is praised’, where the praise is stated of Caesar and yet is not in Caesar but in the one doing the praising. Similarly, when one says ‘A chimera is thought about’ - i.e. a being in thought - where the thought is stated of the chimera and yet is not in the chimera but in the one doing the thinking. ... It must be said, therefore, that the verbs that signify an action that is related to the subject, is in the subject and is said of the subject do not ampliate; but those that signify an action that is related to the subject of which it is said but is not in the subject do ampliate.” Lambert of Auxerre 1988. p. 117. For an even earlier occurrence of the same idea cf. Anonymous author 1967.
15 “Quid enim si quis dicat esse aliquid maius omnibus quae sunt, et idipsum tamen posse cogitari non esse, et aliquid maius eo, etiam si non sit, posse tamen cogitari?” St. Anselm of Canterbury 1968, p.135.
16 Cf. “Aut res loquimur signis sensibilibus, quae sensibus corporeis sentiri possunt sensibiliter utendo; aut eadem signa, quae foris sensibilia sunt, intra nos insensibiliter cogitando, aut nec sensibiliter nec insensibiliter his signis utendo, sed res ipsas vel corporum imaginatione vel rationis intellectu pro rerum ipsarum diversitate intus in nostra mente dicendo.” S. Anselmi Monologion, in: St. Anselm of Canterbury 1968, pp.24-25. This distinction of Anselm’s is also crucial in understanding one of Gaunilo’s objections, referred to below, relying on a difference between mere verbal and essential (as far as this is possible) understanding.
17 Perhaps, in view of these considerations it is not surprising that the idea of an “ontological” proof of the existence of God got intimately connected, especially after Scotus’ work, with a need to prove the consistency of God’s concept, that is, the logical possibility that God exists.
18 Wippel, J.F. – Wolter, A.B. 1969 p. 310. Translation of St. Bonaventure 1891, pp. 45-51.
19 Good selections of relevant recent literature on the topic can be found in: Schwartz, S. P. 1990, and Garfield, J. L. – Kiteley, M. (eds.) 1991.
20 “So, we may tentatively define the speaker’s referent of a designator to be that object which the speaker wishes to talk about, on a given occasion, and believes fulfils the conditions for being the semantic referent of the designator.” Kripke, S. 1991, p.173.
21 Such a guessing game is popular in Hungary and is known as named after Bar Kokhba, the leader of a Jewish uprising against the Roman Empire in the 2nd century A.D. As legend has it, one of his scouts was captured by the dull-witted Romans, who thought that by cutting out his tongue they would prevent him from giving away their military secrets. After his release, however, Bar Kokhba asked him carefully chosen yes/no questions, which he could answer simply by nodding or shaking his head, from which the smart Jewish leader could gain all the information he needed. Nowadays the game is played by two parties, one of whom thinks of something, and the task of the other is to find out what it is by asking questions answerable only by yes or no.
22 And this is the other essential difference of this theory from a Meinongian theory. Cf. n. 12 above. Mere objects of thought do not have the properties under which the persons who think of them conceive of them: they are only thought to have these properties by these persons. Accordingly, mere objects of thought are not individualized by their (“nuclear”) properties, but simply by the intention of the people who think of them. For the Meinongian principle see T. Parsons, op. cit., pp.28-29.
23 “... nominum multiplicitas non attenditur secundum nominis praedicationem, sed secundum significationem, hoc enim nomen homo, de quocumque praedicatur, sive vere sive false, dicitur uno modo. Sed tunc multipliciter diceretur, si per hoc nomen intenderemus significare diversa, puta, si unus intenderet significare per hoc nomen id quod vere est homo, et alius intenderet significare eodem nomine lapidem, vel aliquid aliud. Unde patet quod catholicus dicens idolum non esse deum contradicit pagano hoc asserenti, quia uterque utitur hoc nomine deus ad significandum verum deum. Cum enim paganus dicit idolum esse deum, non utitur hoc nomine secundum quod significat deum opinabilem, sic enim verum diceret, cum enim catholici interdum in tali significatione hoc nomine utantur, ut cum dicitur, omnes dii gentium sunt daemona.” ST1 q.13, a.10, ad 1um.
24 “... dato quod ab omnibus per hoc nomen Deus intelligatur aliquid quo maius cogitari non possit, non necesse erit aliquid esse quo maius cogitari non potest in rerum natura. Eodem enim modo necesse est poni rem et nominis rationem. Ex hoc autem quod mente concipitur quod profertur hoc nomine Deus, non sequitur Deum esse, nisi in intellectu. Unde nec oportebit id quo maius cogitari non potest esse, nisi in intellectu. Et ex hoc non sequitur quod sit aliquid in rerum natura quo maius cogitari non possit. Et sic nihil inconveniens accidit ponentibus Deum non esse: non enim inconveniens est quolibet dato vel in re vel in intellectu aliquid maius cogitari posse, nisi ei qui concedit esse aliquid quo maius cogitari non possit in rerum natura.” ScG I.11.
25 The translation is from Wippel, J.F. – Wolter, A.B. 1969, p.160, somewhat modified on the basis of St. Anselm of Canterbury 1968, p.127. ll. 4-24.
26 The phrase, and the point, is Gadamer’s, of course. Cf. Gadamer, H. G. 1989, esp. pp.245-254, 300-307, 369-379. In fact, I think it is precisely around this point that also Gadamer’s “hermeneutic” approach could be “fused” with the “analytic” approach I followed in this paper. But discussion of this idea would lead too far.
27 I owe thanks to Paddy Blanchette for helpful comments.