The Ontological Argument
Abstract and Keywords
This chapter presents and critically discusses the main historical variants of the “ontological argument,” a form of a priori argument for the existence of God pioneered by Anselm of Canterbury. I assess the contributions of Anselm, Descartes, Leibniz, and Gödel, and criticisms by Gaunilo, Kant, and Oppy among others.
Keywords: Anselm, a priori arguments, arguments for the existence of God, Descartes, existence of God, Gaunilo, Gödel, Kant, Leibniz, ontological argument, Oppy
The term “ontological argument” was Kant's name for one member of a family of arguments that began with Anselm of Canterbury. These arguments all try to prove God's existence a priori, via reasoning about the entailments of a particular description of God. The description almost always involves God's greatness or perfection. Where it does not, the argument has a premise justified by God's greatness or perfection. 1 So these arguments might better be called arguments from perfection.
I deal with the main arguments from perfection and criticisms thereof in historical order.
Anselm: Proslogion 2
Anselm gave the first argument from perfection in his Proslogion ( 1078 ). The key passage (in ch. 2) is this:
We believe [God] to be something than which nothing greater can be thoughtThe Foolwhen he hears“something than which nothing greater can (p. 81 ) be thought,” understands what he hears, and what he understands is in his intellect. (But) it cannot exist in the intellect alone. For if it exists only in the intellect, it can be thought to exist also in reality, which is greater. If therefore itexists only in the intellect, this same thing than which a greater cannot be thought, is a thing than which a greater can be thought. But this surely cannot be. So something than which no greater can be thoughtexistsboth in the intellect and in reality. (Charlesworth 1965 , 116, my translation)
I first explicate Anselm's key phrase “something than which no greater can be thought” (henceforth “a G”). I then take up his reasoning, then the question of whether its premises are true.
“A G” is an indefinite description. Its form lets many things satisfy it (as with “something brown and red” and “something canine”). What the Fool understands is this description. A natural thought would be that what is “in his intellect,” if not just a token string of words, is the property the description expresses, being a G. But as the argument proceeds, it supposes that the Fool “has in mind” some particular thing that has the property, an “it” that cannot exist in the mind alone. Anselm seems to suppose, in short, that by understanding the description a G, one comes into some sort of direct cognitive relation with something that is a G: one thinks of or refers to a particular G. For Anselm, then, being such that no greater can be thought means being such that no one nondivine can refer to a greater possible object, under any description. 2 A G is a greatest possible being to which we can refer. If there is hierarchy of greatness with a topmost level to which we can refer, then, “a G” automatically picks out only something(s) on the topmost level. If we can refer to an unending progression of ever greater possible beings, “a G” does not refer.
“A G” has a modal element: it speaks of items to which we can refer. To make sense of this “can,” I now introduce a bit of technical terminology that will be repeatedly useful. The sentence “Possibly there are ostriches” asserts that in at least one history the universe could have, ostriches would exist. In fact, one such history has taken place. “Possibly Churchill runs a three-minute mile” asserts that in at least one history the universe could have, Churchill pulls off this surprising feat. Churchill has not yet done this, and barring reincarnation or resurrection, he will not. So it appears that actual history is not any of those in which Churchill does this: no such history has taken place. But still, it's in some sense possible that he do so. Every sentence instancing the form possibly P asserts the existence of at least one history the universe could have in which P. Every sentence instancing the form necessarily P asserts that there is no history the universe could have in which ¬P. The sentence “necessarily 2+2=4” asserts that there is no history the universe could have in which this is false; that is that in every possible history, 2+2=4. Every sentence using “can,” of course, is equivalent to one using “possibly” (e.g., “There can be ostriches”).
Philosophers call histories the universe could have possible worlds. So we can (p. 82 ) now explicate Anselm this way: something x is a G only if no nondivine being in any possible world can refer to any being greater than x actually is. Now surely, for every possible being, possibly someone or other nondivine refers to it. If that's so, then possibly something is greater than x only if possibly someone refers to that greater thing. If so, we can simplify our account of a G, for being a G is equivalent to being something than which there can be no greater. From now on, let's take Anselm to be talking of this property.
In Proslogion 5, Anselm reasons that unless it is to be less than we can think it to be, a G must be “whatever it is better to be than not to be” (Charlesworth 1965 , 120), that is, have every attribute F such that having F is better than lacking F. Now if something had every such attribute, it would be a G (a G being one thing it is better to be than not to be). So if something is not a G, it lacks some F a G has, such that having this F is better than lacking F. Thus, Proslogion 5 implies that a G is greater than any possible non-G in at least one respect. Further, there is no respect in which a non-G surpasses a G: if a non-G has some attribute it is better to have than to lack, any G has this too, and only such attributes are respects in which something might surpass a G. 3 So overall, any G is greater than any non-G. As it's obvious that nothing in the material world is a G, we can infer that a G must at least be greater than any actual material object—including the universe. Here is a particularly impressive attribute: being greater than every other possible being in some respect and equaled by no other possible being in any respect. Such a G would be a most perfect possible being. Anselm would almost certainly hold that a G must be a most perfect possible being: if a G were not so, we could apparently think of a greater, namely one that was so. But his argument doesn't make use of this description.
Talk of Gs naturally raises questions like What is greatness? or Greater in what way? Anselm doesn't answer. But he clearly means greatness or being greater to be or involve some sort of value-property the God of Western theism has supremely. So Findlay's ( 1955 ) suggestion that we take these in terms of worthiness of worship can't be too far off the mark: let's say that greatness is either desert of worship or some combination of attributes on which this supervenes. 4 As it turns out, we needn't be more specific than this.
In Proslogion 4, Anselm asserts that
Df. God = that than which no greater can be thought,
the definite description implying that there is just one G. Anselm nowhere argues that there is just one. And this is not obvious. Something without a greater might nonetheless have an equal. If Anselm cannot rule it out that there could be two or more equal Gs, he faces a problem. For his argument will apply to as many possible Gs as there are, prima facie, and so if it works will prove that there are (p. 83 ) many Gs. If there are, the definite description “that than which no greater” will not refer—in which case, Anselm's argument will prove that God does not exist, given (Df). Why just one possible G? One can only speculate:
i. Anselm argues that being a G entails being intrinsically simple, that is, not having distinct purely intrinsic attributes (Proslogion 12; see Monologion 16–17). Suppose that this is so. For any x, being x is intrinsic to x: it is a matter settled entirely within x's boundaries, so to speak. Being simple is also intrinsic. So for any x, if x is simple, being simple and being x must be the same attribute. But then any simple being will be identical to x. So there can be at most one simple being. So if being a G entails being simple, there can be at most one G—and if attribute-identities are necessary, at most one possible G. Thus, there is at least a good argument from premises Anselm clearly accepted to back his belief that at most one possible being is a G.
ii. As the doctrine of divine simplicity is controversial, perhaps a better answer lies with what Anselm means by “greatness.” It's axiomatic in Western theism that whatever precisely worship is, at most one thing deserves it, and this thing coexists with no rivals for worship (see, e.g., Isaiah 40:25, 44:6–7, 46:5, 9). Anselm argues that any G must as such exist necessarily and necessarily be a G. If he's right, and it's also the case that maximal greatness in a possible world W excludes having a rival in W, then in no possible world does a G coexist with another G, and there is at most one possible G.
I now turn to Anselm's reasoning.
The Reasoning
On one reading, Anselm's premises are
1. Someone thinks of a possible object which is a G, and
2. If any possible G is thought of but not actual, it could have been greater than it actually is.
The reductio runs this way. By definition, if a possible object g is a G, no possible object in any possible state is greater than g actually is: g is in a state than which there is no greater. Let g be the G someone thinks of. Then, as a G, g is in a state than which there is no greater. Per (2), if g is not actual, g could have been greater than g actually is. So if g is not actual, g is not in a state than which there is no greater. So if g is not actual, g both is and is not in such a state. So g is actual. So a G exists.
The argument is valid. So let us ask if its premises are true.
(p. 84 ) Ontological Commitments?
(1) is not innocent. It asserts a relation between a thinker and a possible object that is actually a G, and so brings an object into our ontology. Anselm needs it to do so if (1) is to give him a G to which to apply (2). But then if he is not blatantly to beg the question of God's existence, Anselm must also assume that this possible object is there, and is a G, even if it does not exist. And odds are that Anselm did believe in nonexistent objects. 5 But this puts an unflattering gloss on his argument. For then it seems to amount to: grant that something actually is in a state with no greater. This thing either does or doesn't exist. But how could something that didn't so much as exist be as great as all that? And of course, if that's what the argument amounts to, it's hard to see why one should grant that something actually is in such a state. The step from this admission to the conclusion seems vanishingly small.
But Anselm's argument doesn't require his ontology. One could instead read (1) in light of non-Anselmian semantic assumptions. Suppose that one denied nonexistent objects, but held that one can use satisfiable descriptions as if they refer, whether or not they do, and can properly use claims like (2) to reason about satisfiers of descriptions, whether or not the descriptions are satisfied. This would amount to running Anselm's argument within a “free” logic. Such logics carry no ontological commitments. Taken in light of these new assumptions, (1) asserts only that someone tokens an indefinite description that is possibly satisfied. (1), then, turns out no more or less problematic than the claim that
1a. Possibly something is a G.
(2) assigns a degree of greatness to an object even if it does not actually exist; like (1), it must allow for nonexistent objects with greatness if it is not to beg the question. Even if the degree were automatically zero, this would still entail that nonexistents have properties. So we must replace (2) with a premise assigning greatness to nonexistents only in worlds in which they exist. The most straightforward replacement is probably
2a. If possibly something is a G, but actually nothing is a G, then in any possible world W in which something is a G, that G could be greater than it is in W.
If possibly something is a G, there is a world W in which something is a G. So (2a) immediately yields
2b. If possibly something is a G, but actually nothing is a G, then in some possible world W, something is a G but could be greater than it is in W.
(p. 85 )
Free logics let one use names or descriptions that do not refer as if they refer. So they reject the logical rules of universal instantiation (from “for all x, Φx,” infer Φs for any singular term s) and existential generalization (from any statement Fs, infer that there is something which is F; Lambert 1983 , 106–7). Thus, to show that Anselm's argument can go free-logical, one must state his reductio without using these rules. So here it is: given (1a) and (2b), if nothing is a G, then in some possible world W, something is a G but could be greater than it is in W. But it cannot be the case that in some world, a G could be greater than it is in that world: being a G is being in a state with no greater in any world. So it is not the case that nothing is a G. As far as I can see, then, given a free logic, Anselm's reductio goes through.
The Premises
If an argument is valid and its premises are true, its conclusion is true. I will not try to settle whether (1a) is true. But there is a case for (2a). For a G could be greater than it is in W just in case G lacks in W some great-making property compatible with the rest of its attributes in W. If no G exists, any G in any W lacks the property of existing in @, the actual world. But
3. For a G, for any W, existing in @ is great-making in W.
And if it is possible that a G exists, then for some G in some W, existing in @ is compatible with the rest of its attributes.
The controversial premise here is of course (3). There are two cases to consider here: W = @ and W ≠ @. For the first, I support (3) in two ways. One appeals to a general claim,
4. For any F and x, if x would be F were it to exist, then for x, existing in @ is F-making.
Suppose that Leftow would be human were he to exist. Then whoever gives Leftow existence ipso facto makes him be human. So for Leftow, existence is human-making: it makes him actually what he would be were he actual, and so human. But the properties a G would have if actual include being great. So for a G, existing in @ is great-making. Oppy ( 1995 ) suggests that (3) must rest on or be supplanted by some more general principle connecting greatness and existence, which atheists and agnostics would be reasonable to reject: “After all, there seems to be no good reason to suppose that existence in reality is a great-making property solely in the case of a [G]” (10, cf. 11). 6 But the only general principle needed is (4). (4) does (p. 86 ) not connect existence with greatness any more than with any other property, and I cannot see that atheists or agnostics have any particular reason to object to it.
The second line of argument begins that surely
5. Nothing that doesn't exist ought to be worshipped.
For worship is a kind of talking to, and it makes no sense to talk to something that isn't there. Atheists and agnostics will of course insist on (5). If (5) is true, then any G would be more deserving of worship if actual than if merely possible. For a merely possible G does not deserve worship at all, and an actual G does deserve worship. If greatness is worthiness of worship or whatever property(-ies) would subvene it, this implies that any G would be greater if actual than if merely possible, and because it is actual, not merely possible. So a G's being actual surely moves it at least a bit in the direction of maximal greatness. In fact, it moves it all the way, if (as it were) the G is all set to be great save for the little detail of actually existing. But then existing in @ is great-making for Gs.
Suppose, on the other hand, that W ≠ @. We then must ask why existing in some other world contributes to a G's greatness in W. One sort of reply appeals to arguments that necessary existence is great-making: if it is, then a fortiori existing in another world is. Now the claim that being a G entails existing necessarily leads to its own sort of argument from perfection. But it does so only given certain principles of modal logic. Pros. 2 does not commit itself to any such principles. So this sort of support would not make Pros. 2 depend on modal perfection-arguments. It would at most show that Pros. 2 has one root these other arguments do.
Another sort of response begins with two premises: that worship consists largely of giving thanks and praise, and that @, as it happens, contains concrete things whose maker might in some circumstance deserve thanks and praise for them, and for whose existence a G would account if it existed. A being that can have no greater is one than which none can be more worship-worthy. So it must deserve the greatest thanks and praise compatible with its nature. Those who worship, thank and praise God for their existence and for items in the world around them if they seem good. So if a G is to deserve maximal thanks and praise, it must be such as to deserve thanks and praise for whatever should inspire these in worlds it graces. All things in any way good in these worlds thus must owe it their very being; its contribution must suffice for their existence. The more complete this dependence, the greater the thanks and praise deserved. So another axis along which to magnify the thanks/praise a G is owed is depth of dependence: the deeper it is, the greater the thanks/praise deserved. One way dependence can be deeper is this: an item depending on the G could depend on it so thoroughly that it could not exist without the G's causal support. So via “perfect being” reasoning, we can conclude that whatever in any way ought to inspire thanks and (p. 87 ) praise and coexists with a G depends so completely on it for existence that it could not exist without the G.
Turning now to our G in W, @, again, contains many things warranting thanks and praise. Either some of these also exist in W, or none do. Suppose that some do. Then if the G does not exist in @, some things in W could have existed without depending on a G's contribution to their existence. But we've just ruled this out. And so if a G exists in W but not in @, nothing warranting thanks and praise in @ exists in W. If a G exists in W but not in @, nothing in @ could have depended on that G. For if it did, in any world, it would there depend on that G so completely that it could not exist without the G in any world—including @. So if the G does not exist in @, everything in @ is such that that G does not possibly account for its existence. If so, the G of W is not omnipotent: there are perfectly possible contingent beings for whose existence it cannot account. Surely omnipotence is great-making and exemplifiable; surely nothing can be a G without it. So existence in @ follows from a clearly great-making property. This may well make existing in @ great-making. In any case, on the present argument, nothing that does not exist in @ can be a G in any world. And so any G in any world, including W, exists in @.
I submit, then, that the amended, free-logical version of Proslogion 2's argument is valid, and one of its two premises has strong support.
Proslogion 3
In Proslogion 3, Anselm reasons that
something can be thought to be, which cannot be thought not to be. This is greater than what can be thought not to be. Whence if that than which no greater can be thought, can be thought not to be, itis not that than which no greater can be thoughtSo truly does something than which no greater can be thought exist, therefore, that it cannot be thought not to exist. (Charlesworth 1965 , 118)
Some claim that here Anselm gives a second argument for God's existence. They do so by reading Anselm this way:
6. Possibly something is a G, and
7. Being a G entails existing necessarily. So
8. Possibly a G exists necessarily. So
9. A G exists necessarily. So
10. A G exists.
(p. 88 )
I doubt on exegetical grounds that Anselm actually means to give this argument. But as Proslogion 3 has led some to this argument, we can discuss it here.
(6)–(10) is a valid argument in the S5 system of modal logic. Systems of modal logic—the logic of inferences involving “possibly” and “necessarily”—differ in the claims they make about the relations between possible worlds. The distinctive feature of the S5 system of modal logic is that in it, every world is possible relative to every other world: no matter which world were actual, the same set of worlds would be possible. To see how (6)–(10) works in such a set of worlds, let the boxes below represent all the worlds that are possible:
Let existing in at least one box represent being possible, and existing in all the boxes represent existing necessarily. (6) asserts that possibly a G exists. To represent this, we enter a G in one box:
Now (8) asserts not just that it's possible that a G exist, but that it's possible that a G exist necessarily. What this means, in terms of our boxes, is that a G is in one box, and in that box, it's true of the G that it exists in all the boxes (more precisely, all the boxes possible relative to it, which in S5 are all the boxes). So if (8) is true, G is in W1, and in W1 it's true that if G is in W1, it is also in W2–4, so that we have
Thus, given an S5 system of relations among the boxes, (8) does entail (9): G exists necessarily (in all boxes). Now if W1–4 are all the worlds there are, then one of them will turn out to be actual. G is in all of them, so no matter which one is actual, G will be actual with it. So (9) entails (10). In S5, this modal argument from perfection is valid.
Anselm's Real Argument
While Anselm probably did not intend (6)–(10), he did develop the first modal argument from perfection, in a slightly later work, the Reply to Gaunilo:
Whatever can be thought and does not exist, if it existed, would be ablenot to exist. (But) something than which no greater can be thoughtif it existed, would not be ablenot to exist—for which reason if it can be thought, it cannot not exist. (Charlesworth 1965 , 60)
Anselm's reasoning is this: (p. 89 )
11. If it can be thought that a G exists and no G exists, any G would exist contingently if it did exist.
12. It is not possible that a G exist contingently. So
13. It is not the case that it can be thought that a G exists and no G exists.
So
14. If it can be thought that a G exists, some G exists.
15. It can be thought that a G exists.
16. Some G exists.
There are strong a priori arguments for (12). We can recast (11) as
17. If it is possible that a G exists and no G exists, any G would exist contingently if it did exist.
and alter the rest of the argument accordingly. The advantage of doing so is that (17) comes out true within the Brouwer system of modal logic, a weaker system S5 includes. The Brouwer system is weaker than S5 because it makes a weaker claim about possible worlds: rather than assert that every world is possible relative to every other, it asserts that relative possibility is symmetric: that if A is possible relative to B, B is possible relative to A. To see that (17) is true in Brouwer, suppose that these boxes represent all the possible worlds there are:
Let's say that W1 is actual, and relative to W1, W2 is possible. Our G, God, exists only in W2. So actually, God does not exist. But W2 is possible. So it's possible that God exist. Now suppose that W2 had been actual instead of W1. In that case, God would have been actual. But if relative possibility is symmetric, then because W2 is possible relative to W1, had W2 been actual, W1 would have been possible. So had W2 been actual, a world would have been possible in which God did not exist. So had W2 been actual, God would have existed contingently: which is to say that if our G possibly exists and does not, it would exist contingently if it did exist, assuming what the Brouwer system says about relations among possible worlds.
(p. 91 ) It's also worth noting that (6) and (12) suffice on their own to prove God's existence if the correct system of modal logic for metaphysical possibility includes Brouwer. To see this, suppose that these boxes represent all the possible worlds there are:
If W4 is actual, of course, God exists. Suppose instead that W3 is actual. Then if possibly God exists, God exists in at least one box possible relative to W3, and so God exists in W4. Per (12), God exists necessarily in W4. So if W4 were actual, God would exist necessarily, that is, in every world possible relative to W4. Per Brouwer, if W4 is possible relative to W3, W3 is also possible relative to W4. So God is necessary in W4 only if God also exists in W3. So if W3 is actual, God actually exists. So whether W3 or W4 is actual, God exists, and so given (6), (12), and Brouwer, God exists.
Modulo the change from (11) to (17), then, we can credit Anselm with the first valid modal argument from perfection.
Modal arguments from perfection face two difficulties. One lies in showing that the modal systems they invoke really are the correct logics for real metaphysical possibility. The other is epistemological. Consider Plantinga's (1974a) attribute of no-maximality, or being such that one does not coexist with a G. If this attribute is possibly exemplified, then given (12) and S5, being a G is not. A modal argument gives one reason to become a theist only if its proponent offers one not just the argument but some reason to believe the claim that being a G is possibly exemplified rather than the claim that no-maximality is. Many claim that modal arguments from perfection “beg the question” by asserting that being a G rather than no-maximality is possibly exemplified. They do not. Every argument asserts rather than justifies its own premises. If we need reason to believe in being a G rather than no-maximality, this shows not that a modal argument begs the question, but merely that another argument is needed, on behalf of one of its premises.
(p. 92 ) Gaunilo and Parody
Shortly after Anselm published the Proslogion, Gaunilo of Marmoutiers replied with a parody of the Proslogion 2 argument:
(An) island more excellent than all other lands truly exists somewhere in reality (if it exists) in your mind. For it is more excellent to exist not only in the mind but also in reality. So it must necessarily exist. For if it did not, any other land existing in reality would be more excellent. And so the island you conceived to be more excellent will not be more excellent. (Charlesworth 1965 , 164)
This parody isn't quite right, but we can construct the right sort on Gaunilo's behalf: let's take him to have meant that if we replace “a G” with “an island than which no greater can be thought,” the resulting argument works as well as Anselm's. There is no such island. So (says Gaunilo) we know the argument isn't sound, even if we can't pinpoint its flaw.
Unfortunately for Gaunilo, some sorts of parody are easily dismissed. There is no greatest possible island, for there can always be another island better at least for containing more of what makes any other island good (Plantinga 1974b, 91–92). 7 Oppy suggests that perhaps “the greatest possible island will have an infinite surface area andsupply of banana trees (etc.)Given (this) it will not be the case that it could have a greater supply of these things” ( 1995 , 165). Not so: for every order of infinity, there is a higher order. Oppy also suggests that traditional theists must concede the possibility of a greatest island, for their heaven is in effect an island than which no greater is possible, whose greatness lies inter alia in conferring “eternal life and infinite attributes on its inhabitants” (165). But on traditional theist belief, not heaven but God confers eternal life, and heaven is not surrounded by water. A physical heaven might be more like a new universe. But traditional theists don't hold that heaven is a best possible physical universe, only that being in heaven is the best possible state for us—and that it is so because heaven affords each of us our closest contact with God. Further, if greatness is (roughly) worship-worthiness, it's not true that a greatest possible island would be still greater if it existed. Nonexistent islands don't deserve worship, but neither do real ones, however lovely. Here, however, Oppy has a countersuggestion. Perhaps, he wonders, a greatest possible island would have “Godlike powers of providing for its inhabitants,” in which case, theists can rule out a greatest possible island only if they can rule out the possibility of “limited—localized—pantheism” (166). Oppy might have made this particularly pointed by asking Christians whether God could incarnate Himself in an island. But a divine island is great qua divine, not qua island. Despite Oppy, it remains the case that islands as such don't deserve worship. So Oppy has left the realm of Gaunilo's original parody, and moved into talk of what I call almost-Gods.
(p. 93 ) Deity is a kind. Most kinds can have more than one member: there are many cows. If deity is a kind, perhaps it can have many members, or could have had a different one. If it can or could have, parallel arguments from perfection will work for all possible Gods, yielding more Gods than monotheists want. So Anselm needs to show that
NO. There cannot in one possible world be two instances of deity.
One good argument for (NO) stems from a claim argued earlier, that a G must account for the existence of all good things with which it coexists. Gs are good things. So were there two Gs at once, each would have to account for the other's existence. Because —— accounts for ——'s existence is a transitive relation, this would entail that each accounts for its own existence. But this is impossible. Again, we saw earlier that a G's contribution must be both sufficient and necessary for the existence of all good things with which it coexists. If so, there cannot be two Gs at once. For suppose that A and B each suffice on their own for C's existence. Then without B's contribution, C could still exist, if A were still making its contribution. But then it's false that B's contribution is necessary for C's existence.
(NO) is true, and so multiple-G parodies are ruled out. So let's consider parodies via almost-Gods, deities whose only greater is God. Let's call one such being Zod, and say that Zod is just like God save for a slight difference in perfection we cannot conceive. Zod is to us indiscernible from God. But Zod cannot coexist with God. For God is uncreatable and has made everything other than Himself, and Zod would duplicate Him in these respects. And so we cannot accept arguments for both Zod and God. But we might read “a G” as “an almost-God than whom no greater can be thought”—describing a being whose only greater is God, who is not an almost-God. If Anselm can't explain why we should accept (1) and (2) on his reading of them but not on a parody-reading, we ought not assent to them on either reading. Further, if God is a necessary being, so is Zod. So given a modal logic including Brouwer, it's not the case both that Zod and that God possibly exist. 8 But if we can't tell Zod from God, how could we have reason to think one but not the other possible? Thus, parody yields reason to be agnostic about such claims as that being a G is possibly exemplified.
Almost-Gods threaten to multiply: perhaps for any particular degree of likeness to God, an almost-God like Him to that degree would be more worship-worthy if it existed than if it were merely possible. Whether it would, though, depends on what worship is. At least within Western monotheism, whose concept of worship Anselm presumably had in mind, worship is or includes praise without qualification or limit. What deserves only qualified or limited praise thus does not deserve worship. And anything that can have a superior can deserve only qualified or limited praise. It is great—but there can be a greater, and so its praise (p. 94 ) ought to be qualified accordingly. “O god, you are great—but there can be greater”: this does not sound like worship. If it isn't, and yet someone surpassable can deserve no more, nobody surpassable can deserve worship. Nothing can unless it has no possible greater simpliciter. And now here's the rub: an almost-God has no possible greater simpliciter only if it isn't possible that there be an Anselmian G. For as we've seen, a G is greater overall than any other possible being. If a G is possible, then, no almost-God can deserve worship, and so none can be more worship-worthy if actual. And so if a G is possible, one can dismiss this sort of parody—any reason to think a G possible gives one reason simply to ignore it. Perhaps, then, one can so tweak Anselm's property of greatness as to make parody difficult.
Here an objection arises. Polytheists worshipped; what they felt, did, and said is enough like what monotheists feel, do, and say to deserve the label. Some worshipped gods other gods outranked. So one can worship something surpassed. And so there is room for worship of almost-Gods. The tweaking move is at best trivial and at worst question-begging, for it so defines worship that only God can deserve it.
This objection is confused on at least two levels. For one thing, even if polytheists did worship, nothing follows about what deserved their worship: that something is worshipped implies nothing about whether it ought to be. And no polytheist god could deserve what monotheists call worship. In worship, monotheists give all their religious thanks and praise to God. So deserving worship in the Western-monotheist sense includes deserving all of one's religious thanks and praise. No polytheist god deserves all religious thanks and praise, for none is responsible for all of our blessings. So either polytheists misdirected monotheist worship at their gods or, more charitably, what polytheists did “in church” does not count as worship in the sense discussed above. Further, worship for Western monotheists includes the giving of thanks and praise without limit or qualification. Polytheists, just as such, cannot consistently do this for any single god. They must limit and qualify their praise for any god in light of what they must say to other gods: they should not praise Zeus for blessings Hera gave or praise Hera to a degree only Zeus deserves. In worship, monotheists give God all their religious loyalty. Polytheists, as such, cannot give all their religious loyalty in any act of worship. Polytheists' religious loyalties compete: time spent in Venus's temple is not spent in Mars's. Monotheists have only one temple to attend. If polytheists worship, then, their worship differs from monotheists'. There is a kind of worship only monotheists can give, for there are attitudes one can have only to a sole object of worship.
Next epicycle: perhaps one can define the almost-greatness of almost-Gods in terms of deserving almost-worship (or almost-sole-worship, etc.), and say that almost-Gods would be almost-greater if actual. What then? Well, the problem for (p. 95 ) a Pros. 2 parody comes in applying the parallel to (2a). There is no maximal degree of deserving almost-worship (as vs. worship). There is no state than which there is no almost-greater. So for every state an almost-God might be in, there is an almost-greater state something could be in, and so the parody-argument will fail. I now argue the no-maximal-degree claim.
God deserves worship. Maximal likeness to God would be duplication, and so would yield something deserving worship, not almost-worship. If likeness to God is graded on a dense or continuous scale, then there is no maximum likeness to God short of duplication: for every nonduplicate of God, something can be more like God than it is. If God deserves worship, becoming more like God is coming closer to deserving worship. So plausibly, becoming more like God is also coming closer to deserving almost-worship, or (once over the threshold for this) deserving ever more almost-worship. If likeness to God has no maximum short of deserving worship (by duplication), there is no maximum state of almost deserving worship (almost duplicating God). This doesn't entail that there's no maximum state of deserving almost-worship, but it surely suggests it.
Still, it's not implausible that in some cases likeness to God is a granular matter, that is, comes in discrete degrees, with a maximum just shy of duplication. For we can describe such a scale: just like God save for knowing four public truths God knows, or three, or twoOn such scales, if there are maximal states, they are along the lines of being just like God save for not knowing one public truth an omniscient being would know, or being unable to do one task omnipotence, could accomplish, or being able to commit one sin. I doubt that beings like this really are possible—what could keep someone who has all eternity to figure things out, is omnipotent, and knows all the other public truths from learning the last? Be that as it may, someone with just one of these defects would be more like God than someone with all three. But which defect leaves one closest to God? Would someone not quite omnipotent be more like God than someone not quite omniscient? Someone is most like a perfect being if he or she is unlike it only in the least important (“perfecting”) respect, and so this amounts to the question Which is least important: omniscience, omnipotence, or moral perfection? Given the shakiness of all intuitions here, the best reply may be that each one-defect being is more like God in his or her nondefective respects than anything defective in these respects is, but there's no answer to the question Which is most like God overall? This sparks a suggestion: perhaps each one-defect being is in a state with no greater short of being God, and so is maximally Godlike short of duplication. But this suggestion is correct only if there are no relevant gradations within each one-defect state, and that's questionable.
Consider possible beings just one truth short of public-truth omniscience. Some don't know this truth, some that. Which truth they don't know can affect their Godlikeness. Some truths are more important than others. So the lack of (p. 96 ) some truths is more important than the lack of others: it seems less important that God know the weight of a particular gnat in early Mesopotamia than that God know that floods kill. It's more Godlike (“perfecting”) to get important things right. So beings are less Godlike the more important the truths they lack. Again, lacking some truths entails greater cognitive defect than lacking others: not knowing about the gnat is minor, while not knowing that modus ponens is valid is major. But it would take some doing to show that there are least important truths or lacks or defects. If some truths or lacks are more important than others, none are least important, and a being is the more Godlike in knowledge the less important the truth it lacks (or the less important the lack of this truth, or the defect it entails), then not all not-quite-omniscient beings are equally Godlike and there probably is no such thing as a most-Godlike not-quite-omniscient being. Like comments apply to lacks of power and abilities to sin.
The more like God in greatness-relevant ways, the closer to deserving worship. So if there is no greatest nonduplicative likeness to God, for every possible being deserving almost-worship, there is a state something can be in that would put it closer to deserving worship, and so make it deserve more or greater almost-worship. If possibly God exists, then, there is no state than which there is no greater for almost-Gods. Of course, if God is impossible, then again no possible being can duplicate Him, and the points just made about greater likeness to God remain, for they did not turn on the claim that God possibly exists. Possible items can be graded for likeness with impossible ones; the more nearly circular a thing, the more it is like a circular square.
So the last-epicycle parodic argument doesn't go through. On the other hand, almost-Gods make harder the epistemic problem modal arguments face: it's hard to see how to back belief that possibly God exists over belief that possibly Zod exists. And with the modal arguments there in the background, one wonders how well one can argue for (1a). For (it seems) any reason to accept (1a) would have also to be a reason to favor God over Zod. But in fact, the dialectical situation is this. To take a modal argument as reason to believe in God, one must have reason to believe that God rather than Zod is possible. For modal arguments from perfection will work as well for Zod as for God. But to take the Pros. 2 argument as a reason, one need only have reason to believe that God is possible, rather than more reason to believe this than to believe that Zod is.
Considering parodies for the modal argument shows that the existence of God (or Zod) would have modal consequences. If God exists, then given Brouwer, it is not so much as possible that Zod does: it's necessarily false that Zod exists. So the existence of God would have consequences for modal truths not involving the concept of God: God would have a modal footprint. And Anselm in fact held that what necessary truths there are depends on God (Cur Deus Homo II, 17).
(p. 97 ) Descartes
The Fifth of Descartes' Meditations on First Philosophy ([ 1641 ] 1993 ) offers the last fully original argument from perfection. It begins from a general attempt to show that some conceptual truths are not just conceptual truths, but rather reveal facts about natures independent of the mind:
I find within meideas of certain things that, even if perhaps they do not exist anywhere outside me, still cannot be said to be nothing. And althoughI think them at will, nevertheless they are not something I have fabricated; rather they have their own true and immutable natures. For example, when I imagine a triangle, even if perhaps no such figure exists outside my thought anywhere in the world and never has, the triangle still has a certain determinate nature, essence or form which is unchangeable and eternal, which I did not fabricate, and which does not depend on my mind. This is evident from the fact that various properties can be demonstrated regarding this triangle (which) Iclearly acknowledge, whether I want to or not. For this reason they were not fabricated by meAll these properties are patently trueand thus they are something and not nothing. (42–43)
Descartes then suggests that the nature of God is akin to the nature of a triangle in being something mind-independent which the mind grasps:
The idea of God, that isof a supremely perfect being, is one I discover to be no less within me than the idea of any figurethat it belongs to God's nature that he always existsI understand no less clearly and distinctly thanwhen I demonstrate in regard to some figurethat somethingbelongs to the nature of that figureThusthe existence of God ought to have for me at least thecertainty that truths of mathematics (have). (43–44)
This promises a quasi-mathematical demonstration. Descartes' attempt to keep the promise runs this way:
Existence can no more be separated from the essence of God than the fact that its three angles equal two right angles can be separated from the essence of a triangleit isa contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection)it isnecessary for me to suppose God exists, once I have made the supposition that he has all perfections (since existence is one of the perfections)Not that my thought brings this about or imposes any necessity on anything, but rather the necessity of the thing itselfforces me to think this. (44)
Descartes then adds further reasons to believe that his idea of God is “an image of a true and immutable nature” (45). The broad outline of Descartes' argument, then, is this: he grasps what he claims are mind-independent truths about the kind of thing God would be if there were one. And uniquely, in the case of God, (p. 98 ) the mind-independent truths about the kind require that the kind has an instance. To try to show why, Descartes tries to show that “God does not exist” entails a contradiction.
It is surprisingly hard to say exactly what this last phase of Descartes' argument is up to. I offer three readings of it, one of which subdivides.
Meditation V: One Reading
On one reading, Descartes' premises are that
18. If God does not exist, a being with all perfections lacks a perfection, and
19. A being with all perfections lacks a perfection entails a contradiction.
If both are true, Descartes may think, then if God does not exist, a contradiction is true. But (18) is ambiguous, between
18a. If God does not exist, then if anything has all perfections, it lacks a perfection, and
18b. If God does not exist, there is something with all perfections which lacks a perfection. (Van Inwagen 1993 , 80–81)
To get a valid argument with (18a), we must read (19) as
19a. If anything has all perfections, it lacks a perfection entails a contradiction.
But (19a) is false. That conditional does not by itself entail a contradiction. It entails only that nothing has all perfections, which is what one would expect if a perfect being does not exist. So if the argument including (18a) is valid, it is unsound.
For Descartes, God is the sole possible being with all perfections, and so (18b) amounts to
20. If God does not exist, God exists and lacks a perfection.
(20) is false unless God actually does exist necessarily, in which case “God does not exist” is impossible and so implies anything. But then why should an atheist or agnostic accept (20)? It is on its face quite unintuitive. On another reading, (18b) asserts that if God does not exist, He “is” there, in some sense of “is” compatible with nonexistence, and has contradictory properties. This reading clearly commits us to a Meinongian ontology of nonexistent impossible objects, (p. 99 ) for it asserts that if God does not exist, He is one. On such views, “there is” in “there is something with all perfections which lacks a perfection” does not express existence. It is instead a “wide” quantifier ranging over existent and nonexistent objects. To get a valid argument with (18b), we must read (19) as
19b. There is something with all perfections which lacks a perfection entails a contradiction.
But with the quantifier read “widely,” (19b) is false. On a Meinongian ontology, it is no contradiction for there to “be” contradictory nonexistent objects. Such objects are perfectly normal features of reality. What would be contradictory would be for one of them to exist. So the (18)–(19) argument is unsound on two readings, and on a third has a counterintuitive premise supporting which would require another, independent argument for God's (necessary) existence. Let's therefore consider a different analysis.
Meditation V: Second Try
Med. V speaks of what we do and must suppose, that is, of what our idea of God includes. Descartes later offered a “synthetic” presentation of material from his Meditations, and as an argument to what he seems to claim is to the same effect as Meditation V gave:
To say that something is contained in the nature or concept of anything is the same as to say that it is true of that thing. But necessary existence is contained in the concept of God. Hence it is true to affirm that necessary existence exists in Him, or God Himself exists. (HR II 57)
Here the argument is in terms of concepts. There is also a reference to necessary existence, which suggests a modal argument. But by “necessary existence” Descartes means only actual existence the nature of the thing guarantees: that “actual existence is necessarilylinked to God's other attributes” (HR II 20). So Descartes may here suggest that the Med. V argument is really this:
21. For all x, if being F is part of the concept of x, then Fx.
22. It is part of the concept of God that if God's nature is what it is, God exists. So
23. If God's nature is what it is, God exists.
24. God's nature is what it is. So
25. God exists.
(p. 100 )
The problem here is that (21) is false. It's part of the concept of Santa that he has a beard, but it's false that Santa has a beard, for it's false that anything really both is Santa and is bearded. “Santa is bearded” doesn't say anything true. It is just the right thing to say if you're telling Santa stories.
But perhaps (21) is dispensable. All Descartes really needs is
21a. For all x, if being F is part of the concept of God, then Fgod.
One can read Descartes' Meditation III argument about the concept of God as an attempt to warrant (21a). It is, in effect, an argument that the concept of God has contents such that nobody has this concept unless it has an instance—that the causal story behind anyone's having that concept must include a God. If recent externalists are right, there are many such concepts, for example, water. And if the concept of a sort of item is externally determined in the right way, then something like (21a) will hold for it. Suppose that an appropriate externalist story about natural kind concepts is correct, and that water is a natural kind. Then because the concept of water is determined by the real external nature of water, if being H2O is part of that concept, it follows that water is H2O. It's not clear a priori why God or perfect being could not be an externally determined concept. And that Descartes was in general the patron saint of anti-externalism hardly precludes his claiming that there is one exception to it, which the argument from perfection reveals. On the other hand, any argument that externalism holds for the concept of God is ipso facto one that God really exists. If to back a premise in an argument for God, one needs a second, discrete argument for God, then the first argument cannot be stronger than the second and is not independent of it. So if it took such an argument to back (21a), an argument resting on (21a) would be useless.
Meditation V: Third Try
Our third reading of Meditation V begins by noting again its talk of God's essence and what it includes. Descartes later claimed that the Meditation V argument is:
That which we clearly and distinctly understand to belong to the true and immutable nature of anything, its essence, can be truly affirmed of that thingto exist belongs to [God]'s true and immutable nature; thereforeHe exists. (HR II 19)
In accord with this, we might render the Med. V argument as
26. If the “true and immutable nature” of x includes being F, then Fx.
27. The “true and immutable nature” of God includes existence. So
28. God exists.
(p. 101 )
To respect Descartes' claim that this somehow encapsulates Med. V, we might expand the argument by deriving (27) from
29. The “true and immutable nature” of God includes having all perfections, and
30. Existence is a perfection.
Perhaps Descartes did not see (21)–(25) and (26)–(30) as distinct. He distinguishes ideas that grasp “true and immutable natures” from ideas that are just “fictitiousdue to a mental synthesis” (HR II 20). If an idea does not have its content simply due to a mental operation, it grasps a mind-independent truth. That is, it has its content by grasping something that is somehow also extramentally the case. Descartes' thought, then, seems to be that some ideas grasp “natures” that have some status beyond them, the idea of God being one; for these ideas, the “nature” is just the idea's content, and so we can switch indifferently between nature-talk and talk of concepts (ideas' contents).
Descartes' talk of “true and immutable natures” has two functions in (26)–(30). One is trying to lend credibility to (29). If it's part of a thing's nature that it is F, says Descartes, we did not simply dream this up, and so we can trust our impression that such a thing would be F. But apart from this, it also sets up the claim that (27) and (29) concern some entity or truth independent of the mind. If there really is some entity or truth that logically requires that God exist, then there would be a contradiction in objective reality (not just in our ideas about it) if God did not.
Like (21), (26) is dubious but dispensable. All Descartes needs is (27), which we can recast as
27a. There is a “true and immutable nature” P which includes all perfections and is (uniquely) such that if it exists, it has an instance,
whence he can reason that
31. P exists. (27a, simplification)
32. If P exists, it has an instance. (27a, simplification)
33. P has an instance. (31, 32, MP)
Traits of our idea of God are supposed to assure us that it captures a “true and immutable nature.” Why is (27a)'s second conjunct supposed to be true? One story Descartes tells is the (18)–(19) argument. But in at least one place, he tells another story about why existence is uniquely inseparable from the divine essence:
It is not true that essence and existence can be thought the one apart from the other in Godbecause God is His existence. (HR II 228)
That God = God's existence explains the inseparability of God's essence and God's existence only if God = God's essence—a standard part of the doctrine of divine simplicity Descartes inherited from his Jesuit education. So what Descartes is really saying here is that the divine essence = the divine existence. The reason (27a) is true, then, could be that if there is a divine nature, it is identical with the existence of God. If this is so, then if there is in extramental reality such a nature, there is also such an existence—and so God exists. Perhaps Descartes' doctrine of divine simplicity, asserted in Meditation III, can help his argument in Meditation V.
Descartes: Objections and Replies
Publication of the Meditations led to a series of exchanges between Descartes and prominent intellectuals. The best criticisms of Descartes' argument from perfection came from Pierre Gassendi and Johannes Caterus. Caterus wrote:
Though it be conceded that an entity of the highest perfection implies existence by its very name, yet it does not follow that that very existence is anything actual in the real world, but merely that the concept of existence is insepatably united with the concept of highest being. (The) complex “existing lion” includes both lion andexistence, and includes them essentially, for if you take away either it will not be the same complexdoes not its existence flow from the essence of this composite “existent lion”? Yet (this) does not constrain either part of the complex to existTherefore, also, even thougha being of supreme perfection includes existence in the concept of its essence, yet it does not follow that its existence is anything actual. (HR II, 7–8)
One can put Caterus's thought this way: from premises about the content of a concept, only conclusions about the content of a concept can validly follow.
Descartes' reply in a nutshell is that his premises deal in “what belongs to the true and immutable essence of a thing,” not “what is attributed to it merely by a fiction of the intellect” (HR II 19)—that is, are not merely about concepts' contents, but about extramental facts. His criterion for this seems to be that elements of a “merely fictitious” nature can rightly be separated conceptually: winged horse is “fictitious” because we can rightly conceive of horses without wings (HR II 20). On the other hand, if elements FG belong together as part of a “true and immutable nature,” we cannot rightly conceive them apart: being F entails being G, or conversely (HR II 21). Thus, Descartes goes on to try to show that (p. 103 ) existence really does belong to God's “true and immutable nature” without merely reiterating his Med. V argument, by arguing that the nature of God's power itself entails His existence (HR II 21). But if one must show that some divine attribute entails God's existence to show that existence is of God's nature, Descartes has a problem. For if the Med. V argument really does include a premise about God's true, immutable nature including existence, it is then an argument for God the defense of whose premises requires another, independent argument for God's existence. If it is, it is dialectically useless. For if one can demonstrate God's existence a priori in another way, the Med. V argument is unneeded: it can't yield any further, independent warrant for belief in God. If one can't, it has an indefensible premise.
Gassendi wrote:
Existence is a perfection neither in God nor in anything else; it is rather that in the absence of which there is no perfectionthat which does not exist has neither perfection nor imperfection, and that which exists (has) its existenceas that by means of which the thing itself equally with its perfections is in existencenor if the thing lacks existence is it said to be imperfect, (but rather) to be nothing. (HR II 186)
Descartes' reply is that possible existence is a perfection in the case of a triangle, making “the idea of a triangle superior to the ideas of chimeras,” and similarly necessary existence is a perfection in God's case, making the idea of God superior to other ideas (HR II 228–29). This does not immediately address Gassendi's point about mere existence; perhaps Descartes means to add that any property a perfection entails is itself a perfection. This claim would not be implausible, as we see below in discussing Gödel.
Gassendi's second major argument was this:
Although you say that existence quite as much as other perfections is included in the idea of a being of the highest perfection, you (just) affirm what has to be proved, and assume your conclusion as a premise. For I might alsosay that in the idea of a perfect Pegasus (is) contained not only the perfection of having wings but also that of existing. For just as God is thought to be perfect in every kind of perfection, so is Pegasus thought to be perfect in its own kind. (HR II 187)
Descartes offers no reply to the parody. Perhaps he would treat “existing Pegasus” as he did Caterus's “existing lion”: the “complex” captures no “true, immutable nature”—since it's not the case that the attribute of being Pegasus is such that necessarily, if it exists, it has an instance—and so here we do not escape the conceptual order. The Pegasus argument from perfection, Descartes might say, falls to the Caterus objection. But if Descartes cannot support his claim that God's nature includes existence without independent a priori proof that God exists, Gassendi is right that it begs the question.
(p. 104 ) Leibniz
Leibniz worked intensely on arguments from perfection in the 1670s. He held that Descartes' argument was valid but incomplete, needing the addition of a proof that it is at least possible that God exists. His own preferred argument was modal:
If a being from whose essence existence follows is possibleit existsGod is a being from whose essence existence followsTherefore if God is possible, He exists. (Adams 1994 , 137, n.9)
“A being from whose essence existence follows” is just a necessary being. So Leibniz's argument is really that
If possibly a necessary being exists, it exists.
God is by nature a necessary being. So
If possibly God exists, God exists.
The first premise is just an instance of the characteristic axiom of the Brouwer system of modal logic; the argument is sound in Brouwer. The conclusion leaves Leibniz's case for God incomplete, needing, as Leibniz said of Descartes, a proof that possibly God exists. Leibniz tries to provide one.
Leibniz's possibility-argument (Plantinga 1965 , 54–56) treats God as the being whose nature is a conjunction of all and only perfections, perfections being properties that are “simple,” “positive,” and “absolute.” Simple properties do not consist of other properties. They are primitive. Positive properties are those whose natures do not include the negation of other properties. If the property F is a constituent of the property ¬F, every simple property is positive. Positive properties needn't be simple, though. F • G is a positive property if F and G are positive. A property is absolute if and only if its nature involves no limitations of any sort. Leibniz's argument, then, is in essence this: it's possible that God exist just in case all properties in the nature He'd have if actual are compatible. But if properties are simple, they cannot be incompatible because properties of which they consist are incompatible. If properties are positive, their natures do not include the negations of other properties. That is, for all FG, if F and G are positive, F's nature is not and does not include not having G, and G's is not and does not include not having F. But properties F and G are incompatible, thinks Leibniz, only if F includes ¬G, G includes ¬F, some property F includes includes ¬G, or some property G includes includes ¬F. Thus, if any absolute properties are simple and positive, they are compatible.
Leibniz's argument raises a number of questions: Are there simple, absolute, positive qualities? Do they include necessary existence? Do they include colors, (p. 105 ) and do colors pose a problem for the argument? Can the argument be parodied? And what about the gap between consistency and metaphysical possibility?
Simple, Positive Properties
Leibniz wanted this to come out a proof that God possibly exists, and so presumably took perfections to include such properties as omnipotence, omniscience, and perfect benevolence. These involve no limits of quantity or degree. Presumably they need not be instanced by an imperfect subject—they are compatible with “infinity” and “perfection.” So their natures involve no limitations in that respect. It is a limitation to be something with knowledge and will only if there is something better to be, and this is not at all clear. But these are not obviously unanalyzable; plausible accounts of each abound. Leibniz's likely reply would be to say that perfect power, knowledge, and goodness are primitive properties—that although we offer accounts of them in terms of (say) generic power, knowledge, and goodness, in metaphysical fact power (for instance) in general consists in a likeness to the perfect exemplar of power, which thus figures as a primitive constituent in the general, shareable attribute of power. This amounts to applying a resemblance-nominalist account of attributes to the divine case, letting God serve as the paradigm instance: and Leibniz was indeed a nominalist, and speaks of created attributes as imperfect imitations of divine attributes in his Monadology (#48). If the standard divine attributes come out primitive, then they are also positive, and we've already seen that they're “absolute.” Perhaps Leibniz can claim that necessary existence is the paradigm of which nonnecessary existence is an imperfect imitation. This claim is at least standard in theological tradition; one finds it, for example, in Anselm.
Colors
Colors are a problem for Leibniz. Phenomenal redness and greenness seem unanalyzable. They are also positive qualities of experience. They also seem absolute. For what limits are involved in seeming red? Not materiality: a discarnate soul could hallucinate in color, and plausibly in a hallucination something appears red. But no spot in any visual field can have both properties: they are incompatible. Now here Leibniz could perhaps reply that just for this reason, colors are not positive in his sense. Each is, after all, a determinate of a determinable, phenomenal color. And the nature of determinables may come to Leibniz's aid. For a plausible view of determinables would see them as simply disjunctions of their determinates, such that each n-tuple of the properties of which a determinable (p. 106 ) consists is internally inconsistent—in which case, each determinate implies the negation of each other determinate. If this is correct, the phenomenal colors are not Leibniz-positive. Each's nature in some manner contains the negation of the rest: certainly it entails these. So perhaps Leibniz's cause is not utterly hopeless here.
Parody and Possibility
Leibniz's argument does seem vulnerable to parody (Adams 1994 , 150–51). Nothing he says indicates that his simple perfections entail one another. And it's hard to see how he could allow this. If omniscience did entail omnipotence, say, it would not be in virtue of “containing” the negation of nonomnipotence (since it doesn't contain the negation of any property). If the perfections do not entail each other, it seems possible to conjoin all save omniscience with almost-omniscience. For as none contain the negation of any other property, none contain the negation of almost-omniscience. But then the other perfections are consistent with almost-omniscience—or at least Leibniz's argument gives us as much reason to think this as to think that the perfections are all consistent. And so the argument gives us as much reason to grant the possibility of a necessarily existing almost-omniscient almost-God as we do the existence of God. But they can't both be possible. Just because we do see that it is vulnerable to parody, it's clear that Leibniz has a problem with the gap between consistency and real metaphysical possibility. The concepts of God and almost-God are equally consistent, on his showing. But it cannot be that both are possible, for at most one of these beings really exists. So we can't take Leibniz to have shown that it is possible that God or an absolutely perfect being exists.
Kant
Kant's Critique of Pure Reason ([ 1781 ] 1956 ) is often treated as the death knell of arguments from perfection. Kant claimed against Descartes that “ `being' isnota predicatewhich could be added to the concept of a thingIt is merely the positing of a thing” (A598/B626). This denies (30), at least if we assume that every perfection is expressed by a “predicate,” something that describes or characterizes an object. On this assumption, it is very nearly one of Gassendi's moves. Kant also argued this way:
34. All necessary truths are really conditional in form (“The absolute necessity of the judgment is only a conditioned necessity ofthe predicate in the judgment” [A703–4/B621–22]).
35. Any conditional expansion of a purported necessary existential truth would be analytic as well as existential.
36. There are no analytic existential propositions (A708/B626). 9
37. So no necessary proposition asserts the existence of anything.
(36) and (37) follow Hume. But Kant's way of supporting them is, for better or worse, his own. If (36) or (37) is true, then Descartes' argument cannot be sound, if its contention is in effect that “God exists” is analytic. If an argument is unsound, it either has a false premise or makes an invalid inference, and one who asserts that an argument is unsound must back the claim by showing one or the other. Kant's denial of (30) does this.
Kant supports (34) with only an example, that “necessarily a triangle has three sides” is really “necessarily, for all x, if x is a triangle, x has three sides” (A704/B622). His case for (35) is left implicit. In parallel to the triangle example, “necessarily, God exists” would on Kant's account really assert “necessarily, for all x, if x is a God, x exists.” This is an “identical proposition” (A704/B622), since “x is a God” includes the note that x exists, at least on the plausible assumption that only existing things have any attributes at all. If this is an “identical proposition,” it is also an analytic proposition, because its consequent merely makes explicit something its antecedent clearly includes. So if Kant's conditional account of necessity-claims is correct, then any necessary existential proposition is analytic. Kant's denial that existence is a “predicate”—by which he means something that describes or characterizes an object—helps back (36). Analytic propositions unfold the contents of a concept of some item. Concepts characterize their objects, that is, ascribe to them conjunctions of characterizing properties. So analytic propositions can only ascribe characterizing properties. So if existence is not a characterizing property, there can be no analytic existentials.
How much did Kant actually achieve? As to the claim that existence is not a predicate, Anselm's backing for (2), as explained above, does not involve any particular doctrine about the logical status of existence, nor even the claim that existence has some general great-making or perfective aspect. The point about existence doesn't even really cut against Descartes. One version of his argument uses the premise that existence is a perfection, but the having of a perfection could be expressed other than by what Kant would call a “real predicate.” Another version claims that necessary existence is a perfection—but to claim that necessary existence is a property is not to claim that any existential proposition is necessary. Propositions predicating such a property need not be quantified at all. In any case, the claims that existence is not a predicate or a characterizing predicate are quite likely false. We can well understand a woman who concedes that her hus (p. 108 ) band, Harvey, is not as brave as Batman or as brilliant as Lex Luthor, then adds “But at least Harvey exists!” This claim predicates existence of Harvey, telling us something substantive about him that “enlarges our concept” of Harvey, namely, that he is not a fictional character.
As to Kant's other line of attack, mathematics features numerous apparent necessary and nonconditional existential truths, for example, that there is a prime number between one and ten. (Kant's friends might dig their heels in and insist that this is really something like a claim that if anything is a series of natural numbers, it includesBut this would pretty plainly be stretching things.) Note that worries about the ontological status of numbers aren't really to the point here: the truths involved are of this form, whatever precisely it is that makes them true, and even if one assigns some unusual interpretation to the existential quantifier in mathematical contexts. So Kant's (34) seems frail indeed, and without it, (35) is at best irrelevant. If the logicists are right, these necessary truths are all analytic. If they are not, these are synthetic propositions which (pace Kant) do not concern how things must appear to us. Either way, Kant's theory of necessity is in serious trouble.
Gödel
Kant actually said little that earlier writers had not already said, and Kant's objections (I've claimed) were duds. But they were not thought so, and so arguments from perfection found few friends for the next two centuries. In 1970, mathematician Kurt Gödel developed an argument related to Leibniz's. The reasoning keys on a concept of a “positive” property that Gödel did not explain well. C. Anthony Anderson suggests that we take being positive as being “necessary for and compatible with perfection,” or such that “its absence in an entity entails that the entity is imperfect and its presence does not entail (this)” ( 1990 , 297). The two descriptions are equivalent. If a property is necessary for perfection, its absence in A entails that A is imperfect, and conversely. If a property is compatible with perfection, its presence in A does not entail that A is imperfect, and conversely. Gödel's proof (as Anderson emends it) makes these assumptions:
Definition 1. X is divine if and only if x has as essential properties all and only positive properties.
Definition 2. A is an essence of x if and only if for every property B, x has B necessarily just in case x's having A entails x's having B.
(p. 109 )Definition 3. X necessarily exists if and only if every essence of x is necessarily exemplified.
Axiom 1. If a property is positive, its negation is not positive.
Axiom 2. Any property a positive property entails is positive.
Axiom 3. The property of being divine is positive.
Axiom 4. If a property is positive, it is necessarily positive.
Axiom 5. Necessary existence is positive.
Since being perfect is necessary for and compatible with perfection, on Anderson's reading, Definition 1 yields the claim that anything divine is by nature a perfect being. Again, on D. 1, a divine being has essentially every property necessary for perfection. Presumably having every property necessary for perfection suffices for perfection. (If it did not, something more would be necessary to attain perfection.) So D. 1 licenses the use of “perfect being theology” to fill out the concept of a divine being. If entailment is strict implication, Definition 2 encapsulates one standard account of what an essence is. Given D. 2, Definition 3 follows at once.
I now present the argument. Axiom 3 has it that the property of being divine is positive. D. 1 has it that every positive property is essential to a divine being. So being divine is essential to a divine being. D. 2 entails that any being has each of its essential properties in every world in which it exists, for if x has B necessarily, x's having A entails x's having B only if x has A necessarily. So per D. 2, any divine being is necessarily divine—divine in all possible worlds in which it exists. Per D. 1 and A. 5, any divine being is essentially a necessary existent. So any divine being is by nature divine and necessary in every possible world.
Axioms 1 and 2 jointly entail that any positive property is consistent. For a property is inconsistent just in case it entails its own negation. Per Axiom 1, if a property is positive, its negation is not positive. But per Axiom 2, if a property is positive, it entails only positive properties. So no positive property entails its own negation.
If every positive property is consistent, and being divine is positive, being divine is consistent. It is necessarily so per A. 4. We can confirm this another way: being divine is having all and only positive properties essentially. But if positive properties entail only positive properties (A. 2), and no negation of any positive property is positive (A. 1), no positive property entails the negation of any positive property. But then the set of all positive properties is consistent; none of its members entails the negation of any of its members. 10 Suppose now that if being divine is consistent, it is instanced in some possible world. Then given what we've argued so far, there is in some possible world a necessarily existent necessarily divine being: that is, it is possibly necessary that “a divine being exists” is true. Given this and the Brouwer axiom, it follows that a divine being exists.
Gödel's argument faces two basic questions. One is whether there is a con (p. 110 ) tentful, theologically appropriate gloss of “positive” on which the axioms are true. The other is whether there is a sort of possibility such that (a) a concept's being syntactically consistent entails that it is possible in that sense that it be instanced, and (b) the Brouwer axiom is true for that sort of possibility and necessity.
The answer to the first question is yes. Talk of God as a perfect being is certainly appropriate theologically, and perfect being theology has been the main tool to give content to the concept of God philosophically almost as long as there has been philosophical theology. And on Anderson's gloss, the axioms come out true.
Anderson's gloss validates Axiom 1. Suppose that a property F is positive. Then by Anderson's gloss, if A lacks F, A is imperfect. If A has not-F, A lacks F. So if A has not-F, A is imperfect, and so not-F is not compatible with perfection, and so not positive. Anderson's gloss validates Axiom 2. On Anderson's gloss, if a property is not positive, either it is not necessary for or it is not compatible with perfection. If having a property F entails having some property that is not compatible with perfection, having F is not compatible with perfection—and so any property that entails something for this reason nonpositive is itself nonpositive. If a property entails a property not necessary for perfection, it entails a property a divine being can lack. Any property a divine being can lack is not part of its essence. A divine being's essence includes or entails whatever properties it has necessarily (D. 2); so any property a divine being can lack is contingent. But only properties had contingently entail the having of contingent properties. So any property that entails a property not necessary for perfection is itself contingent and not part of a divine being's essence. But a divine being's essence includes all positive properties (D. 1). So any property entailing a property that is not positive in this second way is itself not positive. Axiom 3 seems patent, for given D. 1, being divine amounts to a conjunction of all positive properties, and it's hard to see how such a conjunction could fail to be positive. As to Axiom 4, on Anderson's gloss, a property's being positive consists in two facts about property-entailment. It's plausible that properties entail what they do necessarily. As to Axiom 5, necessary existence is certainly compatible with perfection, and perfect being reasoning suggests that it is necessary for it.
There remains the modal question, of whether a concept of possibility and necessity such that being syntactically consistent (entailing no explicit contradiction) entails being in this way possible also conforms to the Brouwer axiom. Syntactic consistency amounts to “logical possibility,” in one sense of the term. But not all that is possible in this narrow logical sense is really or metaphysically possible: there is no formal, explicit contradiction in the claim that something is red and green all over at once, and yet this claim is not metaphysically possible. So there is a gap between what Gödel establishes and its being metaphysically possible that a divine being exist. And it's a substantive question whether the Brouwer axiom governs real metaphysical possibility. We can describe coherently (p. 111 ) a set of possible worlds in which the Brouwer axiom doesn't hold, and in which, while it's possibly necessary that God exists, God does not exist. We need only two worlds to do so, in fact:
Suppose that W2 is actual, and W1 is possible relative to W2 but not vice versa. Then were W2 actual, W1 would be possible. As we're supposing that there are only these two worlds, a God who exists in W1 exists in every world possible relative to W1, if W2 is not possible relative to W1. So in W1, God exists necessarily (and W2 is impossible). Thus, since W1 is possible relative to W2, in this setup, God is possibly necessary and yet does not exist.
Gödel's argument (as emended) shows us that the concepts of a perfect being and of divinity are consistent, given a reasonable concept of perfection. But the gap between consistency and metaphysical possibility and the need to establish that the logic of metaphysical possibility includes the Brouwer axiom stand between it and the Holy Grail of proving God's existence. As well, as a modal argument, Gödel's faces the epistemic problems we've observed: the portion of the argument that contends that possibly a divine being exists may admit of significant parody. On the other hand, consistency is evidence for possibility, though defeasibly so, and if I've assessed Proslogion 2 correctly, that argument is promising and does not require us to deal with the epistemic problems the modal argument faces. There is (I think) little good to be said for Descartes' argument. But the Pros. 2 argument appears to survive objections; to accept its premise (1a) we needn't have more reason to believe in God's possibility than in Zod's; and we do have evidence that possibly God exists. So while there is of course much more to be said here, perhaps Anselm's argument has a future.
WORKS CITED
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Anderson, C. Anthony. 1990. “Some Emendations of Gödel's Ontological Proof.” Faith and Philosophy 7: 292–303.
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Lambert, Karel. 1983. Meinong and the Principle of Independence. New York: Cambridge University Press.
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(p. 114 ) Plantinga, Alvin, ed. 1965. The Ontological Argument. Garden City, N.Y.: Doubleday.
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FOR FURTHER READING
Adams, Robert. 1971. “The Logical Structure of Anselm's Arguments.” Philosophical Review 80: 647–84.
Alston, William. 1960. “The Ontological Argument Revisited.” Philosophical Review 69: 452–74.
Barnes, Jonathan. 1972. The Ontological Argument. New York: St. Martin's Press.
Chandler, Hugh. 1993. “Some Ontological Arguments.” Faith and Philosophy 10: 18–32.
Clarke, Bowman, 1971. “Modal Disproofs and Proofs for God.” Southern Journal of Philosophy 9: 247–58.
Coburn, Robert. 1963. “Professor Malcolm on God.” Australasian Journal of Philosophy 41: 143–62.
Davis, Steven. 1976. “Does the Ontological Argument Beg the Question?” International Journal for Philosophy of Religion 7: 433–42.
Devine, Philip. 1975. “Does St. Anselm Beg the Question?” Philosophy 50: 271–81.
Dore, Clement. 1984. Theism. Dordrecht: D. Reidel.
Dore, Clement. 1984. “The Possibility of God.” Faith and Philosophy 1: 303–15.
Forgie, William, 1972. “Frege's Objection to the Ontological Argument.” Nous 6: 251–65.
Forgie, William. 1976. “Is the Cartesian Ontological Argument Defensible?” New Scholasticism 50: 108–21.
Forgie, William. 1990. “The Caterus Objection.” International Journal for Philosophy of Religion 28: 81–104.
Forgie, William. 1991. “The Modal Ontological Argument and the Necessary A Posteriori.” International Journal for Philosophy of Religion 29: 129–41.
Gale, Richard, 1986. “A Priori Arguments from God's Abstractness.” Nous 20: 531–43.
Gale, Richard. 1988. “Freedom vs. Unsurpassable Greatness.” International Journal for Philosophy of Religion 23: 65–75.
Gale, Richard. 1991. On the Nature and Existence of God. Cambridge, England: Cambridge University Press.
Gotterbarn, Dale. 1976. “Leibniz' Completion of Descartes' Proof.” Studia Leibnitiana 8: 105–12.
Grim, Patrick. 1979. “Plantinga's God.” Sophia 18: 35–42.
Grim, Patrick. 1979. “Plantinga's God and Other Monstrosities.” Religious Studies 15: 91–97.
Grim, Patrick. 1981. “Plantinga, Hartshorne and the Ontological Argument.” Sophia 20: 12–16.
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Hartshorne, Charles. 1962. The Logic of Perfection. LaSalle, Ill.: Open Court Press.
Hartshorne, Charles. 1965. Anselm's Discovery. LaSalle, Ill.: Open Court Press.
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Notes:
(1.) Leibniz's argument, for instance, reasons simply from the claim that God is a necessary being (see below). But the latter rests on the claims that necessary existence is a perfection and that God is a perfect being.
(2.) Nobody nondivine is clumsy but necessary. Proslogion 15 asserts that God is (p. 112 ) greater than can be thought, using the same language involved in a G. Anselm could not mean to say that God is too great to be thought of or described simpliciter, since he surely thinks that God thinks of Himself. So he must mean a G in terms of thinkers other than God. But Anselm wouldn't want to read a G simply in terms of what we can describe or refer to, for he believes in angels, and surely he'd hold that God is too great for angels as well as humans to describe adequately. Still, since “nobody nondivine” is clumsy, I henceforth replace it with “we.”
(3.) If it is better to lack than to have F—that is, if F is an imperfection—then it is better to have than to lack ¬F, and so a G has ¬F. So a G has no imperfections. So nothing could surpass a G by surpassing one of its imperfections. If an attribute is neither a perfection nor an imperfection—neither raises nor lowers greatness—it's hard to see how it could be a respect in which one being could surpass another. For if being F makes A greater than G, presumably being F raises A's greatness past B's.
(4.) Oppy ( 1995 ) suggests that we need reason to think that a G, if actual, would be “a being of religious significance” since there may well be numbers too great (large) for us to “form a positive conception of” (16). Agreed. The only nonlogical vocabulary in “a G” is “thought of” and “greater.” Since no religious significance attaches to the first, the second must provide some. The Findlay suggestion in effect stipulates that it does. And why not?
(5.) Anselm's argument requires that understanding “the G” puts one in cognitive relation to an entity, the G, which then “exists in intellectu.” On this general approach, understanding “Santa Claus” puts one in cognitive relation with Santa Claus. Santa Claus then is the object of one's thought. But Santa Claus does not exist.
(7.) Can there also always be another being a bit better than any being we pick (Oppy 1995 , 19)? We have the concept of God, which has a number of notes and is supposed in virtue of them to be a concept of the greatest possible being. And we find this connection intuitive: it's pretty hard to think of something better than being necessary, omnipotent, omniscient, morally perfect, and so on. So if one can show it possible that God exist, one can answer the question no. Those who offer arguments from perfection must show that this is possible anyway. So “Is it the case that for any possible being, there is always a greater?” adds nothing to their argumentative task. Moreover, —— is a greatest possible island wears its unsatisfiability on its sleeve. —— is a greatest possible being does not, if only because we're less clear on what makes beings as such “great,” or what greatness is in beings. Further, on the reading of greatness I've suggested, it turns out trivially true that God is the greatest being possible, if God possibly exists.
(8.) To see the need for Brouwer, suppose (contra Brouwer) that relative possibility is not symmetric. Then there could be worlds like these:
For simplicity, suppose that W1–3 are all the worlds there are, that only adjacent boxes bear links of direct relative possibility, and that W2 is actual. Say that W1 and W3 are possible relative to W2, but not vice versa. Then both God and Zod exist necessarily (each exists in the only world possible relative to the world in which it exists). And they do not possibly coexist. But both possibly exist, as W1 and W3 are both possible relative to the actual world.
(9.) Kant also believed in synthetic necessities. (He discussed these under the rubric of “synthetic a priori” truths. But he also held that whatever is knowable a priori is necessarily true.) But these, he held, all concern how things must appear to our senses, and God, he held, cannot appear to our senses.
(10.) Which probably entails that not every prima facie member of the set is actually a member. Being omniscient seems to many a prima facie perfection/positive property. So does being atemporal. Nobody is omniscient who does not know what time it is now. But many think that no atemporal being can know this (e.g., Kretzmann 1966 ). One conclusion from this might be that there are at least two incompatible sets of perfections, differing at least in that one includes atemporality but not omniscience and the other includes omniscience but not atemporality. But if we accept the Gödel/Anderson reasoning, no genuine perfections are incompatible. So on their account, what follows is instead that at most one of atemporality and omniscience is actually a perfection.