Summary: Modern Versions Of The Ontological Argument
Modern Versions of the Ontological Argument
Norman Malcolm
One influential attempt to ground the ontological argument in the notion of God as an unlimited being. As Malcolm describes this idea:
“God is usually conceived of as an unlimited being. He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being.… If God is conceived to be an absolutely unlimited being He must be conceived to be unlimited in regard to His existence as well as His operation. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing. Lack of moisture can prevent trees …show more content…
from existing in a certain region of the earth. But it would be contrary to the concept of God as an unlimited being to suppose that anything … could prevent Him from existing.”
The unlimited character of God, then, entails that his existence is different from ours in this respect: while our existence depends causally on the existence of other beings (e.g., our parents), God’s existence does not depend causally on the existence of any other being.
Further, on Malcolm’s view, the existence of an unlimited being is either logically necessary or logically impossible. Here is his argument for this important claim. Either an unlimited being exists at world W or it doesn’t exist at world W; there are no other possibilities. If an unlimited being does not exist in W, then its nonexistence cannot be explained by reference to any causally contingent feature of W; accordingly, there is no contingent feature of W that explains why that being doesn’t exist. Now suppose, per reductio, an unlimited being exists in some other world W’. If so, then it must be some contingent feature f of W’ that explains why that being exists in that world. But this entails that the nonexistence of an unlimited being in W can be explained by the absence of f in W; and this contradicts the claim that its nonexistence in W can’t be explained by reference to any causally contingent feature. Thus, if God doesn’t exist at W, then God doesn’t exist in any logically possible world.
A very similar argument can be given for the claim that an unlimited being exists in every logically possible world if it exists in some possible world W; the details are left for the interested reader. Since there are only two possibilities with respect to W and one entails the impossibility of an unlimited being and the other entails the necessity of an unlimited being, it follows that the existence of an unlimited being is either logically necessary or logically impossible.
All that is left, then, to complete Malcolm’s elegant version of the proof is the premise that the existence of an unlimited being is not logically impossible – and this seems plausible enough. The existence of an unlimited being is logically impossible only if the concept of an unlimited being is self-contradictory. Since we have no reason, on Malcolm’s view to think the existence of an unlimited being is self-contradictory, it follows that an unlimited being, i.e., God, exists. Here’s the argument reduced to its basic elements: 1. God is, as a conceptual matter (that is, as a matter of definition) an unlimited being. 2. The existence of an unlimited being is either logically necessary or logically impossible. 3. The existence of an unlimited being is not logically impossible. 4. Therefore, the existence of God is logically necessary.
Notice that Malcolm’s version of the argument does not turn on the claim that necessary existence is a great-making property. Rather, as we saw above, Malcolm attempts to argue that there are only two possibilities with respect to the existence of an unlimited being: either it is necessary or it is impossible. And notice that his argument does not turn in any way on characterizing the property necessary existence as making something that instantiates that property better than it would be without it. Thus, Malcolm’s version of the argument is not vulnerable to the criticisms of Anselm’s claim that necessary existence is a perfection.
But while Malcolm’s version of the argument is, moreover, considerably easier to understand than Anselm’s versions, it is also vulnerable to objection. In particular, Premise 2 is not obviously correct. The claim that an unlimited being B exists at some world W clearly entails that B always exists at W (that is, that B‘s existence is eternal or everlasting in W), but this doesn’t clearly entail that B necessarily exists (that is, that B exists at every logically possible world). To defend this further claim, one needs to give an argument that the notion of a contingent eternal being is self-contradictory.
Similarly, the claim that an unlimited being B does not exist at W clearly entails that B never exists at W (that is, that it is always true in W that B doesn’t exist), but it doesn’t clearly entail that B necessarily doesn’t exist (that is, B exists at no logically possible world or B‘s existence is logically impossible. Indeed, there are plenty of beings that will probably never exist in this world that exist in other logically possible worlds, like unicorns. For this reason, Premise 2 of Malcolm’s version is questionable.
Plantinga
Perhaps the most influential of contemporary modal arguments is Plantinga’s version. Plantinga begins by defining two properties, the property of maximal greatness and the property of maximal excellence, as follows: 1. A being is maximally excellent in a world W if and only if it is omnipotent, omniscient, and morally perfect in W; and 2. A being is maximally great in a world W if and only if it is maximally excellent in every possible world.
Thus, maximal greatness entails existence in every possible world: since a being that is maximally great at W is omnipotent at every possible world and non-existent beings can’t be omnipotent, it follows that a maximally great being exists in every logically possible world.
Accordingly, the trick is to show that a maximally great being exists in some world W because it immediately follows from this claim that such a being exists in every world, including our own. But notice that the claim that a maximally great being exists in some world is logically equivalent to the claim that the concept of a maximally great being is not self-contradictory; for the only things that don’t exist in any possible world are things that are conceptually defined in terms of contradictory properties. There is no logically possible world in which a square circle exists (given the relevant concepts) because the property of being square is inconsistent with the property of being circular.
Since, on Plantinga’s view, the concept of a maximally great being is consistent and hence possibly instantiated, it follows that such a being, i.e., God, exists in every possible world. Here is a schematic representation of the argument: 1. The concept of a maximally great being is self-consistent. 2. If 1, then there is at least one logically possible world in which a maximally great being exists. 3. Therefore, there is at least one logically possible world in which a maximally great being exists. 4. If a maximally great being exists in one logically possible world, it exists in every logically possible world. 5. Therefore, a maximally great being (that is, God) exists in every logically possible world.
It is sometimes objected that Plantinga’s Premise 4 is an instance of a controversial general modal principle. The S5 system of modal logic includes an axiom that looks suspiciously similar to Premise 4:
AxS5: If A is possible, then it is necessarily true that A is possible.
The intuition underlying AxS5 is, as James Sennett puts it, that “all propositions bear their modal status necessarily.” But, according to this line of criticism, Plantinga’s version is unconvincing insofar as it rests on a controversial principle of modal logic.
To see that this criticism is unfounded, it suffices to make two observations. First, notice that the following propositions are not logically equivalent:
PL4 If “A maximally great being exists” is possible, then “A maximally great being exists” is necessarily true.
PL4* If “A maximally great being exists” is possible, then it is necessarily true that “A maximally great being exists” is possible.
PL4 is, of course, Plantinga’s Premise 4 slightly reworded, while PL4* is simply a straightforward instance of AxS5. While PL4 implies PL4* (since if A is true at every world, it is possible at every world), PL4* doesn’t imply PL4; for PL4 clearly makes a much stronger claim than PL4*.
Second, notice that the argument for Premise 4 does not make any reference to the claim that all propositions bear their modal status necessarily. Plantinga simply builds necessary existence into the very notion of maximal greatness. Since, by definition, a being that is maximally great at W is omnipotent at every possible world and a being that does not exist at some world W’ cannot be omnipotent at W’, it straightforwardly follows, without the help of anything like the controversial S5 axiom, that a maximally great being exists in every logically possible world.
Indeed, it is for this very reason that Plantinga avoids the objection to Malcolm’s argument that was considered above. Since the notion of maximal greatness, in contrast to the notion of an unlimited being as Malcolm defines it, is conceived in terms that straightforwardly entail existence in every logically possible world (and hence eternal existence in every logically possible world), there are no worries about whether maximal greatness, in contrast to unlimitedness, entails something stronger than eternal existence.
Is the Concept of a Maximally Great Being Coherent?
As is readily evident, each version of the ontological argument rests on the assumption that the concept of God, as it is described in the argument, is self-consistent. Both versions of Anselm’s argument rely on the claim that the idea of God (that is, a being than which none greater can be conceived) “exists as an idea in the understanding.” Similarly, Plantinga’s version relies on the more transparent claim that the concept of maximal greatness is self-consistent.
But many philosophers are sceptical about the underlying assumption, as Leibniz describes it, “that this idea of the all-great or all-perfect being is possible and implies no contradiction.” Here is the problem as C.D. Broad expresses it:
Let us suppose, e.g., that there were just three positive properties X, Y, and Z; that any two of them are compatible with each other; but that the presence of any two excludes the remaining one. Then there would be three possible beings, namely, one which combines X and Y, one which combines Y and Z, and one which combines Z and X, each of which would be such that nothing … superior to it is logically possible. For the only kind of being which would be … superior to any of these would be one which had all three properties, X, Y, and Z; and, by hypothesis, this combination is logically impossible.… It is now plain that, unless all positive properties be compatible with each other, this phrase [i.e., "a being than which none greater can be imagined"] is just meaningless verbiage like the phrase “the greatest possible integer.”
Thus, if there are two great-making characteristics essential to the classically theistic notion of an all-perfect God that are logically incompatible, it follows that this notion is incoherent.
Here it is important to note that all versions of the ontological argument assume that God is simultaneously omnipotent, omniscient, and morally perfect. As we have seen, Plantinga expressly defines maximal excellence in such terms. Though Anselm doesn’t expressly address the issue, it is clear (1) that he is attempting to show the existence of the God of classical theism; and (2) that the great-making properties include those of omnipotence, omniscience, and moral perfection.
There are a number of plausible arguments for thinking that even this restricted set of properties is logically inconsistent. For example, moral perfection is thought to entail being both perfectly merciful and perfectly just. But these two properties seem to contradict each other. To be perfectly just is always to give every person exactly what she deserves. But to be perfectly merciful is to give at least some persons less punishment than they deserve. If so, then a being cannot be perfectly just and perfectly merciful. Thus, if moral perfection entails, as seems reasonable, being perfectly just and merciful, then the concept of moral perfection is
inconsistent.
The problem of divine foreknowledge can also be seen as denying that omniscience, omnipotence, and moral perfection constitute a coherent set. Roughly put, the problem of divine foreknowledge is as follows. If God is omniscient, then God knows what every person will do at every moment t. To say that a person p has free will is to say that there is at least one moment t at which p does A but could have done other than A. But if a person p who does A at t has the ability to do other than A at t, then it follows that p has the ability to bring it about that an omniscient God has a false belief – and this is clearly impossible.
On this line of analysis, then, it follows that it is logically impossible for a being to simultaneously instantiate omniscience and omnipotence. Omnipotence entails the power to create free beings, but omniscience rules out the possibility that such beings exist. Thus, a being that is omniscient lacks the ability to create free beings and is hence not omnipotent. Conversely, a being that is omnipotent has the power to create free beings and hence does not know what such beings would do if they existed. Thus, the argument concludes that omniscience and omnipotence are logically incompatible. If this is correct, then all versions of the ontological argument fail.
Norman Malcolm
One influential attempt to ground the ontological argument in the notion of God as an unlimited being. As Malcolm describes this idea:
“God is usually conceived of as an unlimited being. He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being.… If God is conceived to be an absolutely unlimited being He must be conceived to be unlimited in regard to His existence as well as His operation. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing. Lack of moisture can prevent trees …show more content…
from existing in a certain region of the earth. But it would be contrary to the concept of God as an unlimited being to suppose that anything … could prevent Him from existing.”
The unlimited character of God, then, entails that his existence is different from ours in this respect: while our existence depends causally on the existence of other beings (e.g., our parents), God’s existence does not depend causally on the existence of any other being.
Further, on Malcolm’s view, the existence of an unlimited being is either logically necessary or logically impossible. Here is his argument for this important claim. Either an unlimited being exists at world W or it doesn’t exist at world W; there are no other possibilities. If an unlimited being does not exist in W, then its nonexistence cannot be explained by reference to any causally contingent feature of W; accordingly, there is no contingent feature of W that explains why that being doesn’t exist. Now suppose, per reductio, an unlimited being exists in some other world W’. If so, then it must be some contingent feature f of W’ that explains why that being exists in that world. But this entails that the nonexistence of an unlimited being in W can be explained by the absence of f in W; and this contradicts the claim that its nonexistence in W can’t be explained by reference to any causally contingent feature. Thus, if God doesn’t exist at W, then God doesn’t exist in any logically possible world.
A very similar argument can be given for the claim that an unlimited being exists in every logically possible world if it exists in some possible world W; the details are left for the interested reader. Since there are only two possibilities with respect to W and one entails the impossibility of an unlimited being and the other entails the necessity of an unlimited being, it follows that the existence of an unlimited being is either logically necessary or logically impossible.
All that is left, then, to complete Malcolm’s elegant version of the proof is the premise that the existence of an unlimited being is not logically impossible – and this seems plausible enough. The existence of an unlimited being is logically impossible only if the concept of an unlimited being is self-contradictory. Since we have no reason, on Malcolm’s view to think the existence of an unlimited being is self-contradictory, it follows that an unlimited being, i.e., God, exists. Here’s the argument reduced to its basic elements: 1. God is, as a conceptual matter (that is, as a matter of definition) an unlimited being. 2. The existence of an unlimited being is either logically necessary or logically impossible. 3. The existence of an unlimited being is not logically impossible. 4. Therefore, the existence of God is logically necessary.
Notice that Malcolm’s version of the argument does not turn on the claim that necessary existence is a great-making property. Rather, as we saw above, Malcolm attempts to argue that there are only two possibilities with respect to the existence of an unlimited being: either it is necessary or it is impossible. And notice that his argument does not turn in any way on characterizing the property necessary existence as making something that instantiates that property better than it would be without it. Thus, Malcolm’s version of the argument is not vulnerable to the criticisms of Anselm’s claim that necessary existence is a perfection.
But while Malcolm’s version of the argument is, moreover, considerably easier to understand than Anselm’s versions, it is also vulnerable to objection. In particular, Premise 2 is not obviously correct. The claim that an unlimited being B exists at some world W clearly entails that B always exists at W (that is, that B‘s existence is eternal or everlasting in W), but this doesn’t clearly entail that B necessarily exists (that is, that B exists at every logically possible world). To defend this further claim, one needs to give an argument that the notion of a contingent eternal being is self-contradictory.
Similarly, the claim that an unlimited being B does not exist at W clearly entails that B never exists at W (that is, that it is always true in W that B doesn’t exist), but it doesn’t clearly entail that B necessarily doesn’t exist (that is, B exists at no logically possible world or B‘s existence is logically impossible. Indeed, there are plenty of beings that will probably never exist in this world that exist in other logically possible worlds, like unicorns. For this reason, Premise 2 of Malcolm’s version is questionable.
Plantinga
Perhaps the most influential of contemporary modal arguments is Plantinga’s version. Plantinga begins by defining two properties, the property of maximal greatness and the property of maximal excellence, as follows: 1. A being is maximally excellent in a world W if and only if it is omnipotent, omniscient, and morally perfect in W; and 2. A being is maximally great in a world W if and only if it is maximally excellent in every possible world.
Thus, maximal greatness entails existence in every possible world: since a being that is maximally great at W is omnipotent at every possible world and non-existent beings can’t be omnipotent, it follows that a maximally great being exists in every logically possible world.
Accordingly, the trick is to show that a maximally great being exists in some world W because it immediately follows from this claim that such a being exists in every world, including our own. But notice that the claim that a maximally great being exists in some world is logically equivalent to the claim that the concept of a maximally great being is not self-contradictory; for the only things that don’t exist in any possible world are things that are conceptually defined in terms of contradictory properties. There is no logically possible world in which a square circle exists (given the relevant concepts) because the property of being square is inconsistent with the property of being circular.
Since, on Plantinga’s view, the concept of a maximally great being is consistent and hence possibly instantiated, it follows that such a being, i.e., God, exists in every possible world. Here is a schematic representation of the argument: 1. The concept of a maximally great being is self-consistent. 2. If 1, then there is at least one logically possible world in which a maximally great being exists. 3. Therefore, there is at least one logically possible world in which a maximally great being exists. 4. If a maximally great being exists in one logically possible world, it exists in every logically possible world. 5. Therefore, a maximally great being (that is, God) exists in every logically possible world.
It is sometimes objected that Plantinga’s Premise 4 is an instance of a controversial general modal principle. The S5 system of modal logic includes an axiom that looks suspiciously similar to Premise 4:
AxS5: If A is possible, then it is necessarily true that A is possible.
The intuition underlying AxS5 is, as James Sennett puts it, that “all propositions bear their modal status necessarily.” But, according to this line of criticism, Plantinga’s version is unconvincing insofar as it rests on a controversial principle of modal logic.
To see that this criticism is unfounded, it suffices to make two observations. First, notice that the following propositions are not logically equivalent:
PL4 If “A maximally great being exists” is possible, then “A maximally great being exists” is necessarily true.
PL4* If “A maximally great being exists” is possible, then it is necessarily true that “A maximally great being exists” is possible.
PL4 is, of course, Plantinga’s Premise 4 slightly reworded, while PL4* is simply a straightforward instance of AxS5. While PL4 implies PL4* (since if A is true at every world, it is possible at every world), PL4* doesn’t imply PL4; for PL4 clearly makes a much stronger claim than PL4*.
Second, notice that the argument for Premise 4 does not make any reference to the claim that all propositions bear their modal status necessarily. Plantinga simply builds necessary existence into the very notion of maximal greatness. Since, by definition, a being that is maximally great at W is omnipotent at every possible world and a being that does not exist at some world W’ cannot be omnipotent at W’, it straightforwardly follows, without the help of anything like the controversial S5 axiom, that a maximally great being exists in every logically possible world.
Indeed, it is for this very reason that Plantinga avoids the objection to Malcolm’s argument that was considered above. Since the notion of maximal greatness, in contrast to the notion of an unlimited being as Malcolm defines it, is conceived in terms that straightforwardly entail existence in every logically possible world (and hence eternal existence in every logically possible world), there are no worries about whether maximal greatness, in contrast to unlimitedness, entails something stronger than eternal existence.
Is the Concept of a Maximally Great Being Coherent?
As is readily evident, each version of the ontological argument rests on the assumption that the concept of God, as it is described in the argument, is self-consistent. Both versions of Anselm’s argument rely on the claim that the idea of God (that is, a being than which none greater can be conceived) “exists as an idea in the understanding.” Similarly, Plantinga’s version relies on the more transparent claim that the concept of maximal greatness is self-consistent.
But many philosophers are sceptical about the underlying assumption, as Leibniz describes it, “that this idea of the all-great or all-perfect being is possible and implies no contradiction.” Here is the problem as C.D. Broad expresses it:
Let us suppose, e.g., that there were just three positive properties X, Y, and Z; that any two of them are compatible with each other; but that the presence of any two excludes the remaining one. Then there would be three possible beings, namely, one which combines X and Y, one which combines Y and Z, and one which combines Z and X, each of which would be such that nothing … superior to it is logically possible. For the only kind of being which would be … superior to any of these would be one which had all three properties, X, Y, and Z; and, by hypothesis, this combination is logically impossible.… It is now plain that, unless all positive properties be compatible with each other, this phrase [i.e., "a being than which none greater can be imagined"] is just meaningless verbiage like the phrase “the greatest possible integer.”
Thus, if there are two great-making characteristics essential to the classically theistic notion of an all-perfect God that are logically incompatible, it follows that this notion is incoherent.
Here it is important to note that all versions of the ontological argument assume that God is simultaneously omnipotent, omniscient, and morally perfect. As we have seen, Plantinga expressly defines maximal excellence in such terms. Though Anselm doesn’t expressly address the issue, it is clear (1) that he is attempting to show the existence of the God of classical theism; and (2) that the great-making properties include those of omnipotence, omniscience, and moral perfection.
There are a number of plausible arguments for thinking that even this restricted set of properties is logically inconsistent. For example, moral perfection is thought to entail being both perfectly merciful and perfectly just. But these two properties seem to contradict each other. To be perfectly just is always to give every person exactly what she deserves. But to be perfectly merciful is to give at least some persons less punishment than they deserve. If so, then a being cannot be perfectly just and perfectly merciful. Thus, if moral perfection entails, as seems reasonable, being perfectly just and merciful, then the concept of moral perfection is
inconsistent.
The problem of divine foreknowledge can also be seen as denying that omniscience, omnipotence, and moral perfection constitute a coherent set. Roughly put, the problem of divine foreknowledge is as follows. If God is omniscient, then God knows what every person will do at every moment t. To say that a person p has free will is to say that there is at least one moment t at which p does A but could have done other than A. But if a person p who does A at t has the ability to do other than A at t, then it follows that p has the ability to bring it about that an omniscient God has a false belief – and this is clearly impossible.
On this line of analysis, then, it follows that it is logically impossible for a being to simultaneously instantiate omniscience and omnipotence. Omnipotence entails the power to create free beings, but omniscience rules out the possibility that such beings exist. Thus, a being that is omniscient lacks the ability to create free beings and is hence not omnipotent. Conversely, a being that is omnipotent has the power to create free beings and hence does not know what such beings would do if they existed. Thus, the argument concludes that omniscience and omnipotence are logically incompatible. If this is correct, then all versions of the ontological argument fail.