Because I wasn't able to get to a discussion of it in my philosophy of religion class this week, I'm posting on this blog the main portion of an earlier post outlining and discussing the version of the ontological argument that Norman Malcolm develops in his essay "Anselm's Ontological Arguments."
What Malcolm discovered as he reread Anselm's Proslogion was this: what everyone seemed to take to be just a rewording of the argument Anselm is most famous for is actually a different argument. The first argument holds that existence is, in effect, a great-making property, and that therefore the greatest conceivable being must exist. Malcolm agrees that this argument is unsound, accepting Kant's contention that "existence is not a real predicate." But the second Anselmian argument, rather than focusing on existence, focuses on existing necessarily rather than contingently. Anselm argues, in effect, that it is greater to exist of necessity than to exist contingently. Hence, it is part of the very concept of a greatest conceivable being that this being exist necessarily.
What Malcolm notes is that the property of existing necessarily rather than contingently does meet the test of being a "real" predicate in Kant's sense. That is, it adds to our concept of the thing, describing what it is like rather than merely stating that the thing as described has an instance in the world.
For this very reason, of course, it remains an open question whether there actually exists an entity which possesses its existence in this unique way--necessarily rather than contingently. So we haven't defined God into existence by noting that the very idea of God presupposes necessary existence. We can still reasonably ask, "Does there actually exist a greatest-conceivable being?" If the answer is yes, then that being does not exist merely contingently but necessarily. But Malcolm goes further than this. He argues (and here he is following in the footsteps not only of Anselm but of Leibniz) that the only reason why a greatest-conceivable being wouldn't exist would be because the concept named something whose existence was impossible.
In other words, a crucial feature of Malcolm's development of Anselm's argument is his insight that, as conceived, either "God" names an impossible being or a necessary being that actually exists. Put another way, if God is possible, God is actual.
This is a very interesting result in its own right, but Malcolm goes on to argue (in a manner reminiscent of at least some of Gödel's efforts to construct an ontological argument) that God's existence must be deemed possible.
Another feature of Malcolm's argument is that he sets aside Anselm's language of greatness (perhaps worried about this term being understood in subjectivist ways). Instead of defining God as the "greatest" conceivable being, he defines God as "an absolutely unlimited being." Now certain kinds of properties, he thinks, imply limitation (for example, having a shape--since a shape is defined by its outer boundaries). On this definition, then, God would not have a shape. More generally, physical existence in time and space seems to require boundaries or limits, and so God wouldn't have such spatio-temporal properties. God would be "eternal" and "transcendent." But the possession of power (capacity to do something) does not similarly imply limitation. Nor does the possession of knowledge. If this is right, then these are things an unlimited being would possess without limit.
What Malcolm argues, following Anselm, is that necessary rather than contingent existence is also something that would have to characterize an unlimited being. Here is an outline of his argument for that conclusion:
1. “God” means an absolutely unlimited being
2. Any being whose existence depended on something else, or which could be prevented from existing by something else, would be limited by something else and so would not be an unlimited being.
3. For every proposed being, B, its existence is either possible (but not necessary), necessary, or impossible
4. To say of B that its existence is possible but not necessary is to say that it exists in some possible world (call it PW1), but not in another (PW2)
5. If B existed in PW1 but not in PW2, then either (a) there is something that exists in PW2 that prevents B from existing, or (b) there is something missing from PW2 that B requires in order to exist.
6. Hence, if B’s existence is possible but not necessary, then (a) or (b) is true.
7. If (a) or (b) is true, then B is not an unlimited being.
8. Hence, if B is possible but not necessary, then B is not an unlimited being
9. Hence, if God is possible but not necessary, then God is not an unlimited being
10. Hence, it is not the case that God is possible but not necessary
11. Hence, God is either impossible or exists necessarily
At this point Malcolm takes up the question of whether God, conceived as an unlimited being, is possible. To make his argument here, he invokes two ideas: first, that an entity's existence is impossible only if it is characterized by contradictory properties (e.g., a round square); second, that such contradictions arise only when one property-attribution negates what is affirmed by another property attribution. But to negate what is posited elsewhere, a property attribution must embody, at least implicitly, a limitation. Roundness negates squareness because it imposes boundaries or limits on the space occupied by the object precisely where squareness does not, and vice versa. These concepts, in other words, are partly "negative" concepts--they don't merely ascribe some property to an object, but deny something of it. But an absolutely unlimited being would be such that no real "positive" attribute could be denied of it (we could only deny "negative" properties of it--that is, properties which ascribe absence or limit). As such, Malcolm concludes that an unlimited being cannot embody a contradiction, since that would require the possession of both a positive property and a negative property that denies the former. But an unlimited being would only possess positive properties. This part of his argument can be outlined as follows:
12. In order for the existence of some proposed being B to be impossible, the concept of B must imply, with respect to at least one positive property P, each of the contradictory claims “B has property P” and “B lacks property P.”
13. To lack a positive property is to be limited.
14. If 13, then the conception of an unlimited being cannot include or imply anything of the form “B lacks property P.”
15. Hence, God is not impossible.
16. Hence, God exists necessarily.
Critics of this argument are often skeptical of the idea that the positive and negative property distinction is a meaningful one. If it's not, then we might be forced to say that the failure to possess certain properties is a limitation, whereas their possession would contradict the possession of the opposing property (which one could not deny possession of without imposing limitation). But while it might be difficult to offer definitions of "positive property" and "negative property," there does seem to be an intuitive distinction here. Some property attributions assert that an object lacks something ("ignorant" or "impotent" or "empty"), while others that it has something ("knowledgable" or "capable" or "full"). Others are mixed, in that they assert than an object has this but lacks that ("round" or "green"). Nevertheless, especially when we get to the idea of mixed properties we wade into thorny territory. To use what is perhaps a silly example: Is heat the presence of something and cold the lack of it, such that we must say of God that God is infinitely hot? Or does being the sort of thing that's subject to heat and cold imply a limitation, such that anything of any heat is limited, and an unlimited being would therefore have to be something to which the categories of hot and cold simply do not apply?
Other questions arise, of course, when we consider moral properties. Can there be such a thing as unlimited goodness? And if so, what does that look like? To adhere with traditional theology, we'd need to hold that evil is a lack (something Augustine affirmed), such that any presence of evil implies limitation. If we think of evil as something positive, we get a God who must embody unlimited evil (as well as unlimited good--and hence must embody a contradiction). As such, Malcolm's argument leads us directly into a consideration of the nature of good and evil.
Showing posts with label Norman Malcolm. Show all posts
Showing posts with label Norman Malcolm. Show all posts
Friday, September 30, 2011
Tuesday, October 5, 2010
Norman Malcolm's Ontological Argument
Apologies for not getting this up sooner. I've been unusually busy since getting back from my conference in Detroit, trying to balance my time between work on the new book and preparing a talk I'm giving this afternoon entitled "God and Gays: Rethinking the Traditional Condemnation of Homosexuality."
In any event, here is the promised outline of the ontological argument that Norman Malcolm develops in his essay "Anselm's Ontological Arguments."
What Malcolm discovered as he reread Anselm's Proslogion was this: what everyone seemed to take to be just a rewording of the argument Anselm is most famous for is actually a different argument. The first argument holds that existence is, in effect, a great-making property, and that therefore the greatest conceivable being must exist. Malcolm agrees that this argument is unsound, accepting Kant's contention that "existence is not a real predicate." But the second Anselmian argument, rather than focusing on existence, focuses on existing necessarily rather than contingently. Anselm argues, in effect, that it is greater to exist of necessity than to exist contingently. Hence, it is part of the very concept of a greatest conceivable being that this being exist necessarily.
What Malcolm notes is that the property of existing necessarily rather than contingently does meet the test of being a "real" predicate in Kant's sense. That is, it adds to our concept of the thing, describing what it is like rather than merely stating that the thing as described has an instance in the world.
For this very reason, of course, it remains an open question whether there actually exists an entity which possesses its existence in this unique way--necessarily rather than contingently. So we haven't defined God into existence by noting that the very idea of God presupposes necessary existence. We can still reasonably ask, "Does there actually exist a greatest-conceivable being?" If the answer is yes, then that being does not exist merely contingently but necessarily. But Malcolm goes further than this. He argues (and here he is following in the footsteps not only of Anselm but of Leibniz) that the only reason why a greatest-conceivable being wouldn't exist would be because the concept named something whose existence was impossible.
In other words, a crucial feature of Malcolm's development of Anselm's argument is his insight that, as conceived, either "God" names an impossible being or a necessary being that actually exists. Put another way, if God is possible, God is actual.
This is a very interesting result in its own right, but Malcolm goes on to argue (in a manner reminiscent of at least some of Gödel's efforts to construct an ontological argument) that God's existence must be deemed possible.
Another feature of Malcolm's argument is that he sets aside Anselm's language of greatness (perhaps worried about this term being understood in subjectivist ways). Instead of defining God as the "greatest" conceivable being, he defines God as "an absolutely unlimited being." Now certain kinds of properties, he thinks, imply limitation (for example, having a shape--since a shape is defined by its outer boundaries). On this definition, then, God would not have a shape. More generally, physical existence in time and space seems to require boundaries or limits, and so God wouldn't have such spatio-temporal properties. God would be "eternal" and "transcendent." But the possession of power (capacity to do something) does not similarly imply limitation. Nor does the possession of knowledge. If this is right, then these are things an unlimited being would possess without limit.
What Malcolm argues, following Anselm, is that necessary rather than contingent existence is also something that would have to characterize an unlimited being. Here is an outline of his argument for that conclusion:
1. “God” means an absolutely unlimited being
2. Any being whose existence depended on something else, or which could be prevented from existing by something else, would be limited by something else and so would not be an unlimited being.
3. For every proposed being, B, its existence is either possible (but not necessary), necessary, or impossible
4. To say of B that its existence is possible but not necessary is to say that it exists in some possible world (call it PW1), but not in another (PW2)
5. If B existed in PW1 but not in PW2, then either (a) there is something that exists in PW2 that prevents B from existing, or (b) there is something missing from PW2 that B requires in order to exist.
6. Hence, if B’s existence is possible but not necessary, then (a) or (b) is true.
7. If (a) or (b) is true, then B is not an unlimited being.
8. Hence, if B is possible but not necessary, then B is not an unlimited being
9. Hence, if God is possible but not necessary, then God is not an unlimited being
10. Hence, it is not the case that God is possible but not necessary
11. Hence, God is either impossible or exists necessarily
At this point Malcolm takes up the question of whether God, conceived as an unlimited being, is possible. To make his argument here, he invokes two ideas: first, that an entity's existence is impossible only if it is characterized by contradictory properties (e.g., a round square); second, that such contradictions arise only when one property-attribution negates what is affirmed by another property attribution. But to negate what is posited elsewhere, a property attribution must embody, at least implicitly a limitation. Roundness negates squareness because it imposes boundaries or limits on the space occupied by the object precisely where squareness does not, and vice versa. These concepts, in other words, are partly "negative" concepts--they don't merely ascribe some property to an object, but deny something of it. But an absolutely unlimited being would be such that no real "positive" attribute could be denied of it (we could only deny "negative" properties of it--that is, properties which ascribe absence or limit). As such, Malcolm concludes that an unlimited being cannot embody a contradiction, since that would require the possession of both a positive property and a negative property that denies the former. But an unlimited being would only possess positive properties. This part of his argument can be outlined as follows:
12. In order for the existence of some proposed being B to be impossible, the concept of B must imply, with respect to at least one positive property P, each of the contradictory claims “B has property P” and “B lacks property P.”
13. To lack a positive property is to be limited.
14. If 13, then the conception of an unlimited being cannot include or imply anything of the form “B lacks property P.”
15. Hence, God is not impossible.
16. Hence, God exists necessarily.
Critics of this argument are often skeptical of the idea that the positive and negative property distinction is a meaningful one. If it's not, then we might be forced to say that the failure to possess certain properties is a limitation, whereas their possession would contradict the possession of the opposing property (which one could not deny possession of without imposing limitation). But while it might be difficult to offer definitions of "positive property" and "negative property," there does seem to be an intuitive distinction here. Some property attributions assert that an object lacks something ("ignorant" or "impotent" or "empty"), while others that it has something ("knowledgable" or "capable" or "full"). Others are mixed, in that they assert than an object has this but lacks that ("round" or "green"). Nevertheless, especially when we get to the idea of mixed properties we wade into thorny territory. To use what is perhaps a silly example: Is heat the presence of something and cold the lack of it, such that we must say of God that God is infinitely hot? Or does being the sort of thing that's subject to heat and cold imply a limitation, such that anything of any heat is limited, and an unlimited being would therefore have to be something to which the categories of hot and cold simply do not apply?
Other questions arise, of course, when we consider moral properties. Can there be such a thing as unlimited goodness? And if so, what does that look like? To adhere with traditional theology, we'd need to hold that evil is a lack (something Augustine affirmed), such that any presence of evil implies limitation. If we think of evil as something positive, we get a God who must embody unlimited evil (as well as unlimited good--and hence must embody a contradiction). As such, Malcolm's argument leads us directly into a consideration of the nature of good and evil.
In any event, here is the promised outline of the ontological argument that Norman Malcolm develops in his essay "Anselm's Ontological Arguments."
What Malcolm discovered as he reread Anselm's Proslogion was this: what everyone seemed to take to be just a rewording of the argument Anselm is most famous for is actually a different argument. The first argument holds that existence is, in effect, a great-making property, and that therefore the greatest conceivable being must exist. Malcolm agrees that this argument is unsound, accepting Kant's contention that "existence is not a real predicate." But the second Anselmian argument, rather than focusing on existence, focuses on existing necessarily rather than contingently. Anselm argues, in effect, that it is greater to exist of necessity than to exist contingently. Hence, it is part of the very concept of a greatest conceivable being that this being exist necessarily.
What Malcolm notes is that the property of existing necessarily rather than contingently does meet the test of being a "real" predicate in Kant's sense. That is, it adds to our concept of the thing, describing what it is like rather than merely stating that the thing as described has an instance in the world.
For this very reason, of course, it remains an open question whether there actually exists an entity which possesses its existence in this unique way--necessarily rather than contingently. So we haven't defined God into existence by noting that the very idea of God presupposes necessary existence. We can still reasonably ask, "Does there actually exist a greatest-conceivable being?" If the answer is yes, then that being does not exist merely contingently but necessarily. But Malcolm goes further than this. He argues (and here he is following in the footsteps not only of Anselm but of Leibniz) that the only reason why a greatest-conceivable being wouldn't exist would be because the concept named something whose existence was impossible.
In other words, a crucial feature of Malcolm's development of Anselm's argument is his insight that, as conceived, either "God" names an impossible being or a necessary being that actually exists. Put another way, if God is possible, God is actual.
This is a very interesting result in its own right, but Malcolm goes on to argue (in a manner reminiscent of at least some of Gödel's efforts to construct an ontological argument) that God's existence must be deemed possible.
Another feature of Malcolm's argument is that he sets aside Anselm's language of greatness (perhaps worried about this term being understood in subjectivist ways). Instead of defining God as the "greatest" conceivable being, he defines God as "an absolutely unlimited being." Now certain kinds of properties, he thinks, imply limitation (for example, having a shape--since a shape is defined by its outer boundaries). On this definition, then, God would not have a shape. More generally, physical existence in time and space seems to require boundaries or limits, and so God wouldn't have such spatio-temporal properties. God would be "eternal" and "transcendent." But the possession of power (capacity to do something) does not similarly imply limitation. Nor does the possession of knowledge. If this is right, then these are things an unlimited being would possess without limit.
What Malcolm argues, following Anselm, is that necessary rather than contingent existence is also something that would have to characterize an unlimited being. Here is an outline of his argument for that conclusion:
1. “God” means an absolutely unlimited being
2. Any being whose existence depended on something else, or which could be prevented from existing by something else, would be limited by something else and so would not be an unlimited being.
3. For every proposed being, B, its existence is either possible (but not necessary), necessary, or impossible
4. To say of B that its existence is possible but not necessary is to say that it exists in some possible world (call it PW1), but not in another (PW2)
5. If B existed in PW1 but not in PW2, then either (a) there is something that exists in PW2 that prevents B from existing, or (b) there is something missing from PW2 that B requires in order to exist.
6. Hence, if B’s existence is possible but not necessary, then (a) or (b) is true.
7. If (a) or (b) is true, then B is not an unlimited being.
8. Hence, if B is possible but not necessary, then B is not an unlimited being
9. Hence, if God is possible but not necessary, then God is not an unlimited being
10. Hence, it is not the case that God is possible but not necessary
11. Hence, God is either impossible or exists necessarily
At this point Malcolm takes up the question of whether God, conceived as an unlimited being, is possible. To make his argument here, he invokes two ideas: first, that an entity's existence is impossible only if it is characterized by contradictory properties (e.g., a round square); second, that such contradictions arise only when one property-attribution negates what is affirmed by another property attribution. But to negate what is posited elsewhere, a property attribution must embody, at least implicitly a limitation. Roundness negates squareness because it imposes boundaries or limits on the space occupied by the object precisely where squareness does not, and vice versa. These concepts, in other words, are partly "negative" concepts--they don't merely ascribe some property to an object, but deny something of it. But an absolutely unlimited being would be such that no real "positive" attribute could be denied of it (we could only deny "negative" properties of it--that is, properties which ascribe absence or limit). As such, Malcolm concludes that an unlimited being cannot embody a contradiction, since that would require the possession of both a positive property and a negative property that denies the former. But an unlimited being would only possess positive properties. This part of his argument can be outlined as follows:
12. In order for the existence of some proposed being B to be impossible, the concept of B must imply, with respect to at least one positive property P, each of the contradictory claims “B has property P” and “B lacks property P.”
13. To lack a positive property is to be limited.
14. If 13, then the conception of an unlimited being cannot include or imply anything of the form “B lacks property P.”
15. Hence, God is not impossible.
16. Hence, God exists necessarily.
Critics of this argument are often skeptical of the idea that the positive and negative property distinction is a meaningful one. If it's not, then we might be forced to say that the failure to possess certain properties is a limitation, whereas their possession would contradict the possession of the opposing property (which one could not deny possession of without imposing limitation). But while it might be difficult to offer definitions of "positive property" and "negative property," there does seem to be an intuitive distinction here. Some property attributions assert that an object lacks something ("ignorant" or "impotent" or "empty"), while others that it has something ("knowledgable" or "capable" or "full"). Others are mixed, in that they assert than an object has this but lacks that ("round" or "green"). Nevertheless, especially when we get to the idea of mixed properties we wade into thorny territory. To use what is perhaps a silly example: Is heat the presence of something and cold the lack of it, such that we must say of God that God is infinitely hot? Or does being the sort of thing that's subject to heat and cold imply a limitation, such that anything of any heat is limited, and an unlimited being would therefore have to be something to which the categories of hot and cold simply do not apply?
Other questions arise, of course, when we consider moral properties. Can there be such a thing as unlimited goodness? And if so, what does that look like? To adhere with traditional theology, we'd need to hold that evil is a lack (something Augustine affirmed), such that any presence of evil implies limitation. If we think of evil as something positive, we get a God who must embody unlimited evil (as well as unlimited good--and hence must embody a contradiction). As such, Malcolm's argument leads us directly into a consideration of the nature of good and evil.
Thursday, September 30, 2010
Ontological Arguments for God's Existence
St. Anselm, the 11th Century theologian and philosopher (who also served as archbishop of Canterbury), is best known for two things. Among theologians, he is principally associated with his deeply influential understanding of the Atonement--that is, his account of how Christ's crucifixion is to be understood as securing salvation for sinners. But among philosophers Anselm is better known as the author of the so-called "ontological argument" for God's existence (this name for the argument originated with Kant, who is also credited historically with formulating the most telling objection to the argument).
Until fairly recently it was generally assumed that, in his Proslogion, Anselm offered a single "ontological argument" for the existence of God based on his distinctive formal definition of God as "that than which a greater cannot be thought." Certainly, there is only one "ontological argument" that comes under Kant's scrutiny and becomes the target of his famed (well, famous among philosophers) objection.
That argument runs roughly as follows: Taking "God" to mean "that than which a greater cannot be conceived," let us assume that God in this sense is only an idea in our heads and doesn't actually exist. On this assumption, we can conceived of something that is greater than God--because we can conceive of this God as actually existing, rather than as being nothing more than an idea in our heads (and a God that actually existed would be greater than one that did not). So, on this assumption, it follows that we can conceive of a being greater than that than which a greater cannot be conceived. But, of course, that is impossible. Hence, our assumption has led to a logical impossibility and so has to be rejected. It is not the case that God is only an idea in our head and doesn't exist in reality. Rather, God really exists.
This is the argument that Richard Dawkins, in The God Delusion, calls "infantile" and frames in terms of a school-yard conversation in which one smarmy kid "proves" God's existence by playing with words in a way that makes the argument sound truly silly. Now it is true that most philosophers look at this argument and think there is something fishy going on. But I think it's also true that most philosophers are grateful that the history of reflection on the argument was shaped by serious engagement. In wrestling seriously with this argument (which is formally valid), critics and defenders alike were forced to refine their understanding of what it means to say that something exists, as well as how this kind of statement differs from saying that something is blue or round. One might even wonder about whether the emergence of formal predicate logic as we know it owes something to the lessons of engaging with Anselm (in the symbolic language of predicate logic, an entity's existence is expressed through the use of what is called the existential quantifier, as opposed to being attributed to the entity as a predicate).
In any event, this ontological argument was criticized by Kant on the grounds that, in his terms, "existence is not a real predicate." Put another way, when we say of something that it exists, we don't add to our idea of a thing. Rather, we say that this idea (described in terms of the "real" predicates), has an instance in the world. Thus, to say of God that He exists is not to add to our concept of God. Since positing existence adds nothing to our concept, an existing God is not conceptually different from a nonexistent one. And so there can be no conceptual incoherence with respect to the latter that doesn't also attach to the former.
(Interestingly, I suspect that Anselm would have some sympathy with Kant's objection, because Kant is describing what existence means in its ordinary usage as applied to ordinary things--and Anselm insisted that "God exists" has to mean something very different from "Eric Reitan exists," insofar as God is taken to be the source of existence--or, in Anselm's language, "that through which" things exist, or from which things derive their being. Very roughly, to say that I exist is to say that I participate in existence itself, which is that through which I derive my being; whereas to say that God exists is to say that God is existence itself, that through which other things derive their being. Anselm furthermore attempted to show that existence itself must also be goodness itself, and by implication must be Godlike in the ways that theists have traditionally thought. Whether this element of Anselm's theology can be developed into an answer to Kant, however, is something I won't explore here.)
In any event, many if not most philosophers after Kant found his objection compelling, and the objection has since been expressed in numerous ways--including by Richard Dawkins in The God Delusion. While Dawkins makes no serious effort to carefully articulate this line of objection, he does at least quote part of one philosopher's articulation of it. Unfortunately for Dawkins (at least if he cares about his credentials as a scholar), the philosopher he appeals to for this quote is Norman Malcolm. Even more unfortunate for Dawkins, the quote comes from an article, "Anselm's Ontological Arguments," that is justly famous in the history of discussion about Anselm and his case for God. Since (according to his endnotes) Dawkins extracted the quote from an online encyclopedia article, Dawkins apparently doesn't know that this quote comes from an article in defense of Anselm. As such, Dawkins doesn't know that his dismissal of the ontological argument is, we might say, premature. To put the point more bluntly, Dawkins succeeds in completely ignoring the version of the ontological argument that is still alive today (in the sense of having active defenders) largely by virtue of the efforts of the philosopher Dawkins invokes to justify his dismissal of the argument.
It is true enough that Malcolm accepts the Kantian objection to Anselm. But what Malcolm then does (which is what makes his essay historically important) is to point something out about Anselm's original text that philosophers had historically overlooked. If one looks at that text, one sees Anselm wording his argument in a couple of ways, and it reads as if his second version is intended to be just a different way of saying the same thing. In fact, on a cursory reading it looks like the same argument restated slightly differently.
What Malcolm does in "Ontological Arguments" is show that this cursory reading is a mistake. The two arguments aren't different ways of saying the same thing, but different arguments. While there are important similarities, there is a crucial difference as well. And the difference makes a huge difference: By virtue of that difference, Malcolm argues, Kant's famous objection to the ontological argument doesn't apply. Whereas philosophers had widely assumed that Kant had dealt the death blow to the ontological argument in the 18th century, Malcolm not only showed that there was a version of the argument that avoided Kant's challenge, but he then proceeded to develop the argument in an effort to show that it was, in fact, a powerful and compelling argument for the existence of God--far more compelling, in fact, than the version for which Anselm became famous. Others have followed Malcolm's lead (including Alvin Plantinga) in developing so-called "modal ontological arguments" that trace their lineage to Anselm's second argument.
In addition to these arguments that trace back to Anselm (by way of Malcolm's discovery of the second argument), there are various ontological arguments sketched out by Gödel in his notebooks, especially in terms of the notion of "positive properties," that have come under discussion. Interestingly, however, Malcolm's development of Anselm's second argument develops themes that are also found in Gödel's argument. For these reasons I think Malcolm's version of the argument is especially deserving of closer attention. In my next post, then, I will outline Malcolm's argument.
Until fairly recently it was generally assumed that, in his Proslogion, Anselm offered a single "ontological argument" for the existence of God based on his distinctive formal definition of God as "that than which a greater cannot be thought." Certainly, there is only one "ontological argument" that comes under Kant's scrutiny and becomes the target of his famed (well, famous among philosophers) objection.
That argument runs roughly as follows: Taking "God" to mean "that than which a greater cannot be conceived," let us assume that God in this sense is only an idea in our heads and doesn't actually exist. On this assumption, we can conceived of something that is greater than God--because we can conceive of this God as actually existing, rather than as being nothing more than an idea in our heads (and a God that actually existed would be greater than one that did not). So, on this assumption, it follows that we can conceive of a being greater than that than which a greater cannot be conceived. But, of course, that is impossible. Hence, our assumption has led to a logical impossibility and so has to be rejected. It is not the case that God is only an idea in our head and doesn't exist in reality. Rather, God really exists.
This is the argument that Richard Dawkins, in The God Delusion, calls "infantile" and frames in terms of a school-yard conversation in which one smarmy kid "proves" God's existence by playing with words in a way that makes the argument sound truly silly. Now it is true that most philosophers look at this argument and think there is something fishy going on. But I think it's also true that most philosophers are grateful that the history of reflection on the argument was shaped by serious engagement. In wrestling seriously with this argument (which is formally valid), critics and defenders alike were forced to refine their understanding of what it means to say that something exists, as well as how this kind of statement differs from saying that something is blue or round. One might even wonder about whether the emergence of formal predicate logic as we know it owes something to the lessons of engaging with Anselm (in the symbolic language of predicate logic, an entity's existence is expressed through the use of what is called the existential quantifier, as opposed to being attributed to the entity as a predicate).
In any event, this ontological argument was criticized by Kant on the grounds that, in his terms, "existence is not a real predicate." Put another way, when we say of something that it exists, we don't add to our idea of a thing. Rather, we say that this idea (described in terms of the "real" predicates), has an instance in the world. Thus, to say of God that He exists is not to add to our concept of God. Since positing existence adds nothing to our concept, an existing God is not conceptually different from a nonexistent one. And so there can be no conceptual incoherence with respect to the latter that doesn't also attach to the former.
(Interestingly, I suspect that Anselm would have some sympathy with Kant's objection, because Kant is describing what existence means in its ordinary usage as applied to ordinary things--and Anselm insisted that "God exists" has to mean something very different from "Eric Reitan exists," insofar as God is taken to be the source of existence--or, in Anselm's language, "that through which" things exist, or from which things derive their being. Very roughly, to say that I exist is to say that I participate in existence itself, which is that through which I derive my being; whereas to say that God exists is to say that God is existence itself, that through which other things derive their being. Anselm furthermore attempted to show that existence itself must also be goodness itself, and by implication must be Godlike in the ways that theists have traditionally thought. Whether this element of Anselm's theology can be developed into an answer to Kant, however, is something I won't explore here.)
In any event, many if not most philosophers after Kant found his objection compelling, and the objection has since been expressed in numerous ways--including by Richard Dawkins in The God Delusion. While Dawkins makes no serious effort to carefully articulate this line of objection, he does at least quote part of one philosopher's articulation of it. Unfortunately for Dawkins (at least if he cares about his credentials as a scholar), the philosopher he appeals to for this quote is Norman Malcolm. Even more unfortunate for Dawkins, the quote comes from an article, "Anselm's Ontological Arguments," that is justly famous in the history of discussion about Anselm and his case for God. Since (according to his endnotes) Dawkins extracted the quote from an online encyclopedia article, Dawkins apparently doesn't know that this quote comes from an article in defense of Anselm. As such, Dawkins doesn't know that his dismissal of the ontological argument is, we might say, premature. To put the point more bluntly, Dawkins succeeds in completely ignoring the version of the ontological argument that is still alive today (in the sense of having active defenders) largely by virtue of the efforts of the philosopher Dawkins invokes to justify his dismissal of the argument.
It is true enough that Malcolm accepts the Kantian objection to Anselm. But what Malcolm then does (which is what makes his essay historically important) is to point something out about Anselm's original text that philosophers had historically overlooked. If one looks at that text, one sees Anselm wording his argument in a couple of ways, and it reads as if his second version is intended to be just a different way of saying the same thing. In fact, on a cursory reading it looks like the same argument restated slightly differently.
What Malcolm does in "Ontological Arguments" is show that this cursory reading is a mistake. The two arguments aren't different ways of saying the same thing, but different arguments. While there are important similarities, there is a crucial difference as well. And the difference makes a huge difference: By virtue of that difference, Malcolm argues, Kant's famous objection to the ontological argument doesn't apply. Whereas philosophers had widely assumed that Kant had dealt the death blow to the ontological argument in the 18th century, Malcolm not only showed that there was a version of the argument that avoided Kant's challenge, but he then proceeded to develop the argument in an effort to show that it was, in fact, a powerful and compelling argument for the existence of God--far more compelling, in fact, than the version for which Anselm became famous. Others have followed Malcolm's lead (including Alvin Plantinga) in developing so-called "modal ontological arguments" that trace their lineage to Anselm's second argument.
In addition to these arguments that trace back to Anselm (by way of Malcolm's discovery of the second argument), there are various ontological arguments sketched out by Gödel in his notebooks, especially in terms of the notion of "positive properties," that have come under discussion. Interestingly, however, Malcolm's development of Anselm's second argument develops themes that are also found in Gödel's argument. For these reasons I think Malcolm's version of the argument is especially deserving of closer attention. In my next post, then, I will outline Malcolm's argument.
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