From the Archives: Norman Malcolm's Ontological Argument

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.