Friday, September 30, 2011

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.


  1. Even if we accept Malcolm's argument, what kind of God does it prove? A limitless, necessarily existing being that transcends space and time seems to me to be just the totality of being (i.e. everything that is, the universe--or multiverse, if you prefer--itself) and not the personal God of traditional theistic religion.

    If we grant that Malcolm is successful, he seems to have proved that Spinoza's God or even Tillich's God exists (though Tillich would probably quibble with the language about God "existing"), but such a God is certainly not the God of the Abrahamic faiths.

  2. Hi VeganTrav,

    I think you're right. It's not at all clear how to go from what Malcolm's and other ontological arguments claim to prove to anything like the Christian God.

    In any case, I suspect that all purely logical arguments eventually turn out to be question begging or something like that – although it may be quite difficult to point to actual flaws in specific cases. Do you think Malcolm fails?

  3. Vegan Trav,

    A few quick points. First, it doesn't seem to me as if any of the Medieval theologians took it that their philosophical arguments for God's existence were a replacement for divine revelation, in the sense of giving us a fully fleshed-out picture of the divine to which "special revelation" had nothing to add. Rather, they took it that they could support through reasoned arguments the existence of a divine being in a more generic sense, and that details of the portrait of God would have to come from other sources. Malcolm is following the tradition of these Medieval thinkers (specifically Anselm), and so we can reasonably take him to be arguing for a divine reality in a generic sense. Such a generic God might fit with a range of specific religious conceptions. Within this context, then, your question might be better stated as follows: Does "the God of the Abrahamic faiths" have properties that are consistent with the more generic deity emerging from Malcolm's argument?

    Second, it seems to me that there is a tradition of using the philosophical arguments for God's existence as a basis for building a theological understanding of God that operates, implicitly at least, as a critical corrective to the understandings that emerge from inherited religious narratives alone. Specifically, in the case of the Anselmian-style argument, if God is "the being than which a greater cannot be thought" then certain mythic conceptions of God (being conceptions of something than which a greater can be thought) have to be set aside. If the Anselmian argument works, then it establishes the existence of an absolutely unlimited being--and any being that fell short of this would thus not qualify as the supreme being in the universe. So, if the God of Abraham is taken to be the supreme being in the universe, then the Anselmian style argument has implications for how the God of Abraham is to be conceived.

    Recall that biblical literalism is a relatively new innovation in Christianity, and would have been alien to the thinking of Anselm. While Malcolm would have been well-acquainted with biblical literalism, he would be very much in the spirit of Anselm, whose second ontological argument he was developing. And for Anselm, "the God of Abraham" would not have been the God who literally fits all the descriptions found in the stories of Scripture, but rather the God testified to in those stories--that is, the referent, not the definite description (to borrow some contemporary terminology).


  4. Third, there is the question of whether an "absolutely unlimited being" could be identified with the universe (or multiverse) itself. This is related, I think, to the question of whether Malcolm's God would be "personal." If, you "personal," one means a subjective agent--a being that is conscious and can act--then there is a clear argument for affirming this of Malcolm's God.

    Here's a sketch of the argument: To be absolutely unlimited entails that one possesses every positive quality or property without limit. Consciousness and agency are positive properties. Therefore, an absolutely unlimited being would possess consciousness and agency to an unlimited degree. To possess consciousness in an unlimited degree would be to be perfectly aware of absolutely everything (omniscient?); to possess agency to an unlimited degree would be to be able to perform any conceivable act (omnipotence?). Obviously, there are parts of this argument that would need fleshing out. But this at least gives a sense of why someone might take Malcolm's argument to support the existence of a deity that is "personal." While taking an absolutely unlimited being to possess these traits is not strictly at odds with some sort of pantheism, it would entail that there is far more to the universe than is ordinarily supposed--that the finite consciousness found in the universe is a manifestation of the infinite consciousness of the universe, perhaps.

  5. 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.

    It does not seem to follow. Certainly if (a) or (b) then B does not exist in PW2 but not the other way around.

    The step asserts that if B does not exist in a given world, there must be something preventing it. But why? Certainly we can conceive of two worlds differing only by the presence of some being in one but not in the other.

    Now, to go from this (possibility implies existence) to the existence of an unlimited being (because it's presumably possible) makes some sense, but this is clearly circular.