Tuesday, March 29, 2005

Kurt Gödel's Ontological Argument

Mathematician Christopher Small provides an unabashedly neoplatonic--not to mention lucid and engaging--take on Kurt Gödel's ontological argument.

First reactions: Is this really an argument about God, or is it rather about the Good, perfection, or the perfect being? What is the difference between supremacy of being and perfection of being? Why isn't this a simple case of Being or plain old vanilla lowercase being? What does it mean to talk about an imperfect being? Are philosophers in full agreement about what Parmenides meant by the concept of being, or should claims about the nature of being be regarded with a degree of skepticism?

You see, I have a sense that some kind of order --categorical, logical, natural-- is being superimposed upon or subtended within a discussion of being. Supposedly this is well understood and is addressed by Gödel's positivity operator. Being a logical fool (in a sense) puts me in an akward position. To put it bluntly, I cannot at this time accept the premises of Ansel's Axiom 2 (parallel to Gödel's axiom G0). I question the privileging of necessary being over contigent being, or essence over existence, and cannot see this as being an argument in favor of God's existence. If God does not exist in the strong sense, God quite simply does not exist. And if God were to exist in the weak sense of being merely essential, I can't quite see the objection to remaining agnostic about God's existence, as this view of God may be more or less synonymous with a conception of pure Being, which, other attributions being for the present ancillary, one may treat as a genre of philosophical argument or a specific insight rather than an article of faith.

Small I reckon knows where I'm coming from, and in his conclusion he anticipates the existential objection:

The question of whether every individual has an essence was at the heart of Jean-Paul Sartre's philosophy of existentialism. While he agreed that ordinary individuals such as rocks, trees, dogs and cats have essences, and that essence precedes existence for such things, Sartre argued that for human beings, existence precedes essence in the sense that we exist first and define ourselves secondly.

I feel that's correct, but it may be more relevant to say that existential ontology concieves of existence as surpassing being, or that any proper phenomenological ontology is necessarily transcendental.

But what am I if not a certain internal negation of the in-itself? Without this in-itself which I deny, I should vanish into nothingness. In our Introduction we pointed out that consciousness can serve as the "ontological proof" of the existence of an in-itself. In fact, if there is no consciousness of something, then it is necessary at the start that this "something" have a real being--that is, a being not relative to consciousness. But we see at present that this proof has a larger bearing: if I am able to do something--anything--it is necessary that I exercise my action upon beings whose existence in general is independent of my existence and in particular independent of my action. My action can reveal this other existence to me but does not condition it. To be free is to-be-free-to-change. Freedom implies therefore the existence of an environment to be changed: obstacles to be cleared, tools to be used. Of course it is freedom which reveals them as obstacles, but by its free choice it can only interpret the meaning of their being. It is necessary that they be there, wholly brute, in order that there may be freedom.

Being and Nothingness (trans. Barnes, p. 506)

Sartre's easy slippage between the "I" and "we" should not pass uncommented. The we of Sartre is the one that comprehends the various other Sartres and communicates that comprehension to his readers. Do we, dear reader, need an ontological argument for the existence of Sartre the Author as opposed to the singular Sartre the author of his being, who, though arguably necessary, remains for us more or less in the realm of the heuristic?

Anyway, it seems to me that the potential problems Small sees stemming from the empiricist proposition of esse est percipi may also be explored through phenomological ontology.

Finally, I just have to wonder under what conditions is the Pythagoran intuition expressed or construed as nihilistic?

I don't really understand formal logic, so it should go without saying that I have hardly done justice to Small's presentation. My sense is that he has given adequate consideration to my objections, however, he has done so in a mode that is still somewhat foreign to me. I am sure to be revisiting his treatment of this topic many times.

posted by Fido the Yak at 12:20 AM.


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