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Fr. 355

June 27, 2013

Jorge Luis Borges, “Argumentum Ornithologicum”, The Maker:

“I shut my eyes and glimpse a flock of birds. The image lasts for a second or even less; I don’t know how many birds I saw. Was the number finite or infinite? The problem concerns the existence of God. If He exists, the number is finite, because He knows how many birds I saw. If God does not exist, the number is infinite, because no one could keep tally. In my case, let us say I saw fewer than ten birds and more than one but did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, which is not nine, eight, seven, six, five, etc. This integer is inconceivable; therefore, God exists.”

——–
How is one to understand this proof for god? A formal reading of the proof would seem to be the following:

1. The data of empirically observable (or “objective”) experience are foreseen, guaranteed and verified by god.
2. Imagined or simulated visual experience answers to the same laws as empirically observable experience.
3. Therefore, the data of imagined or simulated visual experience are foreseen, guaranteed and verified by god.

4. Only finite sets, being defined in experience, are conceivable.
5. Infinity, being undefined in experience, is therefore inconceivable.
6. As god can conceive of anything in experience, being all-knowing and all-powerful, that of which god conceives must be conceivable.
7. It follows that, as god can conceive of anything in experience, that of which god conceives must be a finite set.

8. It follows from 2.) that everything in imagined or simulated visual experience is foreseen and conceivable by god.
9. To this can be added 7.), such that everything in imagined or simulated visual experience is thus a finite set.

10. The imagined or simulated visual experience in question concerns a finite set.
11. This finite set is not to be found among the rational finite sets.
12. This set is thus at once finite and inconceivable.
13. As finite, this set could only be guaranteed by god, ergo, god exists.

It is clear from the following that, despite a certain circularity, this proof for the existence of god obeys a strict logic, only to betray that logic in the final set of premises and the overall conclusion. For, as per the second set of premises, one would expect to find side-by-side with 13.):
14. As inconceivable, this set could not be guaranteed by god, ergo, god does not exist.

It is at this point that the rigorous logic of the proof breaks down in favor of a performative rhetorical flourish on the part of an author, for contradictory definitions are simultaneously affirmed in 12.). Accordingly, the proof undoes itself and introduces disorder into what was an ordered, discrete, finite set, resulting, in the end, in a performative reductio ad absurdum. This rhetorical turn is meant to show that, in virtue of its mere form, a proof for the existence of god is ever a futile exercise, specious and anthropomorphic. More specifically, it does this in the final premises by introducing a set of numbers that is, by (human) definition, inconceivable, in order to show just how fallacious it would be to base the existence and knowledge of god, a fundamentally indeterminate being, on that which the human being, a finite entity, can know and reason with.

There is no clear reason, at least from within the framework of reason, why the finite set of numbers of which god can conceive should correspond to those conceivable by humans. Thus, what Borges aims to get at in the end is something like the following: if there exists god, god exists in a fashion quite unlike that in which humanity tends to conceive god. For god is not a personal entity (hence our reason for writing “god” rather than “God”), but rather an alien mind, so unlike the human, that it is perhaps best characterized as “a chaos of vague possibilities” (“Shakespeare’s Memory” in Borges, Collected Fictions, tr. Andrew Hurley, p. 513).

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