St. Borges of Canterbury

In El Hacedor (1960), known in English as Dreamtigers, Jorge Luis Borges includes an ironic ontological argument for the existence of God. The intention might have been ironic, but whether the proof succeeds has nothing to do with the original intentions. So in this essay, I want to analyze whether that argument is valid and whether it is sound. Here is the original Spanish and its translation:

Cierro los ojos y veo una bandada de pájaros. La visión dura un segundo o acaso menos; no sé cuántos pájaros vi. ¿Era definido o indefinido, su número? El problema involucra el de la existencia de Dios. Si Dios existe, el número es definido, porque Dios sabe cuántos pájaros vi. Si Dios no existe, el número es indefinido, porque nadie pudo llevar la cuenta. En tal caso, vi menos de diez pájaros (digamos) y más de uno, pero no vi nueve, ocho, siete, seis, cinco, cuatro, tres o dos pájaros. Vi un número entre diez y uno, que no es nueve, ocho, siete, seis, cinco, etcétera. Ese número entero es inconcebible; ergo, Dios existe. (Borges, 1960/1972, p. 27)

I close my eyes and see a flock of birds. The vision lasts a second or perhaps less; I don’t know how many birds I saw. Were they a definite or an indefinite number? This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count. In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists. (Borges, 1970, p. 29)

Before I discuss the validity and soundness of the paragraph, I want to specify what each of those means. An argument is formally valid if it is impossible that the premises are true and the conclusion is false. So validity doesn’t guarantee the truth of the conclusion. It just means that if the premises are true, so is the conclusion. The soundness of an argument is the real test of its truth value. If the argument is sound, it is both valid and true.

If we break down the paragraph into sections, we get the following:

1. “I close my eyes and see a flock of birds.“

In this section, Borges parodies René Descartes’ third meditation but doesn’t follow him in effacing all images of corporeal things from his mind:

Claudam nunc oculos, aures obturabo, avocabo omnes sensus, imagines etiam rerum corporalium omnes vel ex cogitatione mea delebo, vel certe, quia hoc fieri vix potest, illas ut inanes et falsas nihili pendam, meque solum alloquendo, et penitius inspiciendo, meipsum paulatim mihi magis notum et familiarem reddere conabor.

I will now close my eyes, I will stop my ears, I will turn away my senses from their objects, I will even efface from my consciousness all the images of corporeal things; or at least, because this can hardly be accomplished, I will consider them as empty and false; and thus, holding converse only with myself, and closely examining my nature, I will endeavour to obtain by degrees a more intimate and familiar knowledge of myself. (Descartes, 1641/1912, p. 95)

The image is, of course, unique to Borges. No one can have the same mental image of a flock of birds. But the concept has universal resonance because anyone who engages in the argument imagines a unique flock of birds. And the validity of the proof doesn’t depend on the characteristics of some specific flock of birds. This part is a novelty for ontological arguments. St. Anselm of Canterbury, the inventor of the first and most famous ontological argument, used definitions and concepts to make his argument, not mental images (Anselm, 1078/1903).

2. “The vision lasts a second or perhaps less; I don’t know how many birds I saw.“

Borges knows that he saw several birds but doesn’t know how many. His argument is, therefore, at odds with other ontological arguments. Anselm, Descartes, Leibniz, and others don’t have space for uncertainties. The part about how long the vision lasts is crucial because there cannot be enough time to count all the birds.

3. “Were they a definite or an indefinite number?“

We know that the number of birds Borges or we as readers saw cannot be indefinite. There was a specific image we saw. If only we had that image fixed somewhere, we could look at it again and count the number. So the number of birds must have been finite.

4. “This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count.“

Here we have the main argument. It assumes that the number could have been definite if and only if (iff) some sentient creature knows it. But this isn’t very convincing. No one knows about the existence of some planets, but this doesn’t mean they can’t exist. And we may find later that they exist. Similarly, maybe in 300 years, we will invent a way to go back and rewatch every thought of every human being that ever lived. Of course, if we find out that the flock Borges imagined consisted of 9 birds, this would prove that the number was always definite.

5. “In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists.“

Borges claims that he saw an indefinite number of birds if no one could count them. Therefore, God must exist because indefinite whole numbers between 1 and 10 cannot exist. But again, the main issue is the assumption that if no one knows how many birds I saw, then the number must be indefinite.

If we turn all this into syllogisms, we get:

• P1. If the number of birds is definite, God exists.
• P2. The number of birds is definite.
• ∴ God exists.

• P1′. If God doesn’t exist, the number of birds is indefinite.
• P2′. The number of birds cannot be indefinite.
• ∴ God exists.

The first argument is an example of affirming the antecedent (modus ponens). The second is an example of denying the consequent (modus tollens). So both are deductively valid. Here’s a formalized version to prove their validity:

• P1. p→q (if p, then q)
• P2. p
• ∴ q (therefore q)

• P1′. ¬q→¬p (if not q, then not p)
• P2′. p
• ∴ q (therefore q)

So the arguments are valid, but are they sound? It is almost always impossible to decisively prove the soundness of a philosophical argument, but I believe these arguments aren’t. And Borges would probably agree. They are not sound because premises P1 and P1′ are very dubious. As I already mentioned, the number can be definite even if no one knows it. Criticisms like this one, however, cannot be applied to the ontological arguments proposed by Anselm, Descartes, Leibniz, Gödel, Plantinga, or others because this ironic paragraph by Borges has neither the same intentions nor the same form.

References

• Anselm, St. (1903). Proslogium; Monologium: An Appendix In Behalf Of The Fool By Gaunilo; And Cur Deus Homo. (Sidney Norton Deane Trans.). The Open Court Publishing Company. https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp (Original work published 1078)
• Borges, J. L. (1970). Dreamtigers. E. P. Dutton & Co., Inc.
• Borges, J. L. (1972). El hacedor. Alianza Editorial. (Original work published 1960)
• Descartes, R. (1912). A discourse on method ; Meditations on the first philosophy ; Principles of philosophy. London : Dent ; New York : Dutton. http://archive.org/details/discourseonmetho1912desc (Original work published 1641)