“Mersenne and Guldin were anticipating Borge’s Babel Library ad abundantiam. Not only this, Guldin observed that if the numbers are these, who can marvel at the existence of so many different natural languages?
The art was now providing an excuse for the confusio linguarum. It justifies it, however, by showing that it is impossible to limit the omnipotence of God.
Are there more names than things? How many names, asks Mersenne (Harmonie, II, 72), would we need if were to give more than one to each individual? If Adam really did give names to everything, how long would he have had to spend in Eden?
In the end, human languages limit themselves to the naming of general ideas and of species; to name an individual thing, an indication with a finger is usually sufficient (p. 74).
If this were not so, it might easily “happen that for every hair on the body of an animal and for each hair on the head of a man we might require a particular name that would distinguish it from all others. Thus a man with 100,000 hairs on his head and 100,000 more on his body would need to know 200,000 separate words to name them all” (pp. 72-3).
In order to name every individual thing in the world one should thus create an artificial language capable of generating the requisite number of locutions. If God were to augment the number of individual things unto infinity, to name them all it would be enough to devise an alphabet with a greater number of letters, and this would provide us with the means to name them all (p. 73).
From these giddy heights there dawns a consciousness of the possibility of the infinite perfectibility of knowledge. Man, the new Adam, possesses the possibility of naming all those things which his ancestor had lacked the time to baptize.
Yet such an artificial language would place human beings in competition with God, who has the privilege of knowing all things in their particularity. We shall see that Leibniz was later to sanction the impossibility of such a language.
Mersenne had led a battle against the kabbala and occultism only to be seduced in the end. Here he is cranking away at Lullian wheels, seemingly unaware of the difference between the real omnipotence of God and the potential omnipotence of a human combinatory language.
Besides, in his Quaestiones super Genesim (cols 49 and 52) he claimed that the presence of the sense of infinity in human beings was itself a proof of the existence of God.
This capacity to conceive of a quasi-infinite series of combinations depends on the fact that Mersenne, Guldin, Clavius and others (see, for example, Comenius, Linguarum methodus novissima (1648: III, 19), unlike Lull, were no longer calculating upon concepts but rather upon simple alphabetic sequences, pure elements of expression with no inherent meaning, controlled by no orthodoxy other than the limits of mathematics itself.
Without realizing it, these authors are verging towards the idea of a “blind thought,” a notion that we shall see Leibniz proposing with a greater critical awareness.”
Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 141-3.