- Yesterday, while explaining the possible translations of Latin nouns, all of us fell into a collective astonishment that the indefinite article cannot be plural. You can’t have “a forests”, though this is not because the article is itself singular (there is no mystery to why you can’t say “that forests” or “this planets”, but the impossibility of “a planets” is not the same).
(N.B. see the comments for a discussion of “some” which is indefinite while being both singular and plural.)
-The first explanation anyone ventured was that the article was somehow infinite, and there is only one infinite thing. Someone else objected with a second-hand account of Cantor’s multiple infinities, though everyone saw that we had to give some account of why the idea “infinities” made sense, and so we had to allow that they could be somehow many.
-The indefinite and the infinite are not the same. Mathematics gives a particularly sharp division: it is not the same thing for things to be infinite as it is for them to be undefined. “Undefined” means something like “there is no way to incorporate the thing into an operation” (say, the idea of dividing X by zero, since we’re not sure if the result should be X, or infinite, or zero). Whatever infinite means, it’s not this – even though we don’t know how to deal with “infinity” as though it were exactly the same as a finite quantity (applying basic algebra to ∞ + 1 = ∞ gives us 1=0).
-The infinite is the negation of a terminus or limit; the indefinite is the incompletion of the first act of the understanding. Modernspeak: infinite is either metaphysical or a broad category including the metaphysical and the epistemological; the indefinite is epistemological.
-For St. Thomas, two infinites bookend reality: on the one hand there is an infinite which is such by having no potency at all; on the other hand there is an infinite that is purely potential. David of Dinant identified them.
-This meshed with a text I was reading from Giovanni Gentile, arguing that consciousness was infinite, since for it to recognize anything is to place it within its ambit, and so any possible limit would be placed within it. The point can be generalized to all that exists: no living thing has a terminus that is a part of its being – death is not a part of life; and the corruption or analysis of any form is not a moment in the existence of that form.