Infinite and Indefinite.

We are written from Saint Petersburg on July 1, 1863:

“…In The Spirits' Book, book I, chapter I, no. 2, I noticed this proposition: All that is unknown is infinite. It seems to me that many things are unknown to us without being, for that reason, infinite. As this term appears in all the editions, I asked my guide for the explanation, who answered me: “The word infinite here is an error; the correct word is indefinite.” What is one to think of this?…”

Answer – These two terms, though synonymous in the general sense, each have a special acceptation. The Academy defines them thus:

Indefinite, whose end or limits are not or cannot be determined. Indefinite time. Indefinite number. Indefinite line. Indefinite space.

Infinite, that which has neither beginning nor end, which is without bounds and without limits. Space is infinite. God is infinite. The mercy of God is infinite. By extension, it is said of that to which one cannot assign limits, an end, and, by exaggeration, both in the physical and the moral sense, of all that is very considerable in its kind. It is said particularly for innumerable. An infinite duration. The infinite beatitude of the elect. Stars situated at an infinite distance. I thank you infinitely. An infinite variety of objects. Infinite sorrows. There is an infinite number of authors who have written on this subject. From this it results that the word indefinite has a more particular sense and the word infinite has a more general sense; that the first is used by preference with regard to material things, and the second to abstract things; it is more vague than the other. The more general sense of the word infinite allows it to be applied in certain cases to what is only indefinite, whereas the reverse could not occur. One says equally: an infinite duration and an indefinite duration; but one could not say: God is indefinite, his mercy is indefinite. From this point of view, the use of the word infinite in the above-quoted sentence is not abusive and does not constitute an error. We say, moreover, that the word indefinite would not express the same idea.

As soon as a thing is unknown, it has for thought the uncertainty of the infinite, if not absolute, at least relative. For example, you do not know what will happen to you tomorrow: your thought wanders into the infinite; it is the events that are indefinite; you do not know how many stars there are: it is an indefinite number, but it is also the infinite for the imagination. In the case at hand, it was fitting, then, to employ the term that generalizes the thought, in preference to the one that would give it a restrictive sense.