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I just read Aristotle: The Physics, Books I-IV, and found nowhere the words "potential" and "actual" combined with "infinity", even if the principle is described.

Now I feel these definitions are not originally from Aristotle. Does anyone have any evidence to the contrary?

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They are from translations of Aristotle, who, of course, did not write in Latin, and so used neither actualis nor infinitas. While the last one has a more or less straightforward Greek analogue, the former not so much. Here is from Physics III.6 206a in Hussey's translation, which does not quite put the two together:

"'To be', then, may mean 'to be potentially' or 'to be actually'; and the infinite is either in addition or in division. It has been stated that magnitude is not in actual operation infinite; but it is infinite in division - it is not hard to refute indivisible lines - so that it remains for the infinite to be potentially. (We must not take 'potentially' here in the same way as that in which, if it is possible for this to be a statue, it actually will be a statue, and suppose that there is an infinite which will be in actual operation.)"

And here is the same passage as translated by the Internet Classics archive, which does:

"We must keep in mind that the word 'is' means either what potentially is or what fully is. Further, a thing is infinite either by addition or by division. Now, as we have seen, magnitude is not actually infinite. But by division it is infinite. (There is no difficulty in refuting the theory of indivisible lines.) The alternative then remains that the infinite has a potential existence. But the phrase 'potential existence' is ambiguous. When we speak of the potential existence of a statue we mean that there will be an actual statue. It is not so with the infinite. There will not be an actual infinite."

The subtleties of translation are discussed by Cooper in Aristotelian Infinites. He points out that both energeia and entelecheia in the original text tend to be translated as "actuality", and suggests replacing the traditional translations with "in-activity" and "in-fulfillment", respectively. Accordingly, his translation for the dunamis is "in-capacity":

"Great confusion over the meaning of Aristotle’s claims about the infinite has been caused on all sides of the interpretative debates by the universal habit, until very recently, of misunderstanding the distinction and contrast between dunamis, energeia, and entelecheia as one concerning the metaphysics of modality, and translating dunamis as “potentiality” i.e., possibility, and both the other terms indiscriminately as “actuality.” In fact, as we have seen in our discussion of Metaphysics Θ, the distinction intended is one within the metaphysics of being: it concerns two or in fact three ways in which things can be whatever they are. Being something potentially vs. in actuality has almost no connection with Aristotle’s concerns in this theory, as Beere has clearly and persuasively argued (Doing and Being, esp. chapters 8 and 9)."

"On Aristotle’s theory, nothing is ever in-fulfillment or in-activity (where that means “in-fulfillment”) infinite; when “being-in-capacity F” is intended to contrast with and exclude “being-in-fulfillment F” or being-in-activity F where that terminology is used as the term contrasted with being-in-capacity F, every infinite thing there actually is only is-in-capacity infinite, and never is-in-activity infinite. But that does not prevent Aristotle from saying... that infinite things (magnitudes — both those infinite by division and those infinite by addition, plus number and time) sometimes are-in-capacity infinite and sometimes are-in-activity infinite: here being-in-activity infinite does not mean and in fact contrasts with being-in-fulfillment infinite."

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  • Aristotle's words have mistranslated in order to be misinterpreted by theologians: that is called 'tradition'. It allows us to have e.g. "potential energy".
    – sand1
    Apr 27 '21 at 9:16

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