Time is Always About in the Quad

According to Aristotle, does time depend upon the existence of a mind which perceives (or marks) time? I have not seen the book, but apparently this is what Ursula Coope argues in her recent Time for Aristotle. As the review in NDPR by Andrea Falcon explains:

Aristotle defines time as a kind of number. More precisely, time is "a number of change with respect to the before and after" (219 b 1-2). Coope argues that in defining time as a kind of number Aristotle defines it as something that is essentially countable. On her reading, time gets counted by counting instants of time. Moreover, when we count an instant of time, we mark a potential division in all the changes that are then going on. Counting instants of time turns out to be a way of arranging all the changes that are going on in a single before and after series. ...

A somewhat surprising consequence of Aristotle's definition of time is the claim that time is dependent upon a mind which can count (I should say a soul which can count). For Aristotle the dependence of time upon the mind (the soul) implies that there would be no time without beings that are able to count. But this does not extend to change despite the fact that time and change are intimately connected. Coope focuses on the different way in which time and change relate to the mind (the soul). It follows from the definition of time that time cannot exist in the absence of beings that are able to count because time is defined as something that can be counted. But it does not follow from the definition of change that change depends upon beings that are able to count. Remember that the definition of change is carefully crafted to make no reference, implicit or explicit, to time. In other words, time is essentially countable, whereas change is not. But this is consistent with the claim that there is no change without time and there is no time without change.

I don't know which of the following is Coope's thesis (or perhaps it is some other claim):

(i) For time always to exist, at least one mind must at some time exist;
(ii) Time exists only so long as at least one mind exists that is capable of marking it; or
(iii) Time exists only so long as it is actually being marked (or perceived) by a mind.

(i) seems strange, inelegant, and possibly circular. (ii) also seems strange (and possibly circular as well): why should time exist when it is not marked, just because something exists which can mark it? (If that were so, then wouldn't it exist also if only it were possible that something existed which could mark it?) And yet, on (iii), time would be going in and out of existence, depending upon its being marked or not.

One thinks of sensibles, in response, and yet these admit of a teleological explanation. Do we want to say that time is for the sake of something?

Apart from all this, aren't there texts in Aristotle, referring to time, which can hardly be interpreted to mean that time depends on a mind? I wonder how Coope deals with these. I'll post them tomorrow.