Let us now take up the first charge of circularity, which runs thus: because Aristotle's definition of time includes the term “motion,” and because motion cannot be understood independently of temporal notions, the definition cannot possibly succeed in revealing the essential nature of time – rather, it simply presupposes time.

The charge inherits its force from an intuitive conception of motion, according to which motion is just being at different places at different times. Let us follow Wesley Salmon in calling any such view of motion in terms of pairs of spatio-temporal locations a version of the “at-at theory of motion.” If Aristotle endorses any form of the at-at theory of motion, it's hard to see how the charge of circularity might be avoided. If he does not, it would be desirable to understand in a fairly precise way what his own view is and how it differs from the at-at family of views.

I should begin by clarifying a terminological issue. I have elected to render “kinêsis” as “motion” almost everywhere in this book. But that would be misleading as a strict translation of the Greek term. In the Categories, Aristotle draws several distinctions regarding change and motion. Kinêsis is one genus of metabolê, the highest-level universal of coming-to-be. Kinêsis includes any variety of change with respect to the states of a subject. The other genus of metabolê is change in respect of substance, of which substantial generation (genesis) and corruption (phthora) are the two species.

This is a commentary on Plato's Cratylus. It is a running commentary, because it is not organized by lemmata, but rather proceeds by quoting chunks of text (in my own translation) and then going on to explain them in detail. It is, alas, not a complete commentary, because there are some parts of the dialogue which I comment on only selectively, as I explain at the beginning of chapter 5. It is primarily a philosophical commentary, because what I am chiefly interested in is the purport of the theses advanced in the dialogue and the structure and worth of the arguments for and against them. But it is also a philological commentary, because along the way I discuss many matters of textual criticism and interpretation – some relevant to our philosophical understanding of the dialogue, some (usually confined to footnotes) perfectly irrelevant. Actually, I am afraid all I can say about my choice of focus is that as I was writing I tended, almost unwittingly, to imagine myself reading the dialogue in an open-ended seminar free from any sort of schedule, whose sole concern was to discuss anything that might seem interesting about a given portion of text before moving on to the next one. And so it is that, finally, this is a very long commentary – something for which I won't apologize.

As a consequence of the last feature, the book has been long (everyone around me says too long) in the writing.

One needn't be a metaphysician to have been gripped by puzzles concerning the nature of time. Does it have a beginning? Will it ever come to an end? Why is it that we can remember the past but can only anticipate the future? What happens to objects and events of the past – do they exist in any sense at all? Are any events of the future already determined? Am I identical to any person who existed in the past? How is it that time passes? What is time, anyway? Growing up on our family farm, I would sometimes lie awake nights pondering questions such as these, unsure how I might even begin to find their answers.

As C. D. Broad's remark quoted in the Introduction suggests, much of the difficulty we experience in discussing and contemplating time arises from the language in which we frame the propositions of speech and thought. Certain facts about the English language (e.g. that temporal adverbs are frequently vague or are used ambiguously, that verbs tokened in writing and speech indicate grammatical tense, or even that the word “time” can function as the subject of a sentence) give rise to challenges for those who would inquire into the nature of time.

But these are no less facts about Attic Greek than they are about English, and Aristotle – arguably the first philosopher to explicitly attempt to unravel the snares inherent in language – must have faced the same sort of challenges that arise from them when he composed his own theory of time, an account that he develops in chapters 10–14 of Book iv of the Physics.

In chapter 2 I analysed Socrates' first reactions to Hermogenes' thesis and argued that down to 386d2, where the rejection of Protagoras' relativist doctrine is accomplished, Socrates displays no hostile attitude towards conventionalism. In the sequel, however, what might have seemed just an inquiry into Hermogenes' attitude to Protagoras turns out to have been also, at the same time, the first step of a long and complex defence of naturalism and attack on conventionalism, which will end in 390de with the conclusion that Cratylus is right and Hermogenes is wrong. Our next task is to explore the structure, content and purpose of the arguments which Socrates advances here.

FIRST ARGUMENT: THE NATURALNESS OF ACTIONS (386E–387D)

The naturalness of actions. Cutting and burning (386e–387b)

Socrates' next and crucial step is to argue that actions have an objective nature:

Essentially, I take Socrates to be simply arguing, in accordance with the conclusion of Protagoras' refutation (386de), that actions have an objective nature because everything does.

Aristotle's view concerning the perception of various types of magnitudes has roots in Plato's thought. In the Protagoras, Socrates engages the dialogue's namesake about the importance of “the art of measurement”:

Aristotle's commitment to the instantaneous nature of perception is subject to an immediate and obvious objection. Anyone who cares to reflect on the matter will report that perception seems to occur not in the instantaneous now, but rather in the “specious” now, so called precisely because the present appears to us (specio: “to look at”) to have some temporal thickness. But to the extent that perceptual content simply consists in being appeared to in certain ways, there is no appearance/reality distinction here, and so the way that perception seems to us really is just the way that it is – namely, temporally smeared, not instantaneous.

The objection can be expressed more pointedly. If perception were instantaneous, then (contrary to fact) certain familiar phenomena would not occur. We would not, for instance, perceive the images on a movie theater's screen as moving, but rather would see them as what they actually are: sequences of still images lasting for very brief periods of time. Because that clearly isn't the case, it must be false that perception is instantaneous, and so Aristotle's view is simply mistaken.

The objection so formulated smacks of anachronism, but there are related phenomena with which Aristotle would have been acquainted. For example, anyone who has had occasion to stroll alongside a wooden picket fence will know that looking through even quite small gaps between the boards can provide to one while walking a surprisingly comprehensive image of the space and objects lying behind the fence, and more so the faster one walks.

Both Plato and Aristotle were working against the background of an entrenched popular conception of time when developing their philosophical theories. Hesiod couches his advice regarding the timing of works in terms of celestial events, and the type of chronometer used by the ancients to keep “natural time” (namely, the sundial) functions by tracking the movement of the most prominent heavenly body. The lack of a commonly recognized epoch meant that the calendric conventions employed by common folks and historians alike named years by the number of years removed from some salient event. I argued in Chapter 2 that in the Timaeus Plato accomodates this traditional conception of time to a fairly high degree by defining time in terms of the regular motion of the celestial bodies – that is, as “motion-according-to-number.” Such motion, on Plato's view, is the product of the demiurge's imposition of numerical form onto what were previously disorderly movements:

As part of a larger engineering project, Archimedes needs to determine the maximum velocity that a certain ball attains rolling down a particular incline plane. He knows that velocity is just a ratio of distance to time, d:t. He also knows what distance is and how to measure it. But let us suppose that, being a bit absent-minded, Archimedes is uncertain about the nature of time and how it is measured. He remembers reading about time in the Physics some time ago and wonders where his copy of the text is. So he sets about trying to recall what he might have done with it.

(Commentary: Archimedes' recollection of having read the Physics is a psychic state concerning the past. It is founded upon a compound phantasm consisting of two perceptually induced phantasms, one of whose content is as of his reading the Physics (this is “the movement relative to the thing”) superposed with his current perceptual phantasms. The apparent veracity of each phantasm, along with their joint inconsistency, compels Archimedes to spontaneously regard the event in question as occurring in the past.)

In attempting to determine where his copy of the text might be, Archimedes recalls that immediately after reading about time, he attended a banquet at Conon's home at which Conon mentioned Eratosthenes' interest in Aristotle's discussion of place. Visiting from Alexandria, Eratosthenes didn't have easy access to a copy of the Physics, so Archimedes offered to put his copy on loan.

The hylomorphic interpretation of Aristotle's theory of time quite naturally presents a systematic approach by dividing the task into two stages: first, one should investigate the matter of time, and then one may inquire into the form of time. The burden of this section of the book is to get a conceptual grip on the hulê of time, which is kinêsis, motion.

Here there are a number of issues and questions to be addressed. The first is to sort out Aristotle's claim that time is an aspect of motion (kinêseôs ti). Ursula Coope has produced a reconstruction of Aristotle's argument to this conclusion – which figures as the opening move of Physicsiv.11 – that deserves careful examination. While her reconstruction posits Aristotle's use of a methodological principle familiar from other treatises, I do not believe that she has got the argument in iv.11 right. What I take to be the correct reconstruction of the argument lights the way for the hylomorphic interpretation. I develop my reconstruction in section 3.2 below.

Independent of the question how to understand this particular argument is the larger concern that Aristotle's definition of time is patently circular. How is it possible to read “a number of motion with respect to the before and after” in such a way as to render it non-circular, let alone informative?

Recall from the discussion in the Introduction that temporal passage is one of the three basic elements of the contemporary concept of time and consists in the apparent (or real) “flow” of time from past to future. A natural question to ask about Aristotle's temporal theory is whether he regards this “flow” as a genuine feature of reality. Richard Sorabji and Fred Miller both hold the view that Aristotle's account does incorporate temporal passage, but only equivocally and confusedly so. As Sorabji says:

He goes on to say, “without sharply distinguishing the flowing from the static, Aristotle none the less treats flowing conceptions as essential to the existence of time.” Sorabji maintains that the distinction between flowing and static conceptions of time was not made fully explicit until the Neoplatonist Iamblichus, some six and a half centuries after Aristotle had composed his own theory.

Miller's view is consistent with Sorabji's. He claims that:

I concede that Sorabji and Miller are right to claim that Aristotle does not explicitly distinguish the concepts of temporal extension and temporal passage.

Now, less than two Stephanus pages from the end, comes a turning point: Socrates turns to an explicit – if still provisional – assessment of the flux theory. His arguments, and the final parting of the ways between him and Cratylus, are the subjects of this final chapter.

THE ARGUMENTS (439B–440D)

The lawgivers in a whirl (439bc)

This passage is crucial in several respects, all of which bear on the interpretation and structure of the whole dialogue.

First, Socrates expressly confirms that, as he said at 411bc, he believes that the first namegivers held the flux theory (c1–4). There seems no reason why we should not assume that Socrates is being sincere.

INTRODUCTION (427E–429C)

Preliminary exchanges (427e–428e)

We are now going to hear Cratylus' first words since his laconic ‘if you like’ of 383a3, whereby he allowed Hermogenes to involve Socrates in the discussion. In a few lines he is to become Socrates' only interlocutor down to the end of the dialogue, while Hermogenes remains silent.

A very cautious opening. Hermogenes patiently tries to overcome Cratylus' resistance:

These are the last words we shall hear from him in the dialogue. Socrates adds a very diplomatic invitation, full of Attic courtesy:

Now that we have examined both the matter and the form of time, the hylomorphic analysis is technically complete. However, there are residual issues of importance that need to be addressed. To my knowledge, no commentator of Aristotle has attempted to analyze his notion of simultaneity, but the hylomorphic interpretation has ready to hand an obvious and effective analysis of this temporal relation. The analysis points up the importance of celestial motion within the theory, and we shall have to examine some of Aristotle's remarks in the Physics and other treatises on natural philosophy to fully appreciate the status and role of celestial motion in his account.

The most daunting residual issue concerns Aristotle's treatment of temporal passage and related matters about the present or “now.” There is substantive disagreement over the question of whether Aristotle treats time as being essentially static (as it is in McTaggart's B series) or dynamic (as in his A series). I shall prepare the ground for the hylomorphic view on this issue by examining the interpretations of Richard Sorabji and Fred Miller, both of whom argue that Aristotle fails to integrate temporal passage into his theory in a satisfactory way. Taking this line of argument considerably further, Norman Kretzmann claims that Aristotle, like McTaggart, believes that there is a contradiction inherent in the notion of temporal passage. The hylomorphic interpretation is inconsistent with all of these views.