Philosophy Models

Aristotle (384-322 BC) writes about time and change in book 4 of Physics. The main ideas of his model are:

• Change always involves an underlying thing and two contrary attributes. The underlying persists through the change, while one contrary is lost and the other gained.
• Change can be in substance, quality, quantity, and place.
• Aristotle uses the change in place to explain that change is ordered, meaning that before and after can be defined for it.
• Time is a number referring to the change. As such, it is existentially dependent on change. If there is no change, there is no time. Time, like change, is ordered. The past and present are necessary, while the future is contingent.
• Since time is a number, and numbers exist in intellective souls, time exists just in worlds where intelligent beings exist.

The following OntoUML diagram shows the main classes Aristotle’s model of time:

Class	Description	Relations
Change	“In defining time as a number of change, Aristotle assumes that change is, in an important sense, prior to time. Time is something that is essentially dependent on change, and because of this, a true understanding of time must draw upon a prior understanding of change. This implies that change itself can be defined in a way that makes no reference to time. It thus rules out a certain natural way of using the notion of time to define change. […] What, then, is Aristotle’s account of change? Can he avoid making the nature of change essentially dependent on that of time? He lays out his account of change in books I and III of the Physics. He explains first, in Book I, that change always involves an underlying thing and two contraries. The underlying thing persists through the change, losing one contrary and gaining the other. For instance, when a man becomes musical, the underlying thing is the man. He persists through the change, being first unmusical and then musical. This tells us something about the basic structure of a change, but a full account of change must invoke the notion of potentiality. For such an account, we need to turn to Physics III.1–2. Aristotle says there that change is ‘the actuality (entelecheia) of that which potentially is, qua such’ (201a10–11).“
Before&AfterInChange	Change is ordered and continuous, because change in place is ordered and continuous: “Because there is a before and after in place, there is a before and after in change“	subkind of Before&After; characterizes Change
ChangeInPlace; ChangeInSubstance; ChangeInQuality; ChangeInQuantity	Change according to Aristotle can be in Substance, Quality, Quantity, Place (see [1.3.13]). All these four are superior genus in its ten-fold division (see [1.3.2]).	events inheriting from Change
Before&AfterInPlace	Change in place (motion) is ordered and continuous: “Because there is a before and after in place, there is a before and after in change”	subkind of Before&AfterInChange; characterizes ChangeInPlace
Time	“Aristotle’s account represents time as a kind of universal order and that this is why he defines it, oddly, as a number. It is, he says, a ‘number of change’, a single order within which all changes are related to one another. […] Time is something that is essentially dependent on change […] Aristotle defines time as a kind of number. “It is ‘a number of change with respect to the before and after’ (219b1–2). He introduces this definition as if it is quite uncontroversial. He simply says, ‘for this is what time is . . . ’ (219b1). Though he goes on to explain the sense in which time is a kind of number, he does not really give us an argument for defining it in this way.”	participates in Change; inherits from Number
Past; Present; Future	Past, present and future are phases of time. According to Aristotle past and present is necessary, the future is contingent.	phases of Time
Number	A number.
Before&AfterInTime	“In the Metaphysics, Aristotle presents what I shall call a ‘presentrelative’ view of temporal order. It is a view that defines the temporal ‘before’ and ‘after’ [in time] in terms of distance from the present. This view is striking both because of the central role it accords to the present and because it makes temporal order depend upon duration (upon ‘distance’ from the present). Because of the reference to the present, it is, in a certain sense, a static account of the before and after in time. It describes temporal order as from some particular present and tells us nothing about the relation between this order and temporal order as from some other present.”	characterizes Time; inherits from Before&After
Mind	“Given that time is by definition something countable, the question naturally arises whether its existence depends on the existence of beings, like ourselves, who can count it. Aristotle raises this question towards the end of his discussion (223a21–9). Someone might be puzzled, he says, about whether there could be time if there were no ensouled beings. He presents an argument that there could not be. The argument is that since time is a kind of number, it is necessarily countable. As such, it can only exist in a world in which there are beings that can count. Since the only beings that can count are beings that have intellective souls [minds], there can only be time in a world in which there are such beings. He goes on to point out that this argument gives us no reason to think that change depends on the soul, since change, though it is closely connected to time, is not something that is necessarily countable”	counts Time
Before&After	“Aristotle groups together the before and afters in time, in change, and in place as all being of the same general type. Each of them, he says, is defined relative to some origin. […] Aristotle also invokes the relation of following to explain what he calls ‘the before and after’ (219a14–19). Some explanation of what it is to be before or after is obviously needed in any account of time. In Aristotle’s account, this explanation is of particular importance, as he is going to defne time as ‘a number of change with respect to the before and after’ (219b1–2). This definition will not be very informative unless he also has something to say about what it is to be before or after. But at this crucial point, he says frustratingly little. Such explanation as he gives, draws once again upon the relations between time, change, and magnitude. The before and after is, he tells us, first of all in place. (In this context, ‘place’ seems to be just another word for spatial magnitude.) Because there is a before and after in place, there is a before and after in change, and because there is a before and after in change, there is a before and after in time. As he puts it: ‘Therefore, the before and after is first of all in place. And there it is in position. But since the before and after is in magnitude, it is necessary that also the before and after is in change, by analogy with the things there. But the before and after is also in time, through the following always of the one upon the other of them.’ (219a14–19)”

Sources

• All citations from: Coppe, Ursula, “Time for Aristotle”, Oxford University Press, 2005
• van Fraassen, Bas C., “An introduction to the philosophy of time and space”, Random House, 1970
• Bodnar, Istvan, “Aristotle’s Natural Philosophy”, The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.)

First published: 17/6/2021
Updated: 8/12/2021