Time is the number of movement in respect of before and after

Aristotle on time

Aristotle 384 BC · 322 BCObserve, classify, reason: happiness through virtue.

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What it claims

Time is something real in the world: the before and after of real change, which the soul can count.

Why

Without change we do not feel time; time is what we count in movement when we tell a before from an after.

The same idea through history

Aristotle350 BCAristotle rejects two ready-made ideas: time is not movement itself, and it does not exist without movement or change. He makes it what we count in movement: the before and the after.

Isaac Newton1687Newton takes the opposite view: time flows by itself, whether or not anything moves.

In short

"Time is the number of movement in respect of before and after" is an argument by Aristotle (Physics, IV, 10-14 (c. 350 BC), 350 BC) on the question "Does time really exist?" (answer: time really passes). Its claim: Time is something real in the world: the before and after of real change, which the soul can count. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P5). AskPhilosophy presents 3 objections, 3 of them with a documented reply, and the original text behind each premise, checked word for word.

Physics, IV, 10-14 (c. 350 BC)

Valid with an implicit premise

What is time? One morning you wake up having noticed nothing: no dream, no thought, no sound. You cannot tell whether an hour or a whole night has passed. Aristotle starts from this experience. For him, time is not a separate thing flowing by itself, but it is not a mere illusion either: it is something we count in change, when we say there was a before and an after. Clocks only make this counting precise.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.

Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P5, one could accept everything and still say: there is no real change, only appearances (Parmenides' thesis), so no real time. Aristotle sets this idea aside elsewhere in the Physics. He also admits a limit: with no soul to count there would be no number, so strictly no counted time, but only that of which time is an attribute, movement with its before and after.

The argument is valid. P1 and P2 say that time is neither change nor independent of it. P3 draws from them that time is the number of change, that is, its before and after as counted. P4 says that this before and after are in the change. P5 says that change is real. Then time, which is this before and after, is real.

Analogy. Take a road with milestones. The road exists without the milestones, but distances in kilometres suppose someone who counts. In the same way, for Aristotle, change and its order (before, after) exist in the world, and time is that same order as measured by a mind that counts.

Objections

Each objection is a conversation: click to see who replies and where the debate stands.

Aristotle (the opening difficulties) 350 BC · attacks the conclusion

Aristotle opens his own study by explaining why one might think that time does not exist, or barely: one part of it has been and is not, the other is going to be and is not yet. Yet time, infinite or as short as you like, is made of these parts. What is made of things that do not exist hardly seems able to exist.

Aristote replies

Aristotle

The 'now' links past and future time, and it is their limit: the beginning of one and the end of the other. It divides time only potentially. In so far as it divides, it is always different; in so far as it links, it is always the same, like a point on a line.

Where the debate stands (our summary)Aristotle answers that time is not made of 'nows' set side by side, but of a continuous flow that the now links. Philosophers still discuss whether this is enough to make the past and the future exist, or whether only the present exists.

Augustine 400 · attacks premise 4

Augustine moves the question to the mind: it is in my mind that I measure time, through the impression that passing things leave there and that remains after they have passed. Past and future are then not in things but in the soul, as memory and expectation.

Aristote replies

see the argument

Aristotle

Aristotle asks the question himself: if the soul did not exist, would there be time? Without someone to count, there is no number. But if movement can exist without a soul, and the before and after are attributes of movement, then that of which time is an attribute exists without it.

Where the debate stands (our summary)The core disagreement is about what is 'in the mind'. For Augustine, time (past, future) exists only in the soul that remembers and expects. For Aristotle, the before-after order is in the world and the soul only counts it. Aristotle himself leaves the question open.

Isaac Newton 1687 · attacks premise 2

Newton holds the opposite of P2: there is an absolute, true and mathematical time which flows uniformly without relation to anything external. Movements serve only to measure it approximately, and the duration of things stays the same whether movements are fast, slow or none.

a defender replies

see the argument

No reply possible: objection raised in 1687, after the author's death (-322).

Gottfried Wilhelm Leibniz defender of the argument · 1716

Leibniz replies that the objection of Newton (and Clarke) would hold if time were anything other than the things existing in time. But instants, considered without the things, are nothing at all: they consist only in the successive order of things.

Where the debate stands (our summary)The core question is not settled: is time a kind of container that would exist even in an empty world (Newton), or only the order of events (Aristotle, Leibniz)? Relativity physics in the 20th century gave many physicists good reasons to do without absolute time.