“Aristotle would never have made the mistake of talking about a time before time existed,” claims Woods. (p209)
Woods quotes Aristotle on many occasions throughout Reason in Revolt. It is true that Aristotle believed that the universe was eternal. Yet it is not clear how familiar Woods is with Aristotle’s writing on time, space or infinity. In general, Aristotle takes a contrary position to that of Woods.
If one takes into account the limitations of his epoch, Aristotle achieved some quite remarkable insights into the nature of our universe. Even though Aristotle developed a logic that effectively usurped the ancient dialectics of Anaximander, Aristotle made occasional use of this ancient dialectics when discussing ‘the heavens’.
Woods presents Aristotle’s idea of time using this quote from his Metaphysics: “Movement can neither come into being nor cease to be: nor can time come into being, or cease to be.” Woods sneers: “How much wiser were the great thinkers of the Ancient World than those who now write about ‘the beginning of time’, and without even smiling!” (p145)
Woods is skating on thin ice. In chapter three of Physics, Aristotle discusses the infinite. Aristotle argues, as we have already noted, that there are two sorts of infinity, potential infinity and actual infinity. He concludes very firmly that actual infinity does not exist. It is true, Aristotle explains, that one can always imagine an infinite process, such as in addition. It is not hard to imagine infinity in this sense. This is Aristotle’s potential infinity, but it will always remain finite. Something extra can always be added. So:
there is potentially an infinite… For it will always be possible to take something as extra. Yet the sum of the parts taken will not exceed every determinate magnitude… (Physics, chapter 3, part 6)
Aristotle’s conclusion is spelt out very clearly: “… the infinite has a potential existence. But… There will not be an actual infinite.”
Curiously, Woods does say that Aristotle, “Polemicised against geometers who held that a line segment is composed of infinitely many fixed infinitesimals, or indivisibles.” (p354) This means, in simple language, that Aristotle opposed the idea that something can be infinitely divided, or is comprised of an infinite number of parts. Woods does not state this clearly, but rather in general allows the reader to draw the conclusion that Aristotle supports the same views as Woods.
Aristotle was the first western philosopher to clearly explain the materialist position that there is no such thing as the actual infinite, as a separately existing thing. Woods argues that the infinite does exist, and he makes it a central tenet to the philosophy of dialectical materialism. This introduces an element of idealism (in the philosophical rather than the common or popular sense of the term) into Reason in Revolt and its interpretation of dialectical materialism, because the infinite is a human idea without any proof of its material existence. It is “beyond all human experience”, and yet Woods argues that science should accept this idea as the basis of cosmology.
An idealist approach, in philosophical terms, is one which makes ideas primary and the material world secondary. Idealism explains developments primarily though ideas, and relegates experience to a secondary role, whereas Marxism makes the experience of the material world primary, from which ultimately arises, in a general sense, our ideas about the world. It is important that Woods’ interpretation of dialectical materialism on this question is corrected. The philosophical meaning of the terms ‘idealism’ and ‘materialism’ is discussed in Engels’ Ludwig Feuerbach and the Outcome of Classical German Philosophy.
Woods takes the position that: “The reason why infinity can be used, and must be used, in modern mathematics is because it corresponds to the existence of infinity in nature itself.” (p358) Infinity is not used in this way in mathematics – as Woods concedes later on the same page – because infinity does not correspond to nature itself.
Indeed, Aristotle explains that the type of infinities used in mathematics corresponds to his potential infinity. After explaining the illusion of the actual infinity, Aristotle goes on to say:
Our account does not rob the mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase… In point of fact they do not need the infinite and do not use it. They postulate only that the finite… may be produced as far as they wish… Hence, for the purposes of proof, it will make no difference to them to have such an infinite instead, while its existence will be in the sphere of real magnitudes. (Physics, chapter 3, part 6)
By real magnitudes, of course, Aristotle means concrete, measurable quantities that exist in the real world. This issue will be touched on very briefly in the short chapter, The infinite in mathematics. But more than mathematicians, scientists tend only to use Aristotle’s potential infinity, even among those who defended the idea of an infinite universe. When the Big Bang theory began to gain some adherents, the physicist Fred Hoyle attempted to develop an alternative theory which could explain current cosmological observations on the basis of an infinite universe. In a book popularising his ideas, written in 1955, he simply says: “the word ‘infinite’ should cause no conceptual difficulties. It simply means that however much of the [universe] we consider there is always more of it.” (Fred Hoyle, Frontiers of Astronomy, p277) The reader will perhaps recognise that Hoyle’s definition of an infinite universe avoids Woods’ ‘actual’ infinity and approximates to Aristotle’s potential infinity: it can be “produced as far as [you] wish”. Hoyle’s alternative theory, the Steady State theory, was not successful.
The infinite and the divine
Aristotle makes an exception of time and of the ‘divine’ in On the Heavens. The divine is taken to be infinite by definition. Aristotle explains that all philosophers agree that anything that changes has an origin in time and is finite, because change is a result of the dialectic of the interpenetration of opposites, of coming into being and passing away. If the heavens (by heavens Aristotle means the cosmos) are capable of change then, according to the dialectic of both Anaximander and Aristotle, they must have had a beginning, and will have an ending, and are finite.
But we do not see the heavens change, says Aristotle (apart from their fixed rotation). He says that the stars are “fixed” in the heavens, and that therefore the heavens must be incorruptible, imperishable, unchanging except for their rotational motion through the heavens, since “a thing whose present state had no beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed.” Whereas, “clearly whatever is generated or destructible is not eternal.” (On the Heavens, book 1, part 10)
In other words, for Aristotle, dialectics teaches that if there is change in the heavens, the heavens must have an origin and an end. We now know, since Galileo, that there is change in the heavens – that is to say, in the universe. Galileo, incidentally, was convinced that with the evidence before him, Aristotle would have changed his views.
For Aristotle, the heavens’ eternity reflected the divine. The reason why Aristotle’s aether (the fifth element, the heavens) is eternal, “unaging and unalterable and unmodified”, should be clear to “all who believe in the existence of gods at all”. Aristotle maintains that the aether is the “seat of all that is divine”. (On the Heavens, book 1, parts 3 and 9) While the earth was corruptible, the heavens were not. (In the Renaissance and until the beginning of the twentieth century, the term aether, or luminiferous aether, was used to describe the medium through which scientists thought light propagated.)
Absolute and relative space and time
Woods might have been advised to hesitate before recruiting Aristotle to his cause. He also fails to mention that Aristotle thought the universe, although infinite in time, was a sphere of finite size. Aristotle discusses how concepts of time and space can be meaningful outside this rotating sphere of the heavens. This is fascinating because of its relevance to the concept of the universe that arose from Einstein’s relativity, and therefore from modern speculation about into what substratum the matter, time and space of the Big Bang universe might be expanding.
Firstly, we remember that Aristotle argued that within the heavenly spheres, material things fall down to the earth, because the earth happened to be “down”, at the centre of the universe. (Aristotle appears even to suggest that the earth is simply an aggregate of everything that has fallen “down”.) Fire, on the other hand, heads “up” to the heavens.
This meant that it could be said that for Aristotle time and space were absolute within the bounds of the universe. The earth was the absolute, stationary frame of reference for all motion. For instance, stones fell because the natural place of heavy bodies was the centre of the universe, and that was why the earth was there.
Later, Galileo attacked Aristotle’s views. He pointed out that there was not just one universal frame of reference for motion. For instance, if one was to imagine a game of table tennis below decks on an ocean liner, where the ship is travelling in steady, constant motion in calm seas, without rolling from side to side, one can readily predict that the players will not see any difference in the behaviour of the ball compared to a game on terra firma – all the laws of motion apply, relative to the frame of reference of the steadily moving boat, just as they do on the shore, relative to which the boat is moving.
This is obvious to us. Today, it is second nature to us that motion is relative, not absolute, even if we are not aware of the laws of physics. Yet to Aristotle’s way of thinking, if the boat was in motion (or, more significantly, if the earth was moving through space), the table tennis balls should behave differently, reflecting the forward motion of the ship (or earth), perhaps as though there was an invisible medium through which they and the boat passed, which affected their motion, sweeping the table tennis balls backwards off the table. This is a concept of absolute space and time.
As we shall show, however, although motion is relative, this does not mean that the motion of the table tennis balls is not an objective, measurable phenomenon – there is no lapse into subjective idealism, which is what Woods associates with the concept of relative space and time.
Before time, outside of space
But outside the ‘heavens’, the sphere of stars surrounding the Aristotelian universe, Aristotle concludes that there can be no space or time. Nothing exists outside the heavens, Aristotle says, therefore there can be no movement. But since “time is the number of movement” – time is the measure of change – there is no time outside the heavens:
But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither place, nor void, nor time, outside the heavens. (On the Heavens, book 1, part 9)
Woods asks the defenders of the Big Bang theory: “So what was there before time? A time when there was no time! The self-contradictory nature of this idea is glaringly obvious.” (p210) At least since Aristotle, the answer to the question has not been quite so “obvious”. Since Einstein, the question has to be rephrased: What was there ‘before’ the space-time of our universe?
Woods, however, wishes to distinguish between the measurement of time, which must be relative to some process of change, and the “nature of time itself” (p161), and says: “… in cosmology, the confusion of measurement with the nature of the thing itself leads to disaster in practice.” (p158)
Table 1. Schematic summary of Aristotle’s views
But what is this “time itself” or “thing itself” which is to be abstracted from the measurement of change? It is the old Newtonian concept of time. Newton says, in the Principia: “Time exists in and of itself and flows equably without reference to anything external.” It is truly as if there is somewhere a giant watch, held by a great timekeeper in the sky, keeping track of all celestial matter. We are jumping ahead a little, but for Newton, this timekeeper was god. Einstein did away with the timekeeper. Einstein’s universe, it is often said, is a “democratic universe” with no dictatorial authority laying down on each and every planet the strict time of the universe. Historically, in any case, the notion of a single time from which all clocks must be set arose in that same historical period which gave rise to Greenwich Mean Time, and should be placed in the context of the politics of Britain’s seafaring exploration and conquest of that period.
Woods does not elucidate exactly what “disaster in practice” has occurred as a result of science treating time, since Aristotle, as the measurement of change. Woods concedes, however, that according to this conception: “defining what time is presents a difficulty”, which he does not resolve. Time is indeed a complex phenomenon. But this “time itself” which Woods defends is Newtonian absolute time. On the facing page, Woods correctly asserts the opposing view. “It is impossible to regard [space and time] as ‘things in themselves’.” (p159)
Aristotle’s argument that space and time do not exist if there is no matter is, very roughly speaking, an acceptable hypothesis to science today. There is no meaning, in general, to time and space unless there is matter and energy. This is a materialist position, although it can be hard to grasp. But we will leave it to Galileo to demonstrate aspects of this important concept, which he did when he argued – against the followers of Aristotle – that the earth was in motion.