Eureka! Page 5

  Teleology: the Best of all Possible Worlds

  The fact that the demiourgos created everything in the best possible manner had further important consequences for the way in which Plato explained the world. Plato introduced a type of explanation known as ‘teleological’. This is, literally, an ‘end-directed’ explanation (from the Greek telos, meaning ‘end’). The end that the demiourgos had in mind was to produce the best cosmos possible. Everything in that cosmos was designed to fulfil that purpose. Therefore, according to Plato, we can explain aspects of the cosmos teleologically by saying: ‘It is so because it is best for it to be so.’ Plato believed the stars to have regular and circular motion, because that was the best motion for them to have. Modern physics has done away with teleology entirely. We do not think that there is anything intrinsically ‘good’ about the arrangement of the universe. It just is as it is, and we explain how it works mathematically. The ancients used teleology because they could not see how anything as good (useful, beautiful, well organised, etc.) as animals, humans and the cosmos could come about through blind chance and the like-to-like principle.

  Teleology pervaded a great deal of ancient thought, and in many ways dominated thinking about the cosmos right up to the scientific revolution. It was an aspect of Greek science always open to criticism, especially as some Greeks, notably the atomists, attempted explanations without the use of teleology. While we can plausibly explain the origins of order in the cosmos and the formation and development of living things without resorting to teleology, the ancients could not. The Greeks had good reason to be suspicious of the theories of the atomists on these matters, because with the resources available to the ancient Greeks, they seemed highly implausible.

  Atomism: Let us Trace the Pattern

  We can see a great number of the basic principles of Plato’s world view in action in his atomic theory. Plato did not believe that the standard Greek elements of earth, water, air and fire were the ultimate building blocks of nature. He believed that these elements had a specific structure which could come apart, and that there were two basic entities out of which the elements were made. These were two types of triangle (see Figure 4).

  These triangles did not undergo any change in themselves, and did not break down into anything more fundamental. These, for Plato, were the basic building blocks of nature. Why?

  Of the two triangles the isosceles has one nature, the scalene an unlimited number. Of this unlimited number we must select the best, if we intend to begin in the proper manner. If someone has singled out anything better for the construction of these bodies, his victory will be that of a friend rather than an enemy. We shall pass over the many and postulate the best triangles.

  Figure 4: Isosceles and scalene triangles. For Plato, these were the basic entities of the four natural elements.

  These two shapes were able to come together to form either squares or a complex triangle (Figure 5).

  From these, either a cube, a tetrahedron, an octahedron or an eikosahedron (20-faced object) could be constructed (Figure 6).

  Plato associated these four shapes with the standard four elements of the Greeks. The cubes were earth, the tetrahedra fire, the octahedra water and the eikosahedra air. The properties of the elements could be explained by the shape of their particles. Fire could change and cut up other objects, since its particles were small and had sharp corners, whereas earth, as a cube, was solid and could be well packed.

  These solids – the cube, tetrahedron, octahedron and eikosahedron – are the perfect, or Platonic, solids. They are made up of faces which are all the same shape and size. A demiourgos forming the best possible sort of world would create these basic building blocks to ensure that the elements were properly proportioned as perfect solids. When he imposed shape and number on the chaos, this is how he did it. He also created a certain order for the earth and for the heavens.

  Figure 5: A complex triangle and a square, made up of scalene and isosceles triangles respectively.

  Figure 6: A tetrahedron and a cube – for Plato, these were the basic particles of fire and earth respectively.

  Whatever the merits of Plato’s view on atomism, the basic principle that he introduced to science has been important ever since: although the world appears to be diverse and complex, there is an underlying order which we can capture with mathematics and geometry, and that order is simple, elegant and aesthetically pleasing. Scientists today, especially in the more theoretical and mathematical disciplines, still strive for these qualities in their work. Another interesting aspect of Plato’s atomism was this. The Pythagoreans, who believed that the world was in some way made up of numbers, were perplexed to find irrational numbers, numbers which cannot be expressed as the ratio of two integers. Plato, by contrast, thought that the ultimate constituents of the

  No Slight or Trivial Influence

  Plato was also keen on the use of geometry and astronomy in education. His training for philosophers led from astronomy to geometry to a contemplation of the nature of the good. He was enormously influential in encouraging the study of these subjects, and was always keen to take them to the next level of abstraction, to establish more general and refined theories. Legend has it that the words ‘let no one ignorant of geometry enter here’ were inscribed over the door of Plato’s Academy.

  One can take Plato’s philosophy in many directions, and there have been numerous interpreters of his views. There are elements of his thought that can be interpreted in a mystical and religious manner. Early neo-Platonists laid stress on the soul and God, and how we can best come to know God. Their thinking was enormously important for early Christianity, and played down the importance of the investigation of the physical world. Plato himself certainly emphasised the abstract and the theoretical, and so has been seen by some as downplaying the empirical role in science. His positive legacy, though, is the idea of a mathematically structured cosmos, and the notion that mathematics can play a key role in science. These features of his thought were stressed by Renaissance neo-Platonism, and contributed to the emergence of the scientific revolution. They were also an important alternative to Aristotelian ideas on these matters.

  Aristotle: The Master of Those who Know

  Aristotle was born in Stagira, the son of a doctor to the court of King Amyntas of Macedonia. He was a pupil of Plato at the Academy, where he arrived at the age of seventeen; he studied and worked there for twenty years, to 347 BC. Then came a period of travelling, during which he undertook extensive research in biology, before returning to Athens in 335 BC. He also acted as tutor to Alexander, son of Philip of Macedon, the future Alexander the Great. Aristotle’s Macedonian connections may explain why he left Athens – anti-Macedonian sentiment was very strong there at times. Aristotle finally left Athens in 323 BC, and died in 322. Despite being the best student of the Academy, Aristotle was never offered the headship. He founded his own school, the Lyceum, and had a dedicated band of followers throughout the age of antiquity. The sites of the Academy and Lyceum can still be found in Athens.

  We have many, but not all, of Aristotle’s works. The style of these is in sharp contrast to that of Plato, but we may well have only Aristotle’s lecture notes. Many people in antiquity praised the literary virtues of his finished works, which are now lost. Aristotle wrote on a huge range of subjects, those of particular interest to us being physics, cosmology, meteorology, biology and metaphysics.

  At first a follower of Plato, Aristotle later developed his own distinctive philosophy. While he disagreed with Plato on many matters, there were also considerable similarities. Like Plato, he believed that the cosmos, and living things, had not come about accidentally, but required some sort of teleological explanation. Aristotle’s views had an unparalleled influence. He established a system for thinking about the world that was dominant for 2,000 years, lasting until the seventeenth century. Above all, Aristotle was a great systematiser. He had great breadth of thought, and also an internal coherence and consistency
that made his thinking both plausible and difficult to replace. It could be supplanted only by something at least as comprehensive. Aristotle was the founder of several disciplines, most notably biology and logic. To his later supporters, he was known simply as ‘the philosopher’ or ‘the master of those who know’.

  The Terrestrial Realm

  Aristotle had to answer the question of why things fall to the ground, and why the heavens move as they do, without having a theory of gravity. His answer was that everything had a natural place, and a natural motion in relation to that natural place. Aristotle accepted the usual four Greek elements of earth, water, air and fire. The natural place of earth was at the centre of the cosmos, and the natural motion of pieces of earth was in a straight line towards that centre. So any piece of earth not at the centre would naturally move towards it, unless prevented from doing so. Water also had its natural place at the centre, and its natural motion was to move towards it, but it was not as heavy as earth, so it tended to settle on top of it. Objects did not fall because of gravitational attraction, according to Aristotle, but because of their natural place and their natural motion. This piece of ancient physics demanded that the earth be at the centre of the cosmos. If all of the pieces of earth have their natural place at the centre, and a natural motion towards it, then the earth must be at the centre. If it were ever displaced from there, it would have a natural motion to move back there. So Aristotle’s physics was inherently geocentric. The earth had to be at the centre of the cosmos.

  Air and fire were thought by Aristotle to be light – not less heavy than earth and water, as we would say, but positively light. Their natural motion was away from the centre of the cosmos, and their natural place was at the edge of the terrestrial realm. This reached up to the moon, where the celestial realm of the heavens began. Fire was lighter than air, so it formed the outermost part of the terrestrial realm, with air beneath it. If the elements were to perform only their natural motions, then they would separate out into four concentric rings, with no mixing of the elements.

  Figure 7: Aristotle’s terrestrial realm, as it would be if there were no mixing of the elements.

  Aristotle distinguished between ‘natural’ and ‘enforced’ motion. If earth was thrown upwards, or sideways, that was contrary to its natural motion. Gradually, natural motion would take over again and it would begin to move towards the centre of the cosmos. Enforced motion required the application of force, while natural motion did not. One point on which Aristotle differed radically from modern views was that he believed that no force was necessary to begin natural motion (or end it when a body reached its natural place). We know that any change in motion requires a force. The elements did not completely settle out into separate bands, according to Aristotle, because of the effects of the sun. The sun had daily and seasonal variations, and its heat stirred up and mixed the elements. The sun, as the cause of daily heating and the seasons, was ultimately responsible for all of the mixing of elements in the terrestrial realm.

  The Heavens

  So far we have spoken of the terrestrial realm. For Aristotle, the moon, and everything beyond the moon, was the celestial realm. This contained none of the four elements of the terrestrial realm, but was composed of a fifth element known as ‘aether’. The Greeks saw the heavens as unchanging. For this belief they had the evidence of their own observations, and those of the Babylonians and Egyptians, of which both Plato and Aristotle were aware. No change in the relative position of the stars had been seen. Aristotle saw the terrestrial realm as a place of change, and change typically took place between pairs of qualities, such as hot and cold or wet and dry. He also believed that no enforced motion – and no natural motion in a straight line – could be permanent. So the unchanging heavens must be made of some other substance, not subject to change, without qualities, and having a natural circular motion. This was aether. Aether was neither light nor heavy (not having the same sort of characteristics as the terrestrial elements), so there was no question of the heavenly bodies plunging to earth. Aristotle also believed there to be a ‘prime mover’, something which initiated motion in the heavens but was not itself moved (an ‘unmoved mover’). Effectively this was god, and god spent all of his time thinking about thinking – the supremely pleasant activity, according to Aristotle. A philosopher’s god, if ever there was one! Since Aristotle believed the heavens to be unchanging, he accounted for novae (new stars), comets, etc., by saying that all such phenomena took place in the upper reaches of the terrestrial realm, rather than in the heavens (and these phenomena were likely to be fiery, because that was where fire had its natural place).

  Speculations Upon Matter

  Aristotle disagreed with Plato and the atomists about the elements. Aristotle was not an atomist. He did not believe that matter came in small, discrete packets, nor did he consider this a useful way to think about the question. He did believe in the usual four elements of the Greeks, but thought of them in qualitative terms. The four essential qualities for Aristotle were hot and cold, and wet and dry. Each of the elements possessed a pair of the contrary qualities. This can be represented schematically (see Figure 8).

  Figure 8: Aristotle’s elements. Each element is characterised by a pair of the wet/dry and hot/cold opposites.

  These elements could quite readily transmute into one another. By heating water (cold and wet) one could produce air (hot and wet). As well as not believing in atoms, Aristotle denied that there was any such thing as empty space. For him, the world was full (the technical term is a ‘plenum’), and a true vacuum did not exist.

  Aristotle and Qualities

  Aristotle’s view of matter was essentially a qualitative one. The world was made up of real qualities. The basic qualities of hot, cold, wet and dry could not be broken down or analysed any further. Where we would say that heat is the agitation of small particles, Aristotle would claim it to be a quality of a body. We reduce heat to matter and motion (heat is nothing but matter in motion), but Aristotle thought that there was such a ‘thing’ as heat. If we were to ask Aristotle what the ultimate constituents of the world are, he would reply: the qualities of hot, cold, wet and dry – and not atoms. Thus, Aristotle’s view of the world is said to be a ‘qualitative’ rather than a ‘quantitative’ one.

  Another important contrast between Aristotle and our modern view of the world, and indeed Plato’s view, is the role of mathematics and geometry. Aristotle did not believe that these could provide a good description of objects in the terrestrial realm. He believed that the abstractions of mathematics did not apply to real-life situations. Consider a perfect sphere on a perfectly flat plane, as one might in geometry. There is only one point on this plane where the sphere touches it. But, says Aristotle, in nature we have neither perfect spheres nor perfectly flat planes, and any actual sphere on a flat surface will in fact touch it at many points. In these situations, mathematics describes the ideal and not the actual, and the actual may be very different from the ideal. Aristotle also believed that there were qualities which could not be quantified in any mathematical manner. One might contrast hot, hotter and hottest – that is, make qualitative comparisons – but Aristotle did not think that one could attach numbers to these qualities. One issue here is antiquity’s lack of technology for making such quantifications (i.e., thermometers for measuring heat), but at root Aristotle had a different view of what makes up the world. Atoms might be treatable mathematically, but qualities were not – and qualities, for Aristotle, were the basic constituents of the world.

  Here is a summary of Aristotle’s theory of the elements, including weight, natural place, natural motion and qualities. This theory of the elements and of natural place was retained up to the beginning of the seventeenth century, and the idea of fire as a substance lasted well into the nineteenth century.

  Figure 9: Aristotle’s cosmos (not to scale).

  Explanations

  Aristotle also had a distinctive scheme for explaining the natural world
, which was hugely influential. He required four types of explanation for the full description of a phenomenon. These are sometimes known (rather inaccurately) as the ‘four causes’. Actually, only one of these explanations is like a ‘cause’ in the modern sense, and they are better referred to as the ‘four becauses’. Efficient explanation was close to, but not identical with, our notion of a physical cause. Material explanation told you what something was made of. Formal explanation told you what shape or form something had. Teleological explanation told you the purpose that an object or process had. If we think of a table, we can say that it is made of wood (material explanation), it has the form of a table (formal explanation), it was made by a craftsman (efficient explanation) and it is for writing on or eating off (teleological explanation).