The ‘prehistory’ of philosophy of science (5): What a beautiful world!

We shall conclude with this entry our discussion of Plato’s view of science, the main conclusions of the two former ones being, in the first place, the idea that ‘scientific knowledge’ (epistēmē) consists in the knowledge of eternal, intelligible Forms, whereas material things are imperfect copies of the former, and only graspable with an imperfect species of knowledge (‘opinion’, or dóxa), and, in the second place, that the ultimate foundation of scientific knowledge is the understanding of perfection itself, and, most specifically (applied to the knowledge of the material world), the understanding of how things, and the world, are teleologically organized. Of the immense literary production of Plato, there is only one of his ‘dialogues’, apparently one of his last works (the Timaeus), where he offers a more or less detailed exposition of his views about ‘natural science’, and it is there where we must turn now our attention.

Photo: Casey Horner / Unsplash

Of course, it is impossible to give in this short entry an insightful summary of all the richness (and intricacy, often bordering incomprehensibility) the Timaeus contains, including the famous legend of Atlantis and all the details about the creation of the body and soul of the World, the creation of gods and men, etc. I shall only concentrate in the aspects of Timaeus’ exposition that have the closest connection with the topic of our series, i.e., those that make clearer Plato’s philosophy of science. As it is well known, Plato introduces in this work a kind of mythological figure (the ‘Demiurge’, meaning ‘artisan’) as the responsible for the creation of the cosmos. The mythical character of Plato’s narrative does not allow to determine with certainty to what extent his description of the cosmogenetic process has to be understood more or less literally, or more or less figuratively, as only a kind of ‘allegory’ in the spirit of the ‘simile of the line’ we saw in the past couple of entries, or the classic ‘myth of the Cave’ also in The Republic. Be it as it may, the very fact that Plato feels compelled to frame his explanation into a mythological story gives us a clear hint of what he thought ‘natural science’ or ‘physics’ must (or can) consist in: nothing close to the ideal of exactitude and demonstrative rigour that mathematics had in his own times, or physics itself attained one century later with Archimedes (not to speak of Galilei or Newton), but only something that corresponds, at most, with a merely ‘literary’ standard of argumentation. After all, for Plato knowledge of the material world is intrinsically ‘imperfect’ knowledge, as we have repeatedly seen, and he seems not to have imagined the possibility of a ‘natural science’ more rigorous and accurate than that.

It is true that the Platonic Academy started the idea of astronomy as an attempt to ‘save the phenomena’, i.e., to explain the apparently irregular movements of the planets with the help of precise mathematical models, something that (as we shall see) led centuries later to the development of very precise theories and to the appreciation of exactitude, like in the case of Ptolemy, but Plato himself seems to have been satisfied with (and, more importantly, he seems to have considered that it was impossible to aspire to anything better than) a merely ‘qualitative’ and loose agreement between the mathematical constructions of cosmological theories and the astronomical observations (or ‘phenomena’). Hence, we have not to see in Plato’s view of natural science the notion that ‘accurate predictions’ (and still less ‘unexpected predictions’) is one of the goals of physics, nor even a reasonable goal.

However, Plato’s efforts to ‘rationally explain’ the natural world led to some astounding ideas that (two millennia in the future) greatly influenced the development of modern physics, and that can only be interpreted as a work of absolute genius. We can start by recalling the final reflection of our last entry: how is it that (as in the Phaedrus), Plato frequently grumps about the lack of ‘rationality’ (in the sense of intentional design, or teleology) in other philosophers’ accounts of nature, but instead finds totally alright the absence of such ‘intentionality’ in mathematics? (I mean, couldn’t the natural world be as ‘rational’ as the ‘mathematical world’, without nothing in it resembling an ‘intentional order’?). The answer to this puzzle Plato allows us to glimpse is that ‘the Good’, the supreme Form, is exactly the same as ‘the Beauty’: the Demiurge’s ‘goal’ in giving shape to the world is nothing other than the desire of creating the most possibly beautiful cosmos. All other ‘goals’ or ‘plans’ we can find out within the universe, from the teleological organization of living beings, to the organization of political activities, just to quote a couple of prominent examples, are what they are, according to Plato, as the result of the most basic ‘goal’: that the universe must be as beauty as it can be. Taking this into account, it is not very important whether the ‘creation myth’ narrated by Plato in the Timaeus is understood literally or not, for what is relevant is the idea that beauty is the supreme force in the organization of the cosmos, and perhaps all the story of one god creating the earth, the sky, the people, etc., as a potter creates a vessel or a krater, may have been composed to be taken as just a metaphor. Hence, in philosophy of science, Plato is not only the founder of the teleological paradigm of scientific explanation (one that isn’t living its best moments, to say it all), but also the father of the idea that beauty is the most important virtue a scientific theory must have … because the ultimate truth about the universe must be perfectly beautiful (another idea that, though not as popular now as it has been, hasn’t ceased to exert a powerful influence in fundamental physics).

Timaeus offers many examples of how the search of the maximal beauty constrains the Demiurge’s efforts to shape a lovely world (from the parts of the human organism, to the sizes and organization of planetary orbits –which, obviously, include those of the moon and the sun in Plato’s geocentric system–), but probably the most exciting one is the argument that leads to Plato’s theory of matter: the Demiurge would have attempted to create solid bodies in the most simple and elegant way, which reduces to the construction of the two most simple right triangles from which the regular solids can emerge; these triangles are an isosceles whose acute angles are 45º (so that two of them joined by their hypotenuses form a square) and one whose smaller cathetus length is half of its hypotenuse (so that two of these triangles, joined by their bigger catheti, form an equilateral triangle). Leaving aside the question of why Plato didn’t see the equilateral triangle as ‘elementary enough’, so that it felt the need to ‘derivate’ it from a ‘simpler’ geometrical form (its half), it’s clear how these figures allow the construction of the four regular solids Plato considers in his cosmology: the tetrahedron (four equilateral triangles), the octahedron (eight), the icosahedron (twenty), and the cube (six squares). He had the inspiration of equating each one of these solids to one of the classical ‘elements’ first introduced by Empedocles, and persistent in almost all the scientific views of the world till modern times: in this order, fire, air, water and earth.

Most surprisingly, Plato doesn’t feel totally happy with a theory according to which matter is organized according to a precise mathematical rule (a thesis that, no need to remember, is absolutely essential to modern particle physics), but insists in the fact that material things are intrinsically and necessarily imperfect (i.e., imperfect copies of true mathematical objects), and provides an astonishingly profound conjecture about what the ultimate cause of this imperfection could be. According to him, the lines and surfaces defining the ‘elementary triangles’ cannot be perfect, eternally stable (we would say), because they are ‘made of’ an ‘imperfect’ substrate he often calls ‘the receptacle’ (hypodokhê), or, most simply, ‘space’ (khôra, which perhaps translates better as ‘empty space’), and to which he very often refers with some feminine attributes as ‘mother’ or ‘nurse’, as well as with the name ‘anánke’ (‘necessity’, probably in a sense closer to ‘need’ or ‘lack’, nothing to do with ‘determinism’). This ‘receptacle’ is far from being comparable to the Euclidean absolute, and absolutely inert space of Newtonian mechanics, but is, instead,

not only shaken by the things it contains [i.e., the atoms of the four elements], so that it lurches haphazardly all over the place, but its motion in turn further shakes them. This stirring causes them to be constantly moving in different directions and to become separated. It’s like when things are shaken and sifted by sieves or other devices for cleaning grain. (Timaeus, 53e).

Hence, space is for Plato a kind of eternally moving but chaotic force that permanently ‘shakes’ in fortuitous ways the objects ‘made of’ it, i. e., the lines, surfaces and solids constituting the material atoms. Is not that wonderfully similar to contemporary ideas about ‘quantum space’ or ‘space-time foam’? I only leave this comparison for your consideration.

The last and, from my point of view, more important aspect of Plato’s contribution to the development of the ‘idea of science’, is the fact that with his geometric account of the ‘four elements’, he provides the first great example of what much later will become one of the identity signs of modern natural science: the idea of progress by theoretical unification (or ‘consilience’). After all, what Plato is achieving is nothing less than assembling a wonderfully unified framework of three of the most important insights of the natural philosophers that came before him: Empedocles’ theory of the elements, Leucipus and Democritus’s theory of the atoms, and the Pythagorean conjecture that nature is made of numbers or mathematical entities. These three theories were before Plato totally unconnected to each other: for example, Democritus believed that atoms came in infinite different forms, their shapes having nothing ‘mathematically special’ at all. Instead, Plato provides a very simple explanation (implausible as it unavoidably sounds now to us) of why there are exactly those four elements, i.e., those four types of ‘atoms’ (though probably Plato would rather apply the term ‘atom’ to the edges of his polyhedra). We should wait till the time of an Isaac Newton to witness a comparable move in the history of science.

By the way, if you are wondering what Plato thought about the fifth regular polyhedron (the dodecahedron of twelve regular pentagons), the only, and mysterious thing he says about it is that

one other construction, a fifth, still remained, and this one the god used for the whole universe, decorating it with figures. (Timaeus 55c).

References

Brisson, Luc, and F. Walter Meyerstein, 1995, Inventing the universe: Plato’s Timaeus, the Big Bang, and the problem of scientific knowledge, New York, SUNY Press.

Gregory, Andrew, 2001, Plato’s philosophy of science, London, Bloomsbury.

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