greek philosophy

Aristotle defines elements to be composed of properties that can be felt by touching. He uses two pairs of opposites, hot-cold and wet-dry, to define four elements, which he names fire, earth, water and air. And he identifies wet-dry with soft-hard, viscous-brittle and smooth-rough. Unlike later commonly the case, he does not consistently identify hot-cold with active-passive and light-heavy. If you do, you get a one-to-one correspondence to my previous definition of the elements in terms of in/out and rest/move:

Aristotle defines a fifth element as immutable, moving only in circles and existing only in space, while the other four elements move linearly. And he also arranges the four elements essentially in a circle in which they transform into each other by flipping one of hot↔cold or wet↔dry at each transition, while not completely excluding transitions that flip both at the same time, but considering them more difficult and slower. The shared theme of a circle links the transformation of elements to the fifth element.

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In other words, the same circle as tentatively derived earlier on from my definition of the elements, and a similar meaning related to e5, as also derived earlier.

Passive is inertial in a sense: Outside ero resists more to get into motion than emo resists to get to rest; inside emi resists more to get to rest than eri resists to get into motion. In rough equivalence to inertial and gravitational mass in physics, inert (passive) would be heavy and dense, swift (active) would be light and thin.

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• Aristotle. On Generation and Corruption. Around 350 BCE.
• “Since, then, we are looking for ‘originative sources’ of perceptible body; and since ‘perceptible’ is equivalent to ‘tangible’, and ‘tangible’ is that of which the perception is touch; it is clear that not all the contrarieties constitute ‘forms’ and ‘originative sources’ of body, but only those which correspond to touch.” (Book II, translated by H. Joachim)
• “From moist and dry are derived (iii) the fine and coarse, viscous and brittle, hard and soft, and the remaining tangible differences. For (a) since the moist has no determinate shape, but is readily adaptable and follows the outline of that which is in contact with it, it is characteristic of it to be ‘such as to fill up’. Now ‘the fine’ is ‘such as to fill up’. For ‘the fine’ consists of subtle particles; but that which consists of small particles is ‘such as to fill up’, inasmuch as it is in contact whole with whole–and ‘the fine’ exhibits this character in a superlative degree. Hence it is evident that the fine derives from the moist, while the coarse derives from the dry. Again (b) ‘the viscous’ derives from the moist: for ‘the viscous’ (e.g. oil) is a ‘moist’ modified in a certain way. ‘The brittle’, on the other hand, derives from the dry: for ‘brittle’ is that which is completely dry–so completely, that its solidification has actually been due to failure of moisture. Further (c) ‘the soft’ derives from the moist. For ‘soft’ is that which yields to pressure by retiring into itself, though it does not yield by total displacement as the moist does–which explains why the moist is not ‘soft’, although ‘the soft’ derives from the moist. ‘The hard’, on the other hand, derives from the dry: for ‘hard’ is that which is solidified, and the solidified is dry.”
• “The elementary qualities are four […]. Hence it is evident that the ‘couplings’ of the elementary qualities will be four: hot with dry and moist with hot, and again cold with dry and cold with moist. […] Fire is hot and dry, whereas Air is hot and moist (Air being a sort of aqueous vapour); and Water is cold and moist, while Earth is cold and dry.”
• Aristotle arranges the elements in a cycle fire-air-water-earth:
  “Thus (i) the process of conversion will be quick between those which have interchangeable ‘complementary factors’, but slow between those which have none. The reason is that it is easier for a single thing to change than for many. Air, e.g. will result from Fire if a single quality changes: for Fire, as we saw, is hot and dry while Air is hot and moist, so that there will be Air if the dry be overcome by the moist. Again, Water will result from Air if the hot be overcome by the cold: for Air, as we saw, is hot and moist while Water is cold and moist, so that, if the hot changes, there will be Water. So too, in the same manner, Earth will result from Water and Fire from Earth, since the two ‘elements’ in both these couples have interchangeable ‘complementary factors’. For Water is moist and cold while Earth is cold and dry–so that, if the moist be overcome, there will be Earth: and again, since Fire is dry and hot while Earth is cold and dry, Fire will result from Earth if the cold pass-away. […] (ii) the transformation of Fire into Water and of Air into Earth, and again of Water and Earth into Fire and Air respectively, though possible, is more difficult because it involves the change of more qualities.”
• In On Generation and Corruption, Aristotle considers light-heavy not to be an attribute of any specific elements:
  “(i) heavy and light are neither active nor susceptible. Things are not called ‘heavy’ and ‘light’ because they act upon, or suffer action from, other things. But the ‘elements’ must be reciprocally active and susceptible, since they ‘combine’ and are transformed into one another. On the other hand (ii) hot and cold, and dry and moist, are terms, of which the first pair implies power to act and the second pair susceptibility.”
  But in On the Heavens, he considers air and fire as light and water and earth as heavy, in the order earth-water-air-fire, and postulates the existence of an immutable fifth element that dominates in the sky, is neither light nor heavy and moves in circles, while the first four elements move linearly:
  “[…] all locomotion, as we term it, is either straight or circular or a combination of these two, which are the only simple movements. […] Now revolution about the centre is circular motion, while the upward and downward movements are in a straight line, ‘upward’ meaning motion away from the centre, and ‘downward’ motion towards it. […] For if the natural motion is upward, it will be fire or air, and if downward, water or earth. […] circular motion is necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is a perfect thing. […] These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. […] there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours. […] things are heavy and light relatively to one another; air, for instance, is light relatively to water, and water light relatively to earth. The body, then, which moves in a circle cannot possibly possess either heaviness or lightness. For neither naturally nor unnaturally can it move either towards or away from the centre. […] this body will be ungenerated and indestructible and exempt from increase and alteration […] earth is enclosed by water, water by air, air by fire, and these similarly by the upper bodies.” (Book I, translated by J. Stocks)
• Aristotle appears to consistently consider the pair of opposites hot/cold active and the pair wet/dry passive, see the quote from On Generation and Corruption above, or the following quote from Meteorology:
  “All this makes it clear that bodies are formed by heat and cold and that these agents operate by thickening and solidifying. It is because these qualities fashion bodies that we find heat in all of them, and in some cold in so far as heat is absent. These qualities, then, are present as active, and the moist and the dry as passive, and consequently all four are found in mixed bodies.” (Book IV, translated by E. Webster)
• In the outside world, the elements water and air (essentially liquids and gases or gas-like phenomena like clouds or smoke) appear softer and more fluidly in motion than the element earth (solid matter). The element fire (flames, lightning), however, does not appear to be visibly hard, while, like earth, quite closely related to dryness.
• While many works of Aristotle and Plato have been preserved in their entirety, works of earlier philosophers, as well of many later ones, like the Stoics, have usually only survived as fragmentary quotes by later philosophers, typically around early CE or even later. Since this was also the time in which the “canonical view” on the elements emerged for centuries to follow in astrology, alchemy, medicine, etc., it is difficult to reconstruct other views with certainty. Moreover, it seems that some schools of philosophy might have had oaths which would bind their members not to speak about certain fundamental views, or only in carefully veiled form.
  In a nutshell, the earliest source I know of that attributes fire and air to active, and water and earth to passive is Cicero in Academica (45 BCE), possibly influenced by the Stoics. The first attribution of the same elements to male-female in astrology is Vettius Valens in Anthologia (2nd century CE). Aristotle names Empedocles at least twice as the first to have considered four elements. Plato introduces a fifth element in the Timaeus, most likely predating Aristotle.
  A fragmentary closer look below and in following sections.
• David Sedley writes in chapter 11 of The Cambridge History of Hellenistic Philosophy (2000) that the Stoic’s identification of fire and air with active emerged from medical tradition, from pneuma, breath, which was seen as a mixture of fire and air, and mentions also that this identification was originally not exclusively the only view of the Stoics in their time.
• In Academica (45 BCE), Cicero lets Antiochus of Ascalon say the following, influenced by Aristotle and maybe the Stoics:
  “Accordingly air […] and fire and water and earth are primary; while their derivatives are the species of living creatures and of the things that grow out of the earth. Therefore those things are termed […] elements; and among them air and fire have motive and efficient force, and the remaining divisions […] water and earth, receptive and ‘passive’ capacity. Aristotle deemed that there existed a certain fifth sort of element, in a class by itself and unlike the four that I have mentioned above, which was the source of the stars and of thinking minds.” (Book I 26, translated by H. Rackham)
• A bit later astrological views emerged that see fire and air as male, and water and earth as female. See Vettius Valens’s Anthologia in the 2nd century CE and hints in earlier texts by Dorotheus of Sidon and Marcus Manilius. These views have essentially prevailed, including in medieval alchemy and up to contemporary astrology.
• In contemporary astrology, the element fire is associated with (visual) imagination and impulse, air with (abstract) thinking and communication, water with feelings and faith, earth with pragmatic realism—to give just a rough summary.
• Most things in the sky beyond clouds are round or cyclic: sun and moon are round; planets, as well as stars during night and seasons, move periodically in predictable cycles.
• The fifth element is also called ether or aether and quintessence. Many different views of the fifth element and closely related concepts have emerged over time.
  Plato used the word aether to describe the purest form of air in the Timaeus. But there is also a strong association of the sky with fire, because stars and planets appear to emit light and the sun provides heat, and also because fire was often considered the lightest of the four elements.
  The fifth element is generally considered “divine” because gods were often believed to live in heaven. And it is often also seen as special in other ways, like able to create life, or immortal like the soul or maybe pneuma, or able to create matter and to hold it together, or maybe identified by some alchemists with the philosopher’s stone, which was believed to be able to transform matter, like lead to gold, etc. ?
• Do such associations (historically founded or not) fit well with the definition of e5 simply because they all keep going in circles around the same questions ?
• Apuleius in The Doctrines of Plato in the 2nd century CE:
  “In the first place, the twin pupils of the eyes are very clear, and, shining with a certain light of vision, they possess the office of knowing light; while hearing, by partaking of the nature of air, has a perception of sounds, through messengers in the air; whereas the taste, being a sense more relaxed, is on that account suited to things rather moist and watery; but the touch, as being of the earth and corporeal, perceives things, that are rather solid, and which can be handled and struck against. Of those things likewise, which are changed, when corrupted there is a separate perception. For in the middle of the region of the face Nature has placed the nostrils, by the double door-way of which there passes an odour together with the breath; and that conversions and changes furnish the causes of smelling; and that they are perceived from substances, when corrupted or burnt, or in a mucous or moistened state; […].” (Book I, 14, translated by G. Burges)
  Even though most of what he writes is from Platos’ Timaeus, it seems that a view of see-fire, hear-air, taste-water, touch-earth is something that Apuleius implicitly added. Even more so with the implicit association of transformations of the elements with smell and the 5th element, which would maybe already mirror the definition of e5 in my model…
• According to Diogenes Laërtius in the third century CE, the Stoics would have identified fire with hot, earth with dry, water with wet, and air with cold (and dry):
  “[…] the four elements are all equally an essence without any distinctive quality, namely, matter; but fire is the hot, water the moist, air the cold, and earth the dry—though this last quality is also common to the air. The fire is the highest, and that is called aether, in which first of all the sphere was generated in which the fixed stars are set, then that in which the planets revolve; after that the air, then the water; and the sediment as it were of all is the earth, which is placed in the centre of the rest.” (7. LXIX, translated by C. Yonge)
  The papyrus Anonymus Londinensis from about the first century CE says essentially the same about Philistion (apparently Philistion of Locri, a contemporary of Plato):
  “Philiston thinks that we are composed of four ‘forms’, that is, of four elements—fire, air, water, earth. Each of these too has its own power; of fire the power is the hot, of air it is the cold, of water the moist, and of earth the dry.” (XX 24, translated by W. Jones)
  According to David Hahm in The Origins of Stoic Cosmology (1977), this view might have already been quite common among physicians in classical times. Artistotle’s texts about biology seem to implicitly reflect that view, like that air is inhaled cold and exhaled hot (pneuma). Although there appear to be no contemporary sources that would directly prove such an identification, Hahm’s detailed argumentation that the Stoics aimed for a unified view of the elements (unlike apparently Aristotle) across all fields seems plausible.
  In Stoic belief, the cosmos emerged from fire via air to water to earth, and back (see Hahm for details), essentially along Aristotle’s circle of the elements or light to heavy and back.
• In ancient Greek philosophy there was also the idea of matter consisting of indivisible physical units (atoms). In Plato’s Timaeus, a model is presented that combines both views by associating the elements with the five Platonic solids: fire-tetrahedron, air-octahedron, water-icosahedron, earth-cube and the “roundest” one, the dodecahedron, for the whole world/universe (pan). Kepler’s drawings (1619):

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  Today they are usually paired cube-octahedron, dodecahedron-icosahedron and tetrahedron-itself, because the centers of the surfaces yield the corners of the dual body.
  In 4 dimensions there are 6 generalized Platonic solids, in 5 and more dimensions always only 3, namely generalizations of tetrahedron, cube and octahedron.