1. Anaximenes postulates air as the archê. This may seem to be a throwback to Thales, a step backward after Anaximander; but I will argue that is is not.

  2. Anaximenes is offering a new world view:

    1. Anaximander thought of the basic stuffs and qualities of the world as opposites in conflict.
    2. Anaximenes had a different conception: the basic stuffs and qualities are not opposed, but different stages of a continuum.

  3. Rarefaction and Condensation:

    Read the fragments in Plutarch (21 = B1), Simplicius (16 = A5), and Hippolytus (18 = A7). This is the basic picture:

    Fire [arrow]AIR Wind Cloud Water Earth [arrow]Stone

    The green arrow represents condensation; the blue arrow represents rarefaction. Each kind of stuff in the continuum can rarefy or condense into either of its neighbors (e.g., water can rarefy into cloud, or condense into earth).  As the diagram above shows, then, each kind can either condense or (eventually) rarefy into air.  

  4. Why is air the basic stuff in Anaximenes’ view of the world?  He might have picked any of the items in the continuum.

    1. He rejected the apeiron (perhaps because it was unperceivable, and he could therefore not be certain of its existence).
    2. Among the familiar elements, air is the most like the apeiron as Anaximander conceived it. Air is the most neutral of the elements.
    3. He probably believed that air was the original element, out of which the others developed by the process of rarefaction and condensation.

  5. In what sense is air the archê? There are two possibilities:

    a. Cosmogony (explanation of the origin of the universe).  The key concept: Y was made from X. In this case, Anaximenes’ theory is that everything that exists developed out of the original air.

    b. Constituent analysis. (Cf. Barnes, Presocratics 41.)  The key concept: Y is made of X. In this case, Anaximenes’ theory is that everything that exists is now actually made of air.

    (Barnes thinks that Anaximander would not distinguish these — that he is actually doing both.)

  6. Pitfalls in the interpretation of the principle of Rarefaction and Condensation:

    a. It sounds quantititive — even atomistic — but that can hardly have been what Anaximenes had in mind. For:
    b. The conception of an atom had not yet been invented, and
    c. A particulate (or perhaps even any quantitive) interpretation of Anaximenes’ idea leads to an incoherence in the theory.

  7. The incoherence of Anaximenes’ theory on the particulate interpretation:

    1. If matter is particulate, then a difference in density is a difference in the number of particles per unit of volume.
      Cf. McKirihan, p. 51: “Rarity and density are quantitative notions: more or less of the same stuff in the same place.”
    2. E.g., earth is denser than water in that earth contains more particles per liter than water does.
    3. Particles of what? Presumably, of the basic stuff, i.e., air.
    4. But air itself is one of the natural stuffs in the continuum, along with earth and water. (Air is denser than fire, less dense than water.)
    5. So on the particulate version of Anaximenes’ theory, it should make sense to ask: how many particles (of air) are there per liter of air?
    6. But the question is incoherent. Air cannot be both a natural substance whose nature is determined by its density (measured in terms of number of particles per liter) and the basic particles themselves.
    7. The underlying confusion: air would be both explanans and explanandum. I.e., the basic stuff in terms of which differences are explained, and something whose difference from other natural stuffs also needs to be explained.

  8. Did Anaximenes attempt to explain qualitative differences in quantitative terms? He is often credited with having done so. See, for example, Burnet EGP §26 (endorsed by Guthrie 126-27):

    “… a theory which explains everything as a form of a single substance is clearly bound to regard all differences as quantitative. The only way to save the unity of the primary substance is to say that all diversities are due to the presence of more or less of it in a given space.”

    If this were what he is doing, it would be a very important step (cf. later scientific developments: wave length of light, atomic number, etc.)   This is a tempting interpretation, but unlikely.

    1. Cf. Barnes, Presocratics p. 46:

      “Was Anaximenes really a precocious quantifier, a Presocratic Boyle? Alas, I suspect he was not. Greek scientists were in general averse to, or incapable of, the application of mathematics to physical processes ands phenomena; and there is no evidence that Anaximenes himself had any such application in mind: he had no scale and no instrument for measuring density, and for him density was a quantitative notion only in the weakest sense.”

    2. Cf. McKirihan, p. 51:

      “There is no reason to think that he conceived of analyzing rarity and density in numerical terms. … Moreover, though ‘more’ and ‘less’ are quantitative concepts, it is not clear that Anaximenes understood rare and dense in that way. For us, rarity and density depend on how much of something there is in a given volume, but the idea of ‘a given volume’ is rather sophisticated, and dense and rare themselves can be thought of as qualities just as well as hot and cold can. Anaximenes had the idea of analyzing one feature in terms of another, but it is anachronistic to see him as the originator of the belief that science is essentially quantitative.”

  9. Summary of Anaximenes’ achievement:  See Barnes, Presocratics, p. 47:

    “We need not embrace Anaximenes’ conclusions in order to admire his principles and his methodology: observations of a puzzle situation lead him to form explanatory theories of successively greater generality. And the final theory has many of the hallmarks of science: it is highly general; it is devastatingly simple; it explains the original puzzle; and it applies to, and can therefore be tested against, a mass of superficially unconnected phenomena.”

  10. Anaximander and Anaximenes compared:

    1. They were both monists: they tried to explain diversity in terms of simplicity. To give a single explanation of a variety of different phenomena. (Like contemporary “string theory” — a theory of everything.)

    2. Anaximander had a bold vision: he attempted to explain observable phenomena in terms of a single, basic, unobservable entity (the apeiron).

    3. Anaximenes replaces Anaximander’s basic notion of opposition with that of a continuum of differences.

    4. Anaximenes’ choice of air as the “material substratum” seems retrograde — a throwback to Thales. But there are advantages to Anaximenes’ theory:

      1. It is closer to experience; it does not rely on unobservables.
      2. There is at least a suggestion of trying to reduce qualitative differences to quantitative ones.
      3. There is an actual theory to explain how the process of transmutation works.
      4. An attempt to explain the mechanism of change, to answer the question “how does change occur”?

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