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