Life is an important high-level phenomenon that stands in need of explanation. [Premise]
The most distinctive, common feature of living things is self-movement. [Premise]
Water is self-moving. [Premise]
Moreover, water is necessary for the sustenance of life. [Premise]
So there is reason to believe that water is the source of life. [1-4]
If water is the source of life, water must itself be alive. Â [Premise]
So there is reason to believe that water is itself alive. [5, 6]
Liquid water can realize any shape. [Premise]
Water can realize distinct phases (liquid, solid, gas). [Premise]
The explanation for important high-level phenomena is very likely an adequate explanation for lower-level phenomena. [Premise]
So it’s quite likely that water is the source of everything (the archê). [7-10]
In order to be the source of everything, the archê must be eternal. [Premise]
So as the archê, water must be eternal. [11, 12]
The popular conception of the gods as being alive, eternal, and the source of creation is basically correct. [Premise]
So as the archê, water is divine (“Gods are in everything”). [7, 11, 13, 14]
A Reconstruction of Anaximander’s Reasoning
If water were the archê, then it would be the source of fire, since fire is uncontroversially something that exists. [Premise]
But a sufficient quantity of water will extinguish a fire, and a sufficiently intense fire will annihilate a particular quantity of water. [Premise]
It is highly implausible to claim that the source of a particular kind of stuff would stand in a relation of mutual-destruction with it. [Premise]
So it’s highly implausible to claim that water is the source of fire. [2, 3]
So it’s highly implausible to claim that water is the archê. [1, 4]
The same reasoning applies mutatis mutandis [“making necessary changes”] to each of the four elements. [Premise]
So it’s highly implausible that any of the elements is the archê. [1-6]
So the archê must be distinct from any of the elements and indeterminate with respect to its properties. [7]
So the archê is a quintessence, one we might call “apeiron”. [8]
As the source of everything, apeiron must be eternal. [Premise]
As the source of everything, apeiron would give rise to opposing elements. [Premise]
So the incessant cycle of seasonal change is best understood as the activity of apeiron correcting the imbalance and over-reaching of a particular element (“according to necessity … they pay penalty and retribution to each other for their injustice in accordance with the ordering of time”). [11]
A Reconstruction of Anaximenes’ Reasoning
We have no reason to believe that apeiron exists aside from our inability to identify another kind of stuff that fulfills the requisite theoretical roles. [Premise]
So ceteris paribus [“other things being equal”], an uncontroversial stuff that fulfilled those roles would be a superior choice for the archê, as compared to apeiron. [1]
As one of the four familiar elements, air is a kind of stuff that uncontroversially exists. [Premise]
Air (in the form of breath – pneuma) is even more immediately associated with life than is water. [Premise]
Air is always in motion. [Premise]
Air is the most indeterminate of the four elements. [Premise]
Through the process of condensation, it’s conceivable that air should become wind, clouds, water, earth, and stone. [Premise]
Through the process of rarefaction, it’s conceivable that air should become fire. [Premise]
So it’s conceivable that air is capable of being transformed into the other three elements (earth, fire, and water), and other intermediate substances. [7, 8]
So air fulfills the same requisite theoretical roles as apeiron. [4, 5, 6, 9]
So air is a superior choice for the archê. [2, 10]