- principle of all things the infinite (apeiron), i.e. the unlimited, indefinite.
- question of how to interpret apeiron: infinite in space, time, or indefinite in nature (unlike, e.g., Thales' water)
- one interpretation: different substances are separated from apeiron, and in time balance out through "paying retribution to each other", giving state of justice.
- possible motivation: "opposed" forces in nature, possible without cease, against background of "complete" unity.
- so get an early version of the common Greek pattern of cosmological explanation relying unity and order.
- note: apeiron seems to be a posit, not derived from experience.
- note: argument about Earth's non-motion: idea that Earth at centre of cosmos, so no direction of motion favored; again, note idea of needing a reason for non-motion.
- HoPwaG doesn't say this, but Anaximander's claim about the cylindrical shape of Earth, with us on flat top surface, also seems like the possible product of philosophical argument, viz. we want both that earth preserves its surface shape in three dimensions, but that surface flat and equally elongated in any direction in the plane; what shape fits that bill? a cylinder.
- air as principle of all things; thins and thickens, giving different substances.
- Anaximenes starts with air, rather than other substances, perhaps, because most dynamic and intermediate between other states, hence suitable to play the role of fundamental principle.
- again, idea of explaining cosmos in terms of basic constituents.
- soul (pneuma) as breath (=air); possibly derived from breathing as living; allows comparison of human body with cosmos (i.e. microcosm), another early version of a popular idea in Greek philosophy.
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