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The Etymologies of ἄπειρος

Thomas Davies

Princeton University

This paper explores an important technical term in early Greek philosophy, ἄπειρος. The first known use of the word (in the neuter, ἄπειρον) occurs in a cosmological fragment (DK A9/B1) of Anaximander of Miletus (traditional dates 610–c. 545 BC).

For more than a century, scholars of early Greek philosophy have debated the sense in which Anaximander used this word, with the debate mostly turning on its etymology. It is rare to find a treatment of Anaximander which does not offer an etymology of the word. Unfortunately, few scholars of Anaximander are historical linguists, and proposals range from the unsatisfactory to the insane. This paper offers an informed etymology of ἄπειρος and explores its semantic development and folk-etymological explanations through the Archaic and Classical periods. I conclude with some remarks on the legitimate uses of historical linguistics in ancient philosophy.

Three main accounts of the etymology have been proposed: the majority of commentators understand ἄπειρος as an alpha-privative formed on πεῖραρ ‘limit’ and accordingly render it ‘infinite’ or ‘unlimited’ (Burnet 1930, Jaeger 1947, Vlastos 1947, Guthrie 1962, West 1971, Sweeney 1972, Barnes 1982, Dancy 1989, Couprie 2003, Couprie & Kočandrle 2013, Gregory 2016). An influential minority take it as an alpha-privative formed on πείρω ‘traverse, pass through,’ meaning ‘untraversable’ (Kahn 1960, Graham 2006). A fringe view is that ἄπειρος is an alpha-privative formed on πεῖρα ‘test, experience’ and means ‘that which cannot be experienced’ (first argued by Tannery 1904, and periodically disinterred from the dignity of the grave by e.g. Sweeney 1972, Drozdek 2008, Couprie & Kočandrle 2017).

After a brief summary of the independent problems with these views, I argue that the debate itself is misconceived. The word ἄπειρος was not a new and independent alpha-privative formation, but the product of a collapse of four formally and etymologically distinct words containing the initial element ἀπείρ- into a single o-stem:

  1. ἀπείρων ‘without limits’: an alpha-privative formed on πεῖραρ.
  2. ἀπειρέσιος (metrical allomorph ἀπερείσιος) ‘untraversable’: an East Greek descendant of *aperyet(i)os (< PIE *per-ye/o-) (Vine 1998).
  3. ἀπείριτος ‘uncircumnavigable’: either from *a-peri-itos (after semivocalization of the first /i/ and regular metathesis, as Chantraine, following Schulze 1892), or simply from *a-per-itos (< PIE *per- ‘come through’) with *-per- analogized to (1) and (2).
  4. ἀπείρητος ‘inexperienced’: a regular negative passive adjectival formation from πειράω ‘try, test.’

Near the beginning of the sixth century, ἄπειρος ‘ignorant’ replaced (4). In Ionic, it also replaced (1)–(3), which had already undergone significant semantic bleaching and simply meant ‘vast.’ The Ionic usage of ἄπειρος ‘vast’ spread to Attic and West Greek over the course of the fifth century, resulting in a single o-stem form ἄπειρος meaning both ‘ignorant’ and ‘vast.’ Early on, ἄπειρος ‘ignorant’ was falsely etymologized as an alpha-privative formation to the noun πεῖρα ‘test’ (e.g. Thgn. 571–2). I argue that this provoked reanalysis of its homophone ἄπειρος ‘vast’ into a formation to the noun πέρας, especially in philosophical discourse (Xenoph. B28, Philol. B1–2, Plat. Phlb. 16c10; Arist. Phys. 203b3–15, etc.). The technical meaning of ‘infinite’ therefore arose in the fifth century. I conclude that Anaximander probably would not have found precedent for using ἄπειρος in any sense but ‘very large.’ This does not, of course, preclude his using it in a novel sense, and the paper closes with some methodological remarks on how linguistics should be brought to bear on the interpretation of philosophical texts.

Session/Panel Title

Greek and Latin Linguistics

Session/Paper Number

2.2

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