Ὁ ἄπειρος πρῶτος τὴν ψῆφον βαλέτω. Leaving No Pebble Unturned in Sophistici elenchi, 1

Abstract

Relying on evidence from fifteen epigraphic collections and sixty-odd ancient sources as well as discussing a literature of over five hundred titles, the essay’s highly unorthodox conclusions are a case in point of the micrological ideal of achieving novelty on any given subject by way of transcribing and studying first-hand all relevant materials – edited and unedited alike. The paper’s ambition was to shed new light on one of the most intriguing analogies of the whole Aristotelian corpus, namely the comparison between words and pebbles. A review of all material evidence and virtually all extant sources made short work of two related, albeit mutually exclusive, misconception about ancient reckoning boards and their workings: (1) the idea that – for all practical purposes – the abacus’ arrangement mirrored the decimal system, its columns and rows conveniently matching units, tens, hundreds, thousands, etc. (2) the idea that the inscriptions on several surviving counting boards were a nuisance to the extent that, being inconsistent to a fault with the decimal system itself, they made actual calculations harder than they already were (as opposed to making them easier, as one would expect). The paper demonstrated that the first assumption – the « decimal » bias – is simply mistaken and betrays little or no awareness of the epigraphic and archaeological evidence. The paper also demonstrated that the second assumption – the « abacus riddled with complications » bias – simply defeats the purpose of resorting to the abacus in the first place and betrays a poor understanding of its practical vocation which, most assuredly, was not to add to the very problem it was meant to solve. After bulldozing its way through both misunderstandings, the essay focused on the abacus most distinctive features, that is positionality (i.e. the abacus being a positional system through and through) and hybridity (i.e. the abacus’ place value system being monetary in nature and purpose, as opposed to it being abstract and homogeneous). The final result is an interpretation that moves away from the received views by showing that the prologue of the Sophistici elenchi offers no support to the notion that, when Aristotle referred to counters, he was leaning on a kinship of sorts – or any kinship, for that matter – between abstract calculation and speech. Once we turns the pebble’s simile on its head and set it back upon its feet (Aristotle’s pebble analogy is about pebbles, what else?), it becomes clear that it presupposed numeracy all right, but it was not about numeracy itself. Moreover its goal was not to explain why computational and linguistic symbolisms succeed, but to explain how they fail – failure being the whole point; in this particular instance, failure to detect and prevent abusive value shifts affecting words and counters alike

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