Arithmetic and measurement

Use in the book

At 114c the arithmetician can persuade one person and many about numbers. Socrates uses this to challenge the assumption that private discussion differs essentially from public explanation: knowledge of a subject should remain available regardless of audience size. The simple comparison between one and two at 112e–113a2 had already isolated responsibility for an answer, but the craft example's immediate role is the stability of expertise across audiences.

At 126c–d arithmetic returns as the knowledge that produces concord about numbers. Cities, private persons, and an individual with himself all come under the same standard. Measuring similarly establishes which is greater, a span or a cubit; the comparison extends to weight. The examples give “concord” determinate content: agreement on a subject grounded in a relevant craft.

This is a model for a question, not yet an answer about politics. Socrates wants to know the corresponding civic subject and craft. Alcibiades' move from mathematical agreement to family affection exposes problems when household partners possess different expertise. Nothing here claims that arithmetic by itself reconciles civic interests or makes spouses share every practical judgment. Its argumentative role is to show what an intelligible account of agreement would need to specify.

Places to read

1. 112e–113a2One and two exemplify the respondent’s responsibility for a stated answer
2. 114cAn arithmetician’s competence addresses one or many listeners
3. 126c–126dArithmetic, lengths, and weight supply models of concord grounded in expertise

Translation in this edition

The edition's “measurement” names the craft, while “span,” “cubit,” and “weight” identify the comparisons it governs. The phrase at 126d does not introduce an independently named weighing craft; it says that weight is analogous.

ἀριθμός / ἀριθμητική / ἀριθμητικός

Attested: ἀριθμητικός (arithmētikos; 114c); ἀριθμητικήν (arithmētikēn; 126c). At 114c: The expert in number who can persuade one person or many. At 126c: Arithmetic as the craft producing concord about numbers. Lexical identification: family label: ἀριθμός / ἀριθμητική / ἀριθμητικός. See Arithmetic and measurement.

μετρητική

Attested: μετρητικήν (metrētikēn; 126d). At 126d: Measurement as the craft determining which of two lengths is greater. Lexical identification: lemma: μετρητική. See Arithmetic and measurement.

σπιθαμή / πῆχυς

Attested: σπιθαμῆς (spithamēs; 126d); πήχεος (pēcheos; 126d). At 126d: A span, one of two lengths whose relative size is settled by measuring. At 126d: A cubit, compared with a span in the measurement example. Lexical identification: family label: σπιθαμή / πῆχυς. See Arithmetic and measurement.

σταθμός

Attested: σταθμοῦ (stathmou; 126d). Weight or weighing; another measurable domain in which the relevant art produces agreement. Lexical identification: lemma: σταθμός. See Arithmetic and measurement.