Counting the moon and the formation of a calendar

Use in the book

The Athenian asks how we learned to count (978b). Humans have from the universe a nature able to think one and two; many other living beings lack the capacity even to learn counting from the father. The god first establishes receptivity and then supplies instruction through visible difference. Day and night furnish distinguishable appearances; their repeated alternation teaches one and two and permits thinking three, four, and many (978c–d).

The slowest learner is explicitly included, but only within the class to which the god has given the nature of being able to learn (978e). The passage therefore neither limits elementary counting to a brilliant few nor makes an unqualified claim about every creature. Its lesson depends on repeated appearances and a receptive nature, not on a teacher first reciting an abstract definition of number.

The moon gives the next unit. Appearing larger and smaller, it displays another day until fifteen days and nights; the text then speaks of a circuit if one chooses to set down the whole cycle as one. The wording is compressed. It names a fifteen-day sequence and the formation of a counted whole, but does not provide a complete technical explanation of the modern lunar month. It would be misleading to silently replace its period with a modern numerical value or assert that fifteen days are the full synodic month.

The central educational contrast comes at 979a. Counting each thing one by one differs from continually reckoning number with all things in relation to one another. The god composes months in relation to the year, and number is seen together in relation to number. This is the step from serial accumulation to ordered comparison. The supplied translation retains the god as the subject of the final seeing-together clause, while its later editorial discussion acknowledges another possible construal. The interpretation should remain visible rather than presented as grammatically certain.

The calendar is not isolated from life. Fruits, fertile earth, nourishment, measured winds, and measured rain follow in the account. Poor results are assigned to humans' unjust distribution of their life rather than to divine nature (979a–b). This is an ethical claim about cosmic provision and human ordering; it does not explain every natural disaster or assign individual guilt for every adverse season. Its transition into lawgiving shows the purpose of counting: an intelligible order that bears on how people live together.

Places to read

1. 978bπῶς ἐμάθομεν ἀριθμεῖν — The inquiry asks for the origin of learned counting
2. 978cπαρὰ τοῦ πατρὸς ἀριθμεῖν — The “father” comparison has more than one possible referent
3. 978dτρία καὶ τέτταρα καὶ πολλά — Repeated visible differences permit extension beyond one and two
4. 978d–e2μέχρι πεντεκαίδεκα ἡμερῶν καὶ νυκτῶν — The stated lunar sequence reaches fifteen days and nights
5. 978eτὸν κύκλον ἕνα ὅλον εἰς ἓν τιθέναι — A whole cycle is set down as one unit
6. 979aτὸ δὲ πρὸς ἄλληλα πάντα ἀριθμὸν ἀεὶ λογίζεσθαι — Reckoning considers things in relation to one another
7. 979aμῆνας πρὸς τὸν ἐνιαυτὸν συνεστήσατο — Months are composed in relation to the year
8. 979bοὐκ ἐν δίκῃ διανέμουσαν τὸν αὑτῶν βίον — Human failure concerns unjust distribution of life

Translation in this edition

“Circuit” and “cycle” distinguish periodos and kyklos; “reckon” differs from merely “count.” At 978d Burnet prints ὅταν and deletes the relative ἃς; the English consequently makes Heaven persist in rolling the days and nights, rather than ceasing. At 979a the edition's acknowledged uncertainty about the subject of συνορᾶν should remain part of the reading.

Lunar appearance — φαίνεσθαι (phainesthai)

φαίνεσθαι (phainesthai)

Lunar appearance. The moon appears larger and smaller in the counting lesson; the phrasing describes observed phases without stating that its substance grows and shrinks. Attested: φαινομένη (978d). Counting the moon and the formation of a calendar.

Competence within its limits — ἀριθμητικός (arithmētikos)

ἀριθμητικός (arithmētikos)

Competence within its limits. The capable living being becomes very able to count as far as these elementary phenomena extend, looking at each thing one by one. Attested: ἀριθμητικὸν (978e–979a). Counting the moon and the formation of a calendar.

Lunar counted whole — περίοδος (periodos)

περίοδος (periodos)

Lunar counted whole. The sequence of lunar appearances is called a circuit when its whole cycle is set down as one unit; the text’s fifteen-day wording remains compressed. Attested: περίοδος (978e). Counting the moon and the formation of a calendar.

Calendrical arrangement — συνιστάναι (synistanai)

συνιστάναι (synistanai)

Calendrical arrangement. The god brings months together in relation to the year, making their order a matter of comparison rather than simple accumulation. Attested: συνεστήσατο (979a). Counting the moon and the formation of a calendar.

Learning from visible order — ἀριθμεῖν (arithmein)

ἀριθμεῖν (arithmein)

Learning from visible order. The verb names the elementary learning explained through day, night, and lunar changes, distinct from later reckoning relations among periods. Attested: ἀριθμεῖν (978b). Counting the moon and the formation of a calendar.

A whole counted as one — κύκλος (kyklos)

κύκλος (kyklos)

A whole counted as one. The observer may set down the cycle as a single whole, converting a succession of appearances into one counted unit. Attested: κύκλον (978e). Counting the moon and the formation of a calendar.

Visible basis of counting — ἡμέρα (hēmera)

ἡμέρα (hēmera)

Visible basis of counting. Day is contrasted with night as an appearance from which numerical distinction can be learned, then counted within lunar progression. Attested: ἡμέρας (978c). Counting the moon and the formation of a calendar.

Fertile earth — γῆ (gē)

γῆ (gē)

Fertile earth. Earth is called pregnant in the account of fruits and nourishment made possible by measured seasons. Attested: γῆ (979a). Counting the moon and the formation of a calendar.

Ambiguous source of instruction — πατήρ (patēr)

πατήρ (patēr)

Ambiguous source of instruction. The source from whom other creatures might learn to count, if naturally capable. The edition allows either the god or a creature’s own parent as interpretation. Attested: πατρὸς (978c). Counting the moon and the formation of a calendar.

Stated lunar sequence — πεντεκαίδεκα (pentekaideka)

πεντεκαίδεκα (pentekaideka)

Stated lunar sequence. The number marks the days and nights through which the moon’s differing appearances have passed. The passage does not give a complete modern lunar-period definition. Attested: πεντεκαίδεκα (978d–e2). Counting the moon and the formation of a calendar.

Favorable numerical result — τύχη (tychē)

τύχη (tychē)

Favorable numerical result. Happy fortune qualifies the difficult claim about seeing number together in relation to number; its presence does not retract the surrounding divine pedagogy. Attested: τύχῃ (979a). Counting the moon and the formation of a calendar.

Extension beyond the first pair — τέτταρες (tettares)

τέτταρες (tettares)

Extension beyond the first pair. The neuter τέτταρα is one of the further numbers conceived from recurring appearances after learning one and two. Attested: τέτταρα (978d). Counting the moon and the formation of a calendar.

Elementary achievement — μανθάνειν (manthanein)

μανθάνειν (manthanein)

Elementary achievement. Even the slowest capable learner eventually learns to count sufficiently from the repeated celestial instruction. Attested: μάθῃ (978d). Counting the moon and the formation of a calendar.

Relational calendrical unit — μήν (mēn)

μήν (mēn)

Relational calendrical unit. Months are composed relative to the year, shifting the account from successive units to the comparison of larger ordered periods. Attested: μῆνας (979a). Counting the moon and the formation of a calendar.

Lunar numerical instruction — σελήνη (selēnē)

σελήνη (selēnē)

Lunar numerical instruction. The moon appears larger and smaller and makes another day visible through the stated fifteen-day sequence, enabling a cycle to be counted as one. Attested: σελήνην (978d). Counting the moon and the formation of a calendar.

Visible difference and repetition — νύξ (nyx)

νύξ (nyx)

Visible difference and repetition. Night presents everything differently from day, and its repeated alternation helps teach one, two, and further numbers. Attested: νυκτὸς (978c). Counting the moon and the formation of a calendar.

Seasonal fertility — τροφή (trophē)

τροφή (trophē)

Seasonal fertility. Nourishment for all living beings results from fruits and fertile earth under measured winds and rains. Attested: τροφὴν (979a). Counting the moon and the formation of a calendar.

Relational reckoning — ἀριθμός (arithmos)

ἀριθμός (arithmos)

Relational reckoning. Number is considered in relation to number when months are arranged relative to the year, beyond counting isolated items. Attested: ἀριθμὸν (979a). Counting the moon and the formation of a calendar.

Unit acquired and formed — εἷς (heis)

εἷς (heis)

Unit acquired and formed. The neuter ἕν names one in the first lesson and the unity assigned to a whole cycle; units can be single appearances or an organized whole. Attested: ἓν (978b). Counting the moon and the formation of a calendar.

Production of lunar unity — ἀπεργάζεσθαι (apergazesthai)

ἀπεργάζεσθαι (apergazesthai)

Production of lunar unity. The god’s producing of the moon introduces the larger and smaller appearances by which the learner forms a counted cycle. Attested: ἀπεργασάμενος (978d). Counting the moon and the formation of a calendar.

Measured seasonal rain — ὑετός (hyetos)

ὑετός (hyetos)

Measured seasonal rain. Rains accompany winds that are neither violent nor without measure in the account of earthly nourishment. Attested: ὑετῶν (979a). Counting the moon and the formation of a calendar.

Relations among numbers — λογίζεσθαι (logizesthai)

λογίζεσθαι (logizesthai)

Relations among numbers. Reckoning number with all things in relation to one another is contrasted with counting isolated things; months relative to a year supply the example. Attested: λογίζεσθαι (979a). Counting the moon and the formation of a calendar.

Persistent celestial repetition — ἑλίττειν (helittein)

ἑλίττειν (helittein)

Persistent celestial repetition. Heaven does not cease rolling days and nights around, and therefore does not cease teaching numerical distinctions. Attested: ἑλίττων (978d). Counting the moon and the formation of a calendar.

Relational numerical vision — συνορᾶν (synhoran)

συνορᾶν (synhoran)

Relational numerical vision. Every number is seen together in relation to number. The edition keeps the god as subject but acknowledges another possible construal in its editorial discussion. Attested: συνορᾶν (979a). Counting the moon and the formation of a calendar.

Condition of observing difference — ὄψις (opsis)

ὄψις (opsis)

Condition of observing difference. The observer has sight when passing from day’s kind to night’s part; visible contrast underlies the counting lesson. Attested: ὄψιν (978c). Counting the moon and the formation of a calendar.

Extension to further numbers — ἐπινοεῖν (epinoein)

ἐπινοεῖν (epinoein)

Extension to further numbers. Seeing repeated day-night appearances allows each observer to think of three, four, and many as well. Attested: ἐπινοήσειεν (978d). Counting the moon and the formation of a calendar.

Excluded seasonal excess — ἐξαίσιος (exaisios)

ἐξαίσιος (exaisios)

Excluded seasonal excess. Winds and rains are said not to have this excessive character in the beneficent order described; the phrase does not catalogue every actual storm. Attested: ἐξαισίων (979a). Counting the moon and the formation of a calendar.

Decline of the moon’s appearance — φθίνειν (phthinein)

φθίνειν (phthinein)

Decline of the moon’s appearance. Waning is the paired lunar change through which the god organizes months in relation to the year. Attested: φθίνουσαν (979a). Counting the moon and the formation of a calendar.

Growth of the moon’s appearance — αὐξάνεσθαι (auxanesthai)

αὐξάνεσθαι (auxanesthai)

Growth of the moon’s appearance. The moon’s waxing is paired with waning in the explanation of months arranged relative to a year; the wording does not imply literal growth of its substance. Attested: αὐξανομένην (979a). Counting the moon and the formation of a calendar.

Measured seasonal wind — ἄνεμος (anemos)

ἄνεμος (anemos)

Measured seasonal wind. The plural winds, distinct from pneuma in the navigation example, belong with rains to the favorable conditions sustaining fertility. Attested: ἀνέμων (979a). Counting the moon and the formation of a calendar.

Measure in weather — ἄμετρος (ametros)

ἄμετρος (ametros)

Measure in weather. Winds and rains in the account of beneficent provision are said not to be without measure. Attested: ἀμέτρων (979a). Counting the moon and the formation of a calendar.

Whole for comparing months — ἐνιαυτός (eniautos)

ἐνιαυτός (eniautos)

Whole for comparing months. The year supplies the larger relation within which months are composed; the text does not state a detailed intercalation rule here. Attested: ἐνιαυτὸν (979a). Counting the moon and the formation of a calendar.

Learning from the father (contextual phrase)

παρὰ τοῦ πατρὸς ἀριθμεῖν (978c)

The phrase belongs to the comparison with other living beings that lack the nature enabling this learning. The father may be the god or a creature’s own parent, as the supplied note allows. Neither identification should be silently promoted from plausible interpretation to an uncontested attested name. Counting the moon and the formation of a calendar.

Heaven does not cease rolling (contextual phrase)

ἑλίττων δὴ ταῦτα αὐτὰ ὅταν μὴ παύηται (978d)

The participle completes the verb of ceasing: Heaven does not cease rolling these same days and nights round. It does not mean that Heaven stops and then teaches. Burnet adopts ὅταν and deletes the following relative ἃς; the edition’s English follows that text. Counting the moon and the formation of a calendar.

Fifteen days and nights (contextual phrase)

μέχρι πεντεκαίδεκα ἡμερῶν καὶ νυκτῶν (978d–e2)

This is the precise number in the moon’s sequence of changing appearances. The next sentence calls the sequence a circuit if its cycle is put down as one whole. The compressed formulation should not be silently corrected into a modern month or mistaken for a fully explained statement that a synodic month lasts fifteen days. Counting the moon and the formation of a calendar.

A whole cycle counted as one (contextual phrase)

τὸν κύκλον ἕνα ὅλον εἰς ἓν τιθέναι (978e)

The single whole is treated as a unit of counting. A collection or temporal sequence can thereby enter a higher-order comparison, preparing for months considered in relation to a year. The clause describes the formation of a numerical unit, not merely naming another individual day. Counting the moon and the formation of a calendar.

One by one and in relation to one another (contextual phrase)

τὸ καθ’ ἓν αὐτὸ σκοποῦν· τὸ δὲ πρὸς ἄλληλα πάντα ἀριθμὸν ἀεὶ λογίζεσθαι (979a)

The contrast separates inspecting each item itself, one at a time, from reckoning number with all things in mutual relation. It is the educational step from serial counting to comparison of orders. The following arrangement of months relative to the year gives the contrast concrete calendrical content. Counting the moon and the formation of a calendar.

Months relative to the year (contextual phrase)

μῆνας πρὸς τὸν ἐνιαυτὸν συνεστήσατο (979a)

The accusative object and πρός construction describe months composed in relation to the year. The clause establishes relational organization, not a detailed intercalation procedure. The god is the subject in the supplied translation, and the next seeing-together clause has an acknowledged interpretive difficulty. Counting the moon and the formation of a calendar.

Seeing every number with number (contextual phrase)

πάντα ἀριθμὸν πρὸς ἀριθμὸν ἤρξατο συνορᾶν (979a)

The compounded verb emphasizes seeing together rather than noticing isolated units. The edition retains the god as the subject of began to see, while its later note admits an alternative involving all things as subject. The lexical companion follows the rendering while keeping that uncertainty visible. Counting the moon and the formation of a calendar.