Number

Use in the book

Number enters through a counterfactual test (976d–e). Which knowledge, if absent or removed, would leave human beings most senseless and unintelligent? The answer is the knowledge that has given number to the mortal race. This identifies a pervasive dependency rather than an activity merely more prestigious than the rejected crafts. The giver is then identified as a god, Heaven, not an accidental fortune.

At 977c–d the argument joins numerical discrimination to reason. Someone who does not know two and three, odd and even, cannot give an account of what he has merely perceived and remembered. Without true reason there is no wisdom, and without wisdom there is no complete goodness and consequent happiness. The text expressly allows courage and temperance notwithstanding the deficiency. The foundation is therefore necessary for complete virtue in the argument; the passage does not deny every virtue or every good action to an uncounting being.

The Athenian acknowledges that fully explaining this necessity would take longer than the entire foregoing discussion. His immediate supplementary argument is that all the previously surveyed crafts disappear if arithmetic is removed. Their rejection as wisdom is compatible with their dependence on number. Arithmetic's ubiquity is the point, not an assertion that building, medicine, or navigation are now useless.

At 977e–978b2 the claim grows much stronger. Number is not needed only for small practical things, even though these are important. It enters the distinction of divine and mortal generation and the recognition of reverence for gods; movements and sounds in music must be counted. Finally it is declared the cause of all goods and of no evils, while disorderly motion and whatever shares in evil have been left without number. This is an ethical and cosmological use of numerical order. It cannot be read literally as a denial that a destructive action has a countable duration or uses a measurable instrument. The speech associates goodness with ordered, measured relations, while leaving the most ambitious causal claim asserted more broadly than the preceding examples establish.

The later first study of “numbers themselves,” without bodies (990c), develops number beyond the acquisition of elementary counting. But the opening does not already teach the whole mathematical curriculum. At 979d whether the knower is wise and good still needs an account. Treating number as necessary, treating numerical order as good, and identifying the fully educated wise person are successive argumentative tasks.

Places to read

1. 976eἡ τὸν ἀριθμὸν δοῦσα παντὶ τῷ θνητῷ γένει — The decisive knowledge has given number to mortals
2. 977cἀριθμὸν ἐκ τῆς ἀνθρωπίνης φύσεως ἐξέλοιμεν — The removal test states a dependency
3. 977dἀριθμὸν μὲν ἀνάγκη πᾶσα ὑποτίθεσθαι — Number must be laid down as a foundation
4. 977d–eπάντα δ’ ἀπολείπεται … ὅταν ἀριθμητικήν τις ἀνέλῃ — The other crafts fail if arithmetic is taken away
5. 978aἀγαθῶν ὡς πάντων αἴτιον — The claim is enlarged to number as cause of all goods
6. 978a–bἐπιλέλειπται παντὸς ἀριθμοῦ — Whatever shares in badness is described as left without number
7. 990cἀριθμῶν αὐτῶν ἀλλ’ οὐ σώματα ἐχόντων — The later curriculum begins with numbers themselves, without bodies

Translation in this edition

The translations “number,” “count,” “count out,” “able to count,” and “arithmetic” keep noun, action, capacity, and discipline distinguishable. At 977c Burnet brackets a redundant ἔχοι; it is not an independent assertion of the printed argument. The register should not count deleted words as adopted attestations.

Discipline supporting every craft — ἀριθμητικός (arithmētikos)

ἀριθμητικός (arithmētikos)

Discipline supporting every craft. The feminine substantivized ἀριθμητικήν names arithmetic, whose removal would leave none of the earlier crafts intact. Attested: ἀριθμητικήν (977e). Number arithmetic and the foundation that is not yet the whole answer.

Evil outside numerical order — κακός (kakos)

κακός (kakos)

Evil outside numerical order. Everything that has a share in badness is declared left without number; this is the speech’s expansive ethical claim, not merely a calculation rule. Attested: κακοῦ (978a–b). Number arithmetic and the foundation that is not yet the whole answer.

Complete absence of number — ἀγνοεῖν (agnoein)

ἀγνοεῖν (agnoein)

Complete absence of number. The hypothetical being is altogether ignorant of number, a stronger description than making an occasional calculation error. Attested: ἀγνοοῖ (977c). Number arithmetic and the foundation that is not yet the whole answer.

Divine and mortal generation — γένεσις (genesis)

γένεσις (genesis)

Divine and mortal generation. The consideration of divine and mortal coming into being is offered as a larger field in which number and reverence toward gods become recognizable. Attested: γενέσεως (977e). Number arithmetic and the foundation that is not yet the whole answer.

Dependent on arithmetic — τέχνη (technē)

τέχνη (technē)

Dependent on arithmetic. The earlier candidates are all allowed to count as crafts for the argument that none survives the removal of arithmetic. Attested: τέχνας (977d–e). Number arithmetic and the foundation that is not yet the whole answer.

Motion without order — ἄτακτος (ataktos)

ἄτακτος (ataktos)

Motion without order. Disorder is one feature of the motion associated with the lack of number, alongside failures of reckoning, rhythm, and harmony. Attested: ἄτακτος (978a). Number arithmetic and the foundation that is not yet the whole answer.

Necessary numerical starting point — ὑποτίθεσθαι (hypotithesthai)

ὑποτίθεσθαι (hypotithesthai)

Necessary numerical starting point. Number must be laid down as foundational, although the Athenian says fully explaining the necessity would require a longer account. Attested: ὑποτίθεσθαι (977d). Number arithmetic and the foundation that is not yet the whole answer.

Ethically characterized motion — φορά (phora)

φορά (phora)

Ethically characterized motion. The motion here is characterized as without reckoning, order, seemliness, rhythm, and harmony; the claim concerns ordered quality, not inability to count its duration. Attested: φορά (978a). Number arithmetic and the foundation that is not yet the whole answer.

Foundational requirement — ἀνάγκη (anankē)

ἀνάγκη (anankē)

Foundational requirement. Every necessity is invoked for laying down number as a foundation, while the full account of why it is necessary is expressly deferred. Attested: ἀνάγκη (977d). Number arithmetic and the foundation that is not yet the whole answer.

Indispensable gift — ἀριθμός (arithmos)

ἀριθμός (arithmos)

Indispensable gift. Number is what the decisive knowledge has given to the mortal race and what the Athenian attributes to a preserving god. Attested: ἀριθμὸν (976e). Number arithmetic and the foundation that is not yet the whole answer.

Condition of account-giving — ἀριθμός (arithmos)

ἀριθμός (arithmos)

Condition of account-giving. Removal of number makes intelligence impossible and prevents giving an account beyond perceptions and memories. Attested: ἀριθμὸν (977c). Number arithmetic and the foundation that is not yet the whole answer.

Ethical and cosmic order — ἀριθμός (arithmos)

ἀριθμός (arithmos)

Ethical and cosmic order. Number is asserted as cause of all good and none of evil, extending its significance beyond useful calculations. Attested: ἀριθμὸς (977e–978a2). Number arithmetic and the foundation that is not yet the whole answer.

Discern the decisive dependency — καθορᾶν (kathoran)

καθορᾶν (kathoran)

Discern the decisive dependency. The exhortation asks the speakers to observe which knowledge, if lost or never present, would most diminish human intelligence. The object is an explanatory dependency, not merely something visible to the eyes. Attested: κατίδωμεν (976d). Number arithmetic and the foundation that is not yet the whole answer.

Lack of fitting agreement — ἀνάρμοστος (anarmostos)

ἀνάρμοστος (anarmostos)

Lack of fitting agreement. Unharmonious motion completes the negative series before the claim that all things sharing badness are left without number. Attested: ἀνάρμοστός (978a). Number arithmetic and the foundation that is not yet the whole answer.

Number’s scope — δύναμις (dynamis)

δύναμις (dynamis)

Number’s scope. The extent of the power for which number is responsible reaches beyond the small practical uses of crafts. Attested: δυνάμεως (978a). Number arithmetic and the foundation that is not yet the whole answer.

Counterfactual abolition of arithmetic — ἀναιρεῖν (anairein)

ἀναιρεῖν (anairein)

Counterfactual abolition of arithmetic. Removing arithmetic is the test by which the dependence of every surveyed craft on number is asserted. Attested: ἀνέλῃ (977e). Number arithmetic and the foundation that is not yet the whole answer.

Religious significance of number — θεοσεβής (theosebēs)

θεοσεβής (theosebēs)

Religious significance of number. The substantivized neuter names reverence toward gods as something recognized through considering divine and mortal generation. Attested: θεοσεβὲς (977e). Number arithmetic and the foundation that is not yet the whole answer.

Elementary numerical distinction — δύο (dyo)

δύο (dyo)

Elementary numerical distinction. Two is paired with three in the account of what the uncounting being does not know, and with one in the account of learning through day and night. Attested: δύο (977c). Number arithmetic and the foundation that is not yet the whole answer.

Misshapen or unfitting motion — ἀσχήμων (aschēmōn)

ἀσχήμων (aschēmōn)

Misshapen or unfitting motion. The adjective joins the negative series describing motion without numerical order; it is not a judgment of a named artwork or body here. Attested: ἀσχήμων (978a). Number arithmetic and the foundation that is not yet the whole answer.

Qualified cosmic contrast — σχεδόν (schedon)

σχεδόν (schedon)

Qualified cosmic contrast. The description of motion without reckoning and order begins with this qualifier before the wider claim about everything sharing in badness. Attested: σχεδὸν (978a). Number arithmetic and the foundation that is not yet the whole answer.

Disordered motion — ἀλόγιστος (alogistos)

ἀλόγιστος (alogistos)

Disordered motion. The adjective begins the sequence of negative descriptions of motion left without number and associated with badness. Attested: ἀλόγιστός (978a). Number arithmetic and the foundation that is not yet the whole answer.

Temporal disorder — ἄρρυθμος (arrythmos)

ἄρρυθμος (arrythmos)

Temporal disorder. Rhythmless motion belongs to the series of conditions from which the Athenian contrasts numerical goodness. Attested: ἄρρυθμος (978a). Number arithmetic and the foundation that is not yet the whole answer.

What if the knowledge departed or never arrived? (contextual phrase)

ἐπιστήμη μία διεξελθοῦσα ἢ μὴ παραγενομένη (976d)

The two participles test both loss and original absence of one currently present knowledge. The question is comparative: which missing knowledge would make humans most senseless and unintelligent? Identifying the indispensable foundation does not itself establish that possessing an elementary part of it is sufficient for completed wisdom. Number arithmetic and the foundation that is not yet the whole answer.

A foundation with a fuller explanation deferred (contextual phrase)

ἀριθμὸν μὲν ἀνάγκη πᾶσα ὑποτίθεσθαι (977d)

The infinitive makes number what must be posited underneath the ensuing account. The next clause says that explaining why this is necessary would require a still longer argument. Foundational status is asserted, but the dialogue acknowledges rather than supplies the full explanation at this point. Number arithmetic and the foundation that is not yet the whole answer.

All good and no bad (contextual phrase)

ἀγαθῶν ὡς πάντων αἴτιον, ὅτι δὲ κακῶν οὐδενός (978a)

The compressed clause enlarges number’s significance from useful technique to universal ethical causation. Its contrast should not be weakened to a claim about accurate bookkeeping, but neither should it be paraphrased as proof that harmful events have no measurable duration. The text associates number with good order and leaves the full causal thesis ambitious. Number arithmetic and the foundation that is not yet the whole answer.

Left without every number (contextual phrase)

ἐπιλέλειπται παντὸς ἀριθμοῦ (978a–b)

The perfect marks deprivation as the condition of motion without reckoning, order, shape, rhythm, and harmony, and of everything sharing in badness. The genitive expresses what is lacking. The statement concerns numerical ordering in the argument, rather than literal uncountability of all bad objects. Number arithmetic and the foundation that is not yet the whole answer.

Use in the book

The arithmetic material calls number a multitude composed of monads. Philolaus’ fragment says that all known things have number, since nothing can be conceived or known without it. That wording is more specific than the different claim that all things simply are numbers.

Places to read

1. Arith.6Number is a multitude of monads and numbers stand in ratios.
2. Arith.9Numbers are distinguished from numbered things.
3. I.21.7bPhilolaus connects having number with being knowable.
4. Arith.8Numerical progression and subtraction terminate in a monad.
5. I.49.32.6Different numerical descriptions of soul are distinguished.

Translation in this edition

“Number” renders arithmos; “things that are numbered” renders arithmēta. Keeping the distinction visible avoids turning a claim about intelligibility or counting into an identity of things and numbers.

Images and comparisons

The dramatic account in Arith.1a makes number a discovery that orders a previously confused human life. Its civilizing role is expressed through the contrast between human order and a life likened to that of beasts.

Units, principles, and explanation

Moderatus describes number through progression from a monad and diminution back toward one. The separate reports on monad and dyad distinguish their use as numerical principles from the bodily things that are numbered. Number also enters accounts of soul, but the survey lists several different meanings: simply number, self-moving number, and number related to encompassing rational principles. Calling something numerical therefore begins an interpretive question rather than resolving it.

Use in the book

The political passage makes a multitude’s strength arise from its numbers, while recommending that it learn to contain that strength. In the reflection on concentration, a unity can equal a number, just as a thought can hold a book’s essence. The late comparison of Tacitus and Cicero places exact number beside the weight and measure of words. These examples keep quantity in view while resisting the inference that more units necessarily mean greater excellence.

Places to read

1. I, p. 459, entry 3, ¶1A multitude derives strength from its numbers.
2. II, p. 589, entry 7, ¶1A unity may equal a number in excellence.
3. II, p. 898, entry 2, ¶1Exact number accompanies weight and measure in perfect style.

Translation in this edition

The English translation retains “number” in the literary passages rather than silently paraphrasing it as either quantity or rhythm. Its relation to verbal measure remains available to the reader without an imposed technical definition. The translation note identifies a rhetorical-harmony or cadence sense in the Tacitus comparison, without excluding numerical proportion.

Use in the book

The sequence in Fusées I moves from reciprocal enjoyment at a performance or ball to crowds and then to the maxim ‘Intoxication is a number’. The placement suggests an experience of being more than a single bounded self. It does not explain which arithmetic operation intoxication would literally be. Nor does the passage itself name a philosophical school; assigning a complete numerical metaphysics would supply what the note withholds.

Fusées XXII provides a more concrete model. The actual parts of a ship in motion generate successive imaginary figures in space, and from that multiplication emerges the hypothesis of a living, expressive being. Perception works on real elements but exceeds the inventory of what is physically present. Mon cœur mis à nu XCIII makes the connection explicit in another medium: the arts are number, and number translates space.

Number can also become frightening. Mon cœur mis à nu CIX includes it among the abysses felt in action, desire, memory and beauty. Mon cœur mis à nu XXXV asks whether the number of souls is finite or infinite, leaving the cosmological question unanswered. Thus multiplication can enlarge experience without making its limits secure. The practical addition of daily work and small pleasures in Fusées XX offers another use of counting: repetition contains magnitude in manageable acts, even while the visionary passages expose the self to it.

Places to read

1. Fusées ILe nombre est dans l’individu. L’ivresse est un nombre. — The individual is imagined as internally multiple.
2. Fusées XXIIla multiplication successive et à la génération de toutes les courbes et figures imaginaires — The moving ship turns real elements into an expanding geometry of perception.
3. Mon cœur mis à nu XCIIIle nombre est une traduction de l’espace — The later account of the arts gives number a spatial function.
4. Mon cœur mis à nu CIXdu beau, du nombre — Number belongs among the experienced abysses.

Translation in this edition

The edition preserves the odd singular ‘a number’ in ‘Intoxication is a number’, instead of explaining it as multitude or infinity. That restraint leaves the aphorism's unfinished force intact. ‘Multiplication of number’ likewise sounds less natural than ‘growing numbers’, but keeps the conceptual rather than merely demographic register. In Mon cœur mis à nu XXXV, ‘the number of souls’ remains a question, and the translation does not turn possibly habitable worlds into worlds known to be inhabited.

Use in the book

Number supports several different arguments concerning abstraction, multiplicity, infinity, and soul. In the ascent of Book I, numbers require parts but not spatial position, unlike bodily dimensions. The mind then rises beyond numerical unity, which is accidental, toward substantial unity. Angel likewise contains intelligible distinctions without bodily division, while God is above number as its unifying source. Ficino compares incorporeal number with bodily dimension to explain how intellectual abundance can exceed bodily greatness.

The numbers assigned to angels require careful interpretation. Ficino argues that angelic species far exceed bodily species and describes their multitude as almost or virtually innumerable. This does not itself establish a literally infinite population. Ficino cites Dionysius the Areopagite for the greater abundance of separate intellectual species and Daniel for angelic multitudes. He says that Dionysius uses three and nine chiefly, sometimes seven, and notes twelve in Christian mysteries. He then reports Iamblichus and Proclus dividing the highest angels by three, the middle by nine, the succeeding by seven, and the last into twelve orders. These assignments are attributed classifications rather than an independently established census; the passage does not justify silently treating their reported historical relations as independently verified chronology. A separate distinction concerns determinate species and the indefinitely numerous individuals referred to them; the unity of a kind and the number of its instances are different questions.

Endlessly extendable mathematical thought then supports the argument for infinite divine knowledge. Human mind can always think another number, proportion, or figure beyond a fixed total. If God's knowledge stopped at a number but could proceed, it would retain unrealized capacity; if it could not proceed, human thought could exceed it. Unity is hypothetically imagined as knowing every number potentially contained in it. The image illustrates a source's knowledge of its productive range, not a conscious creature called numerical unity. God does not count through items but knows collectively through one form and act. These uses distinguish enumeration and potential progression from unified divine cognition without offering modern set theory.

Finally, III.1.23 explains the Pythagorean riddle, used by Xenocrates, that soul is a self-moving number. Ficino glosses number as a manifold nature and self-moving as mutable through its own characteristic power. Soul is not absolutely simple unity as God is, and unlike angelic multiplicity it has temporal movement. The five grades are likewise distinguished by different relations of one and many. This particular numerical phrase therefore characterizes soul's composition and activity; it does not reduce a person to an integer or require a hidden calculation.

Further passage references. I.3.12–I.3.1423; I.5.20–I.5.272345678; I.6.4–I.6.52; II.2.7–82; II.4.4; II.10.3–42; II.10.7–10234; III.1.1–82345678; III.1.23.

Places to read

1. II.2.7Many humans and horses are gathered under their respective species-unities
2. II.10.4Unity is hypothetically imagined as knowing its potentially contained numbers
3. II.10.7Indefinitely extendable human thought supports the argument against limited divine knowledge
4. II.10.10Divine cognition does not enumerate step by step
5. III.1.23Self-moving number is glossed as manifold nature mutable by its own property

Translation in this edition

The formula numerum se moventem at III.1.23 is immediately explained, so it should not be literalized into a moving integer. At II.10.4 conscious numerical unity is hypothetical. At II.10.10 enumerando contrasts with a gathered intellectual act rather than proving the absence of distinctions.

numerus / unicus / unire

numerus / unicus / unire. Printed forms: numeri; numero; numerorum; numeros; numerum; numerus; unicum.

Number, uniqueness, and uniting, with numerical and substantial unity distinguished. Human numerical progress is indefinitely extendable; God’s uniqueness is not just occupying first place in a count. References: II.2.7, II.4.4, II.10.4, II.10.7. See Number.

Avicenna (authorities and cited works)

Avicenna. Named in the discussion of the principal angelic minds and their number, and with Algazeles in support of celestial animation. I.5.20; IV.1.88. See Angel; Number; Spheres and stars.

Daniel (authorities and cited works)

Daniel. The prophetic saying concerning innumerable attendants supplies support for angelic abundance. Ficino places it beside discussion of Dionysius and angelic orders. I.5.27. See Angel; Number.

Dionysius the Areopagite (authorities and cited works)

Dionysius the Areopagite. Cited concerning the abundance of separate intellectual species and the numerical orders of angels. Ficino's account connects these classifications with Iamblichus and Proclus. I.5.27. See Angel; Number.

Pythagoras and the Pythagoreans (authorities and cited works)

Pythagoras and the Pythagoreans. Provide compact numerical descriptions of the five grades, soul as self-moving number, and the explicitly marked twelvefold excursion. Apollo's name is interpreted through attributed wordplay. I.2.7; III.1.1–52345, III.1.23; IV.1.40–522345678910111213. See Number; Unity and multiplicity; Twelve; Apollo.

Xenocrates (authorities and cited works)

Xenocrates. Named as using the Pythagorean definition of soul as self-moving number. Ficino glosses number as manifold nature and self-moving as mutable through its own property. III.1.23. See Number; Motion and stability.

Use in the book

After the shadow examples Ficino urges a return into oneself, calling spirit immeasurably broad and body infinitely narrow “if I may speak so.” Numbers approach spiritual nature because they lack position and can number both incorporeal and corporeal objects according to form. They increase without end but do not decrease without end: the downward series reaches unity. Magnitude, in contrast, is given a maximum extension but no final minimum of division.

This is a contrast between indefinite numerical multiplication and the indefinitely divisible finite body, not a claim that all mathematical quantities have identical limits. The assumptions are the passage’s philosophical mathematics, and the rhetoric of infinity must follow the indicated direction. The subsequent geometric ascent likewise distinguishes quantity from power. An indivisible substantial unity can be great in virtus without being great in quantitas. Spiritual amplitude therefore concerns scope and effective independence, not an invisible larger body.

Places to read

1. VI.2.6Number and magnitude run in opposite directions with respect to unlimited increase and decrease.
2. VI.2.19, VI.2.20The geometric ascent culminates in greatness of power without greatness of quantity.
3. VI.12.2, VI.12.3Potential divisibility must later be distinguished from an actually infinite multitude.

Translation in this edition

The apparatus explicitly declines to rationalize away the opposed directions of number and magnitude. “Infinite narrowness” carries ut ita loquar, and “numbers approach spiritual nature” should not be silently strengthened into an identity between numbers and souls.

amplitudo; angustia

amplitudo; angustia. Printed forms: amplitudinem; angustiam; angustiis.

Breadth and confinement, paradoxically opposed between spirit and body. Spiritual amplitude is not physical extension; the passage qualifies its infinite narrowness metaphor with ut ita loquar. References: VI.2.6. See Number and spiritual amplitude.

magnitudo; crescere; decrescere

magnitudo; crescere; decrescere. Printed forms: augmenti; crescunt; decrementi; decrescunt; Magnitudo.

Magnitude and increase or decrease. Numbers increase indefinitely but terminate downward at unity; finite magnitude has no terminal minimum of division in Ficino’s contrast. References: VI.2.6. See Number and spiritual amplitude.

metiri; numerare

metiri; numerare. Printed forms: metiantur; numerentque.

To measure and to number. These functions concern form and apply across bodily and incorporeal objects in the mathematical analogy. References: VI.2.6. See Number and spiritual amplitude.

numerus; replicatio

numerus; replicatio. Printed forms: Numeri; numeri; replicationes.

Numbers and repeated expressions of unity. Numbers lack position and number bodily and incorporeal objects, so they approach spiritual nature. References: VI.2.6. See Number and spiritual amplitude.