Division and indivisibility

Use in the book

The lengthy divisibility argument distinguishes visible, imaginable, and mathematically conceivable parts. A later question proposes a more careful formulation: matter is not divisible into infinitely many imaginable parts, but into a multitude whose infinity can be conceived. The monad passage, meanwhile, pictures a bounded yet indivisible soul through a soap bubble. Physics divided analytically into parts can display apparent incoherence where synthesis shows order. None of these contrasts should be flattened into the claim that Joubert simply denies division.

Places to read

1. I, p. 229, entry 5, ¶1Several meanings of infinite division are interrogated.
2. I, p. 437, entry 3, ¶7A question distinguishes imaginable parts from conceivable infinity.
3. I, p. 236, entry 3, ¶1The monad provides a bounded image of indivisibility.
4. II, p. 768, entry 8, ¶1Analytical division and synthetic order display different aspects.

Translation in this edition

The English translation preserves the questioning form of the later formulation and the distinction between conceive and imagine. These are arguments in the notebooks, not certifications of modern mathematical conclusions.

Use in the book

Philoponus at A872 argues that passages cannot run continuously through the entire body, since all body would then be passage and void. He concludes that there must be solid indivisible portions touching one another and empty intervals between them. This is what he thinks Empedocles must say, not a preserved statement in which Empedocles calls his own constituents indivisible.

Aëtius at A43 supplies a different claim: smallest fragments and masses precede or compose the four elements. The two notices can be compared, but they do not amount to a secure atomic doctrine when combined. Elsewhere in A872 Philoponus explicitly distinguishes occupied passages from void, and the edition notes that no quoted fragment confirms the sub-elemental particle hierarchy.

The Lucretius appendix’s modern note summarizes an opposite critical tradition, that Empedocles allowed no limit to division. The relevant ancient lines are not printed in the appendix. Their evidential status within this particular edition is therefore a report by the editor about the following refutation, not directly inspectable ancient wording. The disagreement is worth retaining rather than choosing one side as a settled physical commitment.

Places to read

1. A 87 (polemical)2Philoponus, On Coming-to-be and Passing-away. Infers indivisible solids as a required consequence of the pore account.
2. A 43 (testimony)Aëtius I 13,1 and I 17,3. Attributes least fragments and masses below the four elements without a full divisibility argument.
3. Appendix I Lucretius (apparatus)Modern editor, commentary after On the Nature of Things I 734–741. Summarizes an unprinted accusation that the elements admit unrestricted division.

Translation in this edition

Neither “small” nor “least” should automatically be translated “atom.” The apparent conflict in the dossier partly reflects differences between reported doctrine, critical inference and editorial summary.

Use in the book

The Latin individuus generally means undivided or indivisible here, rather than an individual person. Ficino distinguishes spatial division, temporal succession, qualitative determination, and intelligible composition; none should be substituted automatically for the others.

Quality supplies an initially qualified case. In I.2.17, dividing a white body leaves the character of whiteness in each piece, so the argument distinguishes the whiteness of a part from a part of whiteness. Yet quality remains dependent upon its bodily subject. III.2.11, explicitly appealing to natural philosophers, instead describes whiteness as extended and divided along with flesh, a larger portion of flesh containing a larger portion of whiteness. The first argument emphasizes the retained qualitative character, while the second invokes a received account of quantitative distribution. Their differing emphases and attribution should remain visible rather than being turned into one unqualified formula.

Soul's indivisibility is substantial. It is wholly present to every bodily part, and its communicated life or vital shadow extends throughout the divided body without cutting the soul into portions. This helps explain its inability to dissolve into bodily components. Similarly, unity present throughout a whole cannot itself be portioned out without requiring another unifier. Nonetheless, indivisibility is not absolute divine simplicity: angelic nature can be free of bodily division while containing distinctions of essence, being, understanding, and objects understood.

Soul can also be called divisible in three qualified respects. Its vital shadow is communicated to a divisible body; its operations are distributed through successive moments; and it inclines toward lower realities that are themselves divided. Correspondingly it remains indivisible in its whole presence, stable substance, and orientation toward higher unified realities. The formula that soul is both divisible and indivisible identifies its middle status between beings divided by neither time nor dimension and lower things subject to both. Ficino relates it to Timaeus of Locri and Plato. It does not assert that soul's substance is at once physically cut into pieces and uncut.

Further passage references. I.2.17; I.3.13–I.3.16234, I.3.29–I.3.332345; I.6.4–I.6.52; III.1.2–5234; III.2.9–22234567891011121314.

Places to read

1. I.2.17Whiteness of each divided bodily part retains its qualitative character
2. III.2.11The received account of whiteness distributed with flesh supplies a contrast to soul
3. III.2.19Soul’s whole presence and stable substance coexist with divided bodily effects and successive activity
4. III.2.22The divisible–indivisible formula is linked to Timaeus of Locri and Plato

Translation in this edition

I.2.17’s partis albedo, “whiteness of a part,” is opposed to pars albedinis, “a part of whiteness.” III.2.11 presents the latter language under secundum physicos, “according to natural philosophers.” Keep that attribution and difference in argumentative emphasis rather than silently forcing both into one formula.

discursio / discerptio family

discursio / discerptio family. Printed forms: discerptam; discerptatur; discursione.

Temporal running-through / tearing into parts. Soul’s successive operation is distinguished from spatial dismemberment; the similar-looking words must not be conflated. References: III.2.21, III.2.22. See Indivisibility.

distinguere / dividere / divisio

distinguere / dividere / divisio. Printed forms: distinguunt; distinguuntur; dividatur; Divisio.

To distinguish or divide; logical determination differs from cutting into parts. Agents distinguish effects, modes distinguish individuals, and continuous quantity is indefinitely divisible. References: II.6.13, II.7.30, II.9.17, II.10.4. See Indivisibility.

dividuus / individuus

dividuus / individuus. Printed forms: dividua; Individua; individua.

Divisible / indivisible. Different respects must be specified: bodily manifestation, temporal activity, stable substance, and orientation to higher or lower objects. References: III.2.19. See Indivisibility.

punctum

punctum. Printed forms: puncta; puncto; punctum.

A point, used geometrically and as an image of indivisibility. Every temporal moment meets eternity’s point in the theory, as every location is said to meet eternal spirit. References: II.6.17, II.6.23. See Indivisibility.

punctum / adstrictus dimensionibus

punctum / adstrictus dimensionibus. Printed forms: adstricta dimensionibus; punctum.

A geometrical point; confined by dimensions. Soul's indivisibility differs from a point's localization; its whole presence enables movement of the whole heaven. References: IV.1.67. See Indivisibility.

Timaeus / Timaeus Locrus

Timaeus / Timaeus Locrus. Printed forms: Locrus; Timaeus.

Timaeus / Timaeus of Locri. The divine preservation knot is attributed to Timaeus; the divisible–indivisible soul account names Timaeus of Locri alongside Plato. References: III.1.5, III.2.22. See Indivisibility.

Timaeus; Timaeus of Locri (authorities and cited works)

Timaeus; Timaeus of Locri. An authority in the account of formless matter and the divine knot preserving otherwise dissoluble things. III.2.22 names Timaeus of Locri alongside Plato concerning soul's divisible and indivisible nature. Distinguish these references from the dialogue title Timaeus. I.3.19; III.1.5; III.2.22. See Matter; Bond, knot, and chain; Indivisibility.

Timaeus (authorities and cited works)

Timaeus. Invoked for divine will and goodness, intellectual ordering, the joining of mind to soul and soul to body, and soul's intermediate composition. II.11.26–272, II.11.38; II.13.3; III.2.22; IV.1.29. See Will; Indivisibility; Degree and mediation.

Use in the book

V.6 asks how a divisible thing could touch an indivisible one. If contact occurs only through a point, the contacting term is itself indivisible, not the divisible body as such. If it occurs through a divisible part, then the contacted thing must correspondingly have parts touched. It would cease to be the indivisible term initially asserted. Ficino takes this dilemma to rule out the soul’s receiving divisible qualities.

He extends the exclusion to direct and reflected contact. Soul neither admits an opposed bodily quality head-on nor is swept along by qualities raging within a body. This is a metaphysical analysis of soul-body interaction, rather than a detailed theory of optical rays. The reflected line illustrates indirect bodily disturbance, which he also refuses to make destructive of essence.

The passage then tests an objection: could an indivisible quality cause corruption instead? Ficino answers that reception of indivisible forms perfects its recipient, as images are received in water, mirrors and the soul without destroying them. A bodily agent seeks to propagate its own form, but a corporeal form has no entry into immaterial essence. A superior source either produces a self-subsistent form separately or communicates a beneficent power. Neither alternative destroys the soul.

The argument excludes particular modes of corruption; it does not make soul incapable of cognition or every relation. Its distinction between a material quality and an image of that quality is indispensable.

Places to read

1. V.5.9Absence of quantitative parts prepares the contact argument.
2. V.6.1The point/part dilemma, direct/reflected contact and nondestructive reception occupy the complete chapter.
3. V.8.3The later reception argument repeats water and mirror examples.

Translation in this edition

The apparatus treats V.6 as one source paragraph, despite the many internal inferences. Individuum must retain the indivisibility sense. The first-printing correction impetu et furore replaces impetu a furore in the language of bodily disturbance.

dividuum / divisibilis

dividuum / divisibilis. Printed forms: dividua; divisibile; divisibilem; divisibilis.

Divisible, admitting quantitative parts. A divisible contact would require corresponding divisible parts in the thing touched, contrary to the hypothesis about soul. References: V.6.1. See Indivisibility and contact.

indivisibilis / individuum

indivisibilis / individuum. Printed forms: individua; individuam; individuum; indivisibile; indivisibilem; indivisibili; indivisibilis; indivisibilium.

Indivisible, without separable quantitative parts. The contact dilemma turns on this property; individuum here should not be mistaken for the modern notion of a person. References: V.6.1. See Indivisibility and contact.

pars / particula

pars / particula. Printed forms: pars; parte; partem; Partes; partes; partibus; particulas; partium.

A part, or smaller part, of a quantitatively divisible whole. Matter's own nature precedes quantitative parts, while bodily parts can be divided without ceasing to belong to the bodily order. References: V.4.5, V.4.9, V.6.1, V.15.1. See Indivisibility and contact.

punctum

punctum. Printed forms: puncta; Puncta; punctis; puncto; punctorum; punctum; Punctum.

A point, the indivisible boundary invoked in the contact argument. If only a point touches the indivisible, the divisible body as such is not the contacting term. References: V.6.1. See Indivisibility and contact.

A nonextended limit of magnitude; it is not an independently actual microscopic body. The three-point dilemma shows why juxtaposed points cannot supply extension or an independent bodily seat for intelligence. References: VIII.4.1, VIII.4.2, VIII.5.1. See Bodily points and the seat of understanding.

rectus / reflexus

rectus / reflexus. Printed forms: rectam lineam; reflexam.

Direct and reflected, two proposed routes of bodily contact or disturbance. Ficino excludes both direct reception of a contrary and indirect capture by qualities raging in body. References: V.6.1. See Indivisibility and contact.

tangere

tangere. Printed forms: tangatur; tangi; tangit; tangitur.

To touch, the proposed physical route by which a bodily quality could affect soul. Ficino tests point-contact and divisible-part contact before distinguishing nondestructive reception of images. References: V.6.1. See Indivisibility and contact.

To touch or make contact. Contact at a line’s endpoints is hypothetical; a touch at a tiny bodily point supplies the whole-awareness example. References: VII.2.2, VII.5.2. See Whole presence and vital intensity.