Point, line and the comparing power · Lexicon

From the book

Marsilio Ficino’s Platonic Theology, Volume II

Marsilio Ficino · Diotimos Editions · 2026

Orientation

At a Glance

The wordThe point and line are argumentative models for indivisibility and extension.
In the Platonic TheologyFicino asks whether the single comparing power is an indivisible point a or a line extending from a to b. Suppose color reaches a alone and voice b alone.
In this editionThe apparatus identifies VII.2.2 as an editorial subdivision within one original source paragraph.
A place to readThe a–b model tests separate and shared reception of color and voice.

Meaning

The point and line are argumentative models for indivisibility and extension. Terminus is an endpoint here, not the goal or limit of organic growth. Vacat altera means that the other power has nothing additional to do: it is redundant, not a physical empty space.

Use in the book

Ficino asks whether the single comparing power is an indivisible point a or a line extending from a to b. Suppose color reaches a alone and voice b alone. Each endpoint then knows its own object and remains ignorant of the other; comparison is not produced. Suppose instead both contents reach both endpoints. Either endpoint already possesses what comparison requires, so the other contributes nothing. Moreover, each successful endpoint now functions as an indivisible power, which is precisely what the divided model was meant to avoid.

The argument is not a proof that a geometrical point is itself a soul. It uses the point’s lack of parts to expose the failure of a distributed knower whose parts have isolated contents. The book later expressly distinguishes soul from body, from a form spread through body, and from a point of such a form. An indivisible source present throughout a living body cannot be reduced to one localized extremity.

The repeated verbs of reaching, touching, crossing and converging make the dilemma vivid but belong to the hypothesis being tested. The conclusion is about unified judgement and the substance able to sustain it, not about trajectories of actual colored or sounded objects traveling along a diagram.

Places to read

VII.2.2The a–b model tests separate and shared reception of color and voice.
VII.5.3The whole soul is explicitly distinguished even from a point of a diffused bodily form.

Translation in this edition

The apparatus identifies VII.2.2 as an editorial subdivision within one original source paragraph. The geometric question therefore continues the two-power comparison of VII.2.1 rather than opening an unrelated mathematical proof. The corrected substantiae preserves the final power–substance relation.

a / b: geometrical labels

a / b: geometrical labels. Printed forms: a; b.

Labels of the endpoints in the hypothetical model of a line-shaped comparing power. The labels distinguish cognitive access at separate endpoints; they are not the names of substances or Latin technical nouns. The letter a also occurs independently as a preposition. References: VII.2.2. See Point, line and the comparing power.

caput / finis / terminus lineae

caput / finis / terminus lineae. Printed forms: caput; finem; termini; terminos; terminum.

Beginning, end and boundary of the hypothetical line. The terms mark cognitive separation in the model, not a literal route for colors or voices traveling inside soul. References: VII.2.2. See Point, line and the comparing power.

indivisibilis / individuus / partibilis

indivisibilis / individuus / partibilis. Printed forms: divisa; individuum; indivisibiles; indivisibilis; partibilem.

Undivided or divisible into parts. The successful comparing power cannot distribute its compared contents among mutually ignorant portions. References: VII.2.2. See Point, line and the comparing power.

pervenire / transire / concurrere

pervenire / transire / concurrere. Printed forms: concurrere; pervenit; transit.

To arrive, cross over and converge. The dilemma contrasts one content reaching one endpoint with both contents converging on both endpoints. References: VII.2.2. See Point, line and the comparing power.

punctum / linea

punctum / linea. Printed forms: linea; lineae; lineam; punctum.

An indivisible point and an extended line used as rival models. The a–b model asks whether separate or shared access at endpoints can explain one comparison. A point is not thereby identified with soul. References: VII.2.2. See Point, line and the comparing power.

vacare

vacare. Printed forms: Vacat altera.

The other power is idle or redundant. One endpoint’s comprehensive perception would do as much as both, so a second contributes no additional comparative work. References: VII.2.2. See Point, line and the comparing power.