Infinite operations and the limits of sensory kinds

Use in the book

Ficino begins with inward circularity. Intellect understands itself, so its activity returns to its own substance rather than ending at an external acquisition whose attainment would stop it. Desire for itself continues to animate this return. He calls the movement everlasting insofar as it is intellectual. Reflection also permits another act beyond any one assigned: knowing something, knowing that one knows it and noticing that notice. Rational appetite, will, has a corresponding recursive range. The earlier chapter allows either successive higher-order acts or one act repeatedly folded upon itself, without settling on a single mechanism.

The catalogue then turns outward. Mind divides bodies further, increases numbers, explores figures and proportions, extends lines beyond the heavens, thinks earlier and later times, conceives wider places and further degrees of qualities. Sight is confined to colour and hearing to sound, but mind compares these classes and reaches beyond any one of them. Past and future enlarge the temporal field; unrealized possibilities and imagined impossibilities enlarge the represented field. Conceiving them does not verify that they exist or even that they are possible. The next unit says that inward products have a reality as representations, comparable to words in air or paintings on a wall, rather than making every depicted object externally actual.

These forms of indefinite reach must be distinguished from the actual simultaneous infinity rejected earlier. In VIII.4.2, a bodily-point theory cannot privilege one potential point as receiver, so it generates infinitely many simultaneously actual forms or acts. In VIII.4.4, repeated bodily division of genus and difference would destroy the bounded comprehensibility of a definition. Those are consequences used against particular hypotheses. VIII.16's indefinitely repeatable operation does not require every extension to have been completed at once, and its universal account can cover indefinitely many instances without enumerating them one by one.

Other senses enter through the ascent beyond finite angels. Whatever finite grade thought has reached, it can conceive a higher one; the regress ends only with an infinite spirit beyond every actual or conceivable finite angel. God is then named infinite act, while matter is infinite potency expressly subject to God and receptive to innumerable forms. This is not a pair of independent equal first principles. The gathering of individuals into species, species into genera and genera toward divine unity supplies yet another route: the many are one in an intelligible account, not physically compressed into one body.

VIII.16.3 adds an argument from proportionate knowledge. To define infinity, mind must in some manner correspond to what it knows. Ficino infers a qualified infinite power from that premise; this is not a modern theorem that defining infinity gives a thinker infinitely much information. The conceptual passage between being and nonbeing provides a further example of unmeasured reach without making nonbeing a spatial region. The argument then changes from cognition to appetite: finite human achievements and knowledge of created things never completely fill the mind's desire, so only infinite God is said to be adequate to it.

The final account is asymmetrical. God's infinity is absolute; mind's intellectual and vital infinity is communicated. Ficino explicitly corrects self-owned power to a divine enlargement continually implanted and preserved. The inference to limitless duration therefore concerns a granted capacity, not an independent infinite substance. Because life is prior in origin to intelligence, he argues that a mind given such scope in understanding and willing must have received an unbounded power of living even more fundamentally. Arithmetic extension, recursive thought, common universals, cognition of infinity and desire for the infinite contribute distinct premises. None should be silently substituted for the whole cumulative argument, and none establishes exhaustive human possession of divine knowledge.

Places to read

1. VIII.4.2An actually infinite simultaneous multiplicity belongs to a rejected bodily hypothesis.
2. VIII.16.1Self-revolution and recursive willing lead into the complete catalogue of unbounded intellectual range.
3. VIII.16.2The ontological status of inward representations and qualified infinity are developed.

Translation in this edition

The text includes quasi, quatenus intellectualis est, forsitan and quodammodo. The apparatus reports the correction from odoribus to coloribus in the sight example. The qualifiers prevent the rhetoric of infinity from becoming an unqualified equation of human mind with God.

aviditas / cupiditas

aviditas / cupiditas. Printed forms: avida; aviditas; cupiditate.

Eager desire for oneself, the motive sustaining inward intellectual return. Ficino treats mind's desire for its own nature as enduring; this technical self-relation is not a clinical description of narcissism. References: VIII.16.1. See Infinite operations and the limits of sensory kinds.

finis (end and absence of end)

finis (end and absence of end). Printed forms: fine; finem; finibus; finis.

An end, goal or limit, including the negation of a final limit. Infinity as endless continuation differs from the infinite end that stops the ascent beyond finite angels; both uses appear in the closing chapter. References: VIII.1.3, VIII.3.6, VIII.3.7, VIII.4.4, VIII.10.2, VIII.15.1, VIII.15.2, VIII.15.3, VIII.16.1, VIII.16.4. See Infinite operations and the limits of sensory kinds.

forte / forsitan / si modo

forte / forsitan / si modo. Printed forms: forsitan; forte; si modo.

Perhaps and provided that, marking conjecture or a stated condition. The text qualifies mathematical bodies, the possibility of invented objects and the premise that knowledge matches its object; these are not flat unconditional assertions. References: VIII.2.7, VIII.4.12, VIII.4.13, VIII.16.1, VIII.16.3. See Infinite operations and the limits of sensory kinds.

infinitus / infinitas

infinitus / infinitas. Printed forms: infinita; infinitam; infinitas; infinitate; infinitatem; infinitati; infinite; infinitis; infinito; infinitos; Infinitum; infinitum; infinitus.

Without the relevant limit; the word's mode must be distinguished in each argument. Simultaneous actual infinity is rejected in the point hypothesis, while recursive range and received intellectual infinity are defended with qualifications. References: VIII.4.2, VIII.4.4, VIII.5.1, VIII.10.1, VIII.14.1, VIII.16.1, VIII.16.2, VIII.16.3, VIII.16.4. See Infinite operations and the limits of sensory kinds.

innumerabilis

innumerabilis. Printed forms: Innumerabiles; innumerabiles; innumerabilia; innumerabilibus; innumerabilis; innumerabiliter; innumere.

Countless or indefinitely many; often emphasizing a range rather than a counted completed total. It describes the many individuals under a universal and the excessive repetitions generated by the bodily cognition hypothesis. References: VIII.1.2, VIII.4.4, VIII.5.1, VIII.15.1, VIII.16.2. See Infinite operations and the limits of sensory kinds.

interminatus

interminatus. Printed forms: interminatam.

Unbounded or without a determinate limit in the specified respect. Ficino introduces the description cautiously, ut ita loquar, for mind’s power as it discovers and defines infinity. The subsequent conclusion remains qualified: intellectual scope is not identical with God’s absolute infinity or with a completed infinite multitude. References: VIII.16.3. See Infinite operations and the limits of sensory kinds.

numerus / figura / proportio

numerus / figura / proportio. Printed forms: comparationes; figura; figurae; Figurarum; figurarum; figuras; lineam; numeri; numeris; numerorum; Numeros; numeros; proportiones.

Numbers, figures, proportions, comparisons and an indefinitely extended line. The catalogue displays mental operations without an assigned final bound, not the completed calculation of an actual infinite set of results. References: VIII.2.7, VIII.4.3, VIII.4.7, VIII.4.10, VIII.4.11, VIII.14.1, VIII.16.1. See Infinite operations and the limits of sensory kinds.

per omnia

per omnia. Printed forms: per omnia.

Through all things, marking an unrestricted range across kinds of objects. The repeated phrase contrasts intellect with sight restricted to colours and hearing restricted to sounds. Its scope includes present, past and future things, unrealized possibilities and imagined impossibilities; representation does not establish external actuality or possibility. References: VIII.16.1. See Infinite operations and the limits of sensory kinds.

posse / fingere / excogitare

posse / fingere / excogitare. Printed forms: excogitat; fingit; numquam; possent; possunt.

Posse means to be able or possible; fingere means to fashion a representation, and excogitare to devise in thought. Numquam, never, qualifies the possibility of what is conceived. Conceiving an object demonstrates cognitive range, but does not verify its external possibility or actuality. References: VIII.16.1. See Infinite operations and the limits of sensory kinds.

quodammodo / quasi / ut ita loquar

quodammodo / quasi / ut ita loquar. Printed forms: quasi; quodammodo; ut ita dixerim; ut ita loquar.

In a certain manner, as if, and if one may speak so: qualifications of an image or claim. They moderate phantasy's incorporeality, mind's infinitude and several spatial metaphors, rather than licensing their removal in summary. References: VIII.1.1, VIII.1.2, VIII.5.1, VIII.7.1, VIII.14.1, VIII.16.3. See Infinite operations and the limits of sensory kinds.

replicare

replicare. Printed forms: replicatur.

Folding back or repeating an intellectual operation. Ficino allows either a succession of higher-order acts or one act repeatedly returning upon itself; no final level is assigned. References: VIII.15.1, VIII.16.1. See Infinite operations and the limits of sensory kinds.

revolutio / orbicularis

revolutio / orbicularis. Printed forms: circumeundo; circumvolutus; orbicularis; Revolutio; revolvitur.

Revolution, circular and circling, images of intellectual activity returning to itself. No external acquisition supplies a final resting point; the model concerns inward self-knowledge rather than the literal rotation of a brain or soul. References: VIII.16.1. See Infinite operations and the limits of sensory kinds.

solus (restrictive)

solus (restrictive). Printed forms: Sola; sola; solis; solo; solum.

Only or alone, restricting a subject, instrument or class of objects as syntax determines. Point alone, extent alone and sight confined to colours illustrate distinct restrictions. Solis can also be the sun's genitive elsewhere, and VIII.10.2 sola qualifies mind. References: VIII.5.1, VIII.10.2, VIII.16.1. See Infinite operations and the limits of sensory kinds.

terminus / terminare

terminus / terminare. Printed forms: terminabitur; terminat; terminatur; termino; terminum; terminus.

Boundary or endpoint; its sense ranges from spatial limit to the limit of a sequence or act. A point bounds magnitude, definition has limits, and inward intellectual motion lacks an externally acquired stopping point. References: VIII.4.1, VIII.4.2, VIII.4.4, VIII.14.1, VIII.15.1, VIII.15.3, VIII.16.1, VIII.16.2, VIII.16.3, VIII.16.4. See Infinite operations and the limits of sensory kinds.