Summary — PART III — COMMENTARY ON ARISTOTLE’S DE ANIMA¶
Analytical Synopsis of Sentencia libri De anima (c. 1267–1268)
Executive Thesis¶
In the Sentencia libri De anima (c. 1267–1268), Thomas Aquinas provides the psychological and cognitive complement to the epistemological division of the sciences established in Super Boetium De Trinitate and the demonstrative logic of the Expositio libri Posteriorum Analyticorum. Whereas logic examines how geometric conclusions flow from immediate principles and metaphysics examines the ontological status of continuous quantity, psychology investigates the incarnate acts by which a human soul united to a body abstracts exact mathematical forms without forfeiting contact with spatial extension. Across the three books of the commentary, Aquinas traces an unbroken arc from the critique of Platonic-Pythagorean reifications of points and numbers (Book I, Lecture 11) and the physics of fluent being in sensory media (Book II, Lecture 16) to the mature doctrine of intelligible matter, turning to the phantasms, and the soul as an intellectual instrument analogous to the human hand (Book III, Lectures 8, 12, and 13).
The pivot of this psychological noetics appears in Book III, Lecture 8 (Pirotta nos. 705–716), where Aquinas establishes the structural proportion governing natural and mathematical definitions: flesh and bones stand to the snub just as the extended continuum—which Aquinas identifies as intelligible matter (materia intelligibilis)—stands to the straight. Because quantity inheres immediately in substance prior to sensible matter (qualities such as hot, cold, white, and black), the \ agent intellect can strip away every sensible quality without falsehood while retaining continuous quantity in the intellect as the individuating substrate of geometric figures. Consequently, just as several men share one specific humanity through diverse parcels of flesh and bones, numerically distinct congruent triangles share one mathematical \ quiddity through distinct parts of the continuum. Yet because the human intellect directly apprehends only the universal quiddity—like a line extended straight—it knows the singular geometric figure only indirectly by bending back in reflection upon the phantasm (redit super phantasmata).
Lectures 12 and 13 of Book III complete this architecture by demonstrating why turning to the phantasms (conversio ad phantasmata) is not merely a genetic stage in learning geometry, as \ Avicenna supposed, but a permanent structural requirement of every act of contemplation (Pirotta nos. 770–777, 790–791). Because \ phantasms stand to the intellective soul as sensible objects stand to external sense, the soul never understands without a phantasm—even when contemplating per se mathematical attributes such as curvature apart from flesh (nos. 780–783). Synthesizing \ Aristotle‘s comparison of the soul to the hand as the organ of organs (organum organorum) and the intellect as the form of forms (species specierum, nos. 789–791), Aquinas reveals human mathematical reason to be neither an angelic intuition of Platonic Ideas nor an empiricist tally of sensory approximations, but an abstractive insight that beholds universal necessity within the determinate spatial diagram.
Key Scholastic & Mathematical Concepts¶
Latin Term |
English Rendering |
Primary Locus |
Doctrinal & Geometric Significance |
|---|---|---|---|
materia intelligibilis |
intelligible matter |
|
Substance considered solely as subject to continuous quantity after all sensible qualities have been mentally removed; provides the intrinsic substrate included in mathematical definitions and the principle multiplying congruent individuals within a single geometric species. |
materia sensibilis |
sensible matter |
|
Corporeal matter subject to sensible qualities (hot, cold, white, black, resistant, soft); essential to natural definitions such as flesh or the snub, but excluded from mathematical definitions such as the curved or the straight. |
phantasma |
phantasm |
|
A particular likeness of a sensible magnitude preserved and formed in the imaginative power; stands to the intellect as the sensible object stands to sense and contains universal intelligibles in potency. |
conversio ad phantasmata (reditus super phantasmata) |
turning to the phantasms |
|
The reflexive return of the intellect upon imaginative representations, required both to know singulars indirectly (like a bent line) and to exercise habitual scientific knowledge in actual contemplation. |
carnes et ossa |
flesh and bones |
|
Common sensible matter included universally in the natural definition of man, while individual natural substances require determinate (‘this’) flesh and (‘these’) bones. |
simum |
the snub |
|
Aristotle’s canonical specimen of a natural form-in-matter (‘concavity in a nose’), whose very definition inseparably posits determinate sensible matter. |
rectum |
the straight |
|
The paradigmatic mathematical attribute whose definition abstracts from all sensible qualities yet necessarily includes the extended continuum as its intelligible matter. |
continuum |
continuum |
|
Unbroken quantitative extension divisible without limit and incapable of being composed from unextended points; serves in geometry as the intelligible matter underlying straightness, curvature, and figure. |
esse fluens (contra esse fixum et quiescens) |
fluent being |
|
The successive, motion-dependent mode of existence characteristic of sound and wave propagation in a medium, contrasted with the permanent and resting being (esse permanens et fixum) of static qualities and magnitudes. |
unitas positionem habens |
unit having position |
|
The classical definition distinguishing the geometric point—situated within the spatial continuum—from the pure arithmetic unit (unitas intellecta), which lacks site and position. |
organum organorum |
organ of organs |
|
Designation of the human hand, which replaces specialized animal appendages by crafting an open-ended array of external instruments; the bodily analogue of the rational soul. |
species specierum |
form of forms |
|
Aristotle’s title for the intellect (explicated by Aquinas as the power receptive of all intelligible forms), through which the human soul intentionally becomes ‘in a way all things’ without possessing any material form restricting its scope. |
Section-by-Section Analytical Breakdown¶
Book I, Lecture 11 — On Democritus’s Account of Motion and How Geometers Imagine a Moving Point Describing a Line¶
Read Primary Text: English (Lib. I, lect. 11) · Latin (Lib. I, lect. 11) · Commentary
In Lecture 11 (Pirotta nos. 168–177), Aquinas expounds \ Aristotle‘s refutation of Xenocrates’s definition of the soul as a ‘self-moving number.’ Aquinas structures the critique first around the substance of the soul through six dialectical arguments (nos. 169–174), and second around its shared philosophical absurdities and inability to ground psychic operations (nos. 175–177). Because a number resolves into units and a soul existing in a body must have spatial location, Xenocrates’s units collapse into ‘units having position’—that is, geometric points. Yet as proved in Physics VIII, every per se self-mover requires a distinction between a moving part and a moved part, which is impossible in an indivisible unit or point (no. 169). Crucially, in the second argument (no. 170), Aquinas invokes the Platonic-geometrical thesis that ‘the motion of a point makes a line, while a moved line makes a surface, and a surface a body,’ concluding that if the soul were a self-moving point, its motion would generate not biological life, but a mere geometric line.
Aquinas further demonstrates that treating the soul as number violates biological continuity—since adding or subtracting a unit alters the species of a number, whereas divided plants and segmented animals retain the same specific soul (no. 171)—and collapses Xenocrates’s mathematical idealism into \ Democritus‘s materialism of spherical soul-atoms, since quantified moving units differ only verbally from indivisible corpuscles (nos. 172, 176). Moreover, soul-points either duplicate the body’s own intrinsic points—allowing infinitely many indivisibles to occupy a single indivisible place—or are identical with them, rendering every body animate (nos. 173, 175), while points cannot be separated from lines and bodies as the intellective soul is separated (no. 174). Finally, weaving together number and motion fails the scientific criterion of definition (Posterior Analytics I), because neither discrete arithmetic nor local motion gives the slightest clue for deducing the soul’s proper operations of reasoning, pleasure, and sorrow (no. 177).
Key Theses:
A geometric point differs from an arithmetic unit solely by adding spatial position (unitas positionem habens, nos. 170, 173).
No indivisible unit or point can move itself per se, because self-motion requires distinct moving and moved parts (continuum, nos. 169, 172).
According to the kinematic mode of speaking used by Platonists and geometers, a moving point generates only a line, not life (no. 170).
Points and lines are ontological boundaries inseparable in real being from surfaces and bodies (no. 174).
A scientific definition must serve as the middle term demonstrating the subject’s per se attributes and operations, which ‘self-moving number’ wholly fails to do (no. 177).
Book II, Lecture 16 — On Sound in Act and Potency and Its Fluent Mode of Being in Motion¶
Read Primary Text: English (Lib. II, lect. 16) · Latin (Lib. II, lect. 16) · Commentary
In Lecture 16 (Pirotta nos. 438–449), Aquinas introduces \ Aristotle‘s treatise on the audible by solving a methodological puzzle: why does De Anima investigate the physical generation of sound, whereas earlier it treated color only insofar as color alters the transparent medium and sight? Aquinas replies with a foundational ontological distinction (no. 438): color, odor, flavor, and tangible qualities possess a ‘permanent and fixed being in their subject’ (esse permanens et fixum in suo subiecto), whereas sound is caused by motion and lacks any ‘fixed and resting being’ (esse fixum et quiescens), consisting instead in a dynamic alteration—what scholastic and neo-Thomist natural philosophy terms fluent being (esse fluens). Consequently, while sound exists in the resonant bell or bronze only in potency, sound in act exists solely in the moved medium and in the sense of hearing (nos. 439–440).
Aquinas then analyzes the triadic mechanics required to actualize sound—a striker, a resistant struck body, and a continuous fluid medium such as air or water (nos. 441–445)—showing that percussion must be swift enough to forestall the dispersion of the air so that the air is struck as a unified mass, like a swiftly struck heap of stones (no. 445). Turning to the secondary generation of sound in echoes (nos. 446–449), Aquinas models acoustic propagation geometrically upon the concentric circular waves (gyrationes) formed when a stone is cast into water: near the center of percussion the circles are small and forceful, while at greater radii they expand and weaken until they either vanish or rebound in the contrary direction from a smooth or concave obstacle, analogous to a rebounding sphere (nos. 446–448) and to the specular versus diffuse reflection of solar rays from polished bronze and water versus opaque bodies (no. 449).
Key Theses:
Unlike color and tangible qualities, which have permanent and fixed being in their subjects, sound has no resting act in the sounding body, but exists in act only in the motion of the medium and in hearing (nos. 438–440).
Actualized sound requires three concurrent principles: a hard, smooth striking body, a resistant struck body, and an undivided continuous medium whose dispersion is forestalled by velocity (nos. 441–445).
Acoustic propagation diffuses radially through air in concentric circular waves whose force diminishes with increasing circumference, parallel to ripples on struck water (nos. 446–447).
Echoes and ambient illumination obey parallel laws of reflection: every wave or ray rebounds, producing a distinct echo from concave enclosures and specular brightness from water or polished bronze, while diffuse reflection from opaque bodies prevents total darkness outside direct sunlight (nos. 448–449).
Book III, Lecture 8 — On the Object of the Intellect: Flesh and Bone vs. the Continuum, the Snub vs. the Straight, and Reflection upon the Phantasm¶
Read Primary Text: English (Lib. III, lect. 8) · Latin (Lib. III, lect. 8) · Commentary
Lecture 8 (Pirotta nos. 699–718) is Aquinas’s decisive psychological analysis of intellectual habit, mathematical abstraction, and the proper object of the human mind. Beginning with the transition of the possible intellect from pure potency to habitual science (first act) and actual contemplation (second act, nos. 699–703), Aquinas refutes \ Avicenna‘s claim that intelligible species are never stored in the possible intellect but must be freshly infused from a separate Agent Intelligence whenever we think (nos. 701–702). Moving to the object of the intellect (nos. 704–709), Aquinas invokes Metaphysics VII to distinguish simple immaterial forms—which are identical with their own quiddities—from composite forms in matter, where individuating principles lie outside the specific essence (‘Socrates is not his humanity,’ no. 705). Crucially, Aquinas extends hylomorphic composition from natural things to mathematics by distinguishing sensible matter from intelligible matter (nos. 706–707): because continuous quantity inheres immediately in substance prior to sensible qualities (white, black, hot, cold), the intellect can remove sensible qualities while retaining continuous quantity (continuum), thereby grounding numerically distinct individuals (such as multiple congruent triangles) within a single mathematical species.
Aquinas then maps cognitive powers onto these ontological levels through a double analogy (nos. 710–716). Just as natural definitions include common sensible matter (flesh and bones for man, the nose for the snub) while abstracting from this flesh and these bones, mathematical definitions include intelligible matter (the continuum for the straight and the curved) while abstracting from sensible qualities altogether (nos. 713–716). To compare universal essences with singular instances, one and the same intellective soul knows both in distinct modes, illustrated by \ Aristotle‘s geometric simile of the bent line (circumflexa, nos. 711–712): extended straight, the intellect directly apprehends the universal \ quiddity; bent back in reflection upon the phantasms (redit super phantasmata), it indirectly knows the singular. Aquinas concludes by refuting three rival epistemologies at once: Platonic realism, which confuses abstraction in thought with separation in real being (nos. 716); representationalism, since the intelligible species is not what is known (quod) but that by which (quo) the extramental quiddity is known (no. 717); and Averroist monopsychism, since numerically distinct intellects share one understood truth through distinct species representing the same real nature (no. 718).
Key Theses:
Habitual science (actus primus) preserves intelligible species in the possible intellect midway between pure potency and actual operation (actus secundus), refuting Avicenna’s separate Agent Intelligence (nos. 700–702).
Continuous quantity inheres in substance prior to sensible qualities; when sensible qualities are mentally removed, substance under continuous quantity remains in the intellect as intelligible matter (nos. 706–707).
The straight stands to the continuum (intelligible matter) just as the snub stands to the nose and man stands to flesh and bones (sensible matter), explaining why multiple triangles exist within a single geometric species (nos. 707, 713, 715).
Like a line extended straight and bent back upon itself, the intellect directly apprehends universal quiddities and indirectly knows singulars by reflecting upon the phantasms (nos. 711–712).
Intelligible species are the formal medium by which (quo) reality is understood, not the primary object which (quod) is understood, overturning both Platonism and Averroist monopsychism (nos. 716–718).
Book III, Lecture 12 — Why the Soul Never Understands Without a Phantasm and How Mathematical Entities Are Understood in Abstraction¶
Read Primary Text: English (Lib. III, lect. 12) · Latin (Lib. III, lect. 12) · Commentary
In Lecture 12 (Pirotta nos. 764–785), Aquinas examines the operation of the intellect in comparison with sensation and appetite. First, he distinguishes physical motion (actus imperfecti, a transitive passage from contrary to contrary that destroys the prior quality) from cognitive and volitional operation (actus perfecti, the immanent activity of a power already perfected by its species, nos. 764–765). While simple sensation parallels intellectual apprehension, sense quasi-affirms or quasi-denies only particular pleasure and pain through the ‘sensitive mean’—likened geometrically to the center of a circle at which all radii from the external senses converge (nos. 766–768, 772)—whereas the intellect strictly affirms and denies universal truth and moves the rational appetite immediately toward universal good (nos. 769–771). From the proportionality sensibles : sense :: phantasms : intellect, Aquinas draws \ Aristotle‘s cardinal psychological law: ‘the soul cannot understand without a \ phantasm‘ (no. 771), reinforcing the unity of the judging intellect through the Euclidean alternation of proportions (permutatio proportionum, a : b :: c : d implies a : c :: b : d, no. 775) and showing how deliberation calculates future contingencies in phantasms as though visually present (nos. 776–779).
Having established the universal necessity of phantasms, Aquinas confronts the crucial test case of mathematics (nos. 780–785): how can an intellect bound to sensory phantasms understand entities separated from sensible qualities? Invoking the principle that ‘there is no falsehood in those who abstract,’ Aquinas distinguishes judging two conjoined things to exist separately (which would be false) from understanding one apart from the other when the latter does not enter its definition (nos. 780–781). Unlike the snub, whose definition includes the sensible nose, curvature does not include flesh in its definition; hence the intellect actually understands the curved without understanding flesh, contemplating mathematical entities ‘as though they were separated, even though they are not separated in reality’ (nos. 781–782). \ Plato‘s failure to grasp this abstractive precision forced him to posit subsistent Mathematicals and Forms, whereas Aristotle posited the \ agent intellect (no. 783). Aquinas closes by deferring the metaphysical question of whether our embodied intellect can know wholly immaterial substances (nos. 784–785).
Key Theses:
Sensing and understanding are not physical alterations (actus imperfecti) but immanent operations of a perfected power (actus perfecti, nos. 764–765).
Both the common sense and the intellect act as an indivisible discriminating center to which diverse sensory lines or phantasms converge, verified by alternation of proportions (a : b :: c : d, nos. 767, 772–775).
Because phantasms stand to the intellective soul as sensibles stand to sense, the human soul never understands without a phantasm (no. 771).
Mathematical abstraction involves no falsehood because the intellect understands the curved without thinking of flesh—not by judging curvature to subsist apart from sensible bodies, a confusion that led Plato to posit separate Forms in place of the agent intellect (nos. 780–783).
Book III, Lecture 13 — How the Soul Is in a Way All Things, the Hand the Organ of Organs, and the Intellect the Form of Forms¶
Read Primary Text: English (Lib. III, lect. 13) · Latin (Lib. III, lect. 13) · Commentary
In Lecture 13 (Pirotta nos. 786–793), Aquinas synthesizes the entire noetics of De Anima around two master theses: how the rational soul is intentionally ‘all things,’ and why human intellection depends intrinsically upon sense and imagination even after scientific habits have been acquired. Recapitulating earlier Greek philosophy (nos. 786–788), Aquinas affirms that the soul is ‘in a way all things’—sensible through sense and intelligible through intellect—not materially, as Empedocles imagined (‘knowing stone by an internal stone’), but intentionally through immaterial species (‘a stone is not in the soul, but the species of the stone,’ no. 788). Hence the soul corresponds to the human hand (no. 789): just as nature gave humanity the hand as the organ of organs (organum organorum) in place of fixed claws, horns, or pelts so that humans might fashion universal instruments for every purpose, so the soul is given in place of fixed innate forms as receptive of all sensible and intelligible forms—making the intellect the form of forms (species specierum).
In the second half of the lecture (nos. 790–793), Aquinas forestalls any Platonist or Avicennian inference that this universal receptivity emancipates human thought from bodily magnitudes. Because neither natural attributes nor mathematical abstractions (ea quae dicuntur per abstractionem) subsist outside sensible magnitudes in reality, no human being can either learn science initially or exercise already-acquired science (utens scientia habita) without simultaneously forming and inspecting a phantasm (no. 790). Against \ Avicenna‘s claim that habitual science dispenses with sense and imagination, Aquinas adduces empirical clinical proof: lesion of the bodily organ of imagination impedes the actual use of previously mastered science (no. 791). Nevertheless, intellectual concepts (primi intellectus) are never reducible to \ phantasms: imagination neither combines concepts into true or false judgments (no. 792) nor represents universals as such, for phantasms depict singulars and contain universal indivisibles only in potency, not in act (no. 793).
Key Theses:
The soul is ‘in a way all things’ not materially like Empedocles’s elements, but intentionally by receiving the sensible and intelligible species of things without matter (nos. 786–788).
Just as the hand is the organ of organs (organum organorum) enabling man to craft every tool, the soul stands in place of all forms, with the intellect functioning as the form of forms (species specierum) receptive of all intelligibles (no. 789).
Because mathematical and natural intelligibles exist ontologically only within sensible magnitudes, both initial discovery and the actual contemplation of habitual science require forming a phantasm (nos. 790–791).
Against Avicenna, bodily lesion of the imaginative organ blocks the exercise of already-acquired science, proving permanent dependence on turning to the phantasms (no. 791).
Primary intellectual concepts are not phantasms, though never without them: phantasms represent particulars and are universal indivisibles only in potency, while truth and falsehood belong to intellectual judgment alone (nos. 792–793).