Summary — PART V — COMMENTARY ON THE METAPHYSICS AND SYSTEMATIC WORKS¶
Analytical Synopsis of Sententia super Metaphysicam, Summa Theologiae, Quaestiones Disputatae de Potentia et de Veritate (c. 1256–1273)
Executive Thesis¶
Part V brings the entire Codex to its metaphysical and epistemological summit by uniting five foundational lectures from St. Thomas Aquinas’s Sententia super Metaphysicam (Books V, VII, and IX) with the systematic syntheses of the Summa Theologiae (Prima Pars, qq. 7, 12, 84, and 85), Quaestiones Disputatae de Potentia Dei (q. 7, a. 2), and Quaestiones Disputatae de Veritate (q. 10, a. 6). Whereas Parts I through IV charted the division of the speculative sciences, the apodictic structure of Euclidean demonstration, the psychological necessity of the spatial \ phantasm, and the physical ontology of the \ continuum, Part V grounds all of these doctrines in first philosophy. In Metaphysics V, lect. 9, Aquinas distinguishes real categorical being—contracted proportionally according to diverse modes of being (modi essendi) and predicating (modi praedicandi), with quantity following upon matter as the first intrinsic accident—from propositional being (esse as the verbal copula signifying the truth of judgment, illustrated by the falsity of the diagonal’s commensurability) and from the division of every category by potency and act (illustrated by the midpoint latent in potency within a continuous line). In Metaphysics VII, lect. 10–11, he resolves the Platonic-Pythagorean temptation to reduce geometric figures to pure numbers by establishing the hylomorphic analogy of mathematics: just as natural species require common \ sensible matter (flesh and bone) in their definition while abstracting from individual sensible matter, mathematical species such as the circle and the right angle dispense with sensible matter (bronze, stone, wood) yet require common materia intelligibilis (the continuum, lines, and surfaces) in their universal definition, while individual mathematical circles grasped in pure imagination are individuated by designated \ intelligible matter and posterior parts such as semicircles.
From the static definition of mathematical essences, Metaphysics IX shifts to the dynamic order of actuality and heuristic discovery. In Metaphysics IX, lect. 3, Aquinas defends real potentiality against Megarian necessitarianism and Protagorean relativism, establishes the modal law of conditional consequence alongside the impossibility of commensurability between the square’s diagonal and side, and formulates the genetic principle that the name and notion of actus (energeia) are first imposed upon sensible motion—what is first evident to us—and extended thence to higher actualities. In Metaphysics IX, lect. 10, this metaphysics of act yields the classical locus on constructive geometric discovery (inventio): geometers discover latent truths by dividing lines and surfaces (dividendo inveniunt), reducing potential constructions into act so that, once the side of a triangle is produced (\ Euclid Elements I.32) or the radius is drawn from the midpoint of the diameter to the circumference (Euclid Elements III.31), the necessary nexus becomes immediately manifest to one inspecting the figure (statim manifestum fit videnti dispositionem figurae). The systematic articles in Summa Theologiae I, q. 84, a. 6–7, q. 85, a. 1, and De Veritate q. 10, a. 6 supply the complete cognitive architecture of this insight: steering an Aristotelian middle course between Democritean materialism and Platonic-Avicennian extrinsicism, Aquinas demonstrates that phantasms serve as the materia causae and instrumental agent under the principal light of the intellectus agens, that actual understanding always requires conversio ad phantasmata to behold the universal nature in the particular exemplar, and that abstraction by simple and absolute consideration isolates mathematical quantity in materia intelligibilis communis without mendacity while implanting the habit of first indemonstrable principles.
Finally, Summa Theologiae I, q. 7, a. 1 and 3, q. 12, a. 4, and De Potentia q. 7, a. 2 crown the Codex with Aquinas’s existential metaphysics of ipsum esse. Contrasting the privative infinity of quantitative division—which approaches matter and underpins the geometer’s operational linea infinita—against the formal perfection of unreceived act, Aquinas declares that esse itself is most formal of all (maxime formale omnium) and, in the celebrated formula of De Potentia q. 7, a. 2, ad 9, the actuality of all acts and on account of this the perfection of all perfections (actualitas omnium actuum, et propter hoc perfectio omnium perfectionum). Because the human intellect can consider in abstraction what it knows in concretion (ST I, q. 12, a. 4, ad 3), resolving concrete composites into both form and esse, it grasps diverse proportional modes of being and affirms objective existential and formal nexuses in judgment. As Peter \ Hoenen S.J. demonstrated across La théorie du jugement d’après St. Thomas d’Aquin (1946) and De Noetica Geometriae (1954)—paralleled by Bernard \ Lonergan‘s Verbum (1967)—and as the GEOMETOR ecosystem realizes computationally across geometor.model, geometor.explorer, and geometor.divine, geometric construction in act is the privileged arena where human intelligence experiences pre-judgmental insight into necessary nexus within intelligible matter before sealing that discovery in rational judgment.
Key Scholastic & Mathematical Concepts¶
Latin Term |
English Rendering |
Primary Locus |
Doctrinal & Geometric Significance |
|---|---|---|---|
Modi essendi / modi praedicandi |
Modes of being and modes of predicating |
|
Establishes that ens is not a genus contracted by extrinsic differences, but analogically diversified into ten categories proportional to real modes of inherence, with quantity following intrinsically upon matter. |
Esse ut veritas propositionis |
Being as propositional truth |
|
Distinguishes the existential and categorical act of being in reality from the copulative est formed by the composing and dividing intellect to signify that an affirmation or negation—including mathematical impossibility or privation—is true. |
Materia intelligibilis communis et individualis |
Common and individual intelligible matter |
|
Defines substance insofar as it underlies pure continuous extension apart from sensible qualities: common intelligible matter (the continuum, lines, surfaces) enters universal geometric definitions, whereas individual intelligible matter individuates particular diagrams in imagination. |
Circulus mathematicus vs. circulus aeneus |
Mathematical circle vs. bronze circle |
|
Illustrates why sensible substrates (bronze, wood, stone) are excluded from geometric essences, yet plurality of equal lines and similar circles in pure phantasia proves that mathematical objects retain individual intelligible matter. |
Actus ex motu derivatus |
Actuality derived from sensible motion |
|
Explains why the name and intelligible conception of actus (energeia and entelecheia) originate from local and qualitative motion—the actuality most manifest to sense—and are analogically extended to immutable forms, intellectual operations, and esse. |
Inventio per divisionem in actu |
Geometric discovery by division in act |
|
Reveals the heuristic mechanism of constructive geometry: drawing auxiliary lines and circles actualizes divisions previously latent in the continuum’s potency, making demonstrative middle terms immediately visible in the diagram. |
Linea infinita geometrae |
The geometer’s infinite line |
|
Clarifies that Euclidean geometry never posits an actually infinite magnitude, which would violate the terminating nature of figura, but uses ‘infinite line’ operationally for an arbitrarily extensible finite segment. |
Resolutio concreti in abstractione |
Resolution of the concrete in abstraction |
|
Identifies the distinctive mark elevating intellect above sense: whereas sight perceives nature only as this concrete singular, created intellect resolves composites so as to consider both concrete form and concrete esse in abstraction. |
Materia causae / agens instrumentale |
Matter of the cause / instrumental agent |
|
Synthesizes sensory empiricism and intellectual immateriality: phantasms act as secondary, instrumental causes supplying determinate structural content, while the intellectus agens acts as principal cause conferring actual intelligibility. |
Conversio ad phantasmata |
Turning to the phantasms |
|
Demonstrates that even after abstracting habitual intelligible species, the embodied human intellect must turn to exemplar phantasms to inspect the universal nature existing in the particular—the exact psychological law governing mathematical diagrams. |
Abstractio per simplicem considerationem |
Abstraction by simple and absolute consideration |
|
Vindicates the truth of mathematics against Platonic hypostatization: considering quantity and figure without considering sensible qualities involves no false judgment of separation, because the mode of understanding follows the knower rather than the mode of material existence. |
Ipsum esse, actualitas omnium actuum |
Being itself, the actuality of all acts |
|
Establishes esse not as an empty genus or minimal substrate, but as the ultimate formal perfection actualizing every substantial and accidental form, contracted by quidditative potency in creatures and subsisting unreceived in God. |
Section-by-Section Analytical Breakdown¶
Metaphysics Book V, Lecture 9 — On the Division of Per Se Being into Ten Categories and Being Signified by Propositional Judgment¶
Read Primary Text: English (Metaph. V, lect. 9) · Latin (Metaph. V, lect. 9) · Commentary
Commenting on \ Aristotle‘s philosophical lexicon (Metaphysics Δ.7, 1017a7–b9), Aquinas distinguishes ens per accidens (accidental predication across a common subject) from ens per se, which he subdivides into three fundamental orders: first, extramental ens perfectum contracted proportionally into the ten categories according to diverse modes of predicating that track diverse modes of being (correcting \ Avicenna‘s claim that accidental terms primarily signify substance); second, intramental esse signified by the verbal copula of propositional composition and division, which expresses the truth of a statement as effect to extramental cause (illustrated by privations like blindness and the negation of the diagonal’s commensurability with the side of a square); and third, the division of all categories by potency and act, illustrated by the statue of Mercury in stone and the midpoint latent in potency within a continuous line.
Key Theses:
Being (ens) cannot be a genus contracted by extrinsic differences, because nothing lies outside being; instead, it contracts into the ten categories proportionally as modi praedicandi follow real modi essendi.
Quantity inheres in substance per se and absolutely as consequent upon matter, whereas quality follows upon form and relation regards another.
Propositional esse formed by the composing and dividing intellect signifies that a statement is true (quia aliquod dictum est verum), extending even to privations and mathematical impossibilities such as the incommensurability of the square’s diagonal.
Every category is divided by act and potency, just as every part of a continuum—such as the midpoint of a line—exists potentially in the whole prior to actual division.
Metaphysics Book VII, Lecture 10 — On Parts of the Form vs. Parts of Matter: Bronze Circle and Mathematical Circle in Intelligible Matter¶
Read Primary Text: English (Metaph. VII, lect. 10) · Latin (Metaph. VII, lect. 10) · Commentary
Expositing Metaphysics Z.10 (1034b20–1036a25), Aquinas resolves whether the parts of a whole are prior to the whole and enter its definition. He distinguishes parts of the form or ratio—which are prior to the composite and belong to the universal definition—from parts into which the concrete whole divides as into matter, which are posterior. Thus the acute angle is defined through the right angle and the semicircle through the circle, not conversely. Crucially, Aquinas distinguishes universal composites (which include common matter) from singular composites individuated by \ designated matter—not only sensible singulars (bronze or wooden circles) but also mathematical singulars (plural equal lines and similar circles grasped by pure phantasia), which are individuated by materia intelligibilis (the \ continuum, surface, or body) and cannot be defined as singulars once they recede from actual inspection.
Key Theses:
Formal parts belong to the quod quid erat esse and are prior to the defined whole, whereas material parts into which a figure is divided—such as the acute angle relative to the right angle or the semicircle relative to the circle—are posterior to the form and defined through it.
Definition belongs solely to the universal species, never to singulars, whether sensible (a bronze circle) or mathematical (this imagined circle), because matter in itself is unknowable save through the universal form.
Plurality within a single mathematical species—such as multiple equal lines or multiple similar figures—proves the existence of mathematical singulars apprehended apart from external sense by phantasia alone.
Intelligible matter (materia intelligibilis) exists in sensible things not insofar as they are sensible, but insofar as they are continuous magnitudes (continuum, surface, or three-dimensional body) underlying mathematical forms.
Metaphysics Book VII, Lecture 11 — How Mathematical Species Are Defined Without Sensible Matter Yet Not Without Common Intelligible Matter¶
Read Primary Text: English (Metaph. VII, lect. 11) · Latin (Metaph. VII, lect. 11) · Commentary
Continuing into Metaphysics Z.11 (1036a26–1037b7), Aquinas confronts the Platonic and Pythagorean error—including the misleading ‘parable of Socrates the Younger’—which argued that just as bronze forms no part of the circle’s essence, neither should flesh and bone belong to human essence nor continuous lines to the essence of the triangle and circle, thereby reducing all mathematical species to pure numbers (such as the dyad for the straight line). Aquinas refutes this hyper-formalism by showing it collapses diverse species sharing a number (a three-sided triangle, a three-term syllogism, a three-dimensional body) into a single species and ultimately reduces all reality to bare unity. Against this, he establishes that mathematical definitions exclude all \ sensible matter yet must retain \ common intelligible matter (lines and the \ continuum), while excluding \ individual intelligible matter (these particular lines or semicircles), so that only pure immaterial substances are wholly identical in reality with their quod quid erat esse.
Key Theses:
Eliminating intelligible matter (the continuum and lines) from geometric definitions reduces triangles and circles to abstract numbers, absurdly identifying a triangle (three lines), a syllogism (three terms), and a body (three dimensions) in species.
The ‘parable of Socrates the Younger’ errs by equating the relation of man to flesh and bone with that of a circle to bronze: natural species require sensible organs ordered to motion, whereas mathematical species abstract from sensible matter while retaining proportionate intelligible matter.
Semicircles are excluded from the universal definition of the circle not because they are sensible like bronze, but because they are material parts of singular circles in individual intelligible matter rather than formal parts of the universal species.
In extramental reality, any substance composed with matter—even if considered logically as universal—differs in the concrete individual from its abstract quiddity; only separate subsistent forms are strictly identical with their quod quid erat esse.
Metaphysics Book IX, Lecture 3 — How the Name and Notion of Actuality Are Derived First from Sensible Motion¶
Read Primary Text: English (Metaph. IX, lect. 3) · Latin (Metaph. IX, lect. 3) · Commentary
Commenting on Metaphysics Θ.3–4 (1046b29–1047b30), Aquinas first refutes the Megarian thesis that potency exists only when acting—showing that it abolishes habitual art and geometry, resurrects Protagorean subjectivism regarding sensible qualities, and destroys all motion and generation—and then refutes the opposite extreme that everything is possible even if impossible consequences follow, citing the geometric impossibility of the square’s diagonal being commensurable with its side. Between these extremes, he defines the possible as that from whose supposition nothing impossible follows, demonstrates the modal theorem that a possible antecedent in a valid conditional entails a possible consequent, and articulates the foundational epistemological principle that because names signify intelligible conceptions and we name first what we understand first, the name and notion of actus (energeia) were first imposed upon sensible motion and thence derived to form, operation, and existence.
Key Theses:
Collapsing potency into act abolishes habitual science and art, reduces sensible qualities to Protagorean appearances, and renders all generation and transition impossible.
Falsehood differs radically from impossibility: that Socrates stands when seated is contingently false yet possible, whereas the commensurability of a square’s diagonal with its side is both false and intrinsically impossible because positing it entails contradiction.
Since spoken names follow the order of human understanding rather than the order of nature, the concept and term actus are first grasped in sensible motion—the actuality most evident to us—and extended analogically to immutable actualities.
In any valid conditional if A, then B, taking possible as opposed to impossible, the possibility of the antecedent A necessarily entails the possibility of the consequent B.
Metaphysics Book IX, Lecture 10 — On Discovering Geometric Truth by Dividing Figures in Act (Euclid I.32 and III.31)¶
Read Primary Text: English (Metaph. IX, lect. 10) · Latin (Metaph. IX, lect. 10) · Commentary
Expositing Metaphysics Θ.9 (1051a4–33), Aquinas first shows why actuality is better than potency in good things (and worse in evils, excluding evil and corruption from eternal beings lacking potency) and then delivers the locus classicus of the entire Aristotelian-Thomistic tradition on geometric discovery (inventio). Geometric diagrams (diagrammata) are discovered in truth by dividing lines and surfaces in act (dividendo inveniunt). Because the parts and auxiliary relations of a \ continuum lie only in potency when a figure is first drawn, the sought theorem remains hidden; once the geometer actualizes those divisions—by extending the base of a triangle to form the exterior angle (\ Euclid I.32) or by bisecting the diameter at the center and drawing the radius to the vertex on the semicircle (Euclid III.31)—the conclusion becomes immediately manifest to one inspecting the figure, because the intellect itself is act and understands things insofar as they are brought into act.
Key Theses:
Geometers discover sought truths by dividing lines and surfaces, reducing into act structural relations that were merely latent in potency in the initial drawing of the figure.
In Euclid Elements I.32, producing side AC of triangle ABC actualizes the exterior angle at C, making it immediately evident (statim manifestum) from the equality of adjacent angles to two right angles that the interior angles equal two right angles.
In Euclid Elements III.31, dividing diameter AC at center D and drawing radius DB actualizes three equal radii (DA, DC, DB) and two isosceles triangles, rendering it immediately manifest to one who knows the principles of geometry that every angle inscribed in a semicircle is right.
Truth is discovered when potentiality is reduced to act because the intellect is itself act, and what is understood must exist in act—hence ‘by making something in act, geometers know’ (facientes aliquid actu cognoscunt).
Summa Theologiae I, q. 7, a. 1 & a. 3; q. 12, a. 4 — Being Itself as Most Formal of All; the Geometer’s Infinite Line; Apprehending Absolute Being¶
Read Primary Text: English (ST I, q. 7, a. 1 & 3; q. 12, a. 4) · Latin (ST I, q. 7, a. 1 & 3; q. 12, a. 4) · Commentary
These three articles from the Prima Pars establish the metaphysical polarity between quantitative limitation and subsistent esse, together with the abstractive power of created intellect. In Question 7, Article 1, Aquinas distinguishes imperfect material infinity (formless indeterminacy) from perfect formal infinity, proving that because ipsum esse is most formal of all (maxime formale omnium), God as unreceived subsistent being is infinito-perfect, whereas figure is the quantitative boundary terminating extension. In Question 7, Article 3, he proves that neither a natural body nor an actually imagined mathematical body can be infinite in magnitude because every actual mathematical body must have a terminating figure, explaining that the geometer’s ‘infinite line’ means only a finite line extensible or subtractable as needed, and that quantitative infinity belongs solely to division toward matter, never addition toward the formal whole. In Question 12, Article 4, he maps the hierarchy of cognitive powers to modes of being and demonstrates in the third reply that because the human intellect can resolve concrete composites to consider form and esse in abstraction, it possesses a natural openness to being elevated by grace.
Key Theses:
Matter is perfected and made finite by form, whereas form’s amplitude is contracted by matter; because ipsum esse is most formal of all, unreceived subsistent esse is supremely infinite and perfect.
No mathematical body can exist in act without some figure (figura), which is the form of quantity enclosed by boundaries; hence an actually infinite magnitude is impossible both physically and mathematically.
When the geometer postulates ‘Let this line be infinite,’ he requires no actually infinite line, but only an actually finite line from which as much may be taken as demonstration requires; quantitative infinity exists solely in potential division toward matter.
Unlike bodily sight, which grasps nature solely in concrete singularity, created intellect resolves what is concrete so as to consider both form and esse in abstraction (per modum resolutionis cuiusdam).
Summa Theologiae I, q. 84, a. 6–7 & q. 85, a. 1 — On the Origin of Science from Sensible Things, Turning to Phantasms, and Threefold Abstraction¶
Read Primary Text: English (ST I, q. 84, a. 6–7; q. 85, a. 1) · Latin (ST I, q. 84, a. 6–7; q. 85, a. 1) · Commentary
In the Treatise on Man, Aquinas delivers his definitive account of human intellectual cognition. Question 84, Article 6 traces an Aristotelian middle path between \ Democritus (who reduced intellect to passive sensory effluxes) and \ Plato (who severed intellect from sense via participation in separate Forms): sense operates in the psychophysical composite, while the incorporeal intellectus agens renders sensory \ phantasms intelligible in act, making sensible cognition not the total cause of science, but the materia causae. Question 84, Article 7 proves from organ lesions and universal introspection—forming exemplary diagrams whenever we strive to understand or teach—that the embodied intellect cannot understand anything in act, even habitual science, without conversio ad phantasmata to behold the universal nature existing in the particular. Question 85, Article 1 refutes the charge that abstraction falsifies reality by distinguishing abstraction via judgmental separation from abstraction via simple consideration, and articulates the canonical hierarchy of individual/common \ sensible matter and individual/\ common intelligible matter across physics, mathematics, and metaphysics.
Key Theses:
Sensible cognition is neither the total efficient cause of intellectual science (Democritus) nor a mere extrinsic occasion awakening innate Ideas (Plato), but serves as the materia causae rendered intelligible in act by the intellectus agens.
Even after acquiring habitual science, the human intellect in this life cannot understand anything in act without conversio ad phantasmata, forming exemplary phantasms in which it inspects the universal nature existing in the particular.
Abstraction by simple and absolute consideration involves no mendacity (abstrahentium non est mendacium), because considering specific or quantitative nature apart from individuating conditions reflects the immaterial mode of the knower rather than asserting real separation in the thing.
Physics abstracts from individual sensible matter while retaining common sensible matter; mathematics abstracts from all sensible matter and from individual intelligible matter while retaining common intelligible matter (substance subject to quantity); metaphysics abstracts even from common intelligible matter.
Disputed Questions on the Power of God, q. 7, a. 2 — That Esse Is the Actuality of All Acts and the Perfection of All Perfections¶
Read Primary Text: English (De Pot. q. 7, a. 2) · Latin (De Pot. q. 7, a. 2) · Commentary
Addressing eleven incisive objections against the identity of essence and esse in God, Aquinas constructs a rigorous causal and metaphysical demonstration. Because all created causes, despite differing in their proper specific effects (fire generating fire, a builder building a house), concur in one universal effect—causing esse—that common effect must derive from the highest universal cause whose own proper nature is esse itself. In the replies, Aquinas deploys the distinction between substantive esse and propositional esse (Metaph. V.9) to explain how we know that God is without knowing what He is (ad 1); distinguishes ens commune (abstraction without precision, open to addition) from esse divinum (subsistent purity excluding all addition, ad 6); distinguishes id quod significatur from our concrete modus significandi (ad 7); explains why ‘God is’ is self-evident in itself—like Every whole is greater than its part—yet demonstrable quoad nos (ad 11); and crowns the article in ad 9 by proclaiming hoc quod dico esse to be the actuality of all acts and the perfection of all perfections, determined by quidditative natures not as potency by act, but as act by potency.
Key Theses:
Whereas Damascene’s statement that ‘that God is, is manifest to us’ refers to propositional esse conceived by the intellect from effects, God’s substantive actum essendi is identical with His essence and exceeds natural comprehension.
Common being (ens commune) abstracts without excluding further determination, whereas subsistent divine esse is individuated by its sheer unreceived purity, excluding any possible addition.
What Aquinas calls esse (hoc quod dico esse) is the actuality of all acts (actualitas omnium actuum) and the perfection of all perfections: no form is understood to exist in act unless esse is posited, and esse is limited by essence as act is contracted by potency.
Like the axiom Every whole is greater than its part for one ignorant of the term ‘whole,’ the proposition ‘God is’ is per se nota secundum se yet requires quia demonstration quoad nos because God’s quiddity is not directly known to us.
Disputed Questions on Truth, q. 10, a. 6 — Whether the Human Mind Receives Knowledge from Sensible Things and on First Indemonstrable Principles¶
Read Primary Text: English (De Ver. q. 10, a. 6) · Latin (De Ver. q. 10, a. 6) · Commentary
In this masterly disputed question on the mind (De Mente), Aquinas classifies and critiques four historical accounts of the origin of science—two purely extrinsic (Platonic separate Ideas and \ Avicenna‘s separate intelligentia agens) and two purely intrinsic (Platonic reminiscence from pre-existent souls and radical Augustinian self-formation)—before establishing \ Aristotle‘s synthesis that human science arises partim ab intrinseco et partim ab extrinseco. Toward external sensible things, our mind stands simultaneously as act to potency (via the intellectus agens, whose participated light derives ultimately from God) and as potency to act (via the intellectus possibilis, receptive of determinate species). In the light of the \ agent intellect, all science is originally implanted in us (originaliter indita) through universal conceptions—first indemonstrable principles arising from sense (sed contra 2)—while in the crucial seventh reply Aquinas formulates the synergy of abstraction: the intellectus agens acts as primary principal agent and the \ phantasms act as secondary instrumental agent, imprinting species in the possible intellect that are both intelligible in act and determinate likenesses of sensible things.
Key Theses:
All human science originally consists in the knowledge of first indemonstrable principles, whose cognition arises in us from sense (Posterior Analytics II.19) under the illuminating light of the agent intellect.
Purely extrinsic theories (Plato, Avicenna) fail to explain why the lack of a bodily sense entails the lack of the corresponding science and why injury to the organ of imagination impedes actual consideration; purely intrinsic theories (pre-existence, pure self-expression) violate the natural hylomorphic union of soul and body.
Human science originates partly from within (the participated light of the intellectus agens, wherein universal first principles are immediately known) and partly from without (determinate forms drawn from sensible things).
In intellectual abstraction, the intellectus agens operates as principal and primary agent while the phantasms operate as instrumental and secondary agent (agens instrumentale vel secundarium), leaving an intelligible species in the possible intellect that bears the imprint of both.