Summary — PART IV — COMMENTARIES ON THE PHYSICS AND ON THE HEAVENS

Analytical Synopsis of In octo libros Physicorum & In libros De caelo et mundo expositio (c. 1268–1273)

Executive Thesis

Across his mature commentaries on \ Aristotle‘s Physics and De Caelo (c. 1268–1273), Thomas Aquinas articulates a unified ontology and noetics of continuous quantity that bridges natural philosophy and pure geometry without collapsing either into Platonic separatism or empiricist atomism. The cornerstone of this synthesis is laid down in In II Physicorum, lectio 3: because dimensive quantity inheres in corporeal substance prior in the order of nature to sensible qualities and physical motion, the intellect can grasp points, lines, surfaces, and solids together with their per se attributes while leaving \ sensible matter out of consideration. Consequently, there is no falsehood in those who abstract (abstrahentium non est mendacium): the geometer does not judge that lines exist apart from physical bodies, but considers in isolation what is intelligibly prior to heat, weight, and resistance, retaining intelligible matter—the homogeneous three-dimensional extension that individuates congruent figures—while leaving behind sensible matter (unlike physical definitions, which resemble the snub in enclosing a determinate sensible subject, whereas mathematical definitions resemble the concave or curved). Conversely, the sciences intermediate between mathematics and physics—optics, harmonics, and astronomy—descend from pure mathematical demonstrations back to sensible matter, demonstrating physical conclusions through formal quantitative middle terms.

This abstractive hierarchy rests on the deeper categorial and topological architecture developed in Physics III, IV, and VI. In In III Physicorum, lectio 5, resolving how a single continuous motion realizes both action (as from the agent) and passion (as in the patient), Aquinas derives all ten Aristotelian categories from modes of predicating proportional to modes of being (modi essendi): substance predicates essence; quantity and quality predicate intrinsic accidents following matter and form respectively (with figure founded as a quality upon quantitative boundaries); relation predicates an intrinsic respect toward another; and the remaining six categories arise by extrinsic denomination from efficient causality (action and passion), extrinsic cosmic measures (when from time, where and position from place), and human rational equipment (having). Within this framework, In IV Physicorum, lectio 7 demonstrates how immobile place becomes known through local translation—the succession of bodies within an invariant containing boundary—and adopts \ Themistius‘s solution for the outermost celestial sphere: a rotating homogeneous \ continuum requires no external container as a whole because its intrinsic parts, consecutive to one another around the circle, exist in place in potency. Crucially, as In VI Physicorum, lectio 1 proves with geometric rigor, no continuum—neither magnitude, motion, nor time—can ever be composed of or resolved into indivisibles. Because partless points have no extremes distinct from a remainder, two points can be neither continuous (sharing one common extreme), nor contiguous (having distinct extremes together without coinciding in position), nor consecutive (since a divisible line always intervenes between any two distinct points); points exist strictly as indivisible boundaries, cuts, and intersections of prior continua.

Finally, in In De Caelo I, lectio 2 and II, lectio 2, Aquinas integrates the topological completeness of three-dimensional extension with the constructive imagination of classical geometry. Body is the sole perfect magnitude because three mutually orthogonal dimensions exhaust divisibility every way (omniquaque), uniting the formal definition of the continuum (parts joined at a common boundary) with its material definition (divisible into things always further divisible). When geometers state that a moving point generates a line, a moving line a surface, and a moving surface a solid, Aquinas explains that they employ an imaginative and genetic mode of speaking (modus loquendi geometrarum) that traces dimensional priority by defect from the complete three-dimensional solid rather than positing physical locomotion of partless atoms. Likewise, In II De Caelo, lectio 2 distinguishes intrinsic biological and dynamical orientations (above and below, before and behind, right and left) from positional directions in inanimate bodies and mathematical figures, which hold no absolute internal principle of motion and acquire directional orientation solely by relational position (positio / situs) relative to a chosen frame or observer—anticipating the invariance of Euclidean figures under rigid translation, rotation, and reflection.

Key Scholastic & Mathematical Concepts

Latin Term	English Rendering	Primary Locus	Doctrinal & Geometric Significance
abstrahentium non est mendacium	there is no falsehood in those who abstract	Phys. II, lect. 3	Epistemological principle guaranteeing the exact truth of geometry: considering dimensive quantity without sensible qualities commits no error because the geometer abstracts by non-consideration rather than asserting separate existence.
materia sensibilis / materia intelligibilis	sensible matter / intelligible matter	Phys. II, lect. 3	Ontological ground of mathematical abstraction: quantity precedes sensible qualities in substance, allowing the intellect to abstract geometric magnitudes from sensible matter while retaining substance under pure extension as intelligible matter.
simum / curvum (concavum)	the snub / the concave or curved	Phys. II, lect. 3	Paradigmatic contrast of definitions: natural definitions resemble the snub by including a sensible subject (a nose) in their essence, whereas mathematical definitions resemble the curved by prescinding from every sensible subject.
scientiae mediae	sciences intermediate between mathematics and physics	Phys. II, lect. 3	Disciplines such as optics, harmonics, and astronomy that apply abstract geometric and arithmetic demonstrations to sensible matter, remaining formally mathematical in their middle terms yet terminally natural in their subject.
modi essendi / modi praedicandi	modes of being / modes of predicating	Phys. III, lect. 5	Architectonic principle of Aquinas’s derivation of the ten categories: being is divided analogically rather than univocally because the fundamental ways predicates are affirmed of a subject mirror the ways reality inheres in or denominates substance.
actio ut ab hoc / passio ut in hoc	action as from this / passion as in this	Phys. III, lect. 5	Resolution of the unity of motion with the duality of causal categories: numerically one continuous motion in the mobile is denominated action as proceeding from the agent and passion as received in the patient.
locus immobilis	immobile place	Phys. IV, lect. 7	The innermost immobile boundary of the containing body, first revealed to the intellect through local translation when distinct bodies successively occupy the same surrounding limit without interpenetrating dimensions.
in loco per partes in potentia	in place through parts in potency	Phys. IV, lect. 7	Themistius’s solution, endorsed by Aquinas against Averroes and Avicenna, explaining rotational motion of an uncontained continuous sphere: while the whole does not change place in subject, its potentially divisible parts succeed one another circularly.
continuum, contiguum (contactum), consequenter se habens	continuous, contiguous, consecutive	Phys. VI, lect. 1	Topological triad governing spatial and temporal order: continuous things share one common extreme, contiguous things have distinct extremes together, and consecutive things have nothing of the same genus intervening between them.
indivisibilia	indivisibles	Phys. VI, lect. 1	Partless boundaries—such as points on a line or nows in time—that possess position or order as extremes of division, but can never touch, overlap partially, or be summed to compose an extended continuum.
continuum divisibile omniquaque	continuum divisible every way	De Caelo I, lect. 2	Definition of three-dimensional body as the complete and perfect genus of magnitude, exhausting all mutually perpendicular directions of continuous extension so that no transition into a fourth spatial genus occurs.
punctus motus facit lineam	a moving point makes a line	De Caelo I, lect. 2; II, lect. 2	The kinematic mode of speaking of geometers (modus loquendi geometrarum), whereby constructive imagination traces higher-dimensional magnitudes from lower-dimensional boundaries to express generative priority without physical atomism.
differentiae positionum	differences of position	De Caelo II, lect. 2	The six directional poles (above and below, before and behind, right and left), which belong intrinsically only to animate self-movers and apply to inanimate bodies and geometric figures purely by relational orientation (quoad nos).

Section-by-Section Analytical Breakdown

Physics Book II, Lecture 3 — How the Mathematician Differs from the Natural Philosopher and Why There Is No Falsehood in Those Who Abstract

Read Primary Text: English (Phys. II, lect. 3) · Latin (Phys. II, lect. 3) · Commentary

Aquinas examines how mathematics and natural philosophy can treat the very same geometric realities—points, lines, surfaces, and solid bodies—without collapsing into a single science. Beginning with two aporiae (that natural bodies possess surfaces, solidities, lengths, and points, and that astronomy simultaneously belongs to mathematics and demonstrates the shapes of natural celestial bodies), Aquinas resolves the difficulty through the distinction of formal perspectives (rationes considerandi). Whereas the physicist investigates surfaces, lines, and points precisely insofar as they are boundaries of a mobile natural body endowed with sensible qualities, the mathematician considers them apart from motion and \ sensible matter. Grounding this epistemic capacity in the ontological order of accidents inhering in substance, Aquinas shows that dimensive quantity accrues to corporeal substance prior to sensible qualities (such as hot, cold, white, or heavy) and the motions rooted in them. Because what is prior in nature does not include what is posterior in its intelligible definition, the intellect can understand quantity and figure with intelligible matter (substance as subject to pure extension) while leaving sensible matter out of consideration—confirming that there is no falsehood in those who abstract, since non-consideration of sensible qualities is not a false judgment of ontological separation.

From this principle Aquinas diagnoses \ Plato‘s twofold error—reifying both mathematicals and natural species into separate Ideas by confusing intellectual abstraction with separate existence—and confirms his solution through two decisive signs. First, natural definitions always resemble the snub (simum), which includes a determinate sensible subject (the nose) in its essence, whereas mathematical definitions—even and odd, straight and curved (curvum), number, line, and figure—prescind from any sensible subject. Second, the sciences intermediate between mathematics and physics (optics, harmonics, and astronomy) invert pure mathematical abstraction by applying abstract geometric and arithmetic theorems back to visual rays, audible sounds, and celestial spheres. Because a science takes its denomination from its terminus, these intermediate sciences are more natural than mathematical, explaining why both the physicist and the astronomer prove that the earth is spherical, yet through distinct middle terms: the physicist from the symmetric downward tendency of heavy parts toward the center, and the astronomer from the curved shadow cast in lunar eclipses and the shifting horizon of visible stars.

Key Theses:

• Mathematics and physics investigate the same extended realities (points, lines, surfaces, and bodies) under distinct formal perspectives: physics treats them as boundaries of mobile natural bodies, whereas mathematics abstracts them from motion and sensible matter.

• Dimensive quantity inheres in substance prior to sensible qualities and physical motions; therefore quantity encloses intelligible matter (substance subject to extension) in its notion without enclosing sensible matter.

• There is no falsehood in those who abstract (abstrahentium non est mendacium), because considering geometric magnitude apart from sensible qualities does not assert that mathematical objects subsist outside sensible bodies, as Plato mistakenly supposed.

• Natural definitions follow the model of the snub by incorporating sensible matter (flesh and bone, though not individual flesh and bone), whereas mathematical definitions follow the model of the curved by excluding sensible matter entirely.

• Sciences intermediate between mathematics and physics (optics, harmonics, astronomy) apply pure geometric and arithmetic principles to sensible matter, sharing conclusions with physics while demonstrating them through formal quantitative middle terms.

Physics Book III, Lecture 5 — On Action and Passion and the Division of Being into Ten Categories Proportional to Modes of Predicating

Read Primary Text: English (Phys. III, lect. 5) · Latin (Phys. III, lect. 5) · Commentary

Commenting on \ Aristotle‘s dialectical investigation into where motion resides relative to mover and moved, Aquinas demonstrates that action (the act of the active principle) and passion (the act of the passive principle) are numerically one and the same continuous motion residing in the mobile subject, yet formally distinct in intelligible definition (ratio). If action and passion were two distinct motions, either motion would reside in the unmoved mover or a single mobile would undergo two simultaneous motions toward the very same specific terminus—both of which are impossible. Conversely, identifying action and passion in subject does not entail that teaching is identical in definition with learning or that every agent undergoes change: just as the road from Thebes to Athens and the road from Athens to Thebes, or an abstract spatial interval taken between opposite endpoints, is one in reality (secundum rem) yet two in directed notion (secundum rationem), so the single continuous motion is action insofar as it proceeds from the agent (ut ab hoc) and passion insofar as it is received in the patient (ut in hoc).

To answer how a merely conceptual distinction within one motion can ground two distinct categories of real being—and how motion can simultaneously belong to quantity, quality, and where—Aquinas unfolds his celebrated systematic derivation of the ten Aristotelian categories. Being is not divided univocally like a genus into species, but analogically according to diverse modes of being (modi essendi), which are strictly proportional to modes of predicating (modi praedicandi). Predicating what pertains to the essence yields substance; predicating what inheres intrinsically yields quantity (on the part of matter, furnishing intrinsic length, breadth, and depth), quality (on the part of form, including geometric figure founded upon lines and surfaces), or relation (an intrinsic respect toward another). Finally, predicating by extrinsic denomination yields action and passion (from external efficient causality), when (from time as extrinsic measure), where and position (from place and the order of parts in place), and having (from external instruments fashioned by human reason). Materially considered as an imperfect act in nature, motion reduces to the category of its terminus (quantity, quality, or where); formally apprehended as a medium between potency and act implying cause and effect, it grounds the categories of action and passion.

Key Theses:

• Action and passion are numerically one continuous motion residing in the mobile patient, distinguished formally as act proceeding from the agent (ut ab hoc) versus act received in the patient (ut in hoc), analogous to one spatial interval traversed in opposite directions.

• Being is divided into the ten categories not univocally, like a genus into species, but analogically according to diverse modes of being (modi essendi) that are proportional to modes of predicating (modi praedicandi).

• Intrinsic inherence generates the categories of quantity (consequent upon matter and providing intrinsic dimensional measure), quality (consequent upon form, with figure founded upon quantitative lines and surfaces), and relation.

• Extrinsic denomination by cause and measure generates action and passion (from efficient causality), when (from temporal measure), where and position (situs, adding the order of parts in place), and having (habitus).

• Motion as an inchoate reality in nature reduces to the category of its terminus (quantity, quality, or where), whereas as a transition from potency to act apprehended between two terms it grounds the categories of action and passion.

Physics Book IV, Lecture 7 — On the Definition of Immobile Place from Local Translation and Themistius’s Solution

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Having established \ Aristotle‘s definition of immobile place as the innermost immobile surface of the containing body, Aquinas confronts the classic cosmological and topological aporia of the outermost celestial sphere: since nothing exists outside the universe to contain it, how can the outermost sphere be in place, given that it manifestly rotates locally? Aquinas first rejects the hypothesis of self-subsistent three-dimensional void space interpenetrating corporeal dimensions as ontologically impossible. He then subjects four historical Peripatetic and Arabic solutions to rigorous critique: Alexander of Aphrodisias’s denial that the outermost sphere moves in place at all; \ Avicenna‘s claim that it moves in the category of position (situs) rather than where (refuted because every species of position consists in an indivisible configuration admitting no per se continuous succession, and moreover presupposes place); Avempace’s proposal that a circularly moving body is located by the convex surface of the inner sphere around which it revolves (violating the axioms that place contains and equals the located); and \ Averroes‘s contention that the outermost sphere is in place per accidens through the fixity of its central body (rejected as incongruous because the center is wholly extrinsic to the substance of the outer shell).

Aquinas decisively endorses the solution of \ Themistius, grounding it in the epistemological origin of the concept of place itself: place would never be sought save on account of local motion (translation), which reveals place through the succession of distinct bodies within one identical spatial bound. Whereas rectilinear translation requires one whole body to vacate a place and another whole body to enter it—demanding an external containing place per se for the whole—circular rotation preserves the whole body within the selfsame spatial region in subject while its parts continuously replace one another in subject around the circumference. Although the parts of a homogeneous continuum (illustrated by water rotating within a vessel) are not actually divided like a heap of contiguous stones, they are divisible and consecutive to one another around the circle, mutually containing and contained in potency. Thus the outermost sphere is in place per accidens by reason of its intrinsic parts existing potentially in place—a minimal, uniform mode of local variation uniquely suited to the first cosmic motion.

Key Theses:

• The existence and nature of place become known through local translation—the observed succession of distinct bodies occupying the same containing boundary—while self-subsistent three-dimensional space interpenetrating bodies is impossible.

• Avicenna’s theory of per se motion in the category of position (situs) fails because each species of situs consists in an indivisible order of parts that admits no continuous succession of more and less apart from local motion.

• Averroes’s claim that the outermost sphere is in place per accidens through the immobility of an extrinsic center violates Aristotle’s definition of per accidens location, which requires inherence or containment within what is located.

• Following Themistius, circular motion does not require the whole rotating continuum to change place in subject, but only its parts to succeed one another continuously in the same spatial positions.

• Unlike a heap of separated, contiguous stones whose parts are in place in act, a homogeneous circular continuum has parts that are consecutive and mutually containing in potency, placing the whole in place per accidens through its intrinsic parts.

Physics Book VI, Lecture 1 — That No Continuum (Line, Time, or Motion) Can Be Composed of Indivisible Points

Read Primary Text: English (Phys. VI, lect. 1) · Latin (Phys. VI, lect. 1) · Commentary

Opening Book VI on the quantitative divisibility of motion, Aquinas presents \ Aristotle‘s apodictic demonstration that no continuum—whether a geometric line, temporal duration, or continuous motion—can be composed out of indivisibles (such as points or nows). Resuming the topological definitions established in Book V—that continuous things are those whose extremes are one, contiguous things (things in contact) are those whose extremes are together, and consecutive things are those with nothing of their own genus intervening between them—Aquinas systematically eliminates every conceivable mode in which partless points could form a line. First, points cannot be continuous or contiguous by their extremes, because an extreme (ultimum) implies a distinction between boundary and bounded part, whereas a partless indivisible admits no internal diversity of parts. Second, if two indivisibles touched at all, neither part-to-part nor part-to-whole contact would be possible; whole would have to touch whole, causing the two points to coincide completely in site (situs) rather than generating distinct spatial positions capable of extending a magnitude. Third, points cannot stand consecutively to one another, because between any two positionally distinct points an extended line always intervenes (and between any two nows, an interval of time).

Aquinas reinforces this topological proof with a second principal demonstration from the Book III definition of the \ continuum as that which is infinitely divisible: since anything is divisible into the elements out of which it is composed, a continuum composed of indivisibles would divide into partless atoms, destroying infinite divisibility. Finally, Aquinas closes every loophole by proving the two supporting lemmas rigorously: any medium separating two non-touching, positionally distinct points cannot be an indivisible (on pain of an infinite regress of intervening gaps) nor a divisible composed of indivisibles, and must therefore be a continuum divisible into things always further divisible—namely, a line; conversely, no continuum can ever be resolved into indivisibles without requiring partless indivisibles to touch one another.

Key Theses:

• From the Book V definitions of continuous (extremes are one), contiguous (extremes are together), and consecutive (nothing of the same genus between), it follows apodictically that no continuum is composed of indivisibles.

• Indivisible points possess no internal distinction between boundary (ultimum) and remainder, and therefore can neither share a common extreme nor place distinct extremes together.

• If two partless points touched, whole would touch whole, collapsing them into a single spatial position rather than producing the positionally distinct parts required for an extended continuum.

• No two points on a line (nor two nows in time) can be consecutive, because between any two positionally distinct points there necessarily intervenes a continuous, infinitely divisible line segment.

• Every continuum is divisible solely into things always further divisible (in semper divisibilia), never into partless atoms; points exist as indivisible boundaries and cuts of continua, not as constituent building blocks.

On the Heavens Book I, Lecture 2 — On the Perfection of Three-Dimensional Body and the Geometers’ Mode of Speaking of a Moving Point

Read Primary Text: English (De Caelo I, lect. 2) · Latin (De Caelo I, lect. 2) · Commentary

Launching the treatise on the corporeal universe, Aquinas synthesizes \ Aristotle‘s dual definitions of the continuum—the formal logical definition of the Categories (that whose parts are joined at one common boundary) and the material physical definition of Physics and De Caelo (that which is divisible into things always further divisible)—in order to define body as a \ continuum divisible every way (omniquaque), that is, across all three dimensions. Dividing continuous magnitude into line (divisible in one direction), plane or surface (divisible in two), and body (divisible in three), Aquinas analyzes Aristotle’s appeal to Pythagorean ternary symbolism, liturgical custom, and universal linguistic usage (where both is said of two, and all first of three) to show that three carries the formal ratio of totality (beginning, middle, and end). Following \ Simplicius, Aquinas makes a crucial methodological observation: Aristotle offers these ternary signs as probable confirmations suited to natural philosophy while presupposing the strict geometric demonstration from mathematics—exemplified by \ Ptolemy‘s proof that no more than three mutually perpendicular lines can meet at one and the same point.

Because all, whole, and perfect share the same formal notion of completeness, three-dimensional body alone is the perfect magnitude, possessing every mode of continuity. From this completeness Aquinas explains a fundamental asymmetry in dimensional generation: whereas geometers imaginatively describe a transition from point to line, from line to surface, and from surface to solid—employing the mode of speaking of geometers (modus loquendi geometrarum) who imagine that a moving point makes a line, a moving line makes a surface, and a moving surface makes a body—no analogous transition can pass from body into a fourth genus of magnitude. Every such dimensional progression arises from a dimensional defect in the lower boundary (just as motion belongs to the imperfect), whereas three-dimensional body exhibits no dimensional lack. Finally, while particular bodies are three-dimensionally complete yet externally bounded by contiguous neighbors (making them imperfect and many), the total corporeal universe is perfect every way, comprehending both all three dimensions and all bodies.

Key Theses:

• Aristotle’s formal definition of the continuum (parts joined at one common boundary) and material definition (divisible into things always further divisible) converge in defining body as a continuum divisible every way (omniquaque).

• While Aristotle adduces Pythagorean ternary arguments and common speech as probable signs in natural science, strict demonstration that spatial dimensions are exactly three belongs to mathematics—as in Ptolemy’s proof that at most three mutually perpendicular lines can meet at one point.

• Because all, whole, and perfect signify formal integrity, three-dimensional body is the sole complete magnitude, whereas line (one-dimensional) and surface (two-dimensional) are dimensionally incomplete boundaries.

• When geometers say that a moving point makes a line, a moving line a surface, and a moving surface a body, they employ an imaginative constructive mode of speaking reflecting dimensional defect, which terminates irreversibly at three-dimensional body.

• Particular bodies are dimensionally complete in genus yet limited by contact with exterior bodies, whereas the universe as a whole is omniquaque perfect both in three-dimensionality and in comprehending all bodies.

On the Heavens Book II, Lecture 2 — On Positional Directions in Natural Bodies and How They Are Considered by Position in Mathematical Figures

Read Primary Text: English (De Caelo II, lect. 2) · Latin (De Caelo II, lect. 2) · Commentary

Investigating whether positional polarities such as right and left belong intrinsically to the celestial sphere as the Pythagoreans claimed, Aquinas develops a rigorous ontology of directional orientation (differentiae positionum) across animate organisms, inanimate physical bodies, and abstract geometric figures. Drawing on On the Progression of Animals, Aquinas establishes that the three directional oppositions—above and below (governing length), right and left (governing breadth), and before and behind (governing depth)—belong per se and intrinsically only to living self-movers endowed with determinate organic parts from which vital motions originate: plants possess only above and below (with the root functioning organically as above by drawing nourishment), sessile animals add before and behind through sense perception, and locally mobile perfect animals possess all six directions. Furthermore, these three axes stand in a strict hierarchy both dimensionally (length precedes breadth and breadth precedes depth, just as line precedes surface and surface precedes body—since according to geometers a moving line generates a surface) and dynamically (above is the primary origin of growth and sensory command, before is the goal of sensory orientation, and right is the starting limb of locomotion).

By contrast, inanimate bodies and artificial or mathematical objects possess no intrinsic active principle of motion in one determinate part rather than another: heavy and light elements move uniformly from every side toward their natural center or periphery, while artificial and geometric figures lack internal self-motion altogether. Consequently, directional terms (above and below, right and left, before and behind) are predicated of inanimate things and geometric figures solely by comparison to us (per comparationem ad nos) in three relational modes: by direct alignment with our own sides (as in augury), by anthropomorphic likeness (as in a statue), or by mirror-image inversion (contraria positio, as in a specular reflection, where right opposes our left). This relational relativity is proved by rotational invariance: turning an inanimate object or geometric figure reverses its right and left relative to us, whereas an organism retains its intrinsic right and left under every rotation. Aquinas concludes by refuting the Pythagorean table of ten opposites for attributing right and left universally to all things while omitting the prior axes of above and below as well as before and behind.

Key Theses:

• The six directional differences (above and below, before and behind, right and left) belong intrinsically and per se only to animate bodies possessing internal principles of nutrition, sensation, and locomotion in determinate organs.

• Dimensionally and genetically, above (principle of length) is prior to right (principle of breadth), and right is prior to before (principle of depth), mirroring the geometric priority of line to surface (where a moving line generates a surface) and surface to solid.

• Inanimate bodies, artifacts, and mathematical figures possess no intrinsic directional polarity, because they lack determinate parts initiating self-motion; when rotated, their apparent right and left invert.

• Positional directions are attributed to inanimate and geometric objects solely by comparison to us (quoad nos) in three ways: direct observer alignment, anthropomorphic correspondence (as in statues), and mirror-image inversion (in speculo).

• The Pythagoreans erred both in projecting right and left onto all things via their moral table of ten opposites and in attributing right and left to the cosmos while neglecting the dimensionally and causally prior principle of above and below.