39. The Continuous, Becoming, and the Unity of Being

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Lecture Notes

Main Topics #

The Philosophy of the Continuous #

• Book VI of Aristotle’s Physics is devoted entirely to the study of continuity
• Continuous quantity is divisible forever and not composed of indivisibles
• The continuous applies to magnitude (line), motion, and time
• The paradox of becoming: how can something that is not become something that is without contradiction?

The Paradox of Becoming (Aristotle’s Solution) #

• The Problem: When an object becomes a circle, is the last instant it is not a circle the same as the first instant it becomes a circle?
  • If yes: the object would both be and not be a circle (contradiction)
  • If no: there must be time in between, but in that time it must either be or not be a circle (infinite regress)
• Aristotle’s Solution: There is no last instant in which something is not a circle, but there is a first instant in which it is a circle
• This distinction (no last instant but a first instant) is crucial and subtle
• Hegel misunderstood this solution and concluded that becoming involves contradiction
• Marxists derived from this error the doctrine that all change is contradiction

Application to Eucharistic Theology #

• The same paradox applies to transubstantiation: when bread becomes the body of Christ
• There is a time when bread and wine are present under the accidents
• There is a time when the body and blood of Christ are present under the same accidents
• Medieval theologians struggled with whether these moments are the same or different
• Thomas Aquinas, using Aristotle’s solution to the paradox of becoming, resolved the theological difficulty
• The solution requires understanding that there is no last instant of the bread’s presence but a first instant of Christ’s presence

The Order of Understanding vs. Order of Being #

• Names come from the continuous because our knowledge begins with continuous sensible things
• We tend to apply categories derived from bodily, continuous reality to immaterial and divine realities
• This causes difficulties because we falsely imagine immaterial things through spatial categories
• God is indivisible not like a point (which is indivisible within the continuous) but outside the genus of continuity altogether
• Thomas teaches (Q. 3, Art. 1) that God is not a body

Thoughts vs. Continuous Magnitudes #

• Aristotle distinguishes thought from continuous quantity (Book III, De Anima)
• Thoughts are like numbers, not like continuous magnitudes
• Between thoughts there is a successor (like numbers: 3 and 4), not an infinite divisibility
• Between premises and conclusion of a syllogism there is the next thought, but no intermediate thought
• Therefore thoughts are not divisible forever, unlike continuous magnitudes

The Meanings of ‘Beginning’ (ἀρχή) #

• The first meaning of archē is spatial: the beginning of this table (something in the continuous)
• God as “Alpha and Omega” requires understanding different meanings of beginning before reaching the divine sense
• This illustrates why understanding the continuous is foundational to ascending to immaterial realities

The Meanings of ‘In’ (ἐν) #

• The first meaning of in is spatial: to be in a place
• This is why we naturally tend to think that whatever exists must be somewhere (common pre-philosophical opinion)
• But to be in a place is properly a property of bodies
• Understanding how to separate in from spatial location is part of ascending to immaterial substances

Time as a Number #

• Time is a number according to Aristotle (the measure of motion)
• But time is not an abstract number; it is a numbered number (numerus numeratus)
• Abstract number is discrete; numbered number (existing in the numbered thing) is continuous
• Time has continuity not from number itself but from the numbered (the continuous motion being measured)
• The abstract number would be discrete (like panis dimidiatus, a half-loaf), but time remains continuous

Unity of Time #

• Some attribute the unity of all temporal things to the unity of eternity (God, the first principle of all duration)
• Others attribute it to first matter, the first subject of motion
• Thomas argues the true cause is the unity of the first motion (motion of the heavenly bodies)
• Since the first motion is the simplest, all other motions are measured by it
• This accords with Metaphysics X: the property of the one is to be a measure
• Time is compared to the first motion as accident to subject (receiving unity from it) and as measure to measured (for other motions)

The Aevum (Ἀιών) and Eternal Beings #

• Two Opinions on Spiritual Substances:
  1. All proceed from God in equality (Origen)
  2. All proceed from God in grade and order (Pseudo-Dionysius, Celestial Hierarchy)
• The Question: Is there one aevum for all eternal things or multiple aeva?
• Since each thing is measured by what is simplest in its kind (Metaphysics X), and spiritual substances are measured by the first eternal being
• The second opinion (hierarchical procession) is more true
• Therefore there is one aevum only, measured by the first eternal being
• This holds even if not all eternal things begin at the same time
• The measure need not be the efficient cause; it need only be simpler than other things measured

Being and the Sensible #

• Our first words and concepts come from sensible things
• We learn language by connecting sounds with what we sense (example: “cookie”)
• Therefore all primary meanings of our words are tied to the sensible and the continuous
• This is why we naturally tend to identify what is with bodies and what exists in bodies
• Most people remain stuck at this less universal level

Ascending to More Universal Understanding #

• In natural philosophy: proceed from general to particular, from less material to more material
• In wisdom (metaphysics): ascend from particular to less universal to more universal (toward the immaterial)
• Most explicitly clear in Book IX of Physics: first consider motion and ability relative to motion; then ascend to universal consideration of act and ability
• In substance: begin with material substances and ascend to understanding substance universally (applicable even to immaterial substances)
• The same ascent occurs in understanding one and many: first the bodily, continuous one; then the most universal one convertible with being
• The division negated in the more universal one is not the division of the continuous but the division of being from non-being

The Property of the One as Measure #

• Aristotle elaborates in Metaphysics X (the book of the one and many) that it is a property of the one to be a measure
• Example: Mozart is a measure of all musicians; Shakespeare of all poets; Aristotle of all philosophers
• This is first understood from the mathematical one (measure of numbers)
• But the principle is carried over by analogy to all genera

Key Arguments #

Argument: Aristotle’s Solution to the Paradox of Becoming #

1. When something becomes F, we ask: is the last instant of not-F identical with the first instant of F?
2. If identical: contradiction (both is and is not F)
3. If different: infinite problem - what about the time in between?
4. Solution: There exists a first instant at which something is F, but there is no last instant at which it is not F
5. This resolves the paradox by denying the assumption that for every interval there must be a first and last instant

Argument: Thoughts Are Not Continuous #

1. Thoughts are compared to numbers, not to continuous magnitudes (Aristotle, De Anima III)
2. Between numbers there is a next number (successor); there is no next longer number
3. Similarly, between thoughts there is a next thought; there is no intermediate thought
4. Therefore, thoughts are not divisible forever
5. This shows that the continuous is not the measure of all things

Important Definitions #

• The Continuous (τὸ συνεχές): Divisible forever, not composed of indivisibles; applies to magnitude, motion, and time
• Numbered Number (numerus numeratus): A number existing in the thing numbered; has continuity from the continuous thing being measured (as opposed to abstract number which is discrete)
• Aevum (ἀιών): The proper duration of eternal creatures (spiritual substances); stands between time and eternity; unchanging but not eternal
• First Motion: The motion of the heavenly bodies; simplest of all motions; serves as the measure of all other motions
• Being of Reason (ens rationis): What exists only in the mind, not in reality
• Privation vs. Negation: Privation is the absence of something in a subject capable of having it; negation is simple non-being

Examples & Illustrations #

The Paradox of Becoming #

• Non-circle becoming a circle: The last instant it is not a circle and the first instant it is a circle cannot be the same (contradiction) nor different (infinite problem). Solution: no last instant of non-circularity, but a first instant of circularity.
• Bread becoming body of Christ: Same logical structure as the becoming-circle problem; solved by Thomas using Aristotle’s solution

Thoughts vs. Lines #

• Succession in numbers: 3, then 4; there is a next number
• No succession in lines: Is there a next longer line? No
• Succession in thoughts: Premise 1, then Premise 2, then Conclusion; there is a next thought
• Therefore thoughts follow the pattern of numbers, not continuous magnitudes

Ascent to Immaterial Understanding #

• Common opinion: Whatever exists must be somewhere (in a place)
  • True of bodies, but not immaterial things
  • Reflects confusion of what is with bodies
• Progress in understanding: Anaxagoras and Plato showed some immaterial things exist; Aristotle systematized this
• The improvement: Our mind gradually separates the notion of what is from the notion of body

Causality and Measure #

• Measure vs. Efficient Cause: A measure need not be the efficient cause; Mozart measures all musicians but does not cause them to exist
• Application to God: God is the measure of all things not necessarily because God causes them, but because all things are measured by the divine simplicity

Questions Addressed #

Why Is Understanding the Continuous Philosophically Important? #

• It is foundational to all our knowledge (we learn through the sensible)
• It introduces the paradoxes of becoming and infinity that require careful metaphysical analysis
• Understanding how to escape false imagination tied to the continuous is necessary for knowing immaterial and divine realities
• Medieval theologians could not resolve Eucharistic difficulties without returning to Aristotle’s solution to the paradox of becoming

How Does Time Have Unity Despite Its Infinite Divisibility? #

• Not through abstract number (which would make it discrete)
• Not through the unity of eternity or first matter alone (these are too remote)
• Through the unity of the first motion (simplest motion), which measures all other motions
• The first motion is both the accident in which time exists (giving it unity) and the measure of all other motions

How Can Eternal Creatures (Angels) Have One Duration (Aevum) Without Beginning Simultaneously? #

• All eternal creatures are measured by the first eternal being (God)
• This unity of measure grounds one aevum for all
• The measure need not be the efficient cause (temporal origin) of all things
• Hierarchy does not prevent metaphysical unity under one measure

How Do We Escape the False Imagination Derived from the Continuous? #

• Recognize that the continuous is only one mode of being
• Thoughts are discrete (like numbers), not continuous
• God is indivisible outside the genus of continuity, not within it
• The first meanings of our words (derived from sensibles) must be refined through abstraction to apply to immaterial realities