58. Place, Time, and the Problem of Change

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Lecture Notes

Main Topics #

The Paradox of Becoming and Change #

• The fundamental difficulty: how can something become what it is not without contradiction?
• Classical formulation: if an object is not-a-sphere, then becomes-a-sphere, what is it at the boundary between these two times?
• If there is time between the state of not-being-a-sphere and being-a-sphere, the object must be either a sphere or not-a-sphere in that intermediate time
• If there is NO time between these states, then the last instant of not-being-a-sphere and the first instant of being-a-sphere must be the same instant—making the object both be and not-be, which violates the principle of non-contradiction
• Hegel admitted contradiction as real rather than solving the problem; Marxist dialectics followed suit
• Aristotle solves this problem in Book 6 of the Physics, but modern philosophers (including Hegel) seem unaware of or ignore his solution

Application to Theological Problems #

• The paradox becomes acute in the doctrine of transubstantiation
• There is a time when bread and wine exist under their accidents, and a later time when the body and blood of Christ exist under those same accidents
• Medieval theologians puzzled over whether the last instant of bread-and-wine existence and the first instant of Christ’s body-and-blood existence are the same instant
• If they are the same instant, both bread and body exist simultaneously (the heresy of Euthra or similar)
• The problem is not merely theological but fundamentally philosophical

Place, Empty, and Motion #

• Democritus argued that the empty (to-mē-on, what-is-not) must exist for motion to occur
• Without empty space, objects would be “packed tight like sardines in a can” and unable to move
• Paradoxically, Democritus admits that what-is-not (the empty) must be in order for change to occur—a verbal contradiction
• Place appears to be the “first” of all things in a particular sense: place can exist without a body in it, but a body cannot exist without a place
• Hesiod claimed place (the yawning gap) came first cosmologically
• However, not all things are in place—immaterial realities like God are not constrained by place

Common and Universal Aspects of Natural Things #

• Place, empty, time, and the continuous are all connected (intrinsically or extrinsically) to motion
• Motion is central to the definition of nature
• These concepts should be studied in general before particular applications because they are common to all natural things and universal
• The study of universals cannot rely on imagination alone; reason must transcend the continuous

Imagination and Transcendence #

• Our imagination cannot transcend the continuous; we never imagine without the continuous or time
• This leads to errors: imagining the soul as a continuous, air-like substance in human shape (as Homer and Dante do)
• The soul is not continuous and cannot be recognized by shape
• Understanding immaterial realities (like God without a body, or pure forms) requires transcending imagination—hence these topics belong to later studies
• Logic helps prepare the mind for theology precisely because logic works with universals that cannot be imagined

The Nature of Definition #

• Descartes and Locke both denied that motion can be defined
• Descartes confused certitude with clear and distinct knowledge; Locke classified motion as a “simple idea” that cannot be defined
• Aristotle knew that not everything can or should be defined; some things are known without definition
• Motion, though infinitely divisible, cannot be defined by its parts (just as a line cannot be defined by dividing it into smaller lines)
• Motion can be defined, however, because it is always “of another”—it depends on a subject
• The point, line, and surface are all indefinable by parts but can be defined through relationship: a point is the limit of a line, a line is the limit of a surface, a surface is the limit of a body
• Even though the point is indivisible, it has a multiplicity in its definition (limit + line), providing the basis for defining it
• Motion similarly can be defined through its relationship to potentiality and actuality

Key Arguments #

The Problem of Temporal Continuity and Instantaneous Change #

1. Assume an object transitions from not-being-F to being-F (where F is any property)
2. Either there is a time interval between these two states, or there is not
3. If there IS a time interval: In that interval, the object must be either F or not-F. Whichever it is, it belongs to one of the original states, contradicting the assumption that there is a distinct intermediate time
4. If there is NOT a time interval: Then the last instant of not-being-F and the first instant of being-F are identical, making the object both F and not-F simultaneously—a contradiction
5. Conclusion: The problem appears unsolvable unless one admits contradiction (Hegel’s approach) or finds the Aristotelian solution in Physics Book 6

Why Motion Can Be Defined Despite Being Divisible #

1. A line cannot be defined by dividing it into smaller lines; division yields only more lines
2. But a point can be defined: a point is the limit of a line (multiplicity: limit + line)
3. Motion is not self-subsisting (it is always the motion OF something; the rolling is not what rolls)
4. Because motion is “of another,” there is inherent multiplicity in its nature
5. This multiplicity provides the foundation for a definition composed of multiple terms
6. Therefore, motion CAN be defined through its relationship to potentiality and actuality

The Primacy of Place #

1. Place appears to be prior to all things because: place can exist without a body in it
2. But a body cannot exist without being in some place (according to the common Greek opinion)
3. However, not all beings are in place (God, immaterial forms, angels)
4. Therefore, place is common to all physical things but not to all beings

Important Definitions #

Place (τόπος, topos) #

• The natural locus or location where a body exists
• Property: a place can exist without a body occupying it, but bodies cannot exist without being in a place
• Common opinion: “Whatever exists must be somewhere; if it isn’t somewhere, it doesn’t exist”
• Exception: immaterial beings are not in place

The Empty (τὸ μὴ ὄν, to-mē-on) / Void #

• That which is not; the negation of body or substance
• Democritus posited it as necessary for motion to occur
• Paradox: Democritus admits that what-is-not must be, in order for motion to be real

The Continuous (τὸ συνεχές, to synechés) #

• Quantity that has parts meeting at a common boundary (unlike discrete quantity, where parts have no common boundary)
• Examples: line, surface, body, time, place
• Our imagination cannot transcend the continuous; we never imagine without spatial or temporal continuity
• Leads to false imaginative conceptions of immaterial realities

Substance (οὐσία, ousia) #

• Etymologically connected to “understanding” (understanding = knowing what stands under something)
• The underlying nature or essence of a thing
• That which is not said of another or in another

Examples & Illustrations #

Packed Objects and Motion #

• Clothing packed tightly in a suitcase cannot move around
• If space were completely full with no empty space, nothing could move—analogous to the packed suitcase
• This explains why Democritus thought the empty must exist

The Recognition of Souls #

• T.J. Kosirik joked: “How do I recognize your soul?” (as opposed to recognizing a body by shape)
• Dante recognizes souls in the Afterlife by their shapes and characteristics, but this is imaginative fiction
• In reality, the soul cannot be recognized by shape because it is not a continuous, spatially-extended thing
• A philosophical colleague might be recognized by “the way he approaches a problem,” but not by recognizing his soul

God Without Body #

• Berquist’s cousin Donald, philosophically trained, tried to explain to his Catholic mother that God has no body
• The mother could not understand this, saying “what difference is that making my head?” (i.e., what use is that knowledge?)
• Most people cannot transcend their imagination to understand immaterial being

The Boundary of Finite Bodies #

• Any finite body has an end (e.g., your body or mine didn’t go on forever; the chair or table didn’t go on forever)
• The end of a body is a surface
• A surface has length and width but no depth (if it had depth, it wouldn’t be the end of the body)
• The end of a surface is a line (length but no width or depth)
• The end of a line is a point (no length, width, or depth)
• Even though a point is indivisible (has no parts), it can be defined as “the limit of a line”

Definition of Square (as borrowed from geometry) #

• Four is a square number (2 × 2); nine is a square number (3 × 3)
• Six is not square but rectangular (2 × 3)
• The term “square” is transferred from geometry to numbers because there is a real connection
• This illustrates how multiplicity can exist in a definition even when the thing itself is simple in some respect

Notable Quotes #

“There’s a time in which it is not a sphere, and then a time in which it is a sphere. Now, is there any time between the end of the time it’s not a sphere and the time it is a sphere?” — Berquist, posing the classical paradox of becoming

“To be or not to be, that is the question. You can’t both be and not be, and you must either be or not be.” — Berquist, referencing Shakespeare and the law of non-contradiction in the context of change

“If you said there was some time in between the two, I’d say in that in-between time, is it or is it not a sphere? It’s got to be one or the other.” — Berquist, demonstrating the logical necessity of the contradiction

“Understanding means knowing what is said to stand under something. Or, knowing something through what is said to stand under it.” — Berquist, etymologically unpacking the meaning of understanding (connected to substance/ὑποκείμενον)

“It is a major thing to understand one of these definitions, like the definition of law, the definition of eternity, or the definition of virtue… And it’s a major thing to understand the definition of motion or place or time.” — Berquist, emphasizing the difficulty and importance of grasping these foundational definitions

Questions Addressed #

How Can Change Occur Without Contradiction? #

• The Problem: If something transitions from not-being-F to being-F, there seems to be no consistent way to describe the boundary between these states without admitting contradiction
• Hegel’s Answer: Admit contradiction as real (rejected by Thomistic philosophy)
• Aristotle’s Answer: Solved in Physics Book 6 (not fully explained in this lecture, but promised for later)
• Berquist’s Point: The problem is not unique to philosophy; it arises in quantum theory when electrons appear to jump between energy levels, and the solution to such apparent contradictions constitutes a genuine discovery

Why Is the Study of Place, Empty, Time, and Continuous Essential? #

• Connection to Motion: These are all intrinsically or extrinsically connected to motion
• Connection to Nature: Motion is in the very definition of nature
• Universality: These concepts are common to all natural things and therefore should be studied generally before particular applications
• Necessity for Theology: Understanding these concepts is necessary for addressing theological problems like transubstantiation

Can Motion Be Defined? #

• Descartes and Locke: No, motion is a simple idea and cannot be defined
• Aristotle’s Position: Yes, motion can be defined, though not by dividing it into parts
• Berquist’s Explanation: Motion is always “of another” (the falling is not what falls), and this dependence on a subject provides the multiplicity necessary for definition
• Analogy: Just as a point (indivisible) can be defined as “the limit of a line,” motion can be defined through its relationship to potentiality and actuality

Why Do Moderns Fail to Grasp Motion’s Definability? #

• Descartes confuses certitude (being sure about something) with clear and distinct knowledge of what it is
• Locke’s distinction between simple and composite ideas leads him to misclassify motion
• Both overlook that Aristotle himself recognized that not everything can be defined, and he knew where the limits were
• Modern philosophers seem unaware that this problem was already solved

How Does Imagination Limit Our Understanding of Immaterial Things? #

• We cannot imagine without imagining the continuous (spatially extended and temporal)
• This leads to false imaginative pictures of immaterial realities (e.g., the soul as an air-like human shape)
• To understand immaterial beings, reason must transcend imagination
• This is why the study of immaterial things belongs to later stages of philosophical development
• Logic helps prepare the mind because it deals with universals, which cannot be imagined

Connections to Prior and Future Material #

Relation to Book 6 of Aristotle’s Physics #

• The solution to the paradox of becoming is found in Aristotle’s treatment of the continuous in Physics Book 6
• This lecture sets up the problem that will be resolved later in the course

Relation to Transubstantiation #

• The theological application of the paradox makes the philosophical problem urgent for medieval and Thomistic theology
• Thomas, knowing Aristotle’s solution, was able to address the theological difficulty
• The problem demonstrates how philosophical precision is necessary for theological clarity

Relation to Modern Philosophy and Science #

• Hegel’s admission of contradiction in change represents a failure to apply Aristotle’s solution
• Quantum theory’s apparent contradictions are structurally similar to the classical paradox of becoming
• The discovery of solutions to apparent contradictions advances science and philosophy

Relation to Logic and Metaphysics #

• Understanding requires grasping what stands under (ὑπο + κείμενον, hypo + keimenon) a thing—connected to substance (οὐσία)
• Universals cannot be grasped through imagination; they require rational understanding
• This connects to the later study of being, substance, and the categories