57. Motion, Continuity, and Natural Philosophy

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Lecture Notes

Main Topics #

• Motion as the Heart of Natural Philosophy: Since nature is defined as “the beginning of motion and change,” understanding motion is essential to understanding nature itself. The remaining six books of the Physics revolve around motion in various ways.
• The Continuous vs. The Discrete: A fundamental distinction that applies to quantity in logic, mathematics, natural philosophy, and even the knowledge of the soul.
• Two Definitions of Continuous: Logic defines the continuous by form (parts meeting at a common boundary); natural philosophy defines it by matter (infinitely divisible).
• Motion as a Property of the Continuous: Motion is continuous rather than discrete, which means it is infinitely divisible and has the property of the unlimited.

Key Arguments #

Why Motion Must Be Studied First #

• Nature is defined by motion; if motion remains unknown, nature remains unknown
• Motion is the most obvious manifestation of nature; “nature loves to hide,” revealing itself through what things do or undergo

The Two Definitions of the Continuous #

In Logic:

• A continuous quantity is one whose parts meet at a common boundary (or “common limit”)
• Example: Two line segments meet at a point; two surfaces meet at a line; two volumes meet at a surface
• This definition emphasizes form and wholeness (how parts compose the whole)

In Natural Philosophy:

• The continuous is that which is divisible forever (infinitely divisible)
• The discrete (e.g., numbers) is not divisible forever
• Example: You can divide a line indefinitely; but you cannot divide the number 7 indefinitely (three and four do not divide further into meaningful parts)
• This definition emphasizes matter and division (how wholes break down into parts)

Why These Different Definitions? #

• Logic is an immaterial science and defines by form
• Natural philosophy defines by matter, which is appropriate to its subject
• Both definitions describe the same reality but from different perspectives

The Significance of Divisibility Forever #

• The continuous is divisible forever; this creates the notion of the unlimited (infinite divisibility)
• This unlimited divisibility appears first and foremost in the continuous
• Time and distance are both continuously divisible: if a slower body covers distance D in time T, a faster body covers D in less time; in that lesser time, the slower body covers less distance; and the faster body covers that lesser distance in even less time

Application to Reason and the Soul #

• Thoughts are like numbers (discrete), not like continuous quantities
• Reason understands even continuous things in a non-continuous way
• This non-continuous character of thought is a sign that reason is not a body (which is continuous)
• Therefore: reason is not matter; reason is not a body

The Problem of Infinite Division in Knowledge #

• Definitions are not divisible forever: eventually you reach something known not by definition but immediately
• Reasoning is not infinitely regressive: eventually you reach statements known without proof
• If definitions or proofs were infinitely divisible, there would be an infinite chain before any knowledge could be attained
• Just as a dictionary cannot define all words by other words (you must eventually associate a word with something sensible), so too reason must reach first principles

Important Definitions #

The Continuous (λογική definition / in Logic) #

• Definition: A quantity whose parts meet at a common boundary or limit (terminus communis)
• Logical Name: Continuous quantity (quantitas continua)

The Continuous (φυσική definition / in Natural Philosophy) #

• Definition: That which is divisible forever (divisibile in infinitum)

The Discrete #

• Definition: A quantity whose parts do not meet at any boundary
• Example: In the number 7, the parts 3 and 4 (or 2 and 5) do not meet in anything; they are simply separated

The Unlimited (ἀπειρον) #

• First appears in the continuous
• Refers to infinite divisibility, not infinite extension
• A property of continuous quantity

Examples & Illustrations #

The Continuous in Geometry #

• Two line segments: continuous at a point
• Two surfaces: continuous at a line
• Two volumes: continuous at a surface

The Discrete in Numbers #

• Seven = 3 + 4: the three and four do not meet at anything
• Seven = 2 + 5: similarly, no common boundary
• Unlike geometric figures, numbers have no position and no common meeting point

Divisibility #

• A line is divisible forever: each segment can be divided again indefinitely
• The number one (in pure arithmetic) is indivisible but has no position
• The point (in geometry) is indivisible but has position
• This is why arithmetic is more certain than geometry: geometry must account for position, adding complexity

Motion and Time #

• If a slower body moves distance D in time T, a faster body moves D in time T-1
• In time T-1, the slower body covers distance D-1
• The faster body covers D-1 in time T-2
• This shows both time and distance are divisible forever

Notable Quotes #

“Since nature is the beginning of motion and change, what motion is then ought not to be hidden from us. For this being unknown, necessarily nature is unknown.” — Aristotle, Physics III.1

“Motion seems to be among the continuous things.” — Aristotle, Physics III.1 (Berquist notes: Aristotle says “seems” because he has not yet proved it; the proof comes in Book VI)

“The unlimited first appears in the continuous.” — Aristotle, Physics III.1

“Thoughts are like numbers; thoughts are discrete, not continuous.” — Aristotle, On the Soul (as discussed by Berquist)

Questions Addressed #

Why Is the Distinction Between Continuous and Discrete Important? #

• For Mathematics: It distinguishes geometry (books I-VI of Euclid, on continuous quantity: lines, angles, figures) from arithmetic (books VII-IX of Euclid, on discrete quantity: numbers)
• For Understanding the Soul: The discrete character of thought shows that reason is not a body, since bodies are continuous
• For Metaphysics: It illuminates the relationship between matter (associated with divisibility) and form (associated with wholeness)

Why Does Aristotle Define the Continuous Differently in Logic vs. Natural Philosophy? #

• Logic emphasizes form and wholeness (parts meeting at a boundary)
• Natural philosophy emphasizes matter and division (infinite divisibility)
• Each definition is appropriate to its discipline and its way of proceeding

How Does the Continuous Dominate Our Knowledge and Language? #

• We first know continuous things through our senses and imagination
• We name continuous things before discrete things
• Names for continuous things (beginning, end, before, in, above, below) are extended metaphorically to other domains
• Even when we discuss discrete things (like numbers), we often borrow language from the continuous (e.g., “continuous proportion” in arithmetic)

Connections to Other Material #

• Book VI of Physics: Where Aristotle proves more explicitly that motion is continuous and develops the philosophy of the continuous
• Book III of On the Soul: Where Aristotle argues that thoughts are like numbers and not continuous, demonstrating the immateriality of reason
• Euclid’s Elements: Books I-VI on geometry (continuous quantity); books VII-IX on arithmetic (discrete quantity)
• Thomas Aquinas: Comments on this distinction and uses it in his theology