63. Time as the Number of Motion: Definition and Nature

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Lecture Notes

Main Topics #

Two False Opinions About Time #

Aristotle first dismisses two crude opinions:

• Opinion 1: Time is the circular motion of the heavens
• Opinion 2: Time is the sphere (the celestial sphere itself)

Berquist notes these fail because they confuse different senses of words (equivocation on “in”) and make time local rather than universal.

The Relationship Between Time and Motion #

Central Problem: Is time itself a motion, or something of motion?

Aristotle argues time is NOT motion through two key arguments:

1. The Localization Argument: Motion exists only where the thing moving is (e.g., the sun’s motion is in the heavens). But time seems to exist everywhere and in all things simultaneously. Therefore, time cannot be motion.
2. The Faster/Slower Argument: Motion can be faster or slower. But fast and slow are themselves determined by time (fast = much distance in little time; slow = little distance in much time). Time is not determined by time. Therefore, time is not motion.

Conclusion: Since time is not motion but also not without motion, time must be something of motion—specifically, an aspect or property of motion.

The Perception of Time Through Change #

We perceive time only when we perceive change:

• If we experience no change (dreamless sleep), we are not aware of time passing
• When change ceases to be distinguished, the earlier and later “now” seem identical
• Only when we perceive before and after in motion are we aware of time

Continuous Magnitude and Divisibility #

Time is continuous because it measures motion over continuous magnitude:

• Every magnitude is continuous and divisible forever
• Motion over a magnitude is therefore continuous
• Time measuring that motion is therefore continuous

Proof of Infinite Divisibility: The faster/slower distinction demonstrates that both distance and time are infinitely divisible. If a slower body covers less distance in the same time, the faster body must cover that lesser distance in less time—an infinite regress.

Before and After in Magnitude, Motion, and Time #

The structure of “before and after” appears in a hierarchy:

• First, before and after exist in magnitude (spatial ordering)
• Second, before and after are found in motion (the moving thing follows a path with before and after)
• Third, before and after characterize time itself

If a road has a before (starting point) and after (ending point), then the motion over the first part comes before the motion over the second part, and correspondingly, the time for the first part comes before the time for the second part.

The Now and Its Paradox #

The “now” (nunc) is indivisible and has no duration. The paradox: How can the now remain the same throughout time if time is always changing?

Resolution: The now is the same as to what it is (it always remains a dividing point between past and future), but it is always other as to its temporal position (it is always before or after other nows). This mirrors how a moving object is the same as to its substance but other as to its location.

Key Arguments #

Argument Against Time Being Motion (Reading 16) #

1. Change or motion exists only where the changing thing is located
2. Time seems to exist everywhere and in all things simultaneously
3. Therefore, time cannot be identical to motion

Supporting Argument: Parts and wholes differ. A part of circular motion is not itself circular motion, yet a part of time is time. This shows time has a different structure than motion.

The Infinite Divisibility Argument #

If motion is continuous over continuous magnitude:

1. A slower body covers distance D in time T
2. A faster body covers distance D in time T’ (where T’ < T)
3. In time T’, the slower body covers distance D’ (where D’ < D)
4. The faster body must cover D’ in time T’’ (where T’’ < T')
5. This process continues infinitely
6. Therefore, both distance and time are infinitely divisible

The Equivocation on “In” #

Melis and others confuse different senses of “in”:

• “All things are in place” (contained spatially)
• “All things are in time” (ordered temporally)
• From these, they falsely conclude: “All things are in the same thing” (time = place)

Berquist emphasizes: These are not the same sense of “in,” though they bear a likeness. As the Fourth Lateran Council teaches, we must note not only likeness between concepts but also the greater unlikeness between them.

Important Definitions #

Time #

“The number of motion according to before and after” — Time is not motion itself but the enumeration or measurement of the successive moments (before and after) in continuous motion. It counts the before-and-after structure inherent in motion.

The Now (nunc) #

The indivisible point that divides the past from the future. It has no duration and is not a part of time but rather its boundary. Analogous to a point on a line.

Continuous (continuum) #

That which is divisible forever; a quantity whose parts meet at a common boundary. All three—magnitude, motion, and time—are continuous.

Before and After #

The ordering of temporal moments; originates in the spatial ordering of magnitude, extends to the ordering of positions in motion, and is essential to the definition of time.

Numbered Number vs. Numbering Number #

• Numbered number: The enumeration itself, the concrete count (e.g., “three days”)
• Numbering number: The abstract number by which we count (e.g., “three” in arithmetic)
• Time is a numbered number, not a numbering number

Examples & Illustrations #

Rip Van Winkle #

Washington Irving’s protagonist falls asleep for ten years but experiences no passage of time because no change occurs during his sleep. He only realizes time has passed when he wakes and observes that things have changed (the tavern sign changed from King George III to George Washington, people have aged, etc.). This illustrates that time awareness depends on perceiving before and after in motion or change.

The Sleeper in the Hospital #

A hospital patient may sleep for two days but believe only one day has passed. The patient perceives no motion or change during sleep and thus joins the “earlier now” (falling asleep) with the “later now” (waking up) as if they were one. No time seems to have passed because there was no distinguishable change.

Shakespeare’s Sonnet on Time #

Berquist quotes Shakespeare: “Like as the ways make towards the pebbled shore, / So do our minutes hasten to their end.” This simile compares the motion of waves (before and after) to the motion of minutes (before and after), illustrating our intuition that time is connected to motion and change.

Richard II in Prison #

Shakespeare’s Richard II, imprisoned and losing his throne, becomes aware of the passage of time through his weeping and emotional turmoil. Shakespeare says time “made me her numbering clock”—showing that we become aware of time through perceiving change in ourselves.

The Ball and Motion #

When a baseball is hit and caught in the outfield, it is the same ball as to its substance but different as to its location at different moments. Similarly, the now is the same in its nature but always other in its temporal position.

The Road Journey #

Traveling from one town to another illustrates the parallel before-and-after structure:

• The road has a before (starting point) and after (destination)
• The motion over the first part of the road comes before the motion over the second part
• The time to travel the first part comes before the time to travel the second part

Thoughts vs. Lines #

Thoughts are discrete (like numbers) with a definite next thought—in a syllogism, the conclusion follows the premises with nothing between. But continuous lines have no next point (any line between two points can be divided). This shows thinking is not continuous even when reasoning about continuous things.

Questions Addressed #

How Can Time Be Connected to Motion but Not Be Motion Itself? #

Resolution: Time is to motion as the now is to a thing in motion. Just as the thing in motion is the same in nature but always other in location, the now is the same in nature but always other in temporal position. Time measures the before-and-after structure of motion without being motion itself.

Why Do We Perceive Time Only When We Perceive Change? #

Resolution: Because time is the number of motion according to before and after. Without distinguishing before and after (which requires perceiving change), we cannot perceive time. The now seems to remain one and undivided when no change occurs, so no time is experienced.

How Can Time Be Everywhere if Motion Is Localized? #

Resolution: Time is not a motion but something of motion. It measures all motions according to their before-and-after structure. The sun’s motion is in the heavens, but the time it takes to go from one point to another applies everywhere—time is universal while motions are particular.

How Is Time Continuous? #

Resolution: Because magnitude is continuous and divisible forever, motion over that magnitude is continuous, and therefore time measuring that motion is continuous. The proof: the faster/slower distinction requires infinite divisibility of both distance and time.

Connections and Context #

Berquist connects this investigation to earlier lectures:

• The equivocation on “in” parallels previous discussions of the eight senses of “in” in the Categories
• The Fourth Lateran Council’s principle about noting both likeness and greater unlikeness between creatures and God applies to understanding how time relates to (but differs from) motion
• The analysis of before and after continues work from the Categories on the meanings of “before”
• The investigation will continue in Book VI of the Physics regarding the continuous