81. The Indivisibility of the Now and Motion

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Lecture Notes

Main Topics #

The Nature of the Now (Nunc) #

• The now is that which is present “through itself and first” (per se et primo), not through another
• The now serves as the indivisible limit or boundary of both past and future time
• Unlike a year, month, day, or hour, which have parts in past and future, the now has no parts
• The now is present to itself, not to some part of itself

The Continuous and Its Limits #

• Continuous time is defined as that whose parts meet at a common boundary
• The past extends up to the now; the future extends from the now
• If past and future had different limits, there would be time between them (a gap), making them discontinuous
• Therefore, the same now must be the limit of both past and future
• The limit cannot be the same kind of thing as what it limits: a point is not a line; time is not the now

The Faster-and-Slower Argument #

If two bodies move at different speeds (e.g., 3:2 ratio) in what is claimed to be an indivisible now:

• The faster body travels through three indivisible magnitudes (A, B, C, D)
• The slower body travels through only two indivisible magnitudes (E, F, G)
• The time is divided into three indivisible units (K, L, M, N)
• The slower body travels distance E-F-G in the full time K-M-N
• But then the slower must cover one and a half indivisibles in the full time
• This requires dividing the indivisible—a contradiction
• Conclusion: If magnitudes and times are indivisible, the faster-and-slower argument shows contradiction; therefore, the now cannot be indivisible in the way supposed

No Motion in the Now #

• Motion requires a before and after (temporal extension)
• The now, being indivisible and present through itself, has no before or after
• Therefore, motion cannot occur in the now
• A body may be in a place at a given now, but this is not motion; it is rest or stasis
• Even though a photograph captures motion, at the instant captured there is no motion occurring

The Distinction: Composed vs. Indivisible #

• Aristotle distinguishes two separate negations:
  1. The continuous is NOT composed of indivisibles
  2. The continuous is NOT indivisible
• These are not the same statement
• A point, for example, is not composed of indivisibles, but it IS indivisible
• The number one (monas) is indivisible but not composed of indivisibles

The Imperfection of Motion #

• Motion “barely is” because it exists nowhere fully present:
  • Not in the now (the only truly present thing)
  • The past is no longer
  • The future is not yet
• Motion exists only divided across time
• This explains why motion is called an “imperfect act” (actus imperfectus)
• Paradoxically, what seems most real to our senses (motion) is least real in being
• What seems unreal to us (eternity, being) is most real

Key Arguments #

The Limit Cannot Be Part of What It Limits #

• A point is the limit of a line but is not part of the line’s length
• A line is the limit of a surface but is not part of the surface’s area
• A surface is the limit of a body but is not part of the body’s volume
• Therefore, the now is the limit of time but is not part of time itself
• The now is in the boundary between past and future but not in the time that is the past or future

The Common Boundary Argument #

• If the end of the past and the beginning of the future were different limits, time would exist between them
• This analogy: if the US-Canada border were not the same line on both sides, there would be a no-man’s-land
• Continuity requires a single common boundary
• Therefore, the same now must be both the end of the past and the beginning of the future

Why the Now Is Indivisible #

• If the now had any temporal extension, it would have parts before and after
• Those parts would not all be “at once” (simul)
• The now would then be present only through part of itself, not through itself and first
• This contradicts the definition of the now
• Therefore, the now must be completely indivisible

Important Definitions #

Nunc (The Now) #

The indivisible limit of time that serves as the common boundary between past and future. It is present through itself and first (per se et primo), with no temporal extension or internal divisibility.

Continuum (The Continuous) #

That whose parts meet at a common boundary (from logic); equivalently, that which is divisible forever into always-divisible parts (from natural philosophy). Time is continuous.

The Limit (Terminus) #

That which bounds a magnitude or time but is not the same kind of thing as what it bounds. The point is the limit of a line; the now is the limit of time.

Motus (Motion) #

An imperfect act that requires temporal extension. Since motion is not fully present in any single now, it barely is—existing only across divisible time.

Examples & Illustrations #

The Divisible Magnitudes #

Berquist walks through the faster-and-slower argument using concrete labels (A, B, C, D for the faster body’s path; E, F, G for the slower body’s path; K, L, M, N for temporal units). This demonstrates how assuming indivisible moments and magnitudes leads to the necessity of dividing indivisibles.

The National Border Analogy #

The boundary between the United States and Canada is a single limit from both sides. If these were different limits, there would be a no-man’s-land between them, and the nations would not be continuous. Similarly, the now is the single common boundary of past and future.

The Tax Deadline #

April 15th at midnight is the deadline for filing taxes. This instant is the limit of the filing period but is not itself a time or duration—one cannot “do” anything in that indivisible instant. Similarly, the now is the limit of time but not time itself.

The Road to Boston #

The road from Springfield to Boston has a definite beginning (at Springfield) and end (at Boston). However, one can begin a journey to Boston from any point along the road. This illustrates that the “beginning” of a journey need not be the ontological beginning of the road.

The Photograph #

A photograph captures a moving object at a single instant. In that captured moment, the object appears stationary, yet it is not truly at rest. It is merely in a place at that now. This illustrates the paradox: no motion occurs in the indivisible now.

The Laminated Counter Surface #

A kitchen counter with a laminated surface appears to have a surface, but this surface has thickness and can be peeled off—making it actually a thin body, not a true surface. A true surface, like the now as limit, must be depthless (indivisible).

The End of the Day #

The “end of the day” is not any hour or time period (like 11:00 PM or the last hour of the day). The end of the day is the indivisible instant when one day becomes the next. This mirrors how the now is not itself time but the limit of time.

Questions Addressed #

Can the Now Be Divisible? #

Question: If we say the now is the limit of time, and if it had any extension, wouldn’t it be divisible?

Answer: Yes, and this leads to contradiction. If the now had extension, it would have parts that are before and after. But then those parts would not all be present “at once,” which violates the definition of the now as that which is present through itself and first. Therefore, the now must be absolutely indivisible.

How Can the Same Now Be the Limit of Both Past and Future? #

Question: Doesn’t the past end at one now and the future begin at a different now?

Answer: If they were different, there would necessarily be time between them. But this would make past and future discontinuous, violating the definition of continuous time. The same now must serve as both the end of the past and the beginning of the future, just as the US-Canada border is the single limit from both sides.

Can Motion Occur in the Now? #

Question: Why can’t something move in an indivisible instant?

Answer: Motion requires a before and after—temporal extension. An indivisible now has no before or after. Therefore, motion is impossible in the now. The faster-and-slower argument demonstrates that assuming motion in an indivisible instant leads to the absurdity of having to divide the indivisible.

If Motion Cannot Occur in the Now, When Does Motion Really Exist? #

Question: If motion is not in the now (the only truly present instant), is motion real at all?

Answer: This is the source of motion’s paradoxical nature. Motion barely is because:

• It is not in the now (which is the only thing fully present)
• The past is no longer
• The future is not yet
• Therefore, motion exists only divided across time, making it what Aristotle calls an imperfect act

Why Does Motion Seem More Real Than Eternity If It Barely Is? #

Question: If motion is least real in being, why does it dominate our perception?

Answer: Motion strikes our senses forcefully. As Shakespeare notes, “Things in motion sooner catch the eye than what not stirs.” We are naturally drawn to change. But what seems most real to us (motion) is actually least real in being, while what seems unreal to us (eternity, God) is most real. This is a fundamental reversal of appearance and reality.

Is the Now Part of Time? #

Question: If the now is the limit of past and future, is it itself part of time?

Answer: No. Just as a point is not part of a line (it is the limit of the line), the now is not part of time. The now is in the boundary (in termino) between past and future, but the past and future are parts of time, and the indivisible now is not divisible enough to be a part of divisible time.