Beginning the Study of Time: Puzzles About the Now

Orientation #

He begins directly with “the beginning of this fifteenth reading” and refers back to “what we saw in the beginning of the book” (that everyone is sure time exists) and to the treatment of place (the glass and the water); he says more will be shown “when you get to the sixth book” and promises a “theological footnote” on the definition of eternity later in the study of time. He also says “next week we’re going away” (trip with his wife; the recording cuts off in an airport anecdote). The previous class finished the eight senses of “in” and noted the primary sense is spatial, which was to matter for time; the next takes up readings sixteen and seventeen on opinions identifying time with celestial motion.

The class, in order #

1. Turning to time: the order of questions (“there remains to go toward time”) #

The point: Thomas pauses on “to go toward time” as Aristotle’s hint that time is hard to understand; the first question is whether time exists at all.

• Augustine, Confessions: if no one asks me what time is, I know; if someone asks, I don’t.
• “External reasons”: he does not know what Thomas means unless dialectical reasons, ones in common circulation “even outside the school.”
• Order of inquiry from the Posterior Analytics: if it is not clear that something exists, ask “does it exist?” before “what is it?” Example: Summa q. 2 on God’s existence before what God is (or isn’t).
• Two alternatives Aristotle poses: time either wholly is not, or “barely exists, and darkly.” Aristotle will not deny time exists; he takes the second: it barely exists, hence hard to know, “dark because there’s hardly anything there to be known.”

2. First argument: put together from non-existents (“what is put together from non-existing things”) #

1. One part of time has come to be and is not (the past); the other is going to be and is not yet (the future).
2. Time is put together from these.
3. What is put together from non-existing things cannot partake of existence. Conclusion: time seems not to exist.

• Hidden assumption (stated explicitly by Aristotle in the third paragraph): the now, the present in the strict sense, is no part of time; no time is in the now.
• Strict vs. loose “now”/“present”: the loose sense includes some past and future. Regress: the present year, month, day, hour, minute each is partly gone and partly to come. Any amount of time has before and after; “now” means being together, not before and after. So no time in the now.
• Hence time is only in past and future, and neither exists: “how can time really be… but it is, huh? It hardly is.”

3. Second argument: parts, and the now is not a part (“the now is not really a part”) #

1. If what has parts is, all or some of its parts must be when it is.
2. Time’s parts: some have come to be, some are going to be; none are, unless the now.
3. The now is not a part: a part measures the whole, and the whole is put together from its parts; time does not seem to be put together from nows.

• “Does not seem” because it will be shown fully in Book VI that a line is not put together from points; the now is to time as the point to the line; in general nothing continuous is put together from indivisibles.
• Against the mathematician’s “line composed of an infinity of points”: to compose is to put together; points would have to touch; having no parts, they can touch only by coinciding; then no more length than one point. Proportionally: lines put together give no width (no square), circles stacked give no depth (no cylinder), unlike pancakes, which have thickness.
• Democritus fragment (Heath, Greek Mathematics, Loeb; handout): a cone imagined as a stack of circles; cut it parallel to the base; the two exposed circles are equal or unequal. If equal wherever you cut, you have a cylinder (rectangle rotated), not a cone (triangle rotated). If unequal, the edge would not be straight. The insoluble problem arises from falsely imagining a stack of circles, which coincide in depth and give no depth.
• Examples of the absurdity of a whole whose parts don’t exist: the chair without legs, seat, back; the word “cat” on the board without c, a, t.
• What he stresses: from the beginning of the book one is “very sure that time exists”; the arguments force the mind to see it exists barely, darkly, “quomodocumque” in the Latin, “very, very tenuous.”
• Parallel, motion: walking from here to my hat, part gone by, part to come; how much motion is in the now? If any, I’d be simultaneously in two places. So motion hardly exists either.
• Parallel, matter: Augustine, not trained by Aristotle as Thomas is, does not know what to say about matter (“a something that is nothing, or a nothing that is something”), because ability [ed.: potency] hardly exists.

4. Is the now always other? When does it cease to be? (“there’s no next now”) #

The point: the now is not a part but the division between past and future; Aristotle asks whether it remains always one and the same, or is other and other, and raises problems for each. Horn one, the now always other:

1. Then the present now must go out of existence and be replaced (even as I talk, a new now).
2. It cannot cease to be when it is; so in some later now.
3. But there is no next now: two nows that are not the same always have time between them (as two points have a line between), else they would touch, coincide, and be one.
4. So whatever later now you pick, there is time and an infinity of nows between, and the present now would coexist with all of them, which is absurd (two nows existing together). Thomas’s text: it cannot cease in itself, nor in another now, “for it is impossible that nows be next to each other, as a point to a point.”

• Line example: end point, later points; no next point, because between any two there is a line, potentially an infinity of points. Likewise no next longer or shorter line, unlike numbers, where eight has a next number.
• Digression, thoughts are like numbers (On the Soul, Book I): the syllogism “every mother is a woman, no man is a woman,” next thought “no man is a mother,” nothing in between; building “square” from quadrilateral, equilateral, right angle; dividing number into odd and even, plane figure into circular and rectilinear, then triangle and quadrilateral: one division comes next after another. So “a line of thought” is a misleading phrase. A good student anticipates the next thought; a professor teaching in order knows it.
• Student’s question: is “no next” a property of the continuous or part of its definition? Answer: it follows from the definition, since the continuous is divisible forever; it is “something additional to be seen.”
• What he stresses: this is “one of the most important ways” we see that reason is not a body: it thinks about continuous things in thoughts that are not continuous, which cannot be explained by what it thinks about; it thinks about bodily things in an unbodily way because it is not a body.
• Book VI definitions previewed: continuous vs. touching vs. next. Continuous: share a common limit. Touching: limits not common but together (place: inner surface of the glass and outer surface of the water are together but not the same surface, else the water would be in the glass as part in whole). Next: nothing of the same kind between, though something may be between (the next house on the block, with bushes and air between; the next student, Anthony, with nothing but no other student between). What continues or touches is also next, but next can be without either.
• Aside: a “theological footnote” will come in the study of time on the definition of eternity (as De Koninck did at the end of his course); like everything about God it involves negation, of things about time and about the now, so both must be understood; and they are connected anyway, since the now is in time.

5. Is the now always the same? (“of no limited divisible thing is there one limit”) #

Horn two, the same now always:

1. Of no limited divisible thing is there one limit, whether continuous in one way or in many: the two ends of a straight line, the bounding lines of a plane figure, the two ends of a cone cannot be the same.
2. The now is a limit of time; a period of time has a now at its beginning and at its end, and if they were the same now there would be no time at all, as two coincident end points give no line.
3. To be simultaneous according to time, neither before nor after, is to be in one and the same now; so if the now were always the same, things a thousand years ago and today would be simultaneous: Aristotle lecturing now, Plato, Thomas (“a nice warm feeling, but I don’t think it’s true”).

• Thomas’s text closes: “let then these many things be in doubt about what belongs to the now.” Left in doubt at this stage.
• Categories: the chapter after before/after is on simul, together, the negation of before and after.
• Aside: the hypothetical, hear one lecture of Aristotle or of Thomas; Warren Murray chose Aristotle, since we know roughly what medieval schools were like but have an inadequate idea of the Lyceum or Academy.

6. Student’s question: are we imagining wrongly? Difficulty in us or in the thing (“in one way difficult and another easy”) #

A student asks whether the puzzles arise because we imagine time wrongly; he answers by turning to Metaphysics Book II (“the second book of wisdom”).

• Knock on each professor’s door at Assumption College: “is it difficult or easy to know the truth?” Most say difficult or impossible; Aristotle: “in one way difficult and another easy.” He shows three ways it is easy (not enumerated here), then asks why it is difficult: the cause is either in us or in the thing, and the chief difficulty is in us.
• The distinction transfers to loving: difficulty loving the common good over the private good is in your heart, since the common good is the greater good; loving a girl for outward appearance over inward virtue, the defect is in you (Bassanio on Portia: “richly left… fair, and fairer than that fair… wondrous virtue”: least lovable for wealth, more for beauty, most for virtue; Alcibiades on Socrates, ugliest man in Athens with something lovable hidden within); difficulty loving God is in you; difficulty loving cancer is in the cancer.
• Understanding other people: a student says it could be both; he agrees. Less reasonable than you: the difficulty is in them (senseless crimes in the newspaper; historians whose choice of Arabic history or Restoration England has no real reason, just an accidental good teacher). More reasonable: the difficulty is in you (the saints; a saint offering twenty dollars for one, since the ratio of eternity to time is infinitely greater; “so reasonable that you can’t understand him”).
• Application to philosophy’s three parts (mathematical, natural, wisdom): natural philosophy and wisdom are both harder than geometry, but for different reasons. Natural philosophy: the cause is in the thing, since motion, time, matter with its potency hardly exist (“barely and darkly,” second paragraph of the reading). Wisdom, approaching angels and God: the cause is in us; God “dwells in light inaccessible,” is most knowable, so if not most known to us, that is our defect.
• Aside: the joke that one “can’t understand a woman” is not necessarily a compliment, depending on where the difficulty lies. Class ends for mass; the airport anecdote is cut off.

His words #

• go toward time; Thomas’s rendering, taken as insinuating the difficulty.
• external reasons; he guesses dialectical, in common circulation outside the school.
• barely and darkly; time’s mode of existence; “quomodocumque” in the Latin.
• now in the strict sense; the present containing no past or future; loose sense includes some of each.
• part; what measures the whole, from which the whole is put together; the now is not one.
• division; what the now is, between past and future.
• compose; to put together; points cannot compose a line.
• ability [ed.: potency]; matter’s mode, which “hardly exists.”
• next; nothing of the same kind between; distinct from touching (limits together) and continuous (common limit).
• natural hearing [ed.: Physics]; “the sixth book of natural hearing.”
• simul, together; negation of before and after (Categories).
• wisdom [ed.: Metaphysics]; “the second book of wisdom.”

Texts #

Read in class

• Thomas Aquinas, Commentary on the Physics, reading 15, opening paragraphs on whether time is, the two arguments, and the problems about the now (Physics IV.10, inferred), read and commented.
• Democritus, fragment on the cone: handout “On the Natural Fragments,” p. 33 (DHB Vol. I, The First Philosophers, p. 146), expounded.
• Shakespeare, The Merchant of Venice, Bassanio’s lines on Portia, quoted. Mentioned
• Augustine, Confessions, on time and on matter.
• Aristotle, Posterior Analytics, order of the questions.
• Thomas Aquinas, Summa theologiae I, q. 2.
• Heath, Greek Mathematics (Loeb, 2 vols.).
• Aristotle, Physics VI (line not from points; continuous, touching, next).
• Aristotle, On the Soul, Book I (thoughts like numbers).
• Aristotle, Categories, chapters on before/after and simul.
• Aristotle, Metaphysics, Book II, opening.
• Plato’s Alcibiades on Socrates (Symposium, inferred).
• Scripture: God dwells in light inaccessible (no locus given).
• De Koninck’s course on time; Warren Murray.

His questions #

• Whether time is among the things that are, or the things that are not? Aristotle takes the second alternative: it exists barely and darkly, hence is hard to know.
• Can you have any amount of time that is present in the strict sense? No; any amount has before and after, and the now means together; so no time in the now.
• Can you put together a line from points? No; points with no parts can touch only by coinciding, giving no length; likewise lines to a square, circles to a cylinder.
• How much of my motion is ever actual, in the now? None; if any motion were in the now I’d be in two places at once; motion hardly exists either.
• When does the present now cease to be? Not when it is, nor in another now, since there is no next now and it would coexist with infinite nows between; absurd.
• Is there a next point on the line, or a next longer line? No, unlike numbers; but there is a next thought, so thoughts are like numbers.
• Is “no next” a property of the continuous or part of its definition? It follows from the definition, divisible forever; an additional thing to be seen.
• Can the now at the beginning and end of a period be the same now? No; no limited divisible thing has one limit, and everything would be simultaneous.
• Is it difficult or easy to know the truth? Aristotle: in one way difficult, in another easy; the cause of difficulty is in us or in the thing, chiefly in us.
• Is the difficulty of natural philosophy in us or in the thing? In the thing, since motion, time and matter hardly exist; for wisdom, in us.