The Now as Indivisible Limit of Past and Future

Orientation #

He opens by saying the previous class “ends the general consideration of the continuous” and that today begins Thomas’s reading 5, which prepares the more particular study of the divisibility of motion; “we may not get all the way through reading five today.” He refers back to Book IV (“we met the now back in Book Four”) and to “the axiom we talked about last time” that the limit of a thing is not the same kind of thing as what it limits (prev. lecture). The previous session concluded Aristotle’s general argument that no magnitude, time or motion is indivisible; the next continues reading 5 with the proofs that nothing moves or rests in the now and that whatever changes is divisible.

The class, in order #

1. What reading 5 will establish; the subject of natural philosophy (“the mobile itself, is what divisible”) #

Point: reading 5 presupposes two things for the study of the divisibility of motion: (a) there is no motion in the now, which requires showing the now is indivisible; (b) the mobile itself is divisible.

• Why (b) matters: Thomas in the proemium says the subject of natural philosophy is ens mobile (in the Ethics commentary, res mobilis), not movable body, even though “everything that moves is a body.” That the mobile is divisible, hence a body, is proven here in Book VI; so “body” is a property/conclusion, not the subject.
• Euclid comparison: triangle is not defined as a figure whose interior angles equal two right angles; that property is proved only at I.32 (after some back-and-forth over the number). The subject is known without its properties at the start of a science.
• Student: isn’t being mobile really a property of body, so the order is only in our knowledge? — Yes, it is the order of our knowledge, reasoning from the more universal to the less; it shows that “the fundamental notion isn’t [body] in our thinking.” Aside: starting from body, “you end up with a mathematical body, Descartes’ bodies.”

2. Digression: titles of Aristotle’s books and the four parts of natural philosophy (“the four parts of natural philosophy, in a certain way, correspond to the four causes”) #

• The second book after the eight books of “natural hearing” (the so-called Physics) is titled in Greek “about the universe/cosmos”; the Latin De caelo et mundo comes from the Greek word meaning both “heavens” and “universe”; since Aristotle also treats earthly bodies, they added et mundo. Titles are a matter of chance: “Physics” transliterates Greek phusis; the three books on the soul are always called by the Latin De anima ("Peri psychēs is too hard to say"). Go back to the original language for the title.
• Thomas’s proemium to the book on the universe: it treats the universe as a whole (limited or unlimited?) and its constituent parts; it is basically about change of place, and to know place you must eventually know the whole universe. Example: his boyhood address ending “the solar system, the universe”; “Where are we?” leads on to the ends of the universe.
• His own observation: each of the four parts of natural philosophy goes furthest with one cause — the eight books arrive at the unmoved mover (mover); generation and corruption goes all the way down to matter; the book on the universe reaches the order of the universe, “kind of like the ultimate form”; the biological books, where the human soul is “the end of nature,” go furthest with purpose. Every part still treats more than one cause.

3. Motion “barely is”; what seems most real to us (“motion seems most real to us because it strikes our senses”) #

Point: if there is no motion in the now, and only the now really is (past gone, future not yet), then motion barely is.

1. All that is really here is the now; the Roman Empire “is really now” only in the sense that now it is in the past.
2. If no motion is in the now, motion is either past or future, i.e. never quite “is” — which makes one “appreciate more calling the motion imperfect act.” Aristotle, Boethius after him, Thomas after both: motion (like time) barely is, hence hard to understand.
3. Yet Aristotle in “his book of wisdom” [ed.: Metaphysics] says motion seems most real to us because it strikes the senses. Shakespeare, Troilus and Cressida: “Things in motion sooner catch the eye than what not stirs.” Example: hiding in the bushes, don’t move. So what seems most real to us (motion) is least real; what is most real (God, eternity, angels) seems unreal to us.

• Aside: to a seminarian asking whether angels exist, “they’re more real than you are”; his teacher Kasurik: at death you will mistake your guardian angel for God. Fra Angelico (beatified, not canonized) alone approaches their magnificence — his brother Richard’s prints, San Marco’s cells; icon painters’ spiritual preparation vs. Western painters painting mistresses as Madonnas; the angel watching you “is like you watching an ant.”
• Aside (student remark accepted): we “falsely imagine eternity to be a frozen now” of time.

4. The now “not through another, but through itself and first” (“not through another, but through itself and first”) #

Point: the text seeks the now in the strict sense — present not by reason of a part, but through itself.

• Series of loose “presents”: the present year (partly past, partly future); the present month on the calendar, present only through one day; the present day, not present “all at once”; the present hour, present only through part of it. The strict now is the one not present through some part being present.
• Aristotle: such a now is necessarily indivisible and “exists in all time.” We met the now in Book IV; we will understand it better here.

5. The now as limit of past and future; two definitions of the continuous (“the same now, be the limit of both times”) #

Text: there is a furthest limit of the past beyond which nothing of the future lies, and of the future beyond which nothing of the past lies; this we say is the limit of both.

• The past may (by reason) extend backward forever — by faith it does not; the future, even by faith, we don’t know how far, only that it ends — but neither extends beyond the now on this side. So the now is end of the past and beginning of the future.
• Fits the definition of the continuous: time is continuous; continuous = parts have a common boundary (circle’s diameter: end of one semicircle, beginning of the other); so past and future share one boundary, the now.
• Student: that is the logic definition; can it be used interchangeably with the natural-philosophy definition (“divisible into always divisibles”)? — They are the same reality seen in contrary directions. Distinction: the line that divides the circle is also the limit at which its two parts are continuous; the point that divides a line is also the common limit of its parts. Logic looks from the parts to the whole (toward form: semicircles making a circle; a parallelogram’s diagonal giving two triangles that together make the parallelogram); natural philosophy looks from the whole to the parts (toward matter). Example: “cat is divisible into c-a-t” vs. “cat is composed of c-a-t.” Backed by the proportion from the four-causes chapter (three parts: naming/defining/exemplifying the causes; three corollaries; the universal understanding, with form : matter :: whole : parts) — so even the three orders of angels are “matter” of the hierarchy in a broad sense. Logic and math are formal sciences; natural philosophy goes down toward matter (from these books to the cosmos, to generation and corruption; from De anima down to anatomy), so it fittingly defines the continuous through its parts. Heraclitus: “the same way up and the same way down.”
• Student: is this table then divisible forever? — Thomas raises how this harmonizes with the arguments against Anaxagoras: here the continuous is considered in general, not yet applied to particular kinds of body; something may impede at the particular level.

6. The limit is not the same kind of thing as what it limits (“the limit of a body is not a body”) #

Point: from the axiom of last time, the now, as limit of time, cannot itself be a time; so it is indivisible.

1. Parts of a line meet at a point, of a surface at a line, of a body at a plane; past and future at the now.
2. Limit of a body is a surface (length and width, no depth); of a surface a line (no width); of a line a point (no length); a point has no limit — “it is the first limit,” not lacking one.
3. So the end of the day is not “the twelfth hour,” nor a minute, nor any time at all: a time would not be all there at the end. If the now were divisible it would be a time, and time would be the limit of time.

• Boundary case: the “surface” of a laminated kitchen counter that can be peeled off is really a body; the true surface is the depthless limit.

7. Why one and the same now (“You’d have time between them”) #

Point: the end of the past and the beginning of the future cannot be two limits, else time would lie between and past would not be next to future.

• Example: the northern limit of the US and the southern limit of Canada are the same limit; otherwise a no-man’s-land, and Canada would border the no-man’s-land, not the US.
• Aside: Palestine/Israel — the only “solution” proposed is a no-man’s-land, another Berlin Wall or Great Wall; “man has his own way of being endless… something endless about our fights.”
• Text: otherwise it would not be now “to itself, but to another” — not the strict now we are after.

8. Is the now “in” the past? The senses of “beginning” in Metaphysics V (“the foundation is the beginning of a what house”) #

Puzzle (student): if the now is the limit of the past, is it in the past? Is the endpoint in the line? — after hesitation: yes, it is in the line.

• Metaphysics V (first word of the book is “beginning”): the book treats the words used in wisdom — of its subject or its parts, its properties, its causes (Thomas: every science has subject, causes, properties). All are equivocal “by reason, not by chance”; Aristotle distinguishes and orders their meanings.
• Meanings of beginning: (1) of a magnitude — point of a line, the edge of the desk, the curb at the campus; (2) where it is most convenient to begin along the road — one need not go to where the road begins (Springfield) to travel to Boston; (3) the fundamental part — the foundation of a house; (4) the mover or maker — the house builder; (5) the starting point of knowledge (definitions, axioms, postulates in geometry).
• Why (3) precedes (4): Thomas — the foundation is a part of the house, the builder is not (“at least he shouldn’t be”); so the foundation is more like the point in the line. Why (5) is last: Thomas — we name things as we know them, first the sensible (a child knows “our land begins at the curb” before he knows axioms), then carried over to the less sensible, last to what cannot be sensed at all; knowledge is inside and hidden. “Aristotle’s ordered it perfectly.”
• On (2): Aristotle compares it to knowing — we begin not from the beginning of the thing but from what is more known to us. Water known before hydrogen, hydrogen before the proton (proton = “first”); Heisenberg: “we never start at the beginning”; if we began at the beginning we would begin with God, the last thing known in philosophy. “She hit me / she’s angry / something made her angry”: effect first, then cause, then cause of cause. Warning: some readers (John Galp, corrected by Msgr. Dionne, as Warren Murray recounted) take that text as being about the beginning of knowledge; that sense is the fifth. Aside: going to the road’s start would be “a neurosis… being a consistent philosopher.”
• Student: is (2) the beginning of a motion, as with “end”? — Yes; the beginning of my motion is the beginning of the distance I travel, not of the road; if I travel the whole road they coincide. Student’s proposed “subjective beginning” rejected: “nothing subjective about it,” it is a reasonable, convenient place.
• Return to the puzzle: the limiting line is in the circle but not strictly a part of it (what has no width is not part of what has width). Likewise the now is in the past and in the future, but the past is an amount of time, a divisible part, and “the indivisible is not a part of the continuous.” So there is no time in the now, and the past is not in the future. Examples: the end of the year is not December; April 15 tax deadline (Patriots’ Day extension in Massachusetts; penalty for not filing worse than for not paying) — the “end” is a postmark by midnight, not the last hour, half hour or minute: “the end of the day is no time at all.”
• Text: if the now had extension, there would be time in both past and future; and it would not all be now, since part would be before and part after — not “to itself and first.”

9. The converse; the now of time vs. the eternal now (“the now that stands still makes”) #

Text: “if it is the same, it is clear that it is indivisible; if divisible, the same things as before will happen again.” Hence there is something indivisible in time, the now.

• Back-reference to the discussion of time and eternity: Boethius — the now that flows along makes time, the now that stands still makes eternity. The eternal now has no before and after; unlike the now of time it does not flow. The now of time is “always and other”: we are losing the future all the time. Boethius defines eternity as a possession; you cannot possess the now of time.
• Aside: his oldest grandchild at her party, “I’m so happy” — “it doesn’t last.”

His words #

• reading five: Thomas’s lectio 5 on Book VI [ed.: lectio].
• ens mobile / res mobilis: movable being, the subject of natural philosophy, as against movable body.
• natural hearing: the eight books, “the so-called physics” [ed.: Physics].
• about the universe / De caelo et mundo: Aristotle’s book on change of place [ed.: De Caelo].
• book of wisdom: Aristotle’s Metaphysics [ed.: Metaphysics]; book five treats “the words especially used in wisdom.”
• imperfect act: motion, which “barely is.”
• the now through itself and first: the strict now, not present by reason of a part.
• continuous (logic): that whose parts meet at a common boundary; (natural philosophy): divisible into always divisibles.
• first limit: the point, which has no limit but is not lacking one.
• equivocal by reason, not by chance: the words of Metaphysics V.
• proton: “first”; the proton is first among water, hydrogen, proton.
• the now that flows / the now that stands still: Boethius on time and eternity; eternity as possession.

Texts #

Read in class

• Aristotle, Physics VI, opening of Thomas’s reading 5 (inferred: ch. 3): the now through itself and first is indivisible and exists in all time; the furthest limit of past and future; the same now is the limit of both; if the same, indivisible.
• Aristotle, Metaphysics V, the meanings of “beginning” (Aquinas, lectio 2; handout “Note for Word Beginning”).
• Shakespeare, Troilus and Cressida (one line quoted).

Mentioned

• Aquinas, proemium to the Physics (subject is ens mobile); Aquinas, commentary on Nicomachean Ethics (res mobilis).
• Aquinas, proemium to De Caelo.
• Euclid, Elements I.32 (interior angles).
• Aristotle, Physics IV (time, the now); Physics II, chapter on the four causes (inferred: ch. 3) with its three parts and the form : matter :: whole : parts proportion.
• Aristotle’s arguments against Anaxagoras (Thomas’s reconciliation with infinite divisibility).
• Boethius on eternity; Heraclitus, “the way up and the way down”; Heisenberg.
• Aristotle, Categories ch. 12 (verified-source match to a handout on “before”; not cited aloud in the transcript).

His questions #

• Is “body” the subject of natural philosophy or a property of it? A property/conclusion: the subject is ens mobile, and that the mobile is divisible, hence a body, is proven in Book VI.
• When really is motion — past, future, or now? Only the now really is; since there is no motion in the now, motion “barely is,” an imperfect act.
• Is the present month present through itself? No, only by reason of one day; the strict now is present through itself and first.
• Could the end of the past and the beginning of the future be two different limits? No: there would be time between them and past would not be next to future (US/Canada).
• Could the limit of time be a time? No: the end of the day is no time at all; a time would not be all there at the end.
• Why is the foundation a more proper “beginning” of a house than the house builder? The foundation is a part of the house, like the point in the line; the builder is not.
• Is the now in the past? Then is the past in the future? The now is in both, but is not a part of either, since the indivisible is not a part of the continuous; no time is in the now.
• Is the second sense of beginning “subjective”? No: it is a reasonable, convenient place to begin one’s motion.
• Is this table divisible forever? Left partly open: here the continuous is considered in general; something may impede at the particular level (Thomas on Anaxagoras).