The Elements of Philosophy: 1.3.19.4

Time (14:155d), like motion and place, received its first definition as a natural concept from Aristotle, who identified it as “the number of motion according to before and after.”  This definition develops from three inductive determinations that successively establish (1) time as something of motion, (2) time as continuous, and (3) time as number.  (1) Time is not the same thing as motion, for many different motions can take place in the same time, and motions can be fast or slow whereas time remains uniform in flow.  On the other hand, time inevitably accompanies motion, for where there is no awareness of motion or change there is no passage of time.  (2) Time is continuous because it is associated with motion that traverses a continuous magnitude.  A continuum is formally one but materially made up of parts:  these parts, joined to each other by indivisibles, constitute an order of local before and after.  A motion that traverses such a spatial continuum has also an order of before and after, as does time’s passage, e.g., when punctuated by the sun’s rising and setting, the moon’s phases, the ebb and flow of the tides, the position of hands on a dial.  (3) Time is numbering of the successive ‘nows’ that serve to mark its passage.  To grasp its being one must visualize a before and after under the common aspect of their being a now (10:547d) and count them as two nows, i.e., as a now-before and a now-after.  These nows, the correlates of the here-before and there-after in motion, are the numbered terminals of the continuum that itself is time.  The numbering referred to here is not that of an absolute or mathematical number [64.1] divorced from passage.  Time is rather numbered number, the number of and in motion that is indissociable from its flux.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §19.  PLACE AND TIME  //  [paragraph] 4  //   [pages] 53 and 54)

Obiter Dicta:   Modern physics speaks of space-time.  The concept of space-time better describes movements in the universe and, especially, is effective in describing relativistic (i.e. near light speed) effects.  Space-time may be an actual thing or a mathematical construct which accomplishes these better descriptions.  Space-time, as either an actual thing or a mathematical construct combines the three dimensions of space with a dimension of time.

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.19.3

Space (14:155d) is a concept related to place; in its physical sense it refers to the fundamental dimensional quality against which one can describe and even measure the motions of bodies.  Whether a purely empty three-dimensional space, i.e. a void (14:741b), has real physical existence in nature has been much debated in the course of history.  Speculative arguments aside, the only evidence for the existence of a void reduces to that for an ether (5:568b) or a physical vacuum (14:510b), neither of which is known to have all the negated properties of completely empty space.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §19.  PLACE AND TIME  //  [paragraph] 3  //   [page] 53)

 

Obiter Dicta:  Modern physics speaks of space-time.  The concept of space-time better describes movements in the universe and, especially, is effective in describing relativistic (i.e. near light speed) effects.  Space-time may be an actual thing or a mathematical construct which accomplishes these better descriptions.  Space-time, as either an actual thing or a mathematical construct combines the three dimensions of space with a dimension of time.

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.19.2

Place (11.49d) is defined by Aristotle as “the innermost motionless boundary of what contains.”  This definition construes place as a container, distinct and separable from the thing contained, but otherwise equal to it and corresponding to it part by part.  Every body surrounded by others is in place, and this is what makes local motion, or change of place, a possibility; the universe as a whole, not being in place, cannot move locally.  The definition also leads to two significant distinctions, one between common and proper place and the other between natural and non-natural place.  Common place is seen as the nearest container or surrounding environment that is immobile, i.e., at rest relatively at least to the body in question.  Proper place is taken in strict accord with the definition—it is equal to the body in place, but its immobility can be purely formal, as part of the whole system contained within an immobile common place.  Natural place is the suitable physical environment of a body, i.e., an environment that is adapted to its proper activity and reactivity in accord with its motive powers and other characteristics, and toward which it has a natural tendency to move.  Non-natural place is any other physical environment.  Two bodies cannot occupy the same proper place in virtue of their impenetrability (7:396a); nor can one body be in two proper places at once, as in bilocation (2:559a), for this would entail a denial of the definition for one or other of the places assigned to it.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §19.  PLACE AND TIME  //  [paragraph] 2  //   [pages] 52 and 53)

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.19.1

“The infinity thus associated with motion is not an actual infinity; rather it is spoken of as a potential infinity, and as such does not preclude measurement of containment.  The measures of most interest for the natural philosopher turn out to be two; place, which can be viewed as a measure of mobile being, and time, which is the measure of the motion the mobile undergoes.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §19.  PLACE AND TIME  //  [paragraph] 1  //   [page] 52)

 

Obiter Dicta:  Aristotle (384 to 322 B.C.) stated in his Physics (Book 4, Chapters 10-13) that time is the measure of change, of the before and after of some given movement.

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.18.8

“By reason of its quantitative aspect motion also involves an element of infinity [§45.3], as can be seen by comparing it with the line segment one might hypothetically traverse in local movement.  The extension of the line segment is related to its terminating points in somewhat the same way as matter is related to form; it itself is a composite, so to speak, of matter and form.  The line segment is also finite by reason of its initial and final terminating points; it becomes infinite only when conceived without one or the other of them.  This can occur by way of increase, since no matter what its actual length the line can always be imagined as without a termination and thus as extending further.  It can occur also by way of decrease, by subtracting parts from the segment in a fixed ration, say by halves, so that no matter how small the remaining part becomes it can become smaller still, because the remainder is similarly divisible.  Now motion is infinite in much the same way as such a line segment.  Infinity is attributed to the line when its extension is viewed as lacking terminating points, and so is linked with a state of potentiality and imperfection.  Similarly motion is infinite under the aspect of successively traversing a distance that is infinitely divisible or augmentable, and sos characteristic of matter that, as potential and imperfect, is in the process of achieving form without having yet come to the intended termination.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §18.  MOTION  //  [paragraph] 8  //   [pages] 51 and 52)

 

Obiter Dicta:  The content of the text quoted immediately above calls to mind Zeno’s paradox regarding a race between a tortoise and a person (Achilles).  Zeno reasoned that if distances are infinitely divisible, should a tortoise be given a head start in this race, Achilles would never be able to overtake the tortoise.  Imagine the tortoise is given a head start in which it is allowed to move along the race path for an amount of time (“T1”) before Achilles begins to run.  At the end of that time “T1”, the tortoise will have reached some specific point along the race path “A”.  Now Achilles is allowed to run and reaches this point “A” in a certain amount of additional time, “T2”.  However, in that same amount of time “T2”, the tortoise will now have reached another spot along the race path, “B”.  By the time Achilles reaches “B”, he will have taken a smaller amount of time “T3”.  However, in that short amount of time (T3), the tortoise will now have moved ahead to a new point “C”.  As long as time and distance are infinitely divisible, it follows that Achilles should never be able to overtake the tortoise.

Obviously, there is something wrong with the seemingly inescapable conclusion reached in Zeno’s paradox, because we know Achilles would quickly overtake the tortoise.  The reality of this possibility seems to point out that either time or distance are not infinitely divisible.  To say that time or distance are not infinitely divisible is to state that in reality there must exist some smallest length and some smallest amount of time; a quantum of length and a quantum of time.  But as yet, physics has not found a quantum of time, and any supposition of the existence of a quantum of distance is dependent on the preliminary existence of a quantum of time, which as yet, has not been found.

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.18.7

“Apart from the qualitative parts or types, motion has also quantitative parts by reason of the distance between contraries that it traverses.  This is best seen in local motion, where the magnitude traversed, known as extension [§64.5], itself manifests all the properties of a continuum [§64.4].  Although motion is continuous, it is not the same as a static continuum such as a line, whereas all the parts co-exist and are known immediately; rather it is a “flowing continuum” whose parts, successive in existence, are known only through the re-presentations of memory.  Because a flowing continuum is a becoming, its parts do not constitute a being in the strict sense; indeed motion exists only by reason of its indivisible [§64.6], i.e., the moment of passage already achieved, and not by reason of its parts, which, as past and future, have already passed out of, or have not yet come into, existence.”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §18.  MOTION  //  [paragraph] 7  //   [page] 51)

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.

The Elements of Philosophy: 1.3.18.6

Action and passion [§9.8] do not constitute separate types of motion, for they are really identified with motion.  Action is motion considered as being from an agent, whereas passion is the same motion considered as in the patient.  None of the other categories found different types of motion for, though changes occur in them, they do so not directly but through one of the three types of motion already discussed (see 10:25d).”  (PART 1.  //  CHAPTER 3 NATURAL PHILOSOPHY  //  [Section] §18.  MOTION  //  [paragraph] 6  //   [page] 51)

 

Obiter Dicta:  In the statement quoted above, the word “patient” does not refer, specifically or primarily to a living being under a physician’s care.  Rather, the word “patient” is used in the general sense of anyone who undergoes or experiences the action of another.  Examples of these understandings of the words “patient” and “agent” include the patient under a physician’s care, or the penitent under the care of a spiritual director, or the batter struck by a pitcher’s pitched fastball.

 

Key:  For an explanation of the reference and cross reference forms used in this book (e.g. [§19.6] and (11:292c), see previous posts in this blog entitled “The Elements of Philosophy:  Preface (7)” and “The Elements of Philosophy:  Preface (8)”.