Space and Time

Philosophy Course Index

—Ancient Greeks were concerned with change. But, change seemed to require that something could be opposite to itself: e.g., both hot and cold, wet and dry, moving at rest, etc. Yet something cannot have both of these properties at once since these properties are contrary. Possible solution: the object has the properties at different times, not at the same time. Yet, this raises the problem of how change/motion relates to time. (Often time was considered to be just a form of change.)

—Myth of Kronos: Greek God responsible for separating Quranos (the sky) from Gaia (the earth) by castrating him with a sickle. Kronos (time) thus separates the sky, the divine world, from the earth, the human world. This rupture is destructive (blood causes vengeance), but also creative (since it created Aphrodite). Time allows human life to appear (and other earthly phenomena). Time is a boundary of the divine/terrestrial, love/death, generation/corruption, etc.

—Anaximander: "apeiron" (unlimited) is the unchanging substratum of all change. All limited things (which are limited by their opposite) must thus be limited in time, because if they were not, they would last forever (and not change).

—Heracleitus: Time produces change in the order of nature. Time has no beginning, and the world may undergo cycles (which suggests that time is not identical with change, since identical cycles of change are the identical time for one who equates time with change).

—Parmenides: Whatever can be spoken of, or conceived, must be complete, without beginning, end, or change. Time is thus unreal because he equates time with change. All things for Par. must be complete (without change or parts), since parts are not "complete" and imply that the object is not perfect (i.e., it contains non-being, which is impossible, since a part is not identical to the whole). So, duration, as a form of time, can’t exist either.

—Plato: Parmenides believed all appearance of change was false, but Plato tried to explain the difference between appearance and reality by positing the "Forms". So, Plato accepts that there must be something underlying change which itself doesn’t change.

—"Forms": They are separate from appearance, but cause them, and do not change (whereas appearances do). The Forms are not in time (Plato's "Parmenides")—if the "one" were in time, then it would be both younger and older than itself (since the "one" would endure through time, and thus have earlier and later stages of itself). But, then the "one" would not be "one" but "many" (which is a contradiction). Par. believed that this showed "appearances" were contradictory, and thus not real.

—"Timaeus": The Demiurge comes across chaotic matter and fashions it into a structured, ordered arrangement—that is, the Demiurge allows the matter to take on the appearances of the "Forms", and thus be intelligible and good, although they are only appearances (copies of the Forms). The universe as a whole is the most perfect of all material things (since it is the totality, and since it does not depend on anything outside itself), while individual material things are less perfect and good (being dependent on other objects, etc.). The world has a soul, as do each individual human.

—Time belongs to the order of appearances, not the greater beings, which are the Forms. Time is created for appearances, whereas the Forms are eternal. But, the Demiurge wanted the World to be as much like the Forms as possible, so "time is the moving image of eternity" that moves according to number. Time differs from eternity in 2 ways: (i) it partakes of change; (ii) it moves according to rational ordered number sequences.

—Circular motion is what makes time an image of eternity (and satisfies both (i) and (ii)) because circular motion is motion that returns to the same place (which is as close to "unchanging" as motion gets). The circular motions of the heavenly spheres accomplishes this feat because the yearly motion of the sphere of the fixed stars returns to the exact same place every year (or, so Plato assumes). This circle of motion is "the circle of the same", yet the spheres containing the 7 planets divide the year into smaller segments of time (months, days, etc.): so, these 7 provide the numbering of time (ii), and are called the "circle of the different". Time is thus created with the motions of the spheres, and is identical to these motions.

—Problems: What occurred before the Demiurge established the order of the universe? Did time have a beginning in time or a non-temporal beginning? Also, we know matter existed before time (in a chaotic) state, so how do you make sense of his theory? Can time begin at some time (ex nihilo)?

—What does it mean to say that there might have been a time before time began: (1) there is no sense (meaning) to the term "before", as used here; (2) there is a second time series (before the first time began) which makes sense of the term "before". Problem: What caused/created the second time series? (Was there a time "before" the second series, so an infinite regress of time series results?) Answer: The second time series does not need a creator or cause. Problem: Why can’t the first time series use this same response?

—If Plato said time was created with matter, then he would have a non-temporal and metaphysical beginning from some cause (Demiurge) which is not in time. Yet, Plato says the Demiurge only fashioned the universe, and didn’t create it. (The world of appearances is the phenomena, while time is its boundary condition; i.e., the bound. cond. of their rational ordering and becoming).

Chapter 2: Aristotle

For Aristotle, time is closely related to change, and motion, but it does not appear to be identical to either.

—Aris. rejects the view that time is identical to the motions of the spheres: since (1) parts of the revolution of a sphere would still be time even without complete revolutions; and (2) if time is motion of a whole sphere, then there would be many times, for there are many different spherical motions—but, there is only one time.

—Aris. rejects view that time is identical with motion because (1) motion is always in the thing that moves, but time is everywhere. Also, (2) there can be faster and slower motions, but "faster" and "slower" are defined by time (as taking less/more time), so time cannot be faster or slower, and thus can’t be identical with motion.

—Aris. believes time is associated with motion, but that it is not identical to motion. Motion is a complex concept identical with change, for Aris. There are 4 types of change; change of place (motion), coming to be or perishing, change in quality (e.g., color), change in size (quantity). Time is involved in all these changes. Time requires change, as well: we can’t tell if time has passed if we don’t know if there has been a change. Example: if we are asleep, we experience no change, and thus no time. Problem: this seems to make an ontological distinction based on epistemological reasons—we can’t experience changeless temporal periods, so there are none. But, can we successfully make this claim?

—Time is the number of motion with respect to before and after (where "before" and "after" refer to the magnitudes involved in all 4 changes—not time). Time partakes of 3 other features of motion: extension, continuity, and transition. For motion to occur, and thus time, there must be an interval separating the before and after that is extended and continuous. Time is the number of what is counted in change (and is not identical to abstract numbers in general). Time is thus dependent on human souls, or some soul, to do the counting; however, motion, and before and after, would still exist—but they would not be numbered or counted (so time is thus not rendered subjective to a soul). Time measures motion, and vise-versa. Once we number an interval between a before and after, we can use this interval to measure other motions (as the spheres are used).

— "Now": what is counted in time? Answer: instants, or "nows". Nows are the basic phenomenon of time (i.e., what we experience), since time is the succession of nows (before and after) counted in motion. Yet, time is not made up/constructed of nows. (Thus time is like a geometrical point, since lines are not composed of points, either). Time, like points, are dense: between any two, there is a third. The now is always the same and always different. It is both (i) the same now (since the "present" is always the same and not something else); (ii) and it is also a different now in that it is always different nows that are being counted (from the before to the after). Aristotle's analogy: A carried thing is both the same thing, but it is different in that it possesses different (position) properties as it is carried. The now both divides and joins intervals of time. The now makes time continuous by connecting the past and future. However, the now is an abstraction, like a geometric point. The nows are limits of intervals of time as the limit at its ends (the before and after). However, limits are parts of the magnitudes that they limit, but the nows are not parts of time, so they are not quite the same as limits (which is also the case for geometric points, since they are not parts of a line, either). Time is continuous and always in transition, but the now is not itself in transition. For there to be a continuous interval of time, there must be two different nows which marks the ends of the interval (if not, it is not an interval of time).

—Here, it should be noted that Aris. never distinguishes the present from an instant. There is no smallest time, for it can be divided infinitely. Yet, sometimes Aris. uses "now" to describe an interval of time.

—For something to be in time, it must be able to be numbered, to be bounded by a before and after and counted by nows. Every change is in time. Every change actualizes a potential (as in the 4 types of change). Anything that doesn’t change (or has the potential to change) is not in time (e.g., mathematical/geometrical figures, Gods, etc.). Changes occur at different times when their before and after are different, and at the same time when they are the same. Time is distinct from any particular change, but several different changes can have the same time if they happen simultaneously and their number (of counted nows) is equal.

—There can be no first or last time, since their can be no first or last number (smallest or greatest number) of (possible?) counted nows. Motion can be measured if the motion is regular, and the most regular motion is the motion of the celestial sphere (so it is the best means of measuring motion). Time does not recur, or is repeated, in the circular motions of the spheres because the cycles each have different before and afters. Time could recur only if one and the same motion recurred. (Question: does this entails a relationalist account of time?) The whole of time is not in time, because it has no first or last instants (before or after).

—Problem of future contingencies: Given a statement, it is either true or false (law of excluded middle). This rule can be applied to statements about the past and present, but raises problem about future. If each statement about the future is either true or false, then their truth value is already determined, so there are no alternatives or possibility of the future turning out different. But, deliberation and action cause future events, and so future events may potentially happen or not happen. If this is so, then there are real alternatives. So, are future events bound by the law of noncontradiction?: Aristotle answers "no"—he claims that "if something is the case, then it is necessarily the case". Future alternatives must be indeterminate, so the law of excluded middle applies only to past and present facts or statements (i.e., what actually, and not potentially, exists). Therefore, for Aris., time is asymmetrical in that the past and present have some form of actual reality, but not the future.

—Skepticism: Sextus Empiricus (200 C.E.). The skeptics were skeptical of the existence of time. There are 3 arguments:

(1) Arguments concerning being limited/unlimited: time is not limited because it is contradictory to think it has limits (since we can imagine time both before and after the limit). But if time is not limited, then there is a real past and future, and not just a present (since a world with only a present is limited, that is, limited to the present). But, if the past and future are real, they must be present, which is absurd. So, time is neither limited or unlimited.

(2) If something changes, then it changes in the present. But if the present is indivisible, then this means that something can change in an indivisible time, which is impossible. So, the present is not indivisible. But, if it is divisible, then its parts must be either past, present, or future. But, if something has parts, then the parts must exist. Yet, the past and future don’t exist, so only the present exists. Thus, time is not divisible. Conclusion: the present is neither indivisible or divisible.

(3) Arguments concerning whether time can be generated or destroyed (or can become): If something is generated or perishes, then it must be generated or perish into something that exists. So, since time can be divided into past, present, and future, and the past no longer exists and the future doesn’t yet exist, if time can be generated or perish, then the future must be generated out of something that doesn’t exist, and the past perishes into something that doesn’t exist. But, this is impossible, so time can’t be generated or perish.

The skeptics acknowledge the appearance of time, but are uncertain of its ontological status.

—Epicurean Time: atoms.

Aris. argued against indivisible motion and place (atoms of motion and place), since it is conceivable that motion can occupy only part of a place, and thus it seems indivisible places and motions are conceivable. There are no time atoms, since time atoms (as "nows") can’t be next to each other (i.e., time atoms violate the "density" of nows, since between any two nows, there exists a third). The Epic. accept time atoms as having a minimal finite duration, and thus comprise longer periods of time of finite duration. They argue that if a finite temporal interval were composed of durationless indivisible nows (as point like entities), this leads to a contradiction, since a collection of durationless parts can’t form a whole that has duration. (This is a possible fallacy of composition: what is true of the parts is true of whole—yet, this isn’t always the case.) For Epic., minimal conceivable times can be constructed from minimal conceivable motions and distances. For Epic., atoms move an atomic distance in an atomic time, which is an atomic motion (which means atoms move at the speed of thought). Yet, there are times shorter than the least conceivable time—this is the time of the "swerve". Epic. accept a 2 level theory of time: (i) perceivable (of ordinary experience); and (ii) conceivable (not of ordinary experience of duration). Time is not a property of matter (it has a unique existence), yet time cannot exist independent of matter. Modern physics is much like Epic. thought: Planck’s constant gives a minimum length to space, and the speed of light (as a maximum speed) allows one to divide the minimum distance by the maximum speed, thereby yielding a minimum time. Of course, smaller distances, times, etc. are conceivable. Also, if two time atoms overlap, they will not be simultaneous, hence smaller temporal periods are conceivable. Yet, physical time may not be the same as conceptual time.

—Stoics: Continuous time

For the Stoics, the universe is material, but everything is continuous with everything else. All bodies interpenetrate one another, so bodies are mixtures within the whole of the world (i.e., bodies are states of the whole). Bodies have no definite boundaries, since their surfaces act only as limits: these limits are not part of the body, but they are not nothing, either. Time is a measure of motion. Time is incorporeal, and (like boundaries or surfaces) it is not body, but it is the limit of both the past and present, since both converge on the present in an infinite series of time intervals. There are no fixed points in time since the present (now) is only a limit, and matter (and time) are in constant flux. Yet, the "present" plays a role in Stoic thought, as well (and can be viewed, from a certain perspective, as the only reality). For the Stoics, there are two levels of time referring to cause and effect: (1) Corporeal time is the causal interactions of all bodies in the mixture of the world in the present. (2) Incorporeal time is the unity of all events which subsist over a period of time, thus over the past and future. Time is thus the unity of all events (which span intervals); so, time is infinite and is continuously divisible. The events are the effects of the causes (which only exist in the interconnected present), so the present causes the events (which exist over temporal periods; i.e., the continuously divisible past and future).

Cosmology: the universe moves in cycles of chaos (a fiery state) and ordered states. The limits of the ordered state of the universe (i.e., the two chaotic states that border an ordered state) are limits which make the time of the ordered state infinite. There is no time in the chaotic states since there is no ordered, sequential existence of matter. So, the time of the ordered state, since it is infinitely divisible, approaches the limit at each boundary in an infinite series where there is no last temporal moment/now. This is similar to the Hawking universe, since the singularity which marks the beginning of time (big bang), and maybe the end of time (big crunch), are points at which the physical equations break down, and thus such points are outside of physical description, and thus outside of time (i.e., they are also limits of an infinite series of temporal moments/durations).

—Plotinus: (205-270 C.E.). Influenced by Aristotle and Plato. Rejects Aris. view that time is motion as measured by number. Three arguments

(1) Some motion is irregular, and can’t be measured, yet time is still involved in the motion. Problem: can there be motion that can’t be counted/measured? Answer: possibly all motions can be counted, even if irregular.

(2) Time is continuous, yet numbers are discrete, so time is not the number of counting. Aris. would probably agree: time is what is counted in motion, and is thus not identical to its particular measure (so the measure reached need not be regular).

(3) If time were a magnitude that measures motion, this does not explain what that magnitude is in itself. So, this magnitude can’t explain completely what time is (once again, Aris. may agree).

For Plot., measuring motion doesn’t bring time into existence. Things undergo temporal progression independently of the act of measuring time. To say otherwise is like saying magnitude doesn’t exist unless someone measures its quantity. When we number time, that action presupposes time (ontologically/logically) prior to the measurement. Time is not the measure of motion (as identical to the measurement) but is something measured by motion. The motion of spheres can be used to measure motion, but it is not identical with it. If the spheres stopped moving, time would still exist. Time is not motion. What serves as the measure of something cannot be its essence: e.g., the scale on a meter stick is not the essence of the length it measures.

—Plotinus’ theory of Ontology or Emanation.

There is a hierarchy of levels of being that emanate from the one (as the unity of all). Eternity is self-identical within the One and is an active manifestation of the One. All of reality is alive, and eternity is the life of the One. The One is both an unchanging unity and alive (how?). Eternity has no sequence, since it is changeless. Temporal language is often used to describe the One, but it should be taken metaphorically. The first emanation of the One is the Intellectual principle (Nous), which contains the Platonic Forms. Eternity also applies to Nous. The second emanation of the One is the World Soul. Time unfold in the World Soul: the World Soul (WS) mediates between the unchanging Forms of Nous and the changing world revealed in sense perception. The sensible world is extended in time (past to future), and while material things don’t completely exist, they strive to exist (as real being). This striving is "becoming", which necessitates a future. If time were eliminated, material things would either disappear or become perfect (like the Forms), which is impossible. Time inheres in the World Soul: it is the differentiation and movement of the life of the WS. The WS is not in time, but its activity is time (for the material inhabitants of the WS).

—Late Neoplatonism: Iamblichus (325 C.E.) has a 2 part theory of time: (1) Static time (which is in Nous) is the sequential ordering, form earlier to later, of Nous (which is the eternal, unchanging order of being). (2) Dynamic time (in the WS) is in constant flux, and marked by the movement of changing things from the unreality of the future, through the existing present, to the unreal past. The 2 kinds of time meet at the now (present). Static time communicates its unchanging permanence and reality to dynamic time at the now. The material world only receives the Forms at the now, and thus gains reality at the now. Thus there is a "flowing" now in 2 senses: (i) the static flow of the now from past to future, and (ii) the dynamic flow (of unreality, to reality, and back to unreality) from the future, to the now, to the past. This theory distinguishes instants of time form the now (since the now flows over instants), but it also explains why "exists" and "is present" are often identified as being equal. Static time interprets the indivisible aspect of being, while dynamic time interprets the unreal aspects of becoming—this process is an Emanation (from static to dynamic). For Plot., time was only in the WS, while Iamblichus places time between Nous and WS.

—Domascius: Time separates event in succession (so they don’t overlap) just as space separates/orders things (so they don’t overlap) which coexist. Time is atomistic, but each time atom, when examined in isolation, can be divided infinitely. This allows time to progress from one unit to another, but also constitute a concrete and real "Now".

—Proclus: Time is a circle whose center is Nous and at rest, while the circumference is the material world and is in motion. Proclus thinks this is a better explanation of time (in Nous and WS) than Iamblichus gave.

Augustine (influenced by Neoplatonists, but adapts their views to his own Christian Theology)

—God is separated from world of form and matter (unlike Neoplatonists). God exists outside of the natural world, which he creates out of nothing. Problem: What was God doing before creation (and where is God)? God can’t will the universe to begin existing because then God’s will can change (and thus God is not eternal: i.e., eternal beings can't change). But, if God always willed the universe to exist, then nature would have always existed. Solution: eternity is separate from time (Neoplat.). God is outside and "prior" to time (not in the temporal sense, but God is "prior" in the causal sense—as in creator to creation). Time itself is created with the world, so there was no time prior to this event (prior to "past, present, future" causally).

—Augustine rejects the view that nature is only a realm of appearances. Aug. also argues that the present can’t be extended: if it were, it would have parts that were past and future (which is impossible). Also, the past and future don’t exist because the past is gone, and the future has yet to exist. Only the present exists, but it exists only insofar as it is constantly passing into non-existence (i.e., time passes). If time didn’t pass, but were static, then the present would be identical to eternity (which is contradictory). But, how can time be only a non-extended present? Answer: only the present exists, while past and future exist only in our minds. Therefore, time exists only while it is passing. But, how can you measure a duration, and thus time, if only a non-extended present exists (and durations are extended)? Solution: our memory retains sensations/images of past experiences and combines/compares them to build up the notion of a "duration". The mind uses "expectations" to build up the idea of future time periods (i.e., we think about the future, plan things, etc.). This makes the past and future dependent on the subjective mind of each person (since each person remembers/expects differently), but the present is a real objective fact of the world. The measure of time is subjective, although time is an objective feature of the world. Aug. denies that time is a measure of motion. The heavens may stop moving, but time continues to exist. Time also measures rest as well as motion, so time is not dependent on motion (same as Neoplat. argument). Time measures motion, and the measure can’t be the same as what is measured. The same temporal interval can measure (i) a motion, (ii) a period of rest—which proves that time is independent of motion.

—Developments in the Middle Ages towards the concept of Absolute time.

(1) Time becomes separated from motion (Scotus, Ockham, Bonet). E.g., Nicholas Bonet (1343): There are as many times as there are motions (so "natural" time exists in the duration of each separate motion). Yet, there is only one "mathematical" time which is the same time for all things (and is a conceptual abstraction from matter and motion). This math. time is independent of all matter and motion in that it flows and measures all things without being influenced/affected by moving bodies (and so it acts like an absolute clock).

(2) The development of mathematical techniques that treat time as an independent variable prior to motion: e.g., Oxford (Merton School) philosophers, Oresme, etc. These philosophers are the first to diagram motion (with a graph) such that the graph of velocity is plotted against a separate line of time, thus separating motion from time (and so velocity becomes a dependent variable of time).

(3) The development of clocks (in large numbers) began to regulate life according to clock time, and not daylight/night.

—Newton: Influenced by Barrow, who held early view of abs. time. Time is real. God exists in time (and infinitely at all times). Time is not created by God, but is a fact of God’s existence (co-existent, co-temporal, but dependent on God). God’s existence and essence are causally, though not temporarily, prior to the existence of time. Newt. distinguishes between absolute, true, mathematical time (independent of matter) and relative, apparent, common time (which is the perceived duration of motions among physical objects). Abs. time is real (not a mathematical abstraction, as for Bonet).

—Locke: How can one construct a true mathematical time form our relative, apparent sensations of time? Locke holds, like Augustine, that time is a measured duration of sensations. Duration comes from a succession of ideas in the mind. We "reflect" on this passing sequence of ideas, compare the temporal "distances between" ideas, and thus arrive at the idea of "duration" (as a complex idea derived from sensations and reflection). We get the idea of succession (as a passing train of ideas) first, and thus form the idea of duration by reflecting on the distance between the idea in this succession. Accordingly, we do not acquire the idea of duration from observing motion, nor from our perceptions of objects in the present (i.e., any single sense perception we have is not extended, and is durationless; thus we do not get the idea of duration directly from a perception—or, put differently, we have no perception of duration itself). We can’t perceive extremely fast or slow movements, since they fail to produce a sequence of ideas in us (because they are either too fast or too slow to produce a distinct succession of ideas). The regularity (periodicity) of a succession of ideas is what is important. Also, we can construct our idea of time even without motion if we simply take an image of a time interval and, repeating it, extend the interval for a longer duration (much as we apply a given length over and over again to produce a greater length even if there is no body possessing that greater length). Given a length of time in our memory we can continue to add to it (which is how we also conceive of eternity). No succession of ideas is ever completely regular, but we can form the idea of a perfectly regular duration from our experience of more/less accurate perceptions of succeeding ideas. Time is not the measure of motion, since we can construct our concept of time directly from the succession of perceptions/ideas in our mind (and this need not involve any moving objects, etc.). Just by holding a single perception/idea in the mind, we can form the idea of succession, since it is not possible to hold an idea in the mind without variation (i.e., the idea changes, thereby producing a succession of idea, and thus it is no longer just one idea in the mind). Moreover, motion depends upon distance and duration, so time (duration) cannot be defined by motion.

—Berkley: Ber. accepts that time is the succession of ideas, but he rejects Locke’s notion of an objective, abstract, uniform time. Since time is a succession of ideas, and since people will (potentially) experience different rates of the succession of ideas in their minds, there will be many different times (relative to each individual). Yet, Ber. doesn’t know what to conclude from this hypothesis.

—Leibniz: Leib. accepts PSR, PII, and concludes that abs. time violates both principles (see notes to Huggett for PSR, PII, etc.): When did God create the world if all times are identical? (which is a PSR violation); furthermore, all empty times would be identical (PII violation). Other arguments: God and Time can’t be co-temporal since this makes time part of God’s existence; but time has parts and God does not; and it would also entail "a subject is in its property". For Leib., time is the order of non-contemporaneous events. Events which are contemporaneous occur at the same time, of course, so the relational order of events (objects) across many non-contemporaneous experiences of objects provides a notion of duration, and thus time. Thus, temporal intervals are relations; i.e., they are abstractions from the relational properties of things. Time is not real, since abstractions from real things are not real. Each thing has its own duration, but not its own time (since time is a much larger relation among many objects).

(NOTE: p.81—If relations are not real things, can they have a quantity (such as, quantity of "ordinal series")? Shoemaker’s theory doesn’t work because there is no way to measure the quantity of the changeless (12 year) incident directly (as is done relative to other parts of the universe for the other changeless periods). One has to guess, as a non-measurable, non-relational hypothesis that it was 1 year—but why not 2, or 3, etc.?)

Rejects Newton’s abs. time since it makes time unknowable (i.e., we only know relative time) and we can’t use relative time (motion of bodies as source of time) to find a motion (time) that most approximates abs. time. Why?: Because we can never know how close the proposed motion really does approximate to the one, true abs. time. Kant also rejects Leibniz’s relational time because it makes time a mere relational property of the phenomena of bodies, and thus unreal (not really true).

—Time is an a priori (Synthetic a priori) pure intuition (see Notes to Huggett). Appearances of objects are not subjective, but objective, and so those objects are objectively real. Yet, objects considered apart from experience (outside appearances) are unknowable. So, time is both empirically real and transcendentally ideal (so time doesn’t apply to things-in-themselves). Where space is the form of outer sense (objects outside us), time is the form of inner sense (flux of our subjective states). Yet, our knowledge only involves appearances, so our subjective states have no special epistemological status (in truth or knowledge). Kant reverses traditional role of change/motion and time: time constitutes an a priori condition/presupposition for the appearance of change and motion. If time were not already given, change would be incomprehensible, since change requires that the same object takes on properties at different times. Time orders appearances in a single order of succession, which is an arithmetical succession, and not a geometric a priori intuition (as with space). Time is a unified infinite span, and an unlimited order of succession. We derive knowledge of arithmetical statements ultimately from time as an a priori pure intuition ("2+2=4"). For Kant, time is not a concept of the understanding because no concept can contain an infinite number of parts, as time does. Only an intuition can contain an infinite number of parts. Also, time is not a priori analytic (since it is not a conceptual truth). However, "concepts of understanding" are necessary (along with pure intuitions) for knowledge of bodies. In short, a means of unifying our experiences of objects into a single unified consciousness must be found in order to have knowledge. If not, different appearances would not belong to the same object (and so the concepts of understanding could not be applied). The "formal unity of consciousness" unites these various perceptions under one unified perspective (as in, "I think"). Yet, time is also necessary for experience—so, time is conjoined to the formal unity of consciousness through "the transcendental imagination". The transcendental imagination allows one to know time; that is past, present, and future, as a span of time, and an interval. We form the concept of time when the transcendental imagination applies the formal unity of consciousness to the pure intuition of time. This also guarantees that concepts of the understanding can be applied to time, and this is accomplished through schemata: quantity and quality of sensations in time, as well as the necessity, possibility, actuality, etc., of how objects are in time.

—Time (and space) lead to antinomies (i.e., valid arguments that lead to seemingly contradictory conclusions). Is the world temporarily infinite or finite? (i) We have no experience of a limit, so time cannot be finite (i.e., we can always imagine more time beyond a limit). (ii) Yet, since all of our experiences are of the finite, we have no idea of an actual infinite since we cannot form a real infinite time from a succession of finite times. So, the magnitude of time in the world is indefinite, and thus time is not infinite, either. Conclusion: there are (apparently) sound arguments which demonstrate that time is finite and time is infinite (?!) Antinomies show that some problems/questions transcend all possible experiences, and so these problems/questions cannot be answered (thus explaining why our reasoning about these concepts, such as time, lead to contradictory results).

Hegel: Hegel tried to reject Kant's concept of "noumena" (things-in-themselves) as unknowable (i.e., as the unknowable realm of real world which would provide answers to the antinomies of time). For Hegel, a more inclusive rational structure subsumes the contradictory elements of phenomena (such as the antinomies) into a greater rational structure. "Becoming" synthesizes being and nothingness (i.e., abstract form and lack of content, respectively) into a unity (which asserts their identity while preserving their difference). Motion and change, as phenomena, presuppose the dynamic structure of becoming; so time is this constant movement of dialectical synthesis. The World Spirit is the subjective basis of all phenomena unified as a whole (since the unity of appearance needs a unified subject). The Spirit is not in time, but time is the constant Becoming of Spirit. Phenomena are in time, but the Spirit, as the unity/totality of phenomena, is timeless.

Nietzche: Neit. rejects Hegel's view of a universal being: there is no transcendent being, or consciousness, that binds and determines an order in Becoming. Without a guiding principle or subject, Becoming is set free and left to itself. The world and time are simply this non-teleological Becoming. For Niet., time does not flow, but pulses. Pulsation is needed for the differentiation of aspects of phenomena. Becoming is the moment of time, which merges past and future, and in which Being comes to be: this moment is time, and thus constantly recurs (because there is no past and future). The "eternal return" of the moment of becoming allows generative elements of phenomena to form (will-to-power). There is nothing beyond appearances; and the being that comes out of Becoming is the will-to-power (which is the principle of the synthesis of forces manifest in appearances). Eternal return, since it is always becoming, and has no teleological goal, is different from all other conceptions of time. A duration is a completed thing, and so can’t return; while a series of recurring events posits the repetition of being, not becoming. All other views of time have a goal for time, or treat time as a being; but, time is becoming. Overall, as Brendan has pointed out to me, this interpretation of Neit. is very dubious, since Neit. never published anything on time (and thus he probably would reject this entire reconstruction of his early views).

Time is not real: nothing that exists can have the property of being in time. Time as experienced is always ordered in 2 distinct series:

A series: dynamic time (which is the passing of time). "Moments" of time are each categorized as "future", "present", "past" in succession. Every moment of time changes with respect to these properties (PPF), and this process constitutes the passage of time.

B series: moments of time stand in relations of "earlier than" and "later than". Moments (or events) possess these properties permanently or "eternally" (since if one moment/event is "earlier than" another, then it is always so). This B-series represents static time.

McTaggarts Argument: the A-series cannot be real since it entails a contradiction. Yet, an A-series is necessary for time because without it, there would be no change–and change is necessary to fully capture our experience of time (i.e., without change, there is no time). Yet, since the B-series theory entails that every event never changes its properties (of "earlier" and "later"), this means that the B-series can’t account for the experience of time alone. Yet, the A-series theory entails that all events have the properties of past, present, and future (PPF). But, these properties are contrary to one another: that is, if an event is past, then it can’t be present, and so on. So, the A-series leads to the contradictory view that each moment (event) possesses contradictory properties (PPF).

–Reply: No event/moment possesses the properties of PPF at the same time, but only in succession (i.e., each event is first Future, then Present, then Past). So, no contradiction arises.

–Counter-Reply (by McTaggart): How are we to understand the claim that no event has all of the PPF properties at the same time? This response appears to involve, or appeal to, some notion of time–but time was supposed to be explained by the A-series; that is, the A-Series was supposed to explain time, but now we need a temporal concept (at the "same time") to explain the A-Series; and this constitutes a case of circular reasoning (i.e., assuming what you are supposed to prove).

2 Possibilities: (i) one could appeal to the B-Series to explain the use of the temporal concepts in the A-Series. Yet, the B-Series cannot account for time (since it is a static concept, as argued above), so this response doesn’t work. In other words, the B-series cannot account for the term "same time", since the B-series only employs the terms, "earlier than" and "later than". (ii) One could appeal to another time series, Time 2 (as opposed to the time of the A-series, which we will call Time 1), in order to provide the concept of time needed to explain the use of "at the same time" in Time 1. Problem: This response leads to an infinite (vicious) regress since the second order time series, Time 2, will have the same problem of the first order time series, time 1, in that any moment of time will be PPF simultaneously. So, Time 2 will need to explain "not at the same time", just as Time 1 did, and so Time 2 needs a third-order time series, Time 3, to explain it. But, then Time 3 will also need a higher time series, Time 4 (for the same reason), and so on for an infinity of time series.

–Other responses: (i) could the experience of time be subjective (relative to each individuals’ experiences, which is often called the "specious present")? Problem: But, then PPF would be different for different individuals, and this contradicts our concept of time as real and objective (since we rely on the objectivity of time to guarantee that all people experience the same moments of time). In other words, experience informs us that PPF are the same for all people, and not relative to each person’s experience. (ii) Could the contradictions (or circulatory) of the A-series be a basic or primitive fact about time that cannot be explained further (and must be simply accepted)? So, time is real although explaining it runs into contradictions (as above). Reply: an explanation can be contradictory (circular) without undermining the concept that is being explained (e.g., morality), but if the concept is itself contradictory (regardless of any explanation of the concept), then the concept must be rejected. And, the fact that each moment of time possesses contrary properties (PPF) is the reason time must be rejected (as unreal). Counter-reply: PPF can be a relative property (relative to different moments) and thus other time series are not needed to explain the A-series.

–The A-Series and B-Series Responses to McTaggarts’ argument: (1) A-series advocates deny that time is unreal, and accept the A-Series. They argue that any concept of time that eliminates the A-series does not accurately reflect our experience of time. The "A-series" is a real aspect of our experience of time that must be retained, and since a clock can reveal the "motion" of the A-series, it is not the case that the A-series is purely subjective. A-series theorists argue that the B-series theory of time treats all moments of time as if they were the same. But, there is a special importance to the "present" which they fail to explain; so, the B-series cannot account for time alone. Problems with the A-series explanation: At what rate does time flow (or the A-series change)? Since "speed=distance/time", any concept of the flow or change of time already presupposes time (which is essentially McTaggart's argument). Some A-theorists reject that a "moving now" accurately explains the A-series, but then how do you understand the A-series? (2) B-series theorists believe that the flow of time (A-series) is just a subjective, psychological phenomenon that has no basis in reality. For the B-series theorist, there is no A-series, and thus no flow or motion of time. Moments (or events) do not change, or come to possess and lose temporal properties (PPF). Thus, there is no special "present" that one moment in time possesses (such that one moment is "present", and all the others moments are either "past" or "future"). Therefore, explaining the change in objects (and not moments/events) is simply explaining how they can have properties that are relative to different moments of time (that form the B-series). These relative properties may be incompatible when viewed from several different moments of time; but incompatible relative properties do not undermine the concept of time (since this can only be accomplished by incompatible objective properties). That is, stating that an object "became cold from time T1 to time T2" does not introduce any irreducible "flow of time" (A-series); rather, this statement can be translated as asserting that an object possessed the property "hot" at T1, and the property "cold" at T2, and that there exists a temporal distance between T1 and T2. Overall, moments (events) stand in different relations to one another, but do not change. By this means, the B-series attempts to explain time (and reject McTaggarts’ belief that the B-series cannot account for time).

A-series theorists tend to appeal to natural languages (i.e., normal languages) and common-sense views of the ontology of the world to justify the A-series. B-series theorists tend to appeal to formal languages (i.e., logical/philosophical reconstructions of natural languages) and to the ontology of science and the scientific world view.

Tensed sentences: a claim whose truth-value differs at different times. E.g., "today is Monday", "I am drinking now". These claims are true at some times (e.g., Monday), and not true at other times.

Tenseless sentences: a claim whose truth value is the same at all times. E.g. "January 22 is Monday", "I am drinking at 11pm, April 7, 2001".

Tensed sentences are used frequently in ordinary language, and seem to support the A-series theory of time since tensed sentences appear to make use of the past, present, and future (PPF) as real properties of events/moments (when the claim is uttered). So, the B-theorist needs to replace tensed sentences with tenseless claims in order to support their theory. B-series theorists must translate all tensed sentences into tenseless sentences. Tenseless sentences are always true or false, and thus don’t seem to invoke PPF as real properties of events. (A-theorists must also translate tenseless sentences, like "E, is earlier than E2" into tensed sentences, like "E, is more past than E2", etc.) A-theorists deny that tensed sentences can be translated into tenseless claims without seriously violating the meaning of the original claim. (B-theorists often use token-reflexive sentences to translate tensed claims into tenseless claims; where a "token-reflexive" sentence refers to the act of uttering the sentence as means of tenseless reference: e.g., "E is now past" is translated into the token-reflexive sentence: "E occurs prior to the utterance of this token sentence".) Conclusion: it seems impossible to translate many tensed sentences into tenseless claims without a loss of meaning. So, the B-theory fails to account for the phenomena of tense in language. E.g., "I am drinking now" is translated into "I am drinking at 11pm, etc."; but, I may not know what time it is (or day, month, year, etc.). So while I know the former claim is true, I don’t know that the latter is true. Yet, if the two statements really are equivalent (i.e., have the same meaning), then their truth values should be the same. But, since the truth values are not identical, it follows that they are not equivalent statements. (In short, propositional attitudes alter their meaning.)

Other problems with the B-series theory: (1) Temporal passage seems an ineliminable, or necessary, feature of our basic experience of the world, but the B-series must deny that this seemingly basic perception has any ontological significance (which is not a plausible conclusion for a B-theorist to reach). (2) What is the ontological status of the B-series? If all events have the same ontological status, then they all equally exist. But, does this mean that all events exist simultaneously (which is a contradiction) or eternally (which may also be a contradiction)–i.e., it seems that temporal properties can be ascribed to the whole B-series. Answer: The B-series entails that the totality of events is not simultaneous or eternal, but successive. In addition, as a counter-reply, to say that something exists must mean more than that it exists "now"; if not, than the A-series claim that "only the present exists" leads to silly claim that "the present exists now". So, the B-series is "successive", and this should be taken as a basic fact. Yet, what does it mean to say that the B-series is "successive"? (McTaggart says that a C-series is a non-temporal series of successive acts, but that the series is symmetrical, without a temporal direction. Thus, he claims that only an A-series can provide a direction to such a time series–and McTaggart's C-series is much like the B-theorist's definition of the B-series as "successive".) What does "successive" imply about the ontology of time (and the B-series)? How does time receive its asymmetry between "earlier" and "later" moments of time (i.e., how can time have a privileged direction from past to future events given the B-theory)? Answer: causal laws or physical factors can provide the "arrow" of time: e.g., laws of thermodynamics, etc. (such that these laws/causal processes provide the arrow of time). Problem: Does physics provide the arrow of time, or does the asymmetrical, basic fact of time’s arrow explain the asymmetry of causal/physical processes? Which is the more basic feature of the world: causal processes or time?

Chapter 11: Phenomenology of Time (Husserl/Merleau-Ponty)

Time is subjective: PPF are subjective phenomena (although Husserl seems to allow for the possibility of an objective, physical "now"; i.e., the present moment). The past (and future) are not memories or brain events which resemble past events, since a memory is a feature of the present (now) and thus fails to identify or represent the past object. (MP argues that a memory of a past event needs some means of ensuring that it correctly identifies the past event; but this implies that some additional mind or framework is needed in our minds to establish the identity; and this quickly leads to a regress of mind inside of minds, of course.) Objects of past perception (such as a melodic phrase) are still perceived even though they are past because temporal objects exist as unified wholes that endure (and are thus continuously perceivable). (NOTE: we are ignoring all the terminology Husserl uses to describe the different aspects of the phenomena of temporal perception.) Past temporal objects are thus still perceived in the present moment (as is reflected in Husserl’s diagram). Temporal objects (like a melodic phase) are experienced as a whole even though much of the object is no longer in the present moment (i.e., we only hear one note at a time of the whole melody, but we still perceive the whole melody). Overall, phenomenology only concerns the phenomena of time; i.e., time as experienced by humans, which is a mental process. Problem: Does this theory conflict with the modern scientific analysis of the brain/mind/perception? (I'm not sure.)

Bergson rejects all attempts to "spatialize" time (i.e., treat time as space). Time is qualitative, and not quantitative (as is space). Qualitative things cannot be added to one another in such a way as to determine a length or magnitude (as can the quantitative, like space). For Berg., the future does not exist; only the present–but the present moment is intertwined with the past. So, the past still exists in the present. Time is not a series (thus he rejects both the A and B series). Time appears to flow, however (so his view is similar to Nietzche): therefore, time is "becoming", or "duree" (as he calls it). Duree (temporal becoming) is an objective fact of the physical world, and not merely phenomenal.