Notes on time


Questions on time

Is time finite in extent or infinite? Is it parcels at the ‘shortest duration’ or continuous, infinitely divisble – going infinitely small, ‘gunky’? Is time linear or cyclic? Is time just an inherent feature of, or the sum of, change or cause? Or is spacetime an entity, the container for all other objects and events? Is time’s passage a subjective phenomenon, or a construction of biological organisms, a biproduct of agency? Does only the present exist or only the past and present, or does all of time exist at once? If all time exists, is the future not already there (and so predetermined)? Or, if the future exists as a set of possibilities, can we really deny there’s something special now (t0) about that potential state of affairs that will (t1) come to pass? How should Special Relativity affect understanding of time, given that the same ‘now’ does not happen everywhere at once? Is the direction of time, if time has direction, arbitrary?   Is time locally representative of its global character? Is time necessary or contingent – does it work the same way at all worlds? Do objects exist ‘all at once’ in each moment, or in temporal parts spread across a set of times? How does truth work in the context of time?


Phenomenal time

The appearance of time is dynamic and asymmetric. Past is locked and receding, future is open and approaching. Pragmatic as we remember the past and use it to plan for the future.


Heraclitean time (origins of presentism)

‘The KOSMOS, the same for all, none of the gods nor of humans has made, but it always was and is and shall-be: an ever-living fire being kindled in measures and being extinguished in measures. (Fragment 30, McKirahan 1994 , 124.)

Heraclitus locates ‘the logos of flux (of transition, of change)’ in the given perception of time, such that truth is in the transition not the moment. He ‘seems to embrace contradictions’ says Hoy, but because language and logic are inadequate for the task of expressing the truth of flux.

In Heraclitus’ camp:

‘Henri Bergson is the best example. Though a mathematician, he complained that any “geometrical” or mathematical or logical-conceptual analysis of time is a falsifi cation of time. Instead, he advocated a purely intuitive (non-conceptual) experience of the flux of Duration (or Absolute Becoming) as the only way to know the reality of time (Hoy and Oaklander 2005 , 34–43)’

Ronald C. Hoy, ‘Heraclitus and Parmenides’ in A Companion to the Philosophy of Time, eds. H.Dyke & A.Bardon, Wiley-Blackwell, Chichester, 2013.


Parmenidian time (origins of eternalism)

Contradiction in talking of time may lead to thesis time isn’t real. There is no change, what is real is uncreated, doesn’t perish (Hoy) no transition, … And how could what is be in the future? How could it come to be? For if it came into being, it is not: nor is it if it is ever going to be in the future. Thus coming to be is extinguished and perishing unheard

of. (KRS, 249–50.)


It [what is] never was nor will it be, since it is now, all together, one, continuous. For what birth will you seek for it? How and whence did it grow?’

Ronald C. Hoy, ‘Heraclitus and Parmenides’ in A Companion to the Philosophy of Time, eds. H.Dyke & A.Bardon, Wiley-Blackwell, Chichester, 2013.


Zeno’s Paradoxes

The Dichotomy

The first [argument] asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal.

( Physics VI 9, 239b11–13 / DK 29 A 25 / KRS 318)

The Achilles Paradox

The second is the so-called Achilles, and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must fi rst reach the point whence

the pursuer started, so that the slower must always hold a lead.

( Physics VI 9, 239b14–17 / DK 29 A 26 / KRS 322)

The Arrow

‘[T]he fl ying arrow is at rest’ ( Physics

VI 9, 239b30 / DK 29 A 27 / KRS 323(a))

‘[H]e says that

[Premise 1] if everything when it occupies an equal space is at rest, and

[Premise 2] if that which is in locomotion is always in a now,

[conclusion] the fl ying arrow is therefore motionless.

( Physics VI 9, 239b5-9 / DK 29 A 27 / KRS 323(b))


It is not the arrow ’s positions that are given to us, such that motion is a construction out of them. Instead, the motion is given to us as a whole, and we abstract instantaneous positions from it.’ Imagine a blurred photograph of a runner. It took a moment to take. Let us imagine that it is particularly blurred in the area of the runner ’ s fast-moving legs. Now ask yourself: How many positions of the legs can be seen? This is an ontological, not an epistemological question. It is about what about the runner ’ s legs really contributed to the making of the picture. (One may, however, ask in addition to that: if instants are empirically inaccessible, how could we possibly see a motion that consists of nothing but instantaneous position?) The first answer that comes to mind today is: infi nitely many positions. This is a deeply Zenonian answer. It is wrong. The correct answer is: one position. Or so one could argue (Strobach 1998 , 220).

This might be some indication of how radical a solution of Zeno ’ s paradoxes, in particular of the arrow paradox, may have to be. Here are a few more attempts at radical solutions:

(1) Stick to instants. At any instant (!) of its flight, the arrow is smeared, in the sense that it is both at a certain position and not at it. This is the true essence of motion. It requires an analysis that goes back to the German philosopher Georg Wilhelm Friedrich Hegel (1770–1831). Of course, endorsing this option implies giving up the principle of non-contradiction, i.e. that “ p ” and “non- p ” cannot be true at the same time. This is what modern paraconsistent logic does anyway, so why not apply it to Zeno, as one of its leading figures, Graham Priest, has done (Priest 1985 )?

(2) Models of time should not be based on instants at all. Their basic entities should be periods of time, and instants should just be introduced as boundaries of them (for a discussion of both the point and the interval view in comparison see Arsenijevi ć and Kapetanovi ć 2008 ).

(3) Models of time should include infinitely small extensions. They might be big enough to contain “more” motion than an instant without any extension. On the other hand, they would not be full-blown periods of time with a defi nite, fi nite extension, so they might have some peculiar properties

(1) Zeno forces us to get clear about the basic notions of the mathematical continuum and its relation to reality. The arrow paradox in particular proceeds from the unproblematic assumption of positions at instants. This assumption has turned out to be not so unproblematic after all. But, still, the idea was that it is relatively easy to assign positions to objects at instants, that there is a procedure for this that will in principle be successful. However, if nature is fundamentally jerky or blurred (at least in a certain realm) this procedure does not always seem to work. Now this is just what nature might be, according to quantum physics. So, at least on a micro-physical level, it seems to be just impossible to press nature into defi nite positions at instants. This might mean that, by inventing the mathematical continuum, we have developed a model that, rather than being too coarse-grained like other modelings of natural phenomena, is too finegrained to fi t reality. So Zeno and all the discussion he provoked might both belong to a paradigm that has today been overcome.

(2) But perhaps it ’ s just the other way around. If Zeno pointed out deep trouble with the continuum, this might have been either in order to promote some atomism of space and time or to at least provide some hint that such a conception is worth considering. Now it might actually be true that in order to cope with quantum gravity, space and time themselves must be seen as quantized in some way. So atomism with regard to space and time itself might turn out to be true in some way. If this is what Zeno advocated, however indirectly, that may count as a triumph for him. The idea has been investigated, with reference to Zeno, by Belot and Earman ( 2001 ). It might be a good idea to google “loop quantum gravity” from time to time in order to stay up to date.’

Niko Strobach, ‘Zeno’s Paradoxes’ in A Companion to the Philosophy of Time, eds. Dyke, H. & Bardon, A., Wiley-Blackwell, Chichester, 2013.


Newtonian time

Absolute Present, Absolute Passage


Kantian idealism about time

‘time-order is bestowed by the mind’

moments of experience . . . [have] their place in a temporal procession, followed and preceded by others.

(Strawson 1966 , 50)

..Kant is also claimed to have controversially put the argument that the mind orders representations of time. (though some say he didn’t, others that this position is untenable).


The Phi Phenomenon

‘The phi phenomenon is a well-known example. Circles of two different colors are flashed on a screen one after the other at two different places. Even though the second circle and therefore

the beginning of stimulation by the second color cannot take place until the second circle has been presented, to the subject the circle appears to move from the fi rst place

to the second and to change to the color of the second circle halfway through . That is to say, the circle appears to change color, and therefore the representation of this change

appears to have begun, before the stimuli causing the appearance have actually arrived, therefore, before the representation of the second color could possibly have begun.’



Einsteinian, relativistic time

No absolute now, only absolute is ‘spacetime distance’ (Hoy) which distant events are simultaneous (e.g., now) is relative to the state of motion of the observer. So, separated and differently moving observers will find different events to be simultaneous (or happening “now”).

‘In this theory, it is mortal hubris, and a factual mistake, to assume that the simultaneity class one mortal observes holds for all observers.’

Ronald C. Hoy, ‘Heraclitus and Parmenides’ in A Companion to the Philosophy of Time, eds. H.Dyke & A.Bardon, Wiley-Blackwell, Chichester, 2013.


Block Universe

Drawing on special relativity, J.J.C. Smart argued for determinism based in ‘Actualism’, the idea that everything that happens has already happened.



Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

(from “Space and Time,” in Problems of Space and Time, ed. J.J.C.Smart, p.297)


‘It is sometimes said, for example, that a light signal is propagated from one part of space-time to another. What should be said is that the light signal lies (tenselessly) along a line between these two regions of space-time. Moritz Schlick has expressed this point well when he says: “One may not, for example, say that a point traverses its world-line; or that the three-dimensional section which represents the momentary state of the actual present, wanders along the time-axis through the four-dimensional world. For a wandering of this kind would have to take place in time; and time is already represented within the model and cannot be introduced again from outside.” And if there can be no change in space-time, neither can there be any staying the same. As Schlick points out, it is an error to claim that the Minkowski world is static: it neither changes nor stays the same. Changes and stayings the same can both of course be represented within the world picture, for example a changing velocity by a curved line and a constant velocity by a straight line.’




C.W. Rietdijk, in A Rigorous Proof of Determinism Derived from the Special Theory of Relativity:

‘there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is “now” for us, (Philosophy of Science, Vol. 33, No. 4 (Dec., 1966), pp. 341-344



If we assume classical physics and take the relation R to be the relation of simultaneity, then, on the view (1), it is true that all and only the things that stand in the relation R to me-now are real.

We now discover something really remarkable. Namely, on every natural choice of the relation R, it turns out that future things (or events) are already real!

(“Time and Physical Geometry,” Journal of Philosophy, 64, (1967) pp.240-247 )



whatever will happen is unavoidable )’there exists now a set of true propositions that, taken together, correctly predict everything that will happen in the future’ (SEP – Time)

(But the SEP notes this thesis is dependent on the notion that ‘every proposition is either true or false – i.e no temporal modality, or by rejection of bivalence (SEP) so that propositons may be neither true or truth value or the value indeterminate).

Ned Markosian, ‘Time’, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), 2014.


Open Future

proposition needs a time to have a truth value (‘p is v at t’) and may ‘have different truth values at different tmes’


Reductionism (or relationism)

‘time does not exist independently of the events that occur in time’ (SEP) time without change is possible


Platonism (or Absolutism or Substantivalism)

..time is a container, which can contain stretches empty of events



only the now exists. Presentism – ‘it is always true that only present objects exist’ (SEP) Runs into problems with Truthmaker.


‘ Just as, for Berkeley, there are no spatially extended sense organs, so, for a presentist, there are effectively no temporally extended sense organs.’

Lorne Falkenstein, ‘Classical Empiricism’


Presentist Ontological Thesis (POT)

Only the present moment exists.


Dynamical Thesis (DT)

The present moves: which moment is the present moment changes



the A- and B-series

a series of positions running from the distant past, through positions of ever-less-distant pastness, to the present, on into the proximate future, and onwards through positions of ever-more-remote futurity. McTaggart called this the A-series. Alternatively, positions in time can be ordered according to their relative positions to each other. This generates a series of positions running from earlier to later times. McTaggart called this the B-series.’ Heather Dyke Time and Tense


(McTaggart [19Z7]). The former represents an event’s occurring now, or in the present, while the latter expresses facts like one event’s occurring earlier

or later than another

On Time and Actuality: The Dilemma of Privileged Position Palle Yourgrau The British Journal for the Philosophy of Science, Vol. 37, No. 4 (Dec., 1986), pp. 405-417



Some argue time doesn’t pass. Time is like dimensions in space. Those who think time is constituted by a B-series (B-theorists) think that there is no objective distinction between past, present and future, and that there is no objective flow of time. The distinction that we draw between past, present and future is best explained as some kind of projection; we perceive reality from a temporal perspective, so we locate events in our past, present or future, but we wrongly project that perspective on to time itself. We mistakenly conclude that events are past, present or future, independently of us. Since there is no such distinction, for the B-theorist, neither is there any associated temporal fl ow. Since there is no ontological privilege involved in being the present moment, that privilege cannot pass from one moment to the next.

…For the B-theory there is no objective present moment, or distinction between past, present and future; there is just a network of events and times related to each other by the temporal relations of precedence, succession and simultaneity



Those who think time is constituted by an A-series (A-theorists) think that there is an observer-independent distinction between past, present and future, and furthermore, they think that time fl ows inexorably with respect to this distinction. The ontological privilege of being the objective present moment continually passes from one moment to the next. So the A-theory comprises a combination of theses: that time is constituted by an A-series, and that this A-series is dynamic.


A-properties and B-relations

‘Another way in which the debate has been characterized is in terms of A-propertiesn and B-relations (Markosian 2010). According to the A-theory there are genuine A-properties in the world: being past , being present and being future , and fi ner gradations thereof. The existence of these properties is not reducible to, or analyzable in terms of the B-relations ( being earlier than , being simultaneous with , and being later than ) that obtain between events. Furthermore, times and events constantly change with respect to the A-properties they possess. Events and times possess futurity, which they shed to acquire presentness, which they shed to acquire pastness. This acquiring and shedding of A-properties is what the passage of time consists in, for the A-theorist. The B-theorist denies that there are any genuine A-properties in the world.’

Linguistic and metaphysical Tense

‘Not only is tense relatively limited as a means for locating events in time, compared to other linguistic expressions, but there are also constraints on the range of expressions of location in time that can be grammaticalized in a language. One of these constraints is that grammatical tense is tied to the notion of a deictic centre; a reference point relative to which events are located in time, which is typically the moment of speech.’



indexed, context dependent statements that refer to context



non-indexed statements that locate events in the context of other events, not a ‘now’..also called ‘tenseless’. Quine turns tensed into tenseless sentences. Have the appeal of always being true.


(Variants of non-presentism)

there are some non present objects..comes in variants including



past and future objects exist as much as present ones


Growing Block Universe

– ‘the universe is always increasing in size, as more and more things are added on the front end (temporally speaking)’ (SEP) Only past and present exist.



Material objects are 3 dimensional, persistant, their identity stretches across the whole of their existence.


Perdurantism or four-dimensionalism

The 4D view ‘temporal extension is perfectly anaogous to spatial extension’ (SEP)


Stage theory

Future counterparts, not temporal parts.


Infinite time

Time can be infinite in two directions, outward, in extent, and inward, or gunkwise.



‘I am not alone in my belief in the possibility of gunk. Anaxagoras believed that, in the actual world, every object is made of gunk: All things were together, infinite both in number and in smallness; for the small too was infinite. Nor is there a least of what is small, but there is always a smaller… (Burnet, 1963, 258)

Leibniz agreed:

There is no atom, indeed, there is no body so small that it is not actually subdivided. (Leibniz, 1989, 33) Presumably Anaxagoras and Leibniz would have accepted the possibility of a gunk world.’



‘If something is made of atomless gunk then it divides forever into smaller and smaller parts—it is infinitely divisible. However, a line segment is infinitely divisible, and yet has atomic parts: the points. A hunk of gunk does not even have atomic parts ‘at infinity’; all parts of such an object have proper parts.

Linear time

Cyclic time

Eternal return


Temporal asymmetry

Time has evolved through stages

‘Perhaps a summary of Fraser’s umwelts would help the reader at this point. According to Fraser (1987), time has evolved through the following levels:

Atemporality describes the world of electromagnetic radiation. “Atemporal conditions do not signify nothingness but rather that the proper time of particles that travel at the speed of light is zero” (p. 368). Prototemporality, the time of elementary particles, “is an undirected, nonflowing as well as fragmented (noncontinuous) time for which precise locations of instants have no meaning. Events in the prototemporal universe may only be located in a statistical, probabilistic manner” (p. 368).  Eotemporality is the temporality of massive matter. “It is a continuous but non-directed, nonflowing time to which our ideas of a present, future, or past cannot be applied” (p. 368).

Biotemporality, the time of living organisms, “characterized by a distinction among future, past, and present, but the horizons of futurity and pastness are very limited…” (pp. 368-369). Nootemporality is the temporality of the fully developed human mind. “It is characterized by a clear distinction among future, past, and present; by unlimited horizons of futurity and pastness; and by the mental present…” (p. 367).

Sociotemporality is “the postulated level-specific reality of a time-compact globe.  The study of sociotemporality encompasses issues in the socialization of time and in the collective evaluation of time” (p. 368).’

Argyros, A, ‘Towards a View of Time as Depth’, Diogenes, 1990; 38; 29


Time and Modality

‘despite the wide currency of early accounts of the interaction between modal and temporal elements in the semantics of certain expressions (e.g., Dowty 1977, 1979), most subsequent work in these areas addressed only one at the exclusion of the other. The standard approaches to conditionals and modality in the 1980s and 1990s dealt with sets of worlds and quantification over them, often paying little attention to the temporal and aspectual properties of the sentences involved. Likewise, theories of tense and aspect typicallydealt with one world at a time, abstracting away from the modal nuances arising with differences between, for instance, past and future reference.’

Stefan Kaufman, ‘Conditional Truth and Future Reference’ Journal of Semantics 22: 231–280



Argyros, A, ‘Towards a View of Time as Depth’, Diogenes, 1990; 38; 29

Hoy, R.C., ‘Heraclitus and Parmenides’ in A Companion to the Philosophy of Time, eds. Dyke, H. & Bardon, A., Wiley-Blackwell, Chichester, 2013.

Kaufman, S., Conditional Truth and Future Reference Journal of Semantics 22: 231–280

Markosian, N., ‘Time’, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), 2014.

Strobach, N., ‘Zeno’s Paradoxes’ in A Companion to the Philosophy of Time, eds. Dyke, H. & Bardon, A., Wiley-Blackwell, Chichester, 2013.

Yourgrau, P., On Time and Actuality: The Dilemma of Privileged Position, The British Journal for the Philosophy of Science, Vol. 37, No. 4 (Dec., 1986), pp. 405-417

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