Hume’s Thoroughly Relationist Ontology of Time

3.1 Standard Relationism: Connecting Time to Change

In his science of human nature, Hume is interested in the capacity of the human mind, and how we acquire ideas, like the idea of time. He rejects infinitesimals based on his copy principle. A simple idea is caused by and resembles a simple impression. We do not have an idea of infinity. We cannot think of an infinitely small or an infinitely large object (T 1.2.1.2–5; SBN 26–8). In thinking anything, we eventually reach a minimally sensible item. The minimally sensible item is the threshold of our thinking. Going over this threshold destroys the idea in question.

In addition to delineating epistemic restrictions, commentators like Brown (2012), Hakkarainen (2012) and Weintraub (2012) have noted that Hume supports a nominalist metaphysics. In the course of denying abstract ideas, Hume is explicit that “everything in nature is individual” (T 1.1.7.6; SBN 19–20). He thinks it is absurd that there could be, for example, a general indeterminate triangle “which has no precise proportion of sides and angles” (Ibid.; see also T 1.3.1.7; SBN 72–3 and Cottrell 2020: Section 4.a) A ‘general triangle’ is not only an absurd term of which we have no idea of, but it is also an absurdity “in fact and reality” (T 1.1.7.6; SBN 19–20). Hence Hume’s copy principle relates to his ontology. The minimal item is the ultimate part of any existent thing; everything that exists is a simple or made of simples.^[13] The simple-complex distinction is ontological (Landy 2018: 30). Simples are more fundamental than complexes and complexes less fundamental than simples. Complexes are made of simples. Whenever we think of something complex that is made of parts—like time—we may divide the complex to parts. Jennifer Wright (2016: 61) sums up Hume’s nominalistically inclined starting point nicely. “In the case of time,” she writes, ultimate parts

are moments. These moments are ontologically fundamental, playing this role in virtue of being simple and indivisible. For Hume, their simplicity entails that, though they compose durations, they themselves possess no duration.

The parts that constitute time are indivisible simples. An object that is a part of succession is a part of time. Yet it is somewhat confusing to say that parts are moments. This is what Hume himself says: “the indivisible moments of time must be fill’d with some real object or existence, whose succession forms the duration, and makes it be conceivable by the mind” (T 1.2.3.17; SBN 39, my emphasis). Moment is a temporal notion.^[14] One unchanging, durationless object alone is not temporal in any way. It constitutes time when it is a member of other indivisible and distinct objects that come one after another. An unchangeable object does not have any duration:

I know there are some who pretend, that the idea of duration is applicable in a proper sense to objects, which are perfectly unchangeable; and this I take to be the common opinion of philosophers as well as of the vulgar. But to be convinc’d of its falshood we need but reflect on the foregoing conclusion, that the idea of duration is always deriv’d from a succession of changeable objects, and can never be convey’d to the mind by any thing stedfast and unchangeable. For it inevitably follows from thence, that since the idea of duration cannot be deriv’d from such an object, it can never in any propriety or exactness be apply’d to it, nor can any thing unchangeable be ever said to have duration (T 1.2.3.11; SBN 37).

Hume allows, in 18th century parlance, that a philosopher and the vulgar commonly believe that changeless objects endure by means of fiction.^[15] Unchanging duration is to be treated as other fictions, like unity of aggregates and continued existence of unperceived objects (Cottrell 2020: Section 5.b). We have certain ways of talking in our every day lives. We might say, for example, that a sports team is one. Hume thinks that a plurality of things is not one thing but many things.^[16] Saying that a society formed by individuals is one thing is a figure of speech. Simple things are more fundamental that complex things because simples constitute complexes and the latter does not exist without the former.

Time is made of many items that are in a succession. For there to be time, the items need to be distinct, so that there is some way to separate the different items. The often-repeated example concerns musical chords. An ongoing chord does not cause the idea of time. It is not temporal in any way, because there is nothing changing in such a sensible object. There should be a chord, another chord, pause, another chord, and so on (Slavov 2019: 398). Only when there is more than one object that is succeeded by another, we may conceive of time:

…we may conclude, that time cannot make its appearance to the mind, either alone, or attended with a steady unchangeable object, but is always discover’d by some perceivable succession of changeable objects (T 1.2.3.7; SBN 35).

As noted before, Hume’s science of human nature studies the way humans acquire ideas (and reason with them). This could suggest that he is not interested in the ontology of time at all. Science of human nature is a foundational, epistemic endeavor.^[17] Perhaps Hume establishes a foundation and a corrective to all other sciences, like parts of natural philosophy. Reasoning in physics, for example, is “in some measure dependent on the science of Man” as it lies “under the cognizance of men, and” is “judged of by their powers and faculties” (T 0.4; SBN xv). I agree that when Hume assesses the notion of time, he is first and foremost concerned on how we conceive of time and experience temporality. To that end, it is enough for him to explain“ the principles and operations of our reasoning faculty, and the nature of our ideas” (T 0.5; SBN xv–vi). This is the main objective of Hume’s principal work, “the sole end of his” logic. His positive answer is that time is an abstract idea that represents “manner of appearance,” that is, moments succeeding each other (T 1.2.3.5; SBN 34). The abstract idea of time presents not a single distinct impression but manners of their disposition (Falkenstein 1997: 179–80).

Still, Hume’s epistemic argument has an ontological stretch. We cannot understand time without change. There is no notion of time without change. We can conceive of an object that does not change. An object like this does not however have a duration. Wright (2016: 54) hits the nail on the head:

His investigation into the concept of time resulted in his tightly binding the concept of time to that of succession. So tightly that he concludes that the idea of time without change is incoherent. This does not tell us that the world exhibits succession and so is temporal. However, it does tell us that, if it does not exhibit succession, there is no sense in our calling it temporal.

Hume is ambiguous on whether there is succession in the mind-independent world without succession of ideas. There could “be a real succession in the objects,” even though we perceive no successions, and even if there is no one to perceive those successions (T 1.2.3.7; SBN 35). Hume is however explicit that if there is no succession, there is no time. In more general terms, if there is no change, there is no time.

Succession and change are related in the following way. The preceding moment and the proceeding moment are distinguished by means of change. We may differentiate earlier and later bits of time only on the condition that change introduces a difference between them (Wright 2016: 86). There might be perfectly stationary objects, but they do not instantiate temporality in any way. “Time cannot make its appearance to the mind […] alone” (T 1.2.3.7; SBN 35), because the term ‘time alone,’ or ‘time itself’ is incoherent. If there is time, there is a succession of objects, that is, change. By connecting change with time, Hume is committed to an ontological thesis.^[18] This is typical relationism. In his own words: “Time is nothing but the manner, in which some real objects exist” (T 1.2.5.28; SBN 64–5). This is relationism also in the sense that it stands in a stark contrast to substantivalism. For Hume, time is not a thing. It is the way things exist.

3.2 Rigid relationism: Standards of Temporal Measurement are Relative

Hume is a rigid relationist because he denies that there is an absolute standard for clock synchronization. Consequently, there are as many times as there are minds or timepieces. Before making this argument, the problem of clock accuracy must be made clear. An accurate clock is a device that ticks evenly. When a typical wristwatch ticks 60 times a minute, it is accurate if all the intervals between its units are equal. The durations 1–2 s, 2–3 s … 58–59 s, 59–60 s should all be the same. Clocks are subject to various disturbances. They drift.^[19] If accuracy is the objective in constructing a clock, there must be some way to synchronize it. This requires a standard of synchronization. There should be a common measure, an ideal clock that ticks perfectly evenly. We could then compare local timekeepers to that ideal standard of time. Different philosophies propose different answers as to what is the correct standard of accuracy. Newton thought it is the absolute, uniform flow of time. Locke thought it is the uniformity of nature, more precisely the regularity of astronomical motions. Berkeley thought it is the goodness of God. Hume thought there is no such standard—or at least we do not have access to it.

Hume does not spill much ink on measurement. He addresses measurement in concert with developing his views on the standards of equality and the status of geometric ratios. In one paragraph, T 1.2.4.24 (SBN 47–9), he analyzes the standards of time-measurement. It is useful to break the paragraph into smaller parts. Hume takes that

1. “A common measure, the notion of any correction beyond what we have instruments and art to make, is a mere fiction of the mind, and useless as well as incomprehensible.”

2. “The fiction however is very natural.”

3. “This appears very conspicuously with regard to time; where tho’ ‘tis evident we have no exact method of determining the proportions of parts […] yet the various corrections of our measures, and their different degrees of exactness, have given us an obscure and implicit notion of a perfect and entire equality.”

According to the first point, a common measure beyond our technology is an illusion. Perhaps the correct standard can be achieved by means of congruity? We can estimate different proportions, greater, less, and equal, by comparing two objects. Perhaps we could make comparisons, develop technology, and carry out ever more precise measurements. However:

We frequently correct our first opinion by a review and reflection; and pronounce those objects to be equal, which at first we esteem’d unequal; and regard an object as less, tho’ before it appear’d greater than another. Nor is this the only correction, which these judgments of our senses undergo; but we often discover our error by a juxta-position of the objects; or where that is impracticable, by the use of some common and invariable measure, which being successively apply’d to each, informs us of their different proportions. And even this correction is susceptible of a new correction, and of different degrees of exactness, according to the nature of the instrument, by which we measure the bodies, and the care which we employ in the comparison (T 1.2.4.23; SBN 47).

By using our senses and instruments to assess proportions, we may never be perfectly certain that we have reached a correct judgment. To understand this point, it is necessary to look at Hume’s classification of judgments on degrees of quality in Treatise 1.3.1. Under closer inspection, he says that it is

impossible to judge exactly of the degrees of any quality, such as color, taste, heat, cold, when the difference betwixt them is very small; yet ‘tis easy to decide, that any of them is superior or inferior to another, when their difference is considerable (T 1.3.1.2; SBN 70).

The consideration above concerns qualitative differences. The basic point can be applied in case of quantities, too. A considerable difference between two objects may be intuited, and hence judged with a high degree of certainty. Small differences are subject to error estimates in measurement. They might be corrected indefinitely by other measurements. Congruity does not provide us an impeccable measure. Accordingly, we do not have access to perfect natural equality.^[20] As Hume remarks concerning the second point, such standard is nevertheless very natural to us. Instinctively we, as well as non-human animals, believe in the uniformity of nature (as Hume details in EHU 5 and 9). Regarding the synchronization of clocks, as Locke pointed out, a supposedly natural uniformity is provided by cyclical celestial motions. But even when we try to standardize our measurements with “some common and invariable measure,” the corrections we make are always “susceptible of a new correction” (T 1.2.4.23; SBN 47). Periodical processes are not temporally equal like the two expressions in a simple algebraic equation. Measures of rotations and revolutions are constantly corrected. Our calendars need to be adjusted by arbitrary means to match celestial phenomena. Investigating natural regularities will never provide us with a perfect equality. The quest for that standard would be a never-ending pursuit.

According to Hume’s third and most decisive point, we do not have an “exact method of determining the proportions of parts” of time (T 1.2.4.24; SBN 47–9). If there is no “perfect and entire equality” to compare ticks of a clock, then there are no absolute criteria for judging which clock is the most accurate.^[21] This position has intriguing consequences. There is in principle an indefinite number of clocks. The readings of clocks might disagree on the intervals among certain events. Compare clocks A and B.

Clock A. Extinction of the dinosaurs – one tick – turn of the third millennium on Greenwich mean time.

Clock B. Turn of the third millennium on Greenwich mean time – billion ticks – my submission of this essay.

This result is highly counterintuitive. If time is relative, then the temporal interval from the extinction of the dinosaurs to year 2000 could be billion times smaller than from the year 2000–2020. Without absolute and universal time, local measures of time are all there is. There is no common measure of time that dictates which local measure is the ‘truest.’ There are as many times as there are minds or devises that tick, or whatever we can use to track time. Hume’s relationism is rigid. According to his ontology of time, temporal intervals—whether they are subjective experiences of the passage of time or measures performed by artefactual machines—are relative.

Although contrary to common-sense expectation, Hume’s relationism is both philosophically and scientifically credible. Take the B-theory of time and the ramifications of relativistic physics. The literature on these issues for the last hundred years is voluminous and growing, so I must be highly selective and concise. According to the B-theory, the earlier/later relation is invariant. Under no circumstances is the second world war earlier than the first, or the first war later than the second. The statements ‘WW1 precedes WW2’ and ‘WW2 succeeds WW1’ are true at all times. A notable fact about the two wars is that the first (at least partly) caused the second. Hume happens to think that causation is temporally asymmetrical. Cause is earlier, and effect is later.^[22] The order of causally related, timelike separated events is not a relative matter (their time-interval is). This is bolstered by the fact that, in a relativistic account of the world, an event is earlier than a later event if an electromagnetic signal, or a signal slower than it, from an earlier event reaches the later event. An observer has a definite past if an event is located within their past light-cone, and a definite future if an event is located within their future light-cone. Grouping together the fixed earlier/later relation of the B-series and the light-cone limitations of the theory of relativity is consistent with the view that a cause begins before its effect. This result holds even in the absence of substantial time. Hume’s relational take on time is therefore not only historically interesting, but credible considering the systematic theories in the metaphysics of time.