WHAT IS PHILOSOPHY?

  

 DRAFT

I

          

NATURE AND DIVISIONS

                                 OF PHILOSOPHY

 

 

 

The philosophy considered in this book arose in ancient Greece. The very word ‘philosophy’ is of Greek origin, literally meaning love (philos) of wisdom (sophia). On the origin of the name, legend has it that, asked what he was, the Greek philosopher Pythagoras would humbly answer that he was not a sage, but only a person in search of wisdom, namely, a philosopher. As we shall see, this answer is illustrative of the difference between the philosopher and the scientist: the philosopher is someone looking for knowledge; the scientist is a person who has sufficient reasons to believe he has found it, to the extent that it makes sense to speak of “finding” knowledge.

 

1. Philosophy and science

One way to try to understand the nature of philosophy is to consider the origin of Western philosophy in ancient Greece around the sixth century B.C. It is well-known that philosophy was conceived as an alternative to mythological and religious explanations of natural phenomena. Rather than continue accepting the explanation of the foundation and origin of our world exclusively by appealing to gods, early Greek philosophers speculatively suggested natural explanatory principles such as water (Thales), fire (Heraclitus), air (Anaximenes), atoms (Democritus), or even abstract principles such as the undefined (Anaximander) and Being (Parmenides). What was the reason for such an extraordinary change in ways of thinking about the world?

   The most plausible explanation is that after earlier Greek thinkers imported scientific knowledge (geometrical, arithmetical, physical, astronomical…) from other cultures, mainly from Egypt, they were the first to consider the nature of such knowledge in itself, as generalizations, in complete abstraction from any conceivable practical applications.[1] The best example is the axiomatization of geometry by Euclid. Although the Egyptians already used geometry in their engineering projects, notably their pyramids, temples and monuments, only the Greeks had the idea of constructing a deductive system of geometry apart from any application. Another example was the development of physical and astronomical laws and explanations. Although Archimedes’ principle of the lever was practically useful, Aristarchus’ genial heliocentric hypothesis, according to which the earth rotates about its axis once a day and revolves around the Sun in a year, the fixed stars being celestial bodies similar to the Sun, although much more distant… was surely useless in his time. And possibly the most striking example of an empirical scientific achievement without any practical application at the time was Eratosthenes’ measurement of the diameter of the earth by by means of triangulation.

   This curiosity going far beyond practical aims can very well explain the birth of speculative philosophy in the thinking of pre-Socratic philosophers. They were also scientists. Thales of Miletus, identified by tradition as the first Greek philosopher, was also an astronomer who once predicted a solar eclipse. This means that these philosophers had already achieved an understanding of the procedures of the sciences, both formal and empirical, that is, they already had a well-formed conception of science. This makes it plausible that Greek philosophy was born from the application of this already incorporated conception of science to speculative issues which were previously addressed exclusively by religion and mythology, such as the question of the ultimate nature of all things or of the origins and fate of the universe. Even if these issues were far from being concretely addressed and explained by the science of their time, they could still be speculatively addressed using the resources of vague ideas like “natural powers”, “abstract entities”, and “personified abstractions”, to borrow some terms of Auguste Comte. Proposing first principles such as water, air, the undefined and Being, was an early attempt to unify the understanding of reality within the framework of highly speculative generalizations.

     If this explanation is correct, if Western philosophy was born from an application of the conception of science to domains in which scientific procedures were objectively impossible, how then can we distinguish the philosopher’s procedures from the scientist’s procedures? It seems that the answer to that question leads us to important considerations about the nature of philosophy itself, or at least parts of it. Even though the rational procedures of philosophers are similar to those of natural scientists (philosophy usually seeks to establish true generalizations from data of some kind, trying to offer explanations based on these generalizations, as much as the natural sciences...), there is a fundamental difference in that for philosophy, unlike science, such rational procedures are merely conjectural or speculative. That was the way it was from the start. What the first Greek philosophers did was to speculate, to proceed by conjectures, and the fact that during more than two millennia these conjectures have come to be argued in more and more refined, complex, and diversified ways, receiving a treatment that tends to become increasingly rigorous and sophisticated, does not transform them into something else.

   On the other hand, philosophy is said to be the cradle of the sciences.[2]  As J. L. Austin explained in an insightful, well-known passage:

 

In the history of human inquiry, philosophy has the place of the initial sun, seminal and tumultuous: from time to time it throws off some portion of itself to take a station as a science, a planet, cool and well regulated, progressing steadily towards a distant final state. This happened long ago at the birth of mathematics, and again at the birth of physics; only in the last century have we witnessed the same process once again, slow and at the time almost imperceptible, in the birth of the science of mathematical logic, through the joint labour of philosophers and mathematicians.[3]

 

Austin’s own speech act theory, explaining the rules of linguistic interaction, is an example of this. He needed many years to develop what is today taught more in linguistics than in philosophy courses. The fact that philosophy is the cradle of the sciences gives rise to another question: how much of philosophy can be considered as a kind of anticipation of science – a protoscience? Its entirety, or only its non-essential domains?

   Another question is: what does it mean to say that an investigation is speculative or conjectural? The answer is: an investigative procedure is purely conjectural (or speculative) whenever the possibility of consensus about its results is totally out of reach. This is, as we shall see, the fundamental difference between philosophy and science: while in science it is relatively easy (or at least not impossible) to obtain a consensus – an interpersonal agreement about results – this consensus remains unattainable for philosophy. The explanation of the effects of levers using the law of the lever offered by the Greek scientist Archimedes can be tested and publicly verified Everyone can agree on this explanation after making a few empirical measurements. In contrast, to explain the generation and destruction of things through the action of the forces of love (philía) and hatred (neîkos) on the four elements (water, air, earth and fire), as the pre-Socratic philosopher Empedocles did, is to embark on an inevitably vague and obscure speculative investigation. This encompasses areas of questioning in which the possibility of achieving free consensual agreement based on empirical methods seems practically impossible.

     The conjectural character of philosophy explains why it is typically an argumentative and aporetic undertaking: where consensus cannot be reached on results, what remains possible is to formulate hypotheses and discuss their possible consequences. The conjectural character of philosophy also explains the lack of linear progress in its domains. The fact that philosophy cannot reach consensus on its results means that in philosophical practice, philosophers find it almost impossible to make decisive inter-theoretical comparisons. While it is generally agreed that relativistic mechanics is superior to Newtonian mechanics, given its greater explanatory power, many do not agree that Berkeley’s proposed nominalism provides more plausible explanations than Platonic or Aristotelian realism, since these are philosophical doctrines.

     Why is it that philosophy cannot reach consensus on results? The answer is that there can only be consensus about results when there is a previous consensus about what is being assumed in research – a kind of agreement that is lacking in philosophy. In philosophy there is no agreement on the adequacy of the questions (many of the philosophical questions, it is suspected, are nothing more than pseudo problems resulting from verbal confusions). Nor is there agreement on the adequacy of the evaluation procedures leading to answers for questions (an argument may seem conclusive to one philosopher and irrelevant to another). Indeed, all these conditions are only really satisfied by science, because only science has consensually accepted assumptions and evaluation procedures. Without satisfying any of these presuppositions, we cannot hope to achieve true consensus concerning results, and are limited to the aporetic discussions typical of philosophy.

   The considerations presented so far vindicate the attempt to clarify the nature of philosophy by developing its similarity and contrast with science. This kind of comparison is impossible if we define science from the reductionist conceptions imposed on us by traditional philosophers of science, especially those of the positivist trend, who improperly extrapolate criteria to all domains of current science that are drawn from the research of a particular fundamental science like physics (Karl Popper, for example, thought that the theory of evolution should not be considered scientific, because it is unable to be the object of repeated observations, as is the case with the theory of relativity). We feel that our idea of philosophical research is one of something too comprehensive and abstract to let itself be possibly captured by any such down-to-earth experimentalist conceptions of science. In contrast to this, it should be noted that this is in no way what we usually mean when most of us – even scientists themselves – talk of science. In what follows I present a conception of science that is liberal enough to encompass any would-be science that could be derived from philosophical speculation.

   We can find this liberal conception of the nature of science in the kind of social conception of science proposed by the physicist J. M. Ziman.  According to him, science in all its forms should be understood as “consensualizable” public knowledge.[4] Under his perspective, the most striking characteristic, common to all sciences, both empirical and formal, is that they contain generalizations able to be consensually accepted as true by members of a scientific community of ideas. This conception of science, in addition to being perfectly in line with what we usually and naturally tend to call science, seems ideal as a means to contrast science with philosophy. Indeed, not only physics, but also chemistry, biology, geology, linguistics, philology, anthropology, and much of psychology and economics, for instance, can be called scientific from this broad perspective.

     Against the conception of science as consensual public knowledge we can make the following objection. There are political, religious, mystical communities in which consensus is imposed from the top down, excluding the possibility of critical evaluation of the issues in question. Notable examples of this were the intrusions of political ideologies into what could or should count as science in Nazi Germany and the former Soviet Union. However, it seems that according to Ziman’s characterization, the results of these ideological intrusions should be admitted as belonging to science, since they were consensually accepted as true by a scientific community. But that cannot be! Therefore, the consensualist-oriented conception of science suggested above seems unable to separate science from ideology.

    The answer to this difficulty is to apply here a distinction between true and false consensus, based on a better characterization of what can be understood as a community of ideas able to produce science. We can call this institution a critical community of ideas, understanding it as one that satisfies conditions like those specified by Jürgen Habermas for what he called the ideal speech situation (ideale Sprachsituation).[5] This means that a critical community of ideas must satisfy some conditions of freedom and rationality for the evaluation of the results of investigations, such as:

 

1.              the condition of making it possible for the members of a community of ideas to hold critical discussions oriented to the truth and free of any coercion, to exclude pressures other than those of the rationality of arguments themselves,

2.              the condition that members of the community of ideas have free access to information and the same chances of offering new ideas, improvements, objections, and critique,

3.              the condition of competence and equivalence in the training of members of the community of ideas.

 

These are conditions for authentic consensus. It is true that conditions like these are never completely met. However, a reasonable satisfaction of such conditions is simply indispensable to establish a consensus suitable for scientific rationality. In fact, scientists can only do science because they idealize a critical community of ideas in their minds when doing their research. And when we hear of a new scientific discovery, we always believe scientific claims for it only if we can reasonably assume that in developing its new findings, the scientific community has satisfied to a sufficient extent conditions such as those mentioned above.[6]

   Beyond this, there are, certainly, the criteria of objectivity, that the members of a scientific community accept necessary assumptions in order to achieve agreement (for instance, the replicability of an experiment in biology). It is this previous agreement on assumptions (methods, data, theories, etc.) which only science has and that is a pre-condition for the possibility of agreement and scientific progress.

   With all this in hand, we are now prepared to present a straightforward comparison between philosophy as anticipation of science (proto-science) and science as consensualizable public knowledge. The contrast is possible insofar as we characterize science as follows:

 

1) Science:  An investigation aimed at obtaining a set of non-trivial generalizations, which will be accepted as consensually true by the members of a critical community of ideas (the so-called scientific community).

 

On the other hand, we characterize philosophy by its similarity and contrast with scientific research, as follows:

 

Philosophy: An investigation aimed at obtaining a set of (non-trivial) generalizations, which is carried out by members of a supposed critical community of ideas (philosophers), but only to the extent that this community is unable to reach any agreement regarding the truth of these generalizations.[7]

 

What this contrast suggests is that everything that belongs to philosophy can in principle, at least, become part of science, insofar as agreement can be established on assumptions that are sufficient to enable authentic consensus about results. In other words: philosophy is what can be done in the impenetrable domains where science – understood as critically consensual knowledge – has not yet been proved possible and perhaps never will be. “Science,” as Russell noted, “is what we know; philosophy is what we don’t know”... “Science is what we can prove to be true; philosophy is what we cannot prove to be false”.[8] With this, the observation made at the beginning of this chapter, that philosophy is the search for truth, and not finding and having it, is better clarified: when philosophy finally finds the truth, it has already lost it to science.

   Surveying the history of science, the idea of philosophy as an anticipation of science has been confirmed again and again. Let’s look at some examples. Mathematics began to separate itself from philosophy already in the ancient world, as Euclidean Geometry shows, though in the ideas of Pythagoras it was still entangled with philosophy and mysticism. Classical logic, though only systematized as a syllogistic by Aristotle, had its law of non-contradiction already anticipated by Parmenides, though still dressed in the garb of metaphysics. Turning to the empirical sciences, according to Karl Popper, the Greek philosopher Anaximander (century VI B.C.)  vaguely anticipated the ideas of inertia and gravitation by suggesting that the earth could be a cylinder floating in empty space, without falling down or to either one side or another, because of its distance from the other stars.[9] The atomist philosophers Leucippus and Democritus, more than two thousand years ago, had already launched the idea of the existence of an infinite number of invisible and physically indivisible particles, which could be aggregated, constituting visible matter, thus explaining its properties. They thus anticipated the scientific discovery of subatomic particles by contemporary physics. The periodic table of current chemistry has taken the place of the long-superseded doctrine of the four elements (water, earth, air and fire) of ancient philosophy. Galileo’s experimental physics replaced Aristotle’s rocking-chair speculative physics of natural places and motions, making possible the scientific development of this fundamental science. Contemporary biology has replaced the vague vitalist theories of philosophers, who flourished from Aristotle to Bergson. The platonic theory of the tripartition of the soul finds a more developed equivalent in the structural theory of mind in Freudian psychoanalysis, which divides it into Ego (Ich), Id (es) and Super-ego (Über-Ich) (although psychoanalysis still falls short of having scientific standards which would make it possible to achieve consensus among its practitioners). And today we believe that when we finally obtain confirmed scientific knowledge of how the human mind actually works – the most puzzling enigma of our time – many problems of our current philosophy of mind and psychology will give way to critical consensus and, therefore, to scientific solutions.

     We cannot for sure say the same about the central fields of philosophy considered in the present book, including metaphysics, epistemology, mind-body relationships, ethics… But it is not impossible. One can argue that it only seems impossible when we consider these fields from a reductionist viewpoint that denies possible scientificity to the presently unmeasurable non-experimental domains of science, as positivist philosophers have done. But when we consider the mutual support that a growing number of different fields of science can give one another, when we consider the idea of science free from prejudices (as in Ziman’s case), this idea ceases to be fanciful.

 

DIVISIONS OF PHILOSOPHY

Starting with Aristotle, philosophy has usually been subdivided into theoretical and practical domains.  We can understand practical philosophy as one which deals with human activity and its products; theoretical philosophy, for want of a better definition, can be negatively defined as the philosophy that does not serve such purposes.

   Under these assumptions, traditionally we find two main subdivisions of theoretical philosophy: epistemology and metaphysics. Epistemology, or theory of knowledge, is concerned with the investigation of the nature, origin, and limits of knowledge. Questions such as “What is knowledge?”, “What is truth?”, “How is knowledge justified?”, “What are the sources of knowledge?”, “How can we answer skeptics?”, can be considered as belonging to epistemology. Metaphysics, on the other hand, is above all[10] an investigation of “being qua being”, better said, the investigation of those things that constitute the broadest domain of knowledge and their relations to one another.[11]  Such things can be universal properties, material substances, states of affairs, space and time, causality, number, etc. The extreme breadth of the domain where we deal with such things marks a difference between metaphysics and particular sciences, since most objects of metaphysics pass through the sciences by being absorbed into their terminology. Thus, the category of property applies simply to all scientific domains, empirical and formal. The category of material substance, as well as of causality, is presupposed by physics, chemistry, biology, and many other empirical sciences. Space and time are assumed by all empirical sciences. The same with the category of number: after all, what science does not presuppose numbers? (because of this, metaphysical categories are also called “framework questions”, though this can be deceptive, suggesting that they are subjective constructs). Furthermore, since Descartes, modern philosophy has considered epistemology and metaphysics as in some way complementary disciplines: as Locke noted[12], only by knowing the limits of what we can know will we be aware of which objects legitimately belong to the domains of our knowledge and what are beyond its possibilities (possibly entities like God, and questions like “Why does the world exist?”). The reciprocal, however, seems equally true: it is only by identifying and examining the objects belonging to the most general domains of knowledge that we acquire methods to evaluate the most general characteristics of our cognitive faculties.

    Traditionally related to metaphysics is today’s much discussed philosophy of mind. It deals with issues such as the nature of consciousness, the relationship between the mental and the physical, mental causality, which allows our identification of persons as remaining the same across time (the so-called problem of personal identity) …

    Regarding practical philosophy, which comprises human activity and purposes, as well as its products, we could include much, much more than this book can cover. Philosophy of action, the complex domain of ethics (which investigates moral action), the philosophy of history (which broadly investigates the changes effected by social action), political philosophy, aesthetics (which investigates artifacts resulting from human action), the philosophy of culture (which investigates human culture and its products like art and even philosophy), the philosophy of life...

   In fact, philosophical questions intertwine in such a way that it can often be difficult to tell which division a problem belongs to. Due to this intertwining of philosophical questions, I chose to divide this book not into general sections, but into chapters, each of them introducing and discussing some central problem of philosophy.

 

 

 

 

---

[1] W. K. C. Guthrie: A History of Greek Philosophy (Cambridge: Cambridge University Press, 1962), vol. 1, p. 36 ss.

[2] Anthony Kenny, Aquinas on Mind (London: Routledge 1993), Introduction.

[3] J. L. Austin, Philosophical Papers (Oxford: Oxford University Press, 1979), p. 232.

[4] This is the thesis on the nature of science advocated by J. M. Ziman in Public Knowledge: An Essay Concerning the Social Dimension of Science (Cambridge: Cambridge University Press 1968), cap. 2. As ne noted: “science, as a corpus of knowledge, as what scientists do, and as an institution, can’t be treated separately, more than a solid can be reconstructed from its projection upon separated Cartesian planes.” p. 42.

[5] See Jürgen Habermas, Wahrheitstheorien, em H. Fahrenbach (ed.), Wirklichkeit und Reflexion (Neske Vlg. Pfullingen 1973).

[6] One point to be emphasized about this characterization is that the exercise of philosophy presupposes a critical community of ideas able to discuss philosophical ideas, even if in some cases, such as those of wrecked philosophers like Vico, Peirce and Nietzsche, in a counterfactual way.

[7] This is not, of course, an all-inclusive definition, since philosophers have also suggested views of what they do that oppose this characterization (e.g. Wittgenstein’s descriptivist view of philosophy). Nevertheless, it agrees fairly well with what we really find in practice.

[8] Apud. afterword by Allan Wood to Bertrand Russell’s book, My Philosophical Development (London: Routledge, 1995).

[9] See K. R. Popper in "Back to the Pre-Socratics", in Conjectures and Refutations, New York 1962, p. 138.

[10] The term ‘metaphysics’ (Aristotle’s first philosophy) has several meanings, this is maybe the most proper.

[11] See G. E. Moore: “What is Philosophy?”, in Some Main Problems of Philosophy, (London: Routledge 2003).

[12] See “Epistle to the Reader”, in J. Locke: An Essay Concerning Human Understanding, (Oxford: Oxfor

SPACE AND TIME

only a draft! 

THE SPATIO-TEMPORAL BACKGROUND

 

 

 

There is something essential about the Now that is just outside the realm of science.

Einstein

 

My intention here is to try to introduce and analyze the concepts of space and time having as points of departure our commonsense perspective. It is true that in modern physics such concepts gain different, unexpected senses. However, physicists’ concepts of space and time developed from common-sense views; and the transformations these concepts have undergone in modern physics should be seen as extensions of the primitive common-sense concepts to domains far beyond the ones to which they were originally applied. A complete rupture is impossible, since it would mean the creation of independent new concepts that would have nothing to do with what we usually understand when using words like ‘space’ and ‘time’.

 

Absolute and relational views of space and time

There are traditionally two competitive conceptions of space, which can easily be extended to time. The first view is called absolutism, or substantivalism, or platonism. It was the view advocated by thinkers such as Plato, Descartes, Isaac Newton and, from a peculiar perspective, by Kant. According to this view, space is absolute in the sense that it does not need anything else to exist. Space is like an infinitely large container occupied by physical objects: an infinitely large, borderless medium in which all things are contained. As Newton wrote in his Principia:

 

absolute space, in its own nature, unrelated to anything external, always remains identical and unalterable.[1]

 

In fact, at least at first view it seems natural that space will not change or depend on the objects contained therein. And there seems to be no sense in talking about space as being finite, at least to the extent that it seems impossible to think of a spatial frontier without admitting the existence of what is “on the other side of it”, that is, space beyond its own limits. Moreover, at least Newtonian absolute space is viewed as totally abstract; it does not interact with the bodies contained within it. And this seems to create difficulties when we consider that according to general relativity, space must be curved when it is near massive bodies, for in this case physical bodies would interact with abstract absolute space, which seems impossible.

   One consequence of the absolute conception of space is that it would continue to exist, even if it could be completely emptied; following this point of view, Kant suggested that because we can imagine there being no object in space, space should be interpreted as absolute.[2] Such an argument, however, could easily be reversed to its opposite. If we imagine that everything contained in space gradually disappeared until nothing was left, it would seem that when nothing occupied it, space itself should also disappear. What Kant suggests makes sense when considered within a particular region of space: I can imagine that all the objects in this room might disappear; as the room would remain, my idea of the nature of the space contained in it seems to be confirmed. However, it does not seem possible to conceive space without any objects to occupy or delimit it, nor the idea of never-ending empty space.

   Considerations like this lead us to the second conception of the nature of space, the relationist or reductionist view proposed by Leibniz. According to that philosopher, space is an “order of coexistence” of things among themselves (while time could be his “order of succession”).[3] We can translate this by saying that space consists of relational properties of material things which have the property of being spatial. When we talk about space, we use relational predicates such as ‘next to’, ‘above’, ‘under’, ‘in front of’, ‘within’... Thus, to communicate the location of the city of Buenos Aires, we use relational predicates, saying that it is situated 900 km south of Porto Alegre, at sea level, bordering the Rio de la Plata. According to the relationist conception, objects are not really located in space, since they themselves are what somehow constitute it, and if there were nothing in the world, there could be no space (and likewise the world itself could not exist).

   There are well-known objections against the relational conception of space. One is that if an object occupies space, then it would seem that the space it occupies could be explained in terms of relationships between spatial subdivisions constituted by the object. However, these spatial subdivisions can also occupy space, requiring that the spaces occupied by them be explicable in terms of relations among their subdivisions, and so on infinitely. The conception of space in relational terms seems to lead, therefore, to an infinite regression. However, this is not a decisive objection. A regression can be vicious or virtuous, and there is no evidence that this is a case of vicious regression.

   Another kind of objection is one that posits topological difficulties. We know, for example, that any asymmetric object has a spatial orientation, given its more extensive axis, and it is possible to object that the orientation transcends the relationships among the parts of the object.

     It is also not too hard to find a plausible answer to this objection. In the case of the orientation of an asymmetric object, we can argue that it only exists if the object is considered in its relationship to other objects. What establishes the direction is obviously the existence of other objects related spatially to the asymmetric object. We usually give a direction to an object, because of our habit of imagining objects always related to something, even if that something is ourselves, unduly anticipating the fact that the world is occupied by other objects. By doing so, the object in question would immediately gain direction, because through it we would then be able to construct a spatially related line to other objects.

   Another objection of the same genre (originally suggested by Kant) is this: my right hand and its reflection in a mirror have identical relational properties with respect to themselves (the reflection corresponds to the left hand). But they are spatially different, which is evidenced by the fact that I cannot put my right hand glove on a hand that is its inverted symmetrical copy – as is the case with my own left hand. Now, my right hand would still be my right hand, even if it were the only object in the world. Therefore, it seems that the notion of space transcends what can be explained in relational terms.

   Something similar can be suggested with respect to my right hand: if it were the only object in the world, it would make no sense to ask if it is a right or left hand, because what we see as my right hand only makes sense to the extent that it is related to what we see as my left hand. I can only say that my right hand glove could not be put on an inverted symmetrical hand, like my left one, because in my mind I relate the glove to both hands, considering for this the relational spatial properties that I see between them. Even if I considered only my right hand and an imaginary left hand glove, I am considering the relationship in space between both objects, one real and the other imaginary. The upshot seems to be that there are relational spatial properties that make my right hand something inevitably different from my left hand. Instead of speaking for absolutism, the answers to this objection, like the above one, seem to speak for relationism.

   The main objection suggested by Newton is the famous example of the rotating bucket.[4] If a bucket filled with water rotates, the water within the bucket will rotate with it, forming a concave surface through centripetal forces. According to Newton, this is so relative to absolute space. There are, however, problems with this example. If the water remains in the bucket, it is because of the earth’s gravitational pull, which means that the phenomenon is in some way relative to the earth and the space occupied by it. A better way to exemplify the point is to imagine a dancing girl turning around herself as the only object existing within absolute space. As she rotates, her arms stretch due to centripetal forces. But how can we know that she is rotating if there is no other object in the space? Maybe precisely when we think she is spinning, it is because she is standing still and the centripetal force in this strange world acts precisely when she stops rotating. We can then imagine that there were rockets attached to her waist that make her rotate rapidly, so that her arms stretch with her movement. Maybe then the thought experiment would work. In this case, absolute space must be at work creating the centripetal forces, since they are relative to its immobility; however, Newton’s absolute space is defined as abstract and unable to interact with any physical body. It thus seems that we can reach no clear conclusion based on this example.

   In a disinterested analysis of our ordinary concept of space, it seems that the relational view has some advantages compared to the notion of absolute space. However, the issue turns out to be much more debatable when we ask whether this conclusion extends to the concept of space accepted by contemporary physics. If we turn to Einstein’s general relativity theory, we can interpret space in different ways. We can think that massive bodies curve spacetime near to them; I would guess that a relationist will suggest that spacetime creates a curved relation between physical bodies; some even exclude physical bodies from their ontology, considering them as “holes” in spacetime, a view that unfortunately (or not) conflicts with the physics of elementary particles.

 

2. The ineffable enigma of time

Time is to some extent like space: just as an object can be located between points in three-dimensional space, an event can be located among other events on the one-dimensional timeline.

   But the dissimilarities are much greater. One is that while objects occupy parts of space, changing their place in it, with time it is different: objects cannot fill time or get stuck in it, as happens in space. Differently from the way things are in space, each co-present object entirely occupies the period of time in which it exists. Moreover, unlike the case of spatial relationships, a temporal process is incongruous with its specular image: a melody played in reverse, for example, ceases to be a melody. And while we can move back and forth in space, time seems to move in only one direction, from the past to the future. If we could travel into the past, then by reversing this direction, it seems that effects could precede their causes, which would generate paradoxes: an adult could, for example, buy a gun and then, traveling into the past, meet himself at the time when he was a child and kill himself; but then, how could he have bought the gun if he was killed when he was a child? Also linked to the direction of time is the fact that we do not have the freedom to move around in time in the same way that we are free to move around in space. Time is different from a videotape. We can’t roll time back, we can’t speed it up, we cannot replay it, and we can’t slow it down. We cannot undo what has happened, and we cannot go back in time and correct our past mistakes, which can never be changed, deleted or reversed. We are driven forward by time regardless of our will and more often against it. Furthermore, although we in some way perceive the passage of time, we have no control over its passage. Also interesting is the way we measure time by means of periodical processes. The human race has counted time by the daily repetitions of sunrise and sunset, the phases of the moon, the seasons of the year, and only much later did we invent clocks, sun dials, water clocks, and hour glasses. It was always a passive way of measurement, different from the active ways we can measure space.

   Now, if time passes, what is its velocity? It is usual to answer that time passes at the rate of one second per second, which seems like a joke. But it is not, at least since Einstein’s relativity theory postulated time dilation. The passage of time can change according to the frame of reference in which it is measured. Time can  slow down for the stationary observer’s clock, either when the observed clock is moving at a relatively much higher speed, or when the observed clock is in a stronger gravitational field. Thus, if someone were moving at half the speed of light, her time would pass approximately 1/10 slower than the stationary observer’s time.

   That we are aware of the passage of time may have been one of the reasons why philosophers reflected much more on the problem of time than on that of space. After all, every human being is subject to the merciless yoke of time, which he can only evade in fantasy. As Baudelaire wrote:

 

In order not to feel the horrible burden of Time that breaks your shoulders and bends you towards the earth, you have to get drunk without pause. But on what? On wine, on poetry, or on virtue, as you wish.[5]

 

And also, as we will soon see, on philosophies of time that deny its very existence.

   Another peculiarity of the investigation into the nature of time is the disparity between the attitude of common sense and the metaphysical attitude towards it. As Augustine wrote, “What is time? If no one asks me, I know. If I want to explain it to someone who asks me, I don’t know”[6]. Time, therefore, seems to us something that is both obvious and yet an incomprehensible mystery. For philosophers such as Wittgenstein, this contrast suggests a therapeutic response: it must be a false enigma[7]. Indeed, it is quite possible that the deeper reason why some philosophers were so easily misled in trying to explain the nature of time is that they considered our statements and intuitions about time under the unconscious pressure of prejudices and psychological motivations. Consequently, that tried to explain the fact of temporality in terms that were not appropriate to understanding it. The healthy attitude could than consist in considering time simply as an irreducible fact of the physical world, as much as space, and not as a deep mystery in search of a metaphysical solution. If we adopt this view, what remains to be done is to analyze our common-sense conceptualizations of this fact, trying to find the best way to reconcile them with our scientific knowledge, always distrustful when we begin to ask ourselves questions for which it no longer seems possible to find any answer.

 

Absolute and relational conceptions of time

To understand time, we also begin with common-sense. After all, we began by searching for ways of counting time. The alternatives correspond to those concerning space: time can also be conceived as either absolute or relational. The absolute conception of time was also proposed by Newton, who wrote in his Principia that:

 

absolute, true and mathematical time, in itself and by its very nature, flows invariably unrelated to anything external.[8]

 

Time is, in the absolute conception, like a kind of “infinite one-dimensional container”, which underlies the events that occur in it. According to the relational conception, defended by Leibniz, time is an “order of succession” of things. For him time is a sequence of moments, and each moment is a set of coexisting events in a network of relations of earlier-than and later-than. Hence, time can be reduced to relationships of time between events and states of affairs. For example, we situate Kennedy’s assassination in time, to the extent that we know that this happened after he was elected president, shortly after the Cuban missile crisis, during the Cold War, before the first man landed on the moon, and well before the fall of the Soviet Empire...

   As the relational conception of time is based on the relations of change of things or events, one conclusion supported by this conception is that there can be no time without change, since time is measured through regular changes, without which nothing could count as objective evidence of the passage of time. Of course, it is entirely possible that nothing ever happens in a certain region of the universe; but this is only imaginable to the extent that things happen in other regions, allowing us to detect and measure the time that has passed between events. We ourselves, the observers, are constantly changing. The assumption that there may be time without change also leads to paradoxical results. If we admit it, then we can assume that the whole world, including ourselves, could “freeze” in time for a period of a year without undergoing any change, after that returning everything to its normal course, as if nothing had happened. Now, assuming that this freeze encompassed the entire universe, we would never know it happened.

   The difficulty with this hypothesis is that it violates a reasonable principle of verifiability, according to which experiences incapable of demonstrating that statements about time are true or false are meaningless. Since the idea of our whole world existing without any change is completely unverifiable, it seems that we can quietly conclude that it makes no sense. It is as absurd as the statement, also completely unverifiable, that the entire universe, along with everything in it, doubled in size while you were reading this paragraph.

   There is an ingenious thought-experiment conceived by Sidney Shoemaker to show that it is not true that the existence of time without change is completely unverifiable.[9] Suppose that the world consists of three regions: A, B and C. The inhabitants of region A of the world observed that region B froze in time for a period of one year every five years; after that B continued its normal course, without the people of region B noticing. The inhabitants of A also found that region C freezes for one year every four years. The inhabitants of regions B and C, in turn, realized that region A freezes for the same period every three years. In a year without freezing, the inhabitants of the three regions meet to discuss the issue, concluding that these freezes not only occur in the regions of others, but also in their own, since the reports of freezing presented by the inhabitants of the other regions correspond to the periodic freezes of events observed by others in them. However, considering this, they will soon discover that after a certain number of years the three regions must freeze simultaneously! In this case, a whole year will pass without the whole world undergoing any change, and this fact will be indirectly verified. Doesn’t it seem that there might be time without change? Or should this year be crossed out of the calendar?

   Against Shoemaker’s proposal, we can conceive the following problem: Imagine that freezing occurs in reverse proportion: in region A there would be one year without freezing every three years, in region B one year without freezing every five years, and in region C a year without freezing every four years. In this case the same number of years should go by without change, with all regions frozen. It seems that now we begin to resist counting time in this manner; we would then prefer to discount the years of total freezing, establishing a variable periodicity for the freezing of each region and discounting the time when all regions are frozen as a timeless time. We can extend this reasoning as we like, supposing, for instance, that for a thousand years the three parts of the world remained in a state of hibernation until one or two or three of them woke up from the frozen period of time… Would they have any reason to believe that time had passed? Similar relativizations suggest that there is no time without change. Finally, one can argue that even in Shoemaker’s thought experiment what supports the hypothesis of a common time without change (the totally frozen period of time) are the changes that regularly occur in the other parts of the world. 

 

The thesis of non-reality of time

The idea that we are prisoners of the merciless yoke of time had strong effects for metaphysical thinkers with a certain propensity to invent intellectual placebos for human suffering. Hence some philosophers have ended by denying the reality of time. The most ingenious attempt in this sense was that of the English idealist philosopher J.M.E. McTaggart.[10]

   He begins by considering two distinct ways of conceiving time. The first one appeals to what he calls the A-series (in fact, a sequence). The A-series is dynamic, basically appealing to the properties of being future, being present, and being past. The second way to conceive time appeals to the static B-series. A B-series is basically characterized by the properties of being earlier and being later.

   According to McTaggart, the B-series doesn’t really explain time, because the concept of time essentially involves change. Such a concept, however, cannot be captured by the consideration of B-series, since it is static; events are dated relative to each other, and this once and for all. Thus, knowing that Kennedy’s death preceded the election of Richard Nixon does not clarify the change, since the relationship of temporal anteriority established between the first and second events is immutable.

   For McTaggart, the only sequence that might be able to explain time is the A-series, which is dynamic. That is what we mean when we talk about the passage of time. It is thanks to the A-series that we can make sense of certain metaphors, such as that humanity steadily marches towards the future, or that time is like a river passing by, or that future events are approaching us, passing by us as they become present and then leaving us behind to be lost in the anonymous obscurity of the past... All of this obviously includes the concept of change. The difficulty arises when we consider that any event in sequence A (say, Kennedy’s death) is forever in the future, is forever present and forever becoming past. This means, according to McTaggart, that three incompatible predicates are applied to A-series events: future, present, and past. Since it is not possible without contradiction to apply incompatible predicates to the same thing – for example, I cannot say that I am sitting and at the same time standing – he concludes that time cannot be real.

     The obvious answer to this argument is that an event can be past, present, and future, but not at the same time. I can perfectly well be seated and standing at different times: I was sitting before; now I’m standing. Similarly, without contradiction the same event can be future at one time and then present and past at two other subsequent times. McTaggart anticipated this objection, though he presented an obscure argument to answer it.[11] I think the best way to make this argument intelligible is by ignoring unimportant details, paraphrasing it as follows:

 

 Even if an event X is only present, past or future at different times, it is alternatively considered present, past or future with respect to a given moment M. But this given moment M can also be considered present, past and future in relation to other moments M1, M2, and M3, which are simultaneous, future or past in relation to it. In this case, it seems that we have again fallen into a contradiction, and if we want to avoid it, we will have to consider that each of these new moments is also past, present or future in relation to other moments M11, M12, M13... and so on infinitely. Hence, either we fall into a contradiction or into an infinite regress.

 

Admitting this paraphrase, a return to infinity can indeed be produced. The problem is that nothing proves it is illegitimate. To highlight this, consider the following analogous reasoning about the incompatible relationships of being equal, smaller, or greater, in the sequence of integers. Suppose we are examining a number that follows another in a sequence. When we get to number 6, we see that it is equal to itself, smaller than 7 and greater than 5. But this is not contradictory, since the concepts of equal, smaller, and greater, are applied here to different numbers. However, here too one can take a step further, analogous to the argument above, suggesting that although 7 is greater than 6, 7 is also equal to itself and smaller than 8, which in turn is greater, equal, and smaller than other numbers, and so on. Should we therefore conclude that this regression to infinity is illegitimate, making the series of integers incoherent? Of course not, since the relationships of being greater, smaller, and equal, although incompatible, are between numbers that are either random or arranged in reverse order. The same can be said about the multiplication of relations between moments alluded to by McTaggart. The fact that it is possible to multiply time relations limitlessly does not make them contradictory, because when incompatible they occur between things that are always random or inversely arranged.

   The thesis that a B-series does not explain change is questionable. According to the B-series form of explanation, we have change when a spatial cross section at a later time is different from the same cross section at an earlier time. The only difference between these sequences is that in the B-series change isn’t subjectively felt, because it is not centered in the observer.

   The real importance of McTaggart’s argument lies the multiplicity of reactions it was able to stimulate. An interesting idea arising from the discussion of this argument is that sequence B is fundamental. Sequence A concerns the course of time from the perspective of a present observer, while sequence B concerns time in abstraction from any particular perspective. We can, by replacing indexical terms such as ‘now’, translate statements relating to sequence A into statements relating to sequence B. For example, instead of saying “Yesterday I went to the dentist”, I can say “On 23/3/2001 C.F.C. says he went to the dentist the previous day”.

   The A-series has an analogue in space: I can say that object A is in front of me, that B is at my side, and that C is behind me. But I can also say that objects A, B, and C are aligned one after the other. In the first case I am talking about space like an A theorist, while in the second case I am talking about space like a B theorist. What clearly distinguishes the A series is that it is subject-centered. And all we can say against sequence B is that it is not its business to provide our subjective feeling of time’s flow.  

 

Presentism, eternalism, growing block theory…

Considering the A-series from an ontological perspective, we find four possible positions: presentism, eternalism, growing block theory, and decreasing block theory.

   According to presentism, only present states of affairs exist. The past once existed, but it no longer does, and the future will exist, but it does not yet exist. This is our common-sense view: we do not care about future and past things in the same way we care about what is around us right now. We feel the present, even if it is only through things happening in the present. Everyone who once felt great pain or was in a situation of great danger knows that the present counts much more than the past, when the pain or the danger is over; and they also know that if the future counts, it is because it can become the present. If we accept the A-sequence view that time can only be present, past, and future, then we can argue that since the past has existed and the future still does not yet exist, then only the present exists. According to eternalism, not only the present, but also the future and the past exist. According to increasing block theory, only the present and the past exist, so that the number of things existing in the universe is constantly increasing. And according to the decreasing block theory, only the present and the future exist, with the result that the number of things existing in the universe is constantly decreasing. Few philosophers would defend the latter view, since we all tend to agree that the future exists only as a possibility, while the past has already existed as a present and therefore has existed (or exists) necessarily and immutably.

   I am a presentist. One problem philosophers have found with presentism, which makes them favor views such as increasing block theory, is that if we accept that only the present exists, we cannot find truth-makers for events that occurred in the past (or will occur in the future). I can find a truth-maker for the statement “I am hungry now”, since I have my present feeling of hunger as its truth-maker; but I cannot find a truth-maker for “I was hungry yesterday”. Or, to give a more compelling example: I can find a truth-maker for the statement “Dogs exist”, since I have a pet dog at home, and its present existence makes the statement true. But consider the statement: “Dinosaurs once existed”. There is no present dinosaur able to make my statement true. How could we relate ourselves to things that no longer exist?

   There are a number of fancy attempts to solve this problem from the presentist viewpoint. However, one way to deal with arguments against presentism is simply to explain them away as metaphysical pseudo-problems. To make this clear, let us first distinguish original truth-makers like my present hunger or my pet dog from secondary truth-makers like my memory of being hungry yesterday or the existence of dinosaur fossils. We have a thousand reasons to believe that these secondary evidences are trustworthy. They are present. The same can be said regarding statements about the future. We know that the following statement about the future is true: “In five billion years our sun will transition to a red giant phase”. Of course, we cannot have access to what will occur in five billion years. Yet a comparison between our sun and the fate of other similar stars that have already passed the present stage of our sun already serves as a secondary truth-maker. The conclusion is that the truth-maker argument against presentism fails miserably.

   There are other difficulties. Consider the statement: “I admire Plato”. It expresses a relation between me and Plato. How can something that exists be related to something that does not? Furthermore, consider the statement “Alexander the Great was born before Napoleon”. How can a relation between two non-existing things be formulated? Finally, the present is very thin, maybe something so thin that it is in danger of disappearing. How can existence or reality be accommodated with such disappearing thinness?

   Consider the statement “I admire Plato”. This is puzzling only if we imagine that this statement implies that I admire someone who never existed. But since Plato existed, and there is plenty of secondary evidence that he did exist, it makes sense to say that I have a relationship of admiration to someone who existed in the past. The same concerning the relation between two things that existed at different times in the past, like Napoleon and Alexander. There is no mystery in the relation between an existing thing and a thing that once existed, or between things that once existed. They do not both need to exist right now to be related. In the same way, there is no mystery in the relation between an existing thing and a fictional one or even between two or more fictional things. All we need is to relate them in our imagination.

   However, the main argument against presentism and for eternalism comes from relativity theory. What is present from the perspective of one observer within a frame of reference can be past or future from the perspective of other observers within other frames of reference moving away from or approaching the observer, and there can be innumerable different frames of reference. This seems to speak for eternalism: since the present might be past or future for different observers, existence must also be past, present, and future.

   Here the answer is also easier than many believe. We neither need to reject modern physics, nor select our own frame of reference (our world here on the surface of the Earth) as the only privileged one, nor search for an absolute frame of reference. What we do need to do is simply to accept the fragmentation of time as a fact about the universe that does not greatly reduce the importance of our observer-centered concepts of future, present, and past. We might accept that there are many futures, pasts, and presents, corresponding to many different frames of reference, though still accepting that our frame of reference here on the surface of the earth is privileged, simply because it is here that we feel the passage of time and live our lives: our own time is what matters to us! At least for this thin kind of anthropocentrism we are correct. The civilized alien inhabitants of a planet similar to the earth located in a very distant galaxy would have the same right to practice their own alien-centrism. This view could be called many-presentism. It admits of many possible presents, with their own pasts and futures, being much more demanding than this mingled and blurred outsider view called ‘eternalism’, which does not deserve the name, since it borrows its meaning from the A-theory, in which eternity would be the sum of all times, without beginning or end. Finally, the fact that the now is frame relative does not mean that the now must be subjective, as some proponents of the B-theory suggest. The now is objective insofar as it can be shared by observers belonging to the same frame of reference; and even if we abstract the existence of human observers, we can consider that if there were human (or non-human) observers within the same frame of reference, they would experience the same now that people are able to presently experience. And even distant events, for instance, what is happening in a spaceship orbiting the planet Jupiter, considering that the earth is approximately 40 light-minutes distant from Jupiter, we can adjust the difference by saying that their present is ~40 minutes later than ours. Moreover, concerning events belonging to a different frame of reference in a very distant place and moving away from or approaching us, we can also adjust their past or future presents in conformity with our own present, taking into account the time dilation predicted by relativity theory (for instance, we can say that because of time dilation a rocket sent to a nearby star ten years ago will only reach our present moment after a calculable amount of time).

   The last remark allows us to give an answer to four-dimensionalism, a metaphysical view that seems to be vindicated by eternalism and contemporary physics.[12] According to four-dimensionalism, material objects cannot be completely present here and now, since they are constituted by temporal parts or stages that complement one another during the time period of their existence. Thus, if Lewis has the intrinsic property of an upright posture when standing, he will have the intrinsic property of a curved back when sitting. Since his existence is four-dimensional, there is no incompatibility between these two properties. My presentist answer is that by having an upright posture, Lewis already has the dispositional property of a curved back, and this dispositional property is obviously present. When Lewis is sitting, he has the dispositional property of standing straight. Even if these properties are intrinsic, they are not essential to Lewis.[13]

   The truth about four-dimensionalism is that it is the result of a confusion between the material object (which has “endurance”), and the process (which has “perdurance”). A process defines itself through its temporal parts (Consider a football game: it is only decided after the game is over; consider the Second World War: one could only evaluate the process after it was over, but not in its beginning; the German defeat at Stalingrad was a decisive “slice” in this process, though it could not be predicted at the beginning of the process. Consider the present invasion of Ukraine by Vladimir Putin, which only began while I was writing this: a process was initiated; the complete identification and further evaluation of this process will only be made afterwards, for instance, by historians in the future, (if humanity still has a future); an individual, for instance, a thief who in the night breaks into your home is someone defined as a thief insofar as he is recognized as such. He is not a semi-thief who broke into your home while the semi-thief who leaves or is caught by the police is another, very different one. The identity of a material object (I assume that a person is in the end nothing but a material object) is something that belongs to the present as something we can objectively identify within our specious present.[14]

 

Space, time, and tropes

Ontological entities like the universals and particulars considered in the first chapter are often located within or outside a space-time background. This was the case of realism. The one-category tropical view of the world can be placed within this background. After all, a trope was characterized by us as a spatio-temporally localizable entity, which means that we will not be able to reduce space and time to tropes, even to relational tropes, without circularity. But at second thought, is this really true?

   Maybe not, if we adopt a relationist view of space and time. Why not introduce the relational space and time relations as tropes that are spatio-temporally localizable? Consider the following example: the Southern Cross constellation. It is made up of five stars. The main axis of the cross is made up of three stars, and the distance between the first and the second is approximately two-thirds of the distance between the second, the central star, and the third one. Considering the arms, they have two stars apparently at (visually) almost the same distance from the central one. Now, the relation of distance between the first and the central star can be considered to be a space-trope of (apparent) distance. Here the objection that by definition a trope is a spatio-temporally localizable property is satisfied without circularity, since the spatial relation between the first and the central stars is located in a network of other spatio-temporally localizable tropes.

   The same could be suggested concerning time. If we accept a relationist view of time, some earlier or later time trope is localizable temporally, but this does not make this characterization circular, since it is within a line of temporally localizable tropes. Thus, suppose that the two-hour time is t2. Consider now the temporal line that includes t2:

 

Ø E1_____t1______E2______t2_______E3_______t3_________E4

 

Event tropes E1, E2… E4 are temporally located, but this does not prevent us from also considering time-interval tropes as temporally localizable: t2 is temporally localizable between E2 and E3, for instance. In principle, at least, according to relationism, space and time can be reduced to tropes. And in modern physics this would not change: why could there not be a dilation of time-tropes? Why could we not have curved space-time tropes? It would be of considerable parsimonious advantage if all the world, space and time inclusive, could be explained only in terms of tropes.

 

Subjective time

It is important to distinguish physical time from psychological and so-called biological time. Psychological time is time as we perceive it. It is physical time as we subjectively measure it. For instance, time seems to pass faster as persons age, and this is a psychological phenomenon. Biological time, for its part, is time regulated by the physiology of living organisms, such as the circadian rhythms of sleeping or of menstruation or the process of aging. Biological time, however, is nothing but physical time as measured based on biological processes.

   Philosophers like Henri Bergson were tempted to put psychological time ahead of physical time, rejecting the reality of the latter. According to him,  objective time is not real, since it is spatialized and intellectualized; the only real time comes from the direct experience of the flux of time in the form of duration (durée). Duration relates to memory, since in memory the past survives in the present. It was already objected that Bergson confuses the memory of the past with the past, treating the problem in a mystifying way. This form of philosophy has served our psychological defense mechanisms by giving more importance to psychological time, since we are more able to access and control it. However, it is a question of survival that our subjective time remains sufficiently similar to objective physical time.

Some provisory conclusions

A-series and B-series are complementary, though only the A-series can be really be translated into the B-series. The A-series explains time from the observer’s point of view. It justifies our presentism. The B-series, on the other hand, explains time from a non-observer centered point of view. Present, future, and past, are observer-centered, and eternalism is a bogus concept. Four-dimensionalism is a mere confusion of objects with processes. I have a bias towards relationism, since I cannot conceive of absolute space or even time. But I confess that I have no good argument for it.

 

---

[1] Isaac Newton: “Absolute Space and Time”, in J. J. C. Smart (ed.): Problems of Space and Time (New York 1964), p. 81.

[2] Immanuel Kant: Critique of Pure Reason, A 24, B 39. In Kant’s idealism, however, space is an a priori pure form of intuition, which does not belong to the world in itself.

[3] Leibniz: “The Relational Theory of Space and Time” (excerpt), in J.J.C. Smart (ed.), Problems of Space and Time, p. 89.

 

[4] Isaac Newton, The Mathematical Principles of Natural Philosophy, Book I, Scholium.

[5] “Pour ne pas sentir l’orrible fardeau du Temps qui brisé vos épaules et vous penche vers la terre, il faut vous enivrer sans trêve. Mais quoi? De vin, de poésie, ou de vertu, à votre guise.” Le Spleen de Paris, XXXIII.

[6] Confessions, XI, 14.

[7] See Ludwig Wittgenstein: Blue Book, Oxford 1958, pp. 6, 26-27 and 108.

[8] Isaac Newton: “Absolute Space and Time”, ibid., p. 81.

 

[9] S. Shoemaker: “Time Without Change”, in R. Lé Poindevin and M. McBeath (eds.): The Philosophy of Time, Oxford 1993.

 

[10] J. McT. E. McTaggart: “Excerpt from The Nature of Existence”, in P. V. Inwagen and D. W. Zimmerman (eds.): Metaphysics: the Big Questions, Oxford 1998.

 

[11] See sec. 331-332.

[12] David Lewis, On the Plurality of Worlds (Oxford: Blackwell Publishing) Ch. 4. Sec. 2.

[13] For my answer to the problem of personal identity, see chapter IV of this book.

[14] The famous Heraclitian dictum, according to which one cannot step into the same river twice is easy to answer, since a river is roughly identified by its course and origins and never by the water that flows in it.