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Logical and Spiritual REFLECTIONS

Book 2. A Short Critique of Kant’s Unreason

Chapter 4. Experience, space and time

Among Kant’s fundamental errors was his assumption that empirical data is initially without unity, being a confused mass of myriad sensations, and that it needs to be united by rational means of some sort, before it can at all constitute an object of perception.

On this basis – and the use of many arbitrary assertions and woefully circular arguments[1] – he argued for the primacy of his a priori “forms of sensibility” (pure intuitions of space and time), i.e. that such “knowledge” of space and time is antecedent to (if not precedent to) any experience to which they are applicable and which they sort out and explain.

On what basis could Kant possibly claim to know that raw data is not unitary and needs unification, if he denies the possibility of access to raw data without a priori categories? How would he know about raw data and about the a priori forms, without reference to them first? How would he explain and justify his claim? Such a claim on his part is (if not plainly self-contradictory) of necessity arbitrary; it constitutes a hidden first premise of his philosophical system that he treats as axiomatic without valid reason. There is nothing obvious or absolute in this assumption of his. It is an unnecessary complication and mystification of the theory of knowledge. No transcendental knowledge of any sort is involved, but just say-so.

On the surface, Kant’s supposition that sensations need to be integrated before perception becomes possible might seem reasonable. If the perception is as commonly described perception of mental products of sensations, i.e. if what we perceive are presumed “representations” rather than the presumed external causes of sensations, then indeed one would expect some mechanism to fuse together the myriad sensory impressions (of the various sense organs, and the many parts of each sense organ). In ancient philosophy, this was called the “common sense”; in neurology, one would refer this task to the brain.

However, this explanation of the role of sensation is a far from certain theory. Indeed, as I argue repeatedly here and elsewhere, it is an internally inconsistent and therefore untenable one. But even ignoring the paradox it entails, just consider the empirical facts involved. We cannot credibly even suppose that sensations are numerous and complex enough to produce images, sounds and other phenomena as rich as those we encounter in perception of physical objects.

When in my daily walks I look at the blue sky, the mountains, the lake, the greenery, the passersby and the colorful ducks, I do not for a moment suppose I am seeing images of such things great and manifold in my head, but naïvely consider that I see the things themselves. To opt for the hypothesis of images would mean that I am producing or reproducing in my mind an enormous quantity of data; just think of the amount of information involved in such an experience. Why suppose I am experiencing a parallel universe in my head, when I can just as easily suppose that I am seeing the universe itself? There is a difficult hypothesis either way, so why not opt for the simpler, more obvious supposition?

If philosophy has any need of a “Copernican revolution”, this admission of perceptual realism (as against the prevalent perceptual idealism) is surely it. It is a revolution much more radical than the one Kant proposed, and much more convincing.

This natural supposition of the common man seems much more reasonable than the one proposed by philosophers and scientists. It compares the qualitative and quantitative characteristics of what we call mental phenomena and what we call physical ones. The contrast in clarity and complexity is all too evident, and sufficient to suggest direct perception of external objects. It is true that some dreams we have are very sharp; some so much so that they seem like ‘visions’. But the large majority of visualizations and dreams are rather vague or approximate. Sensations could never conceivably suffice to reproduce the reality we routinely perceive.

Indeed, some scientists have expressed surprise at the simplicity of sensory messages (electrochemical processes in the nervous system), compared to the complexity of the content of consciousness they are supposed to produce. This suggests that the process of sensation has little if anything to do with perception as such, but rather concerns memorization. Through perception, we independently judge the correctness and reliability of our simultaneous memorizations. Without this distinction, we would be hard put to explain how we evaluate individual memories, and judge them right or wrong; all memories would be uncertain, impossible to evaluate.

Memorization is what makes imagination possible. Imagination is only possible after and as a consequence of memorization, in the way of a rearrangement of memories of experiences or of abstractions from such memories. Mental phenomena are – it is much more reasonable to suppose – merely weak and imperfect reflections of physical phenomena. Imagination, the willful recombination of memories, does not affect what we perceive, but only what we remember. Imagined theses, i.e. hypotheses, can be tested because we can refer to perception independent of memory; if we had no direct perception of externals, but only apparent memories, it would be useless to recombine them, because we could never test them.

Memory of an experience is not identical with the experience. The experience is primary, a given; the memory is secondary, a construct out of sensations. Apparent memories of external objects could not properly be called memories until they are validated through independent, direct perception of those objects. Until then, they have the logical status of mere “impressions or ideas” (to use Hume’s terminology) – i.e. they are just mental items, themselves not validated and therefore incapable of validating others. This is of course the ‘grain of truth’ in Hume’s theory, which gives it some power of conviction. But the ‘husk of falsehood’ in it is Hume’s willful failure to take direct perception into consideration, which results in self-contradiction.

Memories can be ‘good’ or ‘bad’, i.e. accurate or inaccurate renditions of certain experiences. Memories can in time deteriorate (or be lost); we can also train our memory to improve. We judge memories with reference to the experiences they claim to represent or correspond to, using adductive techniques – which means we regard them collectively as somewhat hypothetical. We can instinctively[2] usually tell the difference between a memory and an imagination, but sometimes the latter are confused with the former. This is why we need adduction based on actual experience: to objectively judge the difference.

Mentalists and subjectivists express incredulity as to the possibility of direct consciousness of objects, and aver instead that cognitive processes necessarily produce mirages. It is unthinkable in their view that we directly perceive physical phenomena, but quite conceivable that we directly perceive mental phenomena. I ask: why this prejudice? Surely, the latter is as amazing and inexplicable as the former. In either case, consciousness of one thing by another is something best described as miraculous, for lack of a better word – whatever the presumed substance of its objects or distance from the subject. If we lose this sense of wonder, and regard consciousness as just some other routine “phenomenon”, we are skimming over something very, very surprising.

Those who prefer inner perception to outer have no argument in support of their thesis. The very distinction between inner and outer depends on the presupposition that we can tell a difference between them, if only in appearance. It follows that, at a phenomenological level, inner and outer – i.e. mental and physical – are on the same plane, equally capable of being the true state of affairs. There is no a priori or ab initio basis for a prejudice, one way or the other; the issue can only be resolved in a wider context, with the help of inductive logic.

The phenomenological truth of human knowledge is exactly the reverse of how Kant views it: first we experience raw data, and then only do we mentally process the information so obtained. Raw experience is experience of the totality of the here and now within the immediate range of one’s consciousness. It is essentially pure of rational interference, though reason is quick to try sorting it out almost as soon as it occurs. Thus, experience is initially unitary and only in a second phase is it rationally made to explode into seeming multiplicity, with variations in space, time and circumstance.

This is a truth evident to anyone who has practiced meditation to the stage of contemplation. One is constantly in the here and now, even though the scenery around one changes continuously in various respects[3]. In this cognitive posture, one is observing without comment of any sort (verbal or non-verbal). And indeed, even if thoughts do arise, they are viewed as just part of the scenery. The non-here and/or non-now are mental projections in the here and now; we here and now remember or imagine things beyond the here and now.

The self in fact always resides in the here and now, even if its attention is usually strongly drawn towards some place else and/or some other time. There seems to be a natural force (of varying intensity) pulling us away from the here and now, perhaps for biological reasons of survival. Nevertheless, through a contrary effort of stillness and silence, we can volitionally bring our awareness back in the here and now; and with much training this can become a habit.

Buddhist psychology has, in my view, well explained what it is that draws us out of the ‘here and now’ into the ‘there and/or then’[4]. It is the pull and push of desire (and aversion). We cling to (or away from) some passing content of the ever unfolding here and now, and become absorbed by it. Our attention becomes locked onto it for a while, fed by and feeding memories and fantasies. To avoid this malady, it is necessary to practice non-attachment.

The content of raw experience is essentially a continuous field, not only at any given moment but also from moment to moment. The division of experience into moments is already a rational act; experience itself is one across time. More precisely, experience is only of the present, and any consideration of past (memory) or future (anticipation) is rational rather than experiential. We are always in the present, whose changing appearance is all part of the present. Mental impressions of memory or anticipation may float over more present-seeming appearances, but they must be regarded phenomenologically as in the present too, and only separated out of it by rational reflection.

Similarly, the imaginary cutting up of the visual and other phenomenal fields into distinct parts – and on a later, more abstract plane, the distinction between whole and parts of space as such – this is rational activity that comes after actual experience. Such rational acts presuppose phenomena to act on, and therefore must lag slightly behind the experiences they are applied to. Nevertheless, they do not necessarily rely on memory, because what we experience as “the present” is not an instant, but a moment of time – i.e. the present has a temporal extension, it is not a mere point in time.

Thus, it is we who mentally cut experience up and then bind it together, through various rational acts. These acts occur in the present, like all existing things and events. Before we can locate ‘parts’ of experience variously in space or time, or classify them together in any way, we must differentiate them from each other. For example, we may choose to consider visible blobs of colors as distinct things; thereafter we may regard these items as spatially or temporally separate, or this color and that one to be the same or at least similar (the same to some extent but differing in shade, say).

It is clear from such analysis that locating things in space and time is a relatively complex act of reason. Before we can actually give things spatial and temporal dimensions (positions, shapes and sizes), we have to engage in numerous simpler acts of dividing and discriminating, equating and differentiating, comparing and contrasting, isolating and reassembling. Note that all of these acts involve affirmation and some involve negation; they constitute rational judgments based on experience. But note too that none of these judgments need involve words, though they often do so because this facilitates them (especially when they are numerous and tangled).

Kant would regard all such rational acts as involuntary a priori characterizations of experience, but they are clearly not that. They are essentially voluntary acts of conceptualization, of various degrees of complexity. Usually, such acts are so deeply habitual that they are almost automatic. But in truth, they cannot be claimed automatic, because: (a) very often we lazily skip doing them altogether, and (b) if we do choose to do them, we must make a conscious effort to get them done.

Generally, the simpler conceptual acts tend to be done unthinkingly, whereas the more complex ones require more of an intellectual effort. No doubt, Kant was partly misled by this common observation into regarding space and time as “intuited” instead of as conceived. Contrary to what Kant suggests, no conception is needed to experience raw data. Concepts are later cognitive tools, used to organize the data already experienced, so as to draw inferences from it and build theories around it in pursuit of further information. They are thus far from a priori building blocks of human knowledge; they are quite a posteriori.

Kant proposed his theory of the forms of sensibility (space and time), as well as the forms of understanding (the categories of causality, etc.), in order to explain and somewhat justify our apparent knowledge of a material world beyond our senses, i.e. in the way of an attempt to mitigate Descartes’ mind-body dichotomy and Hume’s problems with induction[5]. In fact, however nice their motive, his proposals aggravated and perpetuated these philosophical difficulties.

Kant suggested, simply because he could think of no better explanation and justification of external knowledge, that reason molds experience in accord with these forms. According to this view, the forms of sensibility act on incoming experience in the way of a pigeonhole, and therefore of a straightjacket. But his assumption of forcible limitation naturally implied a distortion of experience by our faculties, for what is limited somewhat is necessarily twisted out of shape – i.e. it is other than it would otherwise be.

In Kant’s view, if the forms did not structure the raw data provided by the senses, experience would not be at all possible. He thus pretentiously claimed to know and to tell us “what makes experience possible”. But his theory certainly does not greatly elucidate that mystery, and it is doubtful anyone could answer such a question in sufficient detail. In any event, it is untrue that we need to know how experience arises in detail before we can at all rely on experience.

That experience is possible is given by the simple fact that it is, i.e. that we have experience. Experience is empirically given. There is no logical need for any other proof that it is possible! As for the reliability of experience, this is not something that can be proved by deductive means as a starting point. It is however something that can be reasonably assumed to begin with, and ultimately credibly established by use of inductive logic.

The argument in favor of experience would go as follows. Experience (whether by inner or outer perception, or by intuition) is all we have in the way of concrete content of consciousness. There is nothing else to refer to – for abstractions have no existence without previous experiences, i.e. they are evidently rational derivatives of experience.

Our abstract knowledge is simply an attempt to report and remember relatively briefly what we have found in experience so far and to try and anticipate what may come into it later. Such knowledge is mostly tentative – i.e. it may be right or wrong – and the way we determine its validity in each case is with reference to both experience and logic.

If experience is taken phenomenologically, as mere appearance, this starting point is quite sufficient, for it in fact assumes nothing beyond itself. Once we have experienced something, we know what we experienced, and (provided we remember it and remain lucid and honest about it) we will not be fooled by fanciful abstract constructs.

There is of course a need to distinguish between different types of experience: immediate experiences (whether material, mental or spiritual), and their derivatives, viz. memories, imaginations and anticipations (all of which are mental). Such distinction is partly evident at the outset, with reference to the character and intensity of the experiences, and partly the result of later ordering in accord with inductive logic.

There is no rational realm floating in the air, above, below, before, behind or beyond the realm of experience. The rational realm is an outcrop of the realm of experience. Reason helps humans make sense of the world of experience, after the fact. It cannot per se affect, modify or distort experience, because experience (i.e. our experiencing) invariably precedes it.

Reason needs something to act on before it can act at all; it cannot produce experience and it has no power to affect what has already presented itself to us. Reasoning always occurs in relation to some given content of consciousness, in response to some occurring or occurred experience. Reasoning cannot exist apart from some object of consciousness to reason about. This is true at all levels and in all areas of reasoning.

Consciousness per se has no phenomenal attributes, note well. It is the transparent relation between us (the Subjects of consciousness) and our percepts or concepts (the concrete or abstract objects or content of consciousness).

From this phenomenological ground, and the attendant deductive and inductive logical insights in accord with the laws of thought, we can gradually build up a reasonably true to experience body of knowledge. Reason is an efficacious tool of knowledge, if used with due regard to experience and logic.

Kant on the contrary believed that space and time cannot be found in or grasped from experience, and so can only be explained as impositions of specialized faculties that integrate sensations into perceptions. According to him, we cannot experience anything at all until after sensations have been artificially ordered in space and time by these faculties. The “forms of sensibility” thus forcibly give form to the sensible; and such ordering is therefore purely intuitive (in the Kantian sense of that term) and not empirical, a priori and not a posteriori.

The implication of such a viewpoint is that our notions of space and time are given and fixed, for everyone and forever. Yet the documented history of human thought on space and time is that our notions of them are uncertain, varied and changing. Still today, there are doubts and differences of opinion in these matters, and we continue to hope our understanding of them will further evolve.

This historical fact is sufficient proof that Kant’s theory that space and time are not empirical percepts or concepts, but forms somehow imposed by our faculty of sensibility, is wrong. For, to repeat, if Kant’s view were correct, there would be no change across human history in our ideas concerning space and time. We would collectively have a definite, common and static view of them. Our faculties could not adapt to changing data and yield new theories about space and time.

The truth is, our ideas in this field have evolved greatly through history, and also change as we individually grow and become more educated.

The Greek geometers and philosophers developed certain views of space and time. Zeno found certain difficulties in them. In modern times, Descartes invented coordinate geometry. Newton and Leibniz developed their differential and integral calculus. Kant’s deterministic-subjectivist view was itself one stage in the historical development of these notions. Many other philosophers have since had their say on the topics of space and time, notably Husserl.[6]

Among recent physicists, Einstein proposed revolutionary ideas, which tied time to space and adopted non-Euclidean geometry for them. Gödel showed that theory left some unanswered questions[7]. Hawking and others have lately greatly affected our views, with reference to black holes and the Big Bang. And of course, string theory with its additional dimensions no doubt further complicates matters.

All that goes to show that space and time are inductively developed percepts and concepts. Note well that not only the concepts, but even their perceptual basis varies over time: for instance, the discovery of the constancy of the measured velocity of light (through the Michelson-Morley experiments) greatly (thanks to Einstein theory of Relativity) changed our view of space and time. If these percepts and concepts were constitutional or structural as Kant implies, they would be static and independent of all experience.

This simple historical observation demonstrates incontrovertibly the inaccuracy of Kant’s mechanistic view of our knowledge of space and time. Kant’s view is rightly labeled “Idealism” (though not in the sense of Plato’s transcendentally existing Forms or Ideas), because it effectively divorces our percepts and concepts of space and time from experience. His theory implies that they are inventions of our faculties, i.e. ultimately equivalent to figments of the imagination, with no real relevance to or dependence on empirical data.

In my view, space and time are partly percepts directly given in experience, and partly concepts drawn by us from experience using logic (notably, the laws of thought). With regard to space: its first two dimensions are empirical facts evident through perception, while its third dimension requires additional logical work to be projected and so is more conceptual. As regards time: we do not perceive any such thing; it is entirely conceptual, though based on the perception of change. We experience phenomena in flux, and postulate time to make such change more reasonable.

More precisely put, regarding space, every visual experience involves spatial extension, at least in the sense of having two dimensions (though the latter characterization of space, in terms of dimensions, is a later and more conceptual development). What we call the third dimension (again, later, at a still more conceptual level) is the outcome of a rational attempt by us to make sense of certain apparent contradictions in the first two dimensions. For examples, that one thing seems to (over time) move behind or in front of another, or the effects of perspective (proximity and angle from the observer). To resolve such difficulties at the perceptual level, or interpret what we see, we introduce the third dimension, in the way of a successful inductive hypothesis.[8]

The location of auditory phenomena in space is a separate issue. The auditory phenomena are of course perceived, but their placement in space is always an inductive hypothesis, sometimes right and sometimes wrong. Similarly, the precise location of our touch sensations in our body and taste sensations in our mouth depend on an imaginary mapping of space, after physical space has already been visually perceived and understood. Thus, the phenomenon of space is primarily visual and only secondarily involves the other phenomenal modalities.

Furthermore, there seems to be two extensions of space, one mental and one physical. These may overlap transparently, in the sense that we seem capable of projecting some mental phenomena (hallucinations) into outer space side by side with physical phenomena. Moreover, it seems evident that mental phenomena cannot exist if we have not first come into perceptual contact with physical phenomena; that is, mental phenomena rely on memories of physical ones, which by the power of imagination we manipulate (in a second stage), as we will. Thus, mental extension is in a sense a product of physical extension. Nevertheless, the two spaces exist, and it would be an error to speak of the one and ignore the other.

If we consider measurement of extensions (comparing shapes, lengths of lines, areas of surfaces, volumes of bodies), it is possible in both spaces. Such measurement is based on using some concrete thing (like a physical or imaginary ruler) as an intermediary scale, to compare one length to all others. However, mental measurement of internal or external space (the latter by a sort of hallucination) is necessarily approximate (though some people are better at such estimates than others). Physical measurement is considerably more accurate, and we have found many ways to perform it.

The mathematical science of geometry is an attempt to explain and anticipate various apparent regularities in spatial existence. But this science has a great inherent difficulty, in that its basic units of consideration, viz. points, lines and surfaces, are not empirically given, whether in mental or physical space, but require purely verbal negative suppositions to be adequately defined. We cannot actually see a point without any extension, or a line or surface devoid of further thickness[9]. We have to specify by means of verbal negation what we intend concerning them. So the points, lines and surfaces dealt with by geometrical theory are clearly and definitely concepts; they idealize percepts, but are not percepts. They are, at best, abstractions from approximate concretes; they not purely empirical objects.

All the above factors regarding space are mentioned here so as to remind us that what we call “space” has many aspects and involves many considerations. There is space in the purely perceptual sense, as it appears in any and all visual experiences. Visual experience without extension is inconceivable, contrary to Kant’s suggestion. We could not see only a dimensionless point; and in uniform light (or even total darkness) we would still see an extended space (or void). Therefore extension (in two dimensions, to repeat) is given in experience and does not need to be as Kant suggested imposed on experience.

Moreover, there is a subsequent development of the concept of space, first with regard to a third dimension, second in correlation with other phenomenal modalities (sound, touch, taste), and onward using more abstract considerations. By the latter I mean: giving space a name, developing a theory of space, the notion of dimensions, evolving a geometry of space, first Euclidean and then non-Euclidean, and so forth. At an advanced stage, we realize the relativity of spatial and temporal measurements, and develop a theory of relativity, then a theory linking space and time. And the conceptualization of space goes on and on, for there are still many unsolved mysteries.

Similarly, the word time refers to many levels of consideration, from the pure perception of motion in space and qualitative changes (visual or otherwise) – to very abstract concepts and complex theories. Time is not itself perceived but largely conceived with reference to experiences of motion and mutation. Time is a concept, and not at all a percept (unlike the first two dimensions of space). Indeed, the most perceptual part of change is that which is evident now (in the present); change occurring in the past and more so in the future requires still more conceptual means to grasp (notably reliance on memory and on imagination). Propositions have to be formulated and justified.

What is given to us in experience is motion and change; but since these seem to us to imply contradictions, we invent the concept of time to resolve the contradictions somewhat. We say: though this thing or moment differs from its predecessor or successor in my experience, there is no contradiction because they are in different positions in a “time” dimension. We thus invent time, somewhat in analogy to space, although such analogy has its difficulties, since it presents time as static rather than dynamic and fails to clearly distinguish between present, past and future.

We notice, too, that there are apparently an inner time and an outer one. That is to say, mental events call for a harmonizing concept of time just as physical events do[10]; and since these two sets of events seem to occur in separate domains, we can effectively speak of two time streams. Or eventually, perhaps, one time stream to explain both sets of events. Here again, the issue of measurement arises, using a physical clock or mental metronome (i.e. using certain standard motions or changes for comparison with others).

And here again, the concept becomes more and more abstract and complicated, as we seek to better understand it and build theories around it, and relate it to other things (like space, in the theory of relativity). Certainly, the concept of time is full of difficulties, which I need not go into here, for they are widely known. E.g. How stretched in time is the present? Where have past instances of the present gone, and where will future instances of the present come from? We hope over time we will overcome more of these epistemological and ontological difficulties and others we do not yet notice. Yet the concept of time is very useful, so we continue to use it anyway.[11]

What here should be stressed is that our concepts of space and time are built up inductively from various percepts. Inductively means using generalization and particularization, adductive logic (confirmation, rejection of theories). These concepts do not, as Kant implies, antedate and themselves form the percepts in some way. We should not confuse the formation of concepts out of percepts, with the Kantian idea that the percepts are formed out of sensations. For it is such confusion that gives Kant’s theory a verisimilitude it does not deserve.

For instance, Kant’s theory of space seems justified by our common belief that our eyes subdivide the light coming from a physical object, producing visual sensations that are reassembled in the brain to give us a complete image, which is what we allegedly see. But this scenario leads to logical difficulties, as discussed elsewhere. We must therefore on the contrary assume that we perceive the physical object itself, or at least the physical light from it, and not a mental image of it stored in the brain. In that case, the internal consistency of Kant’s theory is too shaky and the theory must fall.

Furthermore, we should not be overly impressed by the fact that Kant’s ideas on space and time inspired new thinking in subsequent philosophy and science. Most famously, Einstein acknowledged some debt to Kant in this domain. A not-entirely-accurate viewpoint (like Kant’s novel subjectivism of space and time) can still lead to correct views (like Einstein’s more objectivist relativity of observations to observers). Fanciful notions can give rise to good ideas.

[1] Which I will not get into the details of here – to avoid turning this essay into another thick book. Some replies to Kant’s arguments are effectively given in this section further on, when I present an alternative thesis.

[2] That is, by introspection or intuition, perhaps by “feeling” the different ways they are stored in the brain.

[3] This perspective perhaps explains the Zen koan “Bodhidharma didn’t come to China” (Dogen, p. 152). It means: China came to Bodhidhama. That is to say, the stream of appearances associated with going to, being and traveling in China, including the appearances of Bodhidharma’s body in the midst of these geographical locations, was present in front of (or all around) him – but he never moved, never went anywhere (other than where his soul was all along).

[4] Which we might identify with nirvana and samsara, respectively (though I do not pretend to have personally consciously experienced nirvana). Many useful illustrations are suggested by Zen masters in this context, such as: the still and empty self experiencing passing things and events is likened to the hub of a wheel; imaginations relate to other objects of experience like clouds in the sky, floating around in the foreground without really affecting the background. Note that the here and now is not a narrow expanse: since it has no boundary, it is potentially and therefore ultimately the “vast emptiness” of all space and time (to borrow a phrase from Bodhidharma in Dogen, p. 138).

[5] One of Kant’s motives in formulating his doctrine of space and time seems to have been to differentiate the two phenomenal domains, the physical and the mental. But this is not truly possible, because these concepts have instances in both domains equally.

[6] We should also keep in mind that there have been reflections on these topics in the East. See for instance, 13th century Japanese Zen master Dogen’s essay “The Time Being” (pp. 69-76). Kapleau, who includes part of this essay in his book, considers its insights, “realized … introspectively … through zazen” to “parallel … to a remarkable degree” modern scientific beliefs (pp. 307-11). I don’t know about that, finding it difficult to understand fully. But it any case it is interesting and challenging.

[7] See Yourgrau’s instructive and interesting book on this topic.

[8] Note that we could conceivably adopt an alternative, more positivistic hypothesis, and regard things as really disappearing when they go behind others and regard things as really changing size and shape as they change distance and direction relative to us (or we do relative to them). This possible interpretation of perspectives is not favored because it is much more difficult for the individual to manage in practice, and more importantly because of the irreconcilable contradictions it implies between the experiences of different individuals.

[9] We only perceive rough approximations of those geometrical units: e.g. extended dots rather than points, and so forth. See my discussion of this in my Phenomenology chapters 8.2 and 8.3.

[10] Note this well – it is not merely physical time that presents us with difficulties, but equally mental time. So, it cannot be argued that the difficulties are specifically physical, or specifically mental either.

[11] See also my discussions of issues relating to space and time in Phenomenology chapters 2.4 and 6.1-6.3.

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