Chapter 5
    
    An Argument That Objects Phenomenally Look To Have z Coordinates
    
    1
    
    The z Coordinate Constraint
    
    In chapter 4 I argued for primitivism, the view that the position properties that objects phenomenally look to have are absolute, primitive properties, which are such that it is not metaphysically possible for objects to have them. In this chapter I shall address the question whether these position properties consist of two coordinates or three coordinates.
    
    It is uncontroversial that objects phenomenally look to have horizontal and vertical coordinates, or x and y coordinates. It is intuitive that there may be three objects, A, B and C, such that the position that B phenomenally looks is further along in a horizontal direction from the position that A phenomenally looks, and such that the position that C phenomenally looks is further along in a vertical direction from the position that A phenomenally looks. It is controversial, however, whether objects phenomenally look to have coordinates on a forwards/backwards axis, or a z axis. Traditionally this question has been expressed in terms of
    
    whether one can visually perceive depth properties, for instance whether an object can phenomenally look at a certain point on an axis extending forwards of one.
    
    In chapter 1, I argued that there is the following constraint on the possibility of objects phenomenally looking to have z coordinates:
    
    The z Coordinate Constraint:
    
    If it is possible that objects phenomenally look to have z coordinates, then it is possible that there are three objects, o1, o2, o3, such that o1 and o2 phenomenally look to o3 to have the same x and y coordinates, but distinct z coordinates.
    
    Analogues of the z coordinate constraint for x and y coordinates are easily met. For instance, consider looking at a red cube at t1 against a white background. Suppose that, between t1 and t2, the cube moves to the left by a small distance. The x coordinates that the cube phenomenally looks to have will be different at t1 and t2, and the y coordinates and, if applicable, the z coordinates, that the cube phenomenally looks to have will be the same at t1 and t2.
    
    Suppose that between t2 and t3 the cube moves up a small distance. The y coordinates that the cube phenomenally looks to have will be different at t2 and t3, and the x coordinates and, if applicable, the z coordinates, that the cube phenomenally looks to have will be the same at t2 and t3.
    
    It is less easy to imagine how the z coordinate constraint might be met. For instance, suppose that between t3 and t4, the cube moves further away from one. This situation is illustrated in figure 1. Figure 1 is a bird’s eye perspective of a horizontal cross section of oneself and the cube at two different times, t3 and t4.
    
    Figure 1
    
    The cube at t4 C1 C2 The cube at t3 C1 C2
    
    The x and y coordinates that the cube phenomenally looks at t3 and at t4 will be different. Indeed, the set of x and y coordinates that the cube phenomenally looks to have at t4 will be a subset of the set of x and y coordinates that the cube phenomenally looks to have at t3. C1 and C2 are the two ends of the top of the side of the cube that one is looking at. Suppose, for instance, that, at t3, C1 phenomenally looks to have x coordinate x5, and C2 phenomenally looks to have x coordinate x10. At t4, C1 and C2 will phenomenally look to have x coordinates that are phenomenally closer together than x5 and x10 are. For instance, at t4, C1 may phenomenally look to have x6, and C2 may phenomenally look to have x8.
    
    Thus, this example does not provide a way of satisfying the z coordinate constraint. To satisfy the z coordinate constraint, we need to ensure that the object phenomenally looks to have the same x and y coordinates at t4 as it phenomenally looks to have at t3.
    
    One way to ensure this, given that the cube has moved away from one, is to enlarge the cube by an appropriate amount. Let us suppose that some enlarging of the cube takes place between t4 and t5. This enlarging is such that, at t5, the facing side of the cube is at the same distance away from one as it is at t4, and that the facing side of the cube phenomenally looks to have the same x and y coordinates that it phenomenally looks to have at t3. This situation is illustrated in figure 2. As with figure 1, figure 2 is a bird’s eye perspective on a horizontal crosssection of oneself and the cube.
    
    Figure 2
    
    The cube at t5, having been appropriately enlarged.
    
    The cube at t4 The cube at t3
    
    Will the cube phenomenally look to have different z coordinates at t3 and t5? It seems that there will in fact be no visual phenomenal difference between the way the cube phenomenally looks at t3, and the way the cube phenomenally looks at t5. Given the phenomenal character principle, it follows that there is no difference in any z coordinate that the cube phenomenally looks to have at t3 and at t5.
    
    2
    
    The Possibility of Objects Phenomenally Looking To Have z
    
    Coordinates
    
    In this section I will argue that, by considering the possibility of 360 degree vision, one can show that two objects can phenomenally look to some being to have the same x and y coordinates, but different z coordinates, and therefore that the z coordinate constraint can be met. In the next section, I will argue that objects phenomenally look to have z coordinates to us. If
    
    objects do phenomenally look to us to have z coordinates, then the correct response to the argument in the paragraph above is to say that the cube phenomenally looks to have the same z coordinate at t3 and t5.
    
    Consider a cubical being, which we shall call Cube, that has eyes covering all of its six sides. Figure 3 is a bird’s eye perspective of a horizontal cross-section of Cube:
    
    Figure 3
    
    Cube has 360 degree vision, and the information from its various eyes is all integrated into one global visual experience. Just as the information from our two eyes is integrated into one visual experience, so the information from all of Cube’s eyes is integrated into one global visual experience.
    
    There is good evidence that certain animals, such as woodcocks, have 360 degree vision (Waldvogel 1990). It is less easy to demonstrate that information from the eyes of such animals is integrated into one visual experience, but there does not seem any obvious obstacle to this being the case. If we reflect on our own experiences, we can imagine that our field of vision, which is approximately 140 degrees, might be increased, to 200 degrees, say by our acquiring a
    
    third eye on one side of our heads. There does not seem any obstacle to the information received from this additional eye being integrated into the same visual experience as the information from our existing two eyes. And the same point seems to apply to fourth, fifth and sixth eyes that we might acquire, which would give us 360 degree vision. Thus it seems reasonable to assume that the information from all of Cube’s eyes is integrated into one global visual experience.
    
    Let us suppose that, as illustrated in figure 4, Cube sees two apples, apple1 and apple2. Apple1 is on one side of Cube, and apple2 is on the opposite side of Cube. My central argument will be that apple1 and apple2 phenomenally look to Cube to have exactly the same x and y coordinates. Since apple1 and apple2 clearly do not phenomenally look to Cube to have exactly the same position, apple1 and apple2 must phenomenally look to have different coordinates on some third axis, a z axis. Figure 4
    Apple1
    
    z axis
    
    Apple2 y axis
    
    x axis
    
    I have labelled the axis going across the page the x axis, the axis going up the page the z axis, and the axis going into the page the y axis. The axes are labelled as such since figures 3 and 4 are how a horizontal cross-section of Cube would look from above. These are the axes of physical space that Cube is in; for clarity I will henceforth refer to them as physical axes.
    
    If our treatment of the perspective problem in chapter 4 is correct, then the position properties that objects phenomenally look to Cube to have are not coordinates on these physical axes. That is, the position properties that objects phenomenally look to Cube to have are not ones that they actually have. The perspective problem applies to Cube as well as to us. Suppose that Cube, and another similar being, Cube2, are sitting opposite each other, looking at two adjacent circles, one red and one green. The two circles phenomenally look to be in different positions to Cube and Cube2. Since the circles presumably cannot have two different position properties at once, for the reasons mentioned above, the option that seems most plausible is that the circles do not have the position properties that they phenomenally look to Cube and Cube2 to have.
    
    From now on, to avoid confusion, I will refer to the coordinates that objects phenomenally look to have as phenomenal coordinates, and the coordinates that objects in fact have as physical coordinates. Thus, the question we are addressing at present is whether objects phenomenally look to have phenomenal z coordinates.
    
    In my argument I will also be appealing to the relations introduced in section 4.1 in chapter 4 of being to the phenomenal right/left of, and being phenomenally above/below.
    
    Let us suppose that apple1 phenomenally looks to Cube to have phenomenal x and y coordinates, x5 and y5. A central premise in my argument that objects phenomenally look to Cube to have phenomenal z coordinates is that apple2 may also phenomenally look to Cube to have phenomenal x and y coordinates, x5 and y5. That is, a central premise in my argument is that apple1 and apple2 may phenomenally look to Cube to have the same phenomenal x and y coordinates.
    
    The following is an argument for this premise. Suppose that apple2 phenomenally looked at a different phenomenal x coordinate from apple1. Would the position property that apple1 phenomenally looks to have be to the phenomenal right or to the phenomenal left of the position property that apple2 phenomenally looks to have? If apple2 phenomenally looks to have a different phenomenal x coordinate from apple1, then the phenomenal x coordinate that apple2 phenomenally looks to have must be either to the phenomenal right or to the phenomenal left of the phenomenal x coordinate that apple1 phenomenally looks to have. Suppose, for the sake of argument, that apple2 phenomenally looks at phenomenal x10, that is, that the phenomenal x coordinate that it phenomenally looks to have is to the phenomenal right of the phenomenal x coordinate that apple1 phenomenally looks to have.
    
    Let us now suppose that, between t1 and t2, Cube expands to the right and left, so that it becomes an oblong. And suppose that it acquires enough new eyes that it continues to have eyes all over the surface of its body. The expanded Cube is illustrated in figure 5.
    
    Figure 5
    
    Apple1
    
    Apple3
    
    z axis
    
    1
    
    Apple2 y axis
    
    x axis
    
    Figure 5 illustrates Cube’s shape after the expansion at t2. We assume that, at t2, apple1 still phenomenally looks to have phenomenal x5. And we also assume that, at t2, apple2 still phenomenally looks to have the same phenomenal x coordinate that, at t1, it phenomenally looked to have, which, by hypothesis, is x10.
    
    It seems that the effect of expanding Cube to the right and left is that objects moving along the side marked ‘1’ in figure 5 can now phenomenally look to Cube to have a wider range of phenomenal x coordinates. For instance, let us suppose that, at t1, an object moving along side 1 could phenomenally look to have phenomenal x coordinates ranging from x3 and x7. It seems plausible to suppose that, at t2, an object moving along side 1 might phenomenally look to have phenomenal x coordinates ranging from x0 and x10.
    
    Given this, it seems plausible to suppose that, at t2, apple3 phenomenally looks to have phenomenal x10. After all, the effect of the expansion is that objects can phenomenally look
    
    further to the phenomenal right than they could before the expansion. So it seems plausible to suppose that apple3 may phenomenally look to Cube to have phenomenal x coordinate x10.
    
    Since, by hypothesis, apple2 also phenomenally looks to have x10, at t2, apple3 and apple2 phenomenally look to have the same phenomenal x coordinate. It is this kind of claim that forms a central premise in my argument. That is, what is central to my argument is that Cube sees two objects on opposite side of it, and these two objects phenomenally look to it to have the same phenomenal x and y coordinates.
    
    For the purposes of my argument, it does not matter whether it is apple2 and apple3 that phenomenally look to have the same phenomenal x coordinate, or whether it is apple1 and apple2 that phenomenally look to have the same phenomenal x coordinate. We began supposing that apple1 and apple2 phenomenally look to have the same phenomenal x coordinate. When we considered a challenge to this premise, we showed that if apple2 and apple1 do not phenomenally look to have the same phenomenal x coordinate, then at least apple2 and apple3 phenomenally look to have the same phenomenal x coordinate. Since the aim is to show that two objects on opposite sides of Cube can phenomenally look to Cube to have the same phenomenal x coordinate, it does not matter whether this claim holds for apple3 and apple2, or apple1 and apple2. For simplicity, I will assume that it holds for apple1 and apple2, as we originally assumed. Thus apple1 and apple2 phenomenally look to Cube to have the same phenomenal x coordinate.
    
    Mutatis mutandis, the same argument as above will show that it is safe to take as a premise that apple1 and apple2 phenomenally look to have the same phenomenal y coordinate.
    
    Thus, we assume that apple1 and apple2 phenomenally look to Cube to have the same phenomenal x and y coordinates. It is clear that apple1 and apple2 phenomenally look to Cube to have different position properties. If apple1 and apple2 phenomenally looked to Cube to have the same position property, then there would be no visual phenomenal difference between Cube seeing apple1 on its own, and Cube seeing apple1 and apple2 together. In fact, however, there is a significant visual phenomenal difference between Cube seeing apple1 on its own, and its seeing apple1 and apple2 together. The visual phenomenal difference is due in part to the fact that when Cube sees apple2 in addition to seeing apple1, apple2 phenomenally looks to have a different position property from apple1.
    
    There seems to be only one way to accommodate the fact that apple1 and apple2 phenomenally look to Cube to be in different positions, and that is to allow that apple1 and apple2 phenomenally look to have different phenomenal z coordinates. We started off this section by considering the following constraint on its being possible for objects phenomenally to look to have phenomenal z coordinates.
    
    The z Coordinate Constraint:
    
    If it is possible that objects phenomenally look to have z coordinates, then it is possible that there are three objects, o1, o2, o3, such that o1 and o2 phenomenally look to o3 to have the same x and y coordinates, but distinct z coordinates.
    
    It seems that the state of affairs illustrated in figure 4 meets this constraint. Apple1 and apple2 phenomenally look to Cube to have the same x and y coordinates but different z coordinates.
    
    The point that originally gave us grounds for suspicion that objects phenomenally look to us to have z coordinates was that it does not seem straightforward to bring about a situation in which there is an isolated change in the phenomenal z coordinate that objects phenomenally look to us to have. That is, it does not seem straightforward to bring about a situation in which an object phenomenally looks to us to have the same phenomenal x and y coordinates between t1 and t2, but distinct phenomenal z coordinates. By contrast, it does seem straightforward to bring about an isolated change in the phenomenal x and y coordinates that objects phenomenally look to have. It does seem straightforward, for instance, to bring about a situation in which an object phenomenally looks to have the same phenomenal y and z coordinate between t1 and t2, and a different phenomenal x coordinate.
    
    The same restriction may well apply to Cube. It might well be the case that, at any given time, only two of the three phenomenal coordinates that an object phenomenally looks to Cube to have can change. For instance, suppose that, between t1 and t2, apple1 moves further away from Cube on the physical z axis, as illustrated in figure 6.
    
    Figure 6
    
    Apple1 (at t2)
    
    Apple1 (at t1)
    
    z axis
    
    Apple2 y axis
    
    x axis
    
    The phenomenal z coordinate that apple1 phenomenally looks to have may not change. In fact, if Cube is like us, all that will happen is that, at t2, apple1 will phenomenally look to have phenomenal x and y coordinates that are closer together than the phenomenal x and y coordinates that apple1 phenomenally looks to have at t1.
    
    Suppose that, between t2 and t3, apple1 moves down the left-hand side of Cube. This is illustrated in figure 7.
    
    Figure 7
    
    Apple1 (at t2)
    
    Apple1 (at t1)
    
    z axis
    
    Apple1 (at t3)
    
    Apple2 y axis
    
    x axis
    
    Between t2 and t3 the phenomenal z coordinate that apple1 phenomenally looks to have will change. However, it is not so clear that, whilst this is happening, the phenomenal x coordinate that apple1 phenomenally looks to have can change. For instance, suppose that, between t3 and t4, apple1 moves away from the left-hand side of Cube on the physical x axis. This is illustrated in figure 8.
    
    Figure 8
    
    z axis
    
    Apple1 (at t4)
    
    Apple1 (at t3)
    
    Apple2 y axis
    
    x axis
    
    If Cube is like us, it seems that when apple1 moves away from Cube on the physical x axis between t3 and t4, the phenomenal y and z coordinates that apple1 phenomenally looks to Cube have will become closer together (here I am using the description ‘the phenomenal y and z coordinates that apple1 phenomenally looks to Cube to have’ non-rigidly; similar descriptions below are also used non-rigidly). It does not seem that the phenomenal x coordinate that apple1 phenomenally looks to have need change between t3 and t4.
    
    There is still reason to believe, however, that as apple1 is travelling down the left-hand side of Cube between t2 and t3, there is some phenomenal x coordinate that apple1 phenomenally looks to Cube to have. After all, suppose that, at t3, apple2 is travelling up the right-hand side of Cube, and that it phenomenally looks to have the same phenomenal z and y coordinates as apple1. This is illustrated in figure 9.
    
    Figure 9
    
    Apple1 (at t2)
    
    Apple1 (at t1)
    
    z axis
    
    Apple1 (at t3)
    
    Apple2 (at t3)
    
    x axis y axis
    
    Clearly, apple1 and apple2 phenomenally look to have different position properties to Cube, and to accommodate this we must allow that, at t3, apple1 and apple2 phenomenally look to Cube to have different phenomenal x coordinates.
    
    It may be that, as apple1 is rounding one of Cube’s corners, it can phenomenally look to Cube to change all three of its phenomenal coordinates. For instance, suppose that apple1 moves to the top left corner of Cube, as in figure 10.
    
    Figure 10
    
    Apple1 2 1 4 3 z axis
    
    Apple2 y axis
    
    x axis
    
    It could be that Cube can see apple1 out of the eyes on side 1 and out of the eyes on side 2. When apple1 moves along side 1, the phenomenal z coordinate it phenomenally looks to have changes, and when it moves along side 2, the phenomenal x coordinate it phenomenally looks to have changes. Thus, it is possible that when apple1 moves diagonally in the directions of the double-headed arrow in figure 10, both the x and z phenomenal coordinates that it phenomenally looks to have change. And, by moving upwards at the same time, the phenomenal y coordinate that it phenomenally looks to have can change too.
    
    Another way in which the phenomenal x, y and z coordinates that an object phenomenally looks to a subject to have could change all at once is if the subject was L-shaped, as in figure 11.
    
    Figure 11
    
    z axis
    
    1
    
    Apple1
    
    2 y axis
    
    x axis
    
    Let us call the being in figure 11 L. As apple1 moves along side 1 of L, the phenomenal z coordinate that it phenomenally looks to have changes. As apple1 moves along side 2 of L, the phenomenal x coordinate that it phenomenally looks to have changes. Thus, if apple1 moves in a diagonal direction from sides 1 and 2, in the directions of the double-headed arrow, then both the phenomenal z and the phenomenal x coordinate that apple1 phenomenally looks to have may change at the same time. And if apple1 moves upwards at the same time, then the phenomenal x, y and z coordinates that apple1 phenomenally looks to have may change at the same time.
    
    There is a slight difficulty when considering apple1’s movement away from L’s sides. Suppose that apple1 moves towards side 2 between t1 and t2, as in figure 12, whilst remaining the same distance from side 1.
    
    Figure 12
    
    z axis Apple1 at t1 1 Apple1 at t2
    
    2 y axis
    
    x axis
    
    When objects move closer to us, the phenomenal x and y coordinates that the boundary points of those objects phenomenally look to have become further apart. If we were simply considering how things phenomenally look to side 2 of L, as opposed to L as a whole, it would be natural to suppose that at t2, the phenomenal x and y coordinates that the boundary points of apple1 phenomenally look to have become further apart. However, apple1 is the same distance from side 1 at t2 as it was at t1, and thus, if we were considering how things phenomenally look from the perspective of side 1, we would not expect the phenomenal x and y coordinates that the boundary points of apple1 phenomenally look to have to change (thanks to Maria Lasonen for this point).
    
    However, since we are supposing that the information from L’s eyes is integrated into one global visual experience, we cannot suppose that the phenomenal x and y coordinates that the boundary points of apple1 phenomenally look to have both change and do not change. Thus L’s visual system must somehow reconcile the conflicting information that it is receiving from its eyes. At t2, the image that apple1 is projecting onto the retina of L’s eyes on side 2 is larger than the image that apple1 is projecting onto the retina of L’s eyes on side 1. The information that
    
    L’s visual system is receiving from its eyes on side 2 suggests that the visual system should make apple1’s boundary points phenomenally look further apart at t2 than at t1; and the information that L’s visual system is receiving from its eyes on side 1 suggests that the visual system should not make apple1’s boundary points phenomenally look further apart at t2 than at t1.
    
    It seems an empirical question how L’s visual system would resolve this conflict. Perhaps side 1 dominates, and L’s visual system would resolve the conflict by not making the boundary points of apple1 phenomenally look further apart at t2 than at t1. Or perhaps L’s visual system would average out the information from the eyes on side 1 and side 2, and make the boundary points of apple1 phenomenally look slightly further apart at t2 than at t1. Both of these options seem possible.
    
    One might think that all of the questions that we have been considering in this section are ones for empirical science, and not ones that are amenable to armchair analysis. How can we know how things would phenomenally look to Cube? However, the assumptions that we made in the example of Cube were quite weak. They were 1.) 360 degree vision is possible, 2.) the information from the eyes on Cube would be integrated into one visual experience. The first assumption is well supported by empirical evidence. The second assumption seemed quite plausible when we considered how 360 degree vision might be realized in our own case; I will not repeat the argument here. Thus it does not seem too ambitious to think that the armchair approach can deliver results in the case of examples such as Cube.
    
    3
    
    Objects Phenomenally Looking To Have z Coordinates to Us
    
    We have established that objects phenomenally look to Cube to have z coordinates. It remains to be shown that objects phenomenally look to have phenomenal z coordinates to us. The intuitive challenge to the hypothesis that objects phenomenally look to have phenomenal z coordinates to us that we considered earlier was that, although there can be isolated changes in the phenomenal x coordinates that objects phenomenally look to us to have, and isolated changes in the phenomenal y coordinates that objects phenomenally look to us to have, it is not straightforward that there can be isolated changes in the phenomenal z coordinates that objects putatively phenomenally look to us to have.
    
    However, this challenge can be answered. Apple1 phenomenally looks to Cube to have a phenomenal z coordinate even though, when apple1 restricts its movements to the side of Cube that it is on in figures 4 and 5 (and does not go around the corners of Cube), there cannot be any changes in the phenomenal z coordinate that apple1 phenomenally looks to have; apple1 phenomenally looks to have the same phenomenal z coordinate throughout. Our answer to the intuitive challenge, then, is that the fact that there are no changes in the phenomenal z coordinate that objects putatively phenomenally look to us to have is compatible with there being some phenomenal z coordinate that those objects phenomenally look to have.
    
    I shall now argue that there is some reason to think that objects phenomenally look to us to have phenomenal z coordinates. Consider the situation illustrated in figure 13.
    
    Figure 13
    
    C B A
    
    D
    
    Supposing that I am the subject represented in figure 13, object A is at the left-hand edge of my field of view. Put informally, my argument that objects phenomenally look to us to have phenomenal z coordinates is as follows. D phenomenally looks as far from C as B phenomenally looks from A. However, D phenomenally looks further to the phenomenal right of C than B does from A. A, B, C and D phenomenally look to have the same phenomenal y coordinate. These points are consistent only if A and B phenomenally look to have different phenomenal z coordinates.
    
    Put more precisely, the argument is as follows. We will call the position properties that A, B, C and D phenomenally look to have LA, LB, LC and LD respectively.
    
    1.) There is some phenomenal distance w, such that LA is w from LB, and LC is w from LD. 2.) Whilst the phenomenal x coordinate in LD is some phenomenal distance w from the phenomenal x coordinate in LC, phenomenal x coordinate in LB is less than w from the phenomenal x coordinate in LA. 3.) A, B, C and D phenomenally look to me to have the same phenomenal y coordinate.
    
    Therefore: 4.) LA contains a distinct phenomenal z coordinate from LB.
    
    The argument for 1.) is that it seems as though A phenomenally looks as far apart from B as C phenomenally looks from D. The argument for 2.) is that whilst LB may be a little to the phenomenal right of LA, it does not seem as much to the phenomenal right of LA as LD seems to be from LC.
    
    The argument for 3.) is that A, B, C and D are all at the same height relative to me, and thus they all phenomenally look to have the same phenomenal y coordinate.
    
    It follows from 1.), 2.) and 3.) that LA contains a distinct phenomenal z coordinate from LB, and therefore that A phenomenally looks to have a distinct phenomenal z coordinate from B.
    
    1.) and 2.) are the crucial premises in this argument. When one introspects on one’s visual experiences, they come to seem plausible. For instance, at the moment my computer processor and my printer are arranged as A and B are respectively, and the left-hand and righthand edges of the screen of my computer are arranged as C and D are respectively. That is, my computer processor and printer are to the left of me, and my computer screen is in front of me. My computer processor phenomenally looks as far from my printer as the right-hand edge of my computer screen phenomenally looks from the left-hand edge of my computer screen. But my printer does not phenomenally look as far to the phenomenal right of my computer processor as the right-hand edge of my computer screen phenomenally looks from the left-hand edge of my
    
    computer screen. All of the objects in question phenomenally look to have the same phenomenal y coordinate. The only way of reconciling the above points is to suppose that my computer processor phenomenally looks to have a different phenomenal z coordinate from my printer. This seems an intuitive result: in this situation, it does seem natural to say that the printer phenomenally looks forward of the computer processor.
    
    In our discussion of Cube above, we established that if we came to have 360 degree vision, then objects would phenomenally look to have phenomenal z coordinates. Furthermore, we showed that, as we acquired eyes on the sides of our heads, then objects moving up and down our left and right hand would phenomenally look to have changing phenomenal z coordinates. That is, it is the objects moving in certain directions at the left-most and right-most extremities of our field of view that, in such a situation, would phenomenally look to have changing phenomenal z coordinates. This observation, based on thought experiment, is the same as the introspective observation that we made when considering figure 13 above: it is at the left-most and right-most extremities of our field of view, where the angle of vision is the greatest, that perceived objects can phenomenally look to us to have different phenomenal z coordinates.
    
    4
    
    Conclusion
    
    In this chapter I have argued that it is metaphysically possible for objects phenomenally to look to have phenomenal z coordinates, and, furthermore, that there is some introspective evidence to suggest that objects do phenomenally look to have phenomenal z coordinates.

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