Is there more to life than being happy?

Suppose there are two men, Bob and Rob, whose mental lives are exactly similar. Both are very happy throughout the majority of their lives. There is, however, an important difference between them: Bob lives in the real world, while Rob lives alone in the Matrix, never to discover his predicament. None of Rob's family and friends are real.* His love is directed towards people who don't exist, and his accomplishments are appreciated by no one. No one shares in his joys or comforts him in his times of sorrow. Now, my question is this: would you rather live a life like Bob's or a life like Rob's? If you would rather live a life like Bob's, your choice cannot be based on any subjective difference between Bob and Rob, for they are exactly alike when it comes to their thoughts and feelings. So if you prefer a life like Bob's you want more for yourself than just being happy. What this “more” is is hard to characterize. Personally, I think it involves the notion that sharing one's life with others is intrinsically good, and that sharing one’s life in this way is something which is not desirable for the sake of any effect it has on our subjective well-being. But what primarily interests me here is what the reader has to say.

*I will stipulate that the simulations Rob encounters are not conscious. If one thinks such simulations must be conscious, imagine an equivalent scenario with a Cartesian demon running the show instead.

Dialetheism and Hume's Principle

Suppose the dialetheic treatment of the logical and / or semantic paradoxes is correct; in particular, that sentences of the liar family express propositions which are both true and false. Then consider the following list, which I will call List A:

(1) All whales are mammals.

(2) Nothing can escape a black hole.

(3) (3) is not true.

How many statements on List A are true? Well, both (1) and (2) are true, and under our assumption of dialetheism so is (3). Since these statements are all distinct from each other, it follows that there are three true statements on the list. But (3) is also false, so what it says is not true; hence it is also true that there are only two true statements on the list. So the number of true statements on List A is both two and three. By a parity of reasoning, we can conclude that the number of false statements on the list is both zero and one.

What if we bring Hume’s Principle to bear on this case? According to Hume’s Principle, the number of F’s equals the number of G’s if and only if there is a one-to-one correspondence between them. Suppose, now, that Jones has three books on his coffee table, which we will call Book A, Book B and Book C. Is the number of books on Jones’ coffee table the same as the number of true statements on List A? Invoking Hume’s principle tells us that the number of books is the same as the number of true statements if and only if each book can be paired off with exactly one true statement and vice versa. Can this be done? On the assumption of dialetheism, the answer is “Yes and no”: Book A can be paired off with (1) and Book B with (2), but can Book C be paired with (3)? Insofar as (3) is merely a statement Book C can indeed be paired with it. But in being paired with (3), is Book C paired with a true statement? Since (3) is both true and false, it follows that Book C both is and is not paired with a true statement. Because of this, while it is true that Book A, Book B and Book C are each paired with a different true statement in List A, it is also false that they are thus paired. Hence, if Hume’s Principle holds, we get the result that the number of books on Jones’ table both does and does not equal the number of true statements on List A. What follows from this? If the number of books on the table is three, and the number of books on the table both does and does not equal the number of true statements on List A, shouldn’t it follow that three does not equal three? After all, if there are three books on the table and the number of true statements on List A equals this, there must be three true statements on List A. If the number of true statements on List A is also not equal to three, how can it fail to hold that three, which does in fact number the true statements, is not equal to three? Now, as equality does not depend upon context, if three is not equal to three in this case, it is not equal to three in any case, and I take it that this would be a Very Bad Thing. However, a dialetheist need not embrace this result. Even though, on Hume’s Principle, the number of books on the table is both equal and not equal to three, it does not follow that “the number of books on the table” picks out some one thing that is not equal to itself. Instead, the dialetheist should hold that the phrases “the number of books on the table” and “the number of true statements on List A” are really descriptions which falsely presuppose uniqueness because they contain the definite article ‘the’. In truth, what’s going on here is that there is more than one number which exhaustively numbers the true statements on List A, and this in no way entails that there is some one number which is unequal to itself. All that follows is that the numbers involved are not equal to each other. Yet it remains true that there both is and is not a one-to-one mapping from the books on Jones’ table to the true statements on List A. From this, I think dialetheists should conclude that the number of F’s can be different from the number of G’s even if there is a one-to-one mapping between them, and can be the same even if there is not. They should hold that Hume’s Principle, in dialetheic contexts, is a biconditional which fails in both directions, and as such cannot be used to provide a criterion of identity for numbers.

Points and Platonism

In this post I want to discuss the ontological status of points and its significance for semantic arguments for Platonism. No, not geometrical points; the points I’m talking about are the ones you gain or lose in playing certain kinds of games (including sports).

Suppose a Platonist argues as follows:

Let’s say that John has ten points in a game. Surely, then, these points must exist: Nothing is true of the non-existent, so if John really has ten points, there must be ten points which John has. Or consider the statement: “John is two points ahead of Fred”. This seems to assert a relation between the number of points John has and the number of points Fred has. If one thing stands in a relation to another they both must exist, so if “John is two points ahead of Fred” is true there must be points which each of them has. “And if one holds that points don’t exist,” the Platonist might add, “who should be the one to tell poor John and Fred that they both lose because they have no points?”

What is one to think of such reasoning? I have chosen this example because it resembles the sort of semantic arguments Platonists often use in other domains, in particular semantic arguments for properties and mathematical objects. In this case, however, the nature of the objects posited is particularly problematic. First, it seems difficult to conceive what these points would be: Besides trivially essential properties—properties such as being identical to itself, which are shared by everything that exists—and those such as being a point belonging to John, what properties would points have? This might not be so bad in itself, for there are more respectable abstract objects--sets, for example--which also seem to have no properties besides the kind mentioned above and those attributed to them by set theory. But one can ask more troubling questions. For example, if John loses a point and Fred gains one, is the point John lost the same point as the one Fred gained, or a different one? If questions of identity and difference make no sense for points, I think that is a good (though arguably not indefeasible) reason for rejecting such entities. But the plight of points is worse yet: Suppose John and Fred are playing a game where, so the rules prescribe, it is possible to have a negative number of points. We can imagine that they are playing a board game where you roll dice and move your piece the indicated number of spaces, and in which landing on a penalty box costs a player five points even when the number of points they have is less than five. The player who has the most points after twenty moves have been made wins. So, for example, if John has -25 points and Fred has -10 after twenty moves, Fred wins the game. Should the Platonist conclude from this example that, since points really exist, it is possible to have a negative number of something? Or should they say instead that, since there can’t be a negative number of anything, this game is somehow illegitimate?

As with other abstract objects, there are also epistemological problems with accepting the existence of points. If points are independently existing entities, how can we be sure we really gain or lose them in the manner the rules of the game prescribe? Could it be that, if the rules of the game say that move m is worth five points, one might only gain three points on executing move m because of some ontological glitch? For Humeans who reject necessary connections between distinct existences, it should appear suspicious that anything could guarantee that something we do causes us to stand in some contingent (or “external”) relation to independently existing abstracta.

If one finds the prospect of answering these bizarre questions distasteful, one will want to find some way of rejecting points while retaining the ability to make sense of our game-related talk and behavior. One might seek a nominalistic paraphrase of statements ostensibly about points, or perhaps try to give a Wittgensteinian account in which our talk of points is treated as moves in a language-game which is practically indispensable to our keeping score. Whatever one says here, I think it is clear that the semantic argument for points faces serious difficulties. If it can’t be made to work here, why should it fare any better with respect to other kinds of abstract objects? I wouldn’t say that other sorts of abstract objects can’t exist—on the contrary, I think some do. But if they do, it seems to me, we need far better arguments for believing in them.

Some reflections on phenomenology

The following consists of some more or less random thoughts I've had on phenomenology. Originally they were meant to be organized into an introduction to a longer work, but at this point I don't think I'll ever get around to completing it, so I thought I may as well dump them here. Enjoy them, such as they are, as an illustration of the weird things you can think of when you have too much free time on your hands. :-P





As I open my eyes, I am treated to a menagerie of colors and shapes. Far from being randomly strewn about, they appear organized into various objects at various distances from each other and from me. These objects, or at any rate most of them, seem to curve or budge outward in a three dimensional space. I see them arranged in depth with respect to each other, according as they are closer to or farther away from me in the direction of my line of sight. This sense of depth is diminished if I close one eye. The objects look somehow flattened, even though I know intellectually that this is not so. Yet I can still tell that they are closer to or farther away from me because in my experience closer objects occult farther ones: If I situate myself (and/or the objects) so that the closer object is “in front of” the farther one, I can no longer see part of it, even though I believe no less strongly that it is still there. (A priori, there is no reason that this should be true of all possible visual experience. If you put one of your hands in front of the other, the sensation[1] you have in the closer hand in no way occults the sensation you have in the farther hand, yet it is not as though the sensation in the closer hand is “transparent”, both seem entirely “solid”, just as the color of an opaque object seems “solid”. If it is possible to sense one solid sensation as being in front of another without the closer occulting the farther, I see no reason why this should be impossible in principle with color in the case of vision.) Something similar is the case with pictures and paintings: The figures depicted are apprehended by me as being in depth, and, after a fashion, as three dimensional, even though I do not perceive the depth or trideminsionality as I do in normal binocular vision. The sense of depth is even less than in monocular (single-eye) vision. The closer an object is, the more the visual background is occulted by it, and in that sense it appears larger the closer it is, even though I do not judge it to increase in size.

An interesting question confronts me: What do these objects seem to be distant from? “My head” would be one commonsensical answer, but my head is not represented in this space—the only time I normally see my head is in a mirror or a picture, or perhaps on a closed-circuit television screen. And whenever I do see it, as in a mirror, it still appears to be distant from my vantage point. My vantage point, or point of view, seems only to be definable as a focal point of my perceptual space. In my unreflective moments, it seems that my point of view is my inmost here—a place behind my eyes from which I’m looking out.[2] The distance and direction of everything I see seems to be defined relative to this point.

Sounds seem to be organized about this same focal point. Sounds are curious beasts: Although they occupy space, they seem neither to be points nor to have any shape. Who can hear the blare of a trumpet and say whether it is flat, spherical, or triangular? Synesthetes perhaps[3], but not the rest of us. In spite of this, sounds do seem to possess distance and direction. Most of us ask where a sound is coming from, not where it is. On the folk conception, sounds have a focal point where they are “made” or “emitted”, and suffuse the space around this point, growing fainter the farther away they are from it. This is a good approximation when interpreted as regarding sound waves in the air, but not as regarding aural experiences, which are in the mind or brain of the observer.[4] Our minds may make mistakes in attributing sounds, as when one attributes the sounds which come from television speakers to the mouths of the actors one apparently sees through the television screen.

It has been argued by some—such as Kant—that one must always think of space as being infinite, and cannot imagine that it comes to an end. How does this belief come about? I imagine it arises from a thought experiment such as this: Imagine any colored shape, such as a square, or if you're feeling more creative, a tree. Regardless of the shape, you always represent it as being against some background, whether black, or white, or blue, but it is always some color. From this, you may come to the conclusion that for any colored area, there must be a colored border. But this conclusion is problematic. Does your visual field[5] stretch on to infinity? The answer, I think, is no. If you hold your index finger about an inch outward from your face, and move it straightly to the right, after a couple feet you'll find that you can't see it any more. The farther something is from the center of the visual field, the more “blurred” or "indistinct" it appears, until you cannot see anything at all. So if your visual field comes to an end, what lies outside it? Your visual field, as presented in experience, is itself a colored area outside of which there is no colored border. Yet it seemed a short while ago to be impossible to imagine that space of any sort could come to an end. So what’s going on here? The answer, I think, goes something like this: Everything that you see lies in your visual field, and thus within its borders. In order for you to see where the visual field ends, its borders would have to be brought within themselves, which is impossible. Because you cannot “see” its boundary as you could the juncture of two colored areas, you conclude it has no boundary at all.

There are many senses grouped together under the grab-bag label “touch”. One of these is proprioception, which is the feeling of how one’s limbs are situated with respect to each other and one’s torso. Another is the sensation one has “in” the various parts of one’s body. This feeling is difficult to describe; it might be characterized as a sensation of existence or ownership, even a feeling of space being “filled”. What it is is brought to light in contrast with its absence, as when some part of one’s body, such as one’s leg, “falls asleep”. I can note that I never experience this sensation in objects which are not part of my body, though if I did I would probably come to regard the object as a part of me. Touch, of course, also includes the sensations of textures of the objects my skin comes into contact with, from the roughness of sandpaper to the smoothness of silk. Neither can I leave out the feelings of pressure and tension on my skin, nor those of heat and cold. Touch seems to be “coupled” to sight: It does not seem to me that I have two right arms, one felt and one visible, but rather one arm both felt and visible. This can result in some interesting experiences: If you bring your hand closer and closer to your face, its image grows, taking up more and more of the background, and yet your hand doesn’t feel as though it’s getting any bigger. The feeling you have in your right hand and its corresponding visual image still seem to fit together, in spite of the fact that one changes while the other remains constant.

Taste and smell may be regarded with justice as two branches of the same sense. Most of the richness of a given food’s flavor is derived from my sense of smell, as the tongue can discern only sweet, sour, salty, bitter, and umami. Taste and smell must be very similar; otherwise we would never confuse them as we do. Something can both smell sweet and taste sweet, but try to imagine a confusion between sight and hearing, or between taste and touch, and I think you’ll come up empty. Nevertheless, taste and smell are still distinguishable. Taste is apprehended as being concentrated on the tongue, whereas smell is presented as suffusing the space in front of one.

The perceptions which I have discussed so far do not exhaust the realm of experience. In addition to ordinary experiences of external objects, there is also the phenomenon of imagination, or mental imagery. One notable feature of mental imagery is something that, following David Hume, I will call “faintness”. The term is being used here in an analogical sense, as is evidenced by the fact that, for example, a normal sound or visual experience can be so faint that I cannot determine what it is I am seeing or hearing. By contrast, if I imagine seeing or hearing something I can determine what it is I am imagining quite well enough, it simply that the imagined sight or sound, though “cognized” in some sense, is neither seen nor heard. By the “faintness” of mental imagery one should understand the fact that though these experiences are determined, they are not apprehended in the same way genuinely perceptual experience is. Perhaps an example can make the nature of this distinction clearer. For my part, if I imagine (form a visual image of) a tree, it looks to be in front of me. That is, I don't see it, from a first person perspective, as being on the side of me or behind my head. Yet in spite of its being in front of me, it doesn't look at all "transparent"; I don't "see through it" to the things in my normal visual field, and neither are they obscured by the image. They both look "solid" in their own way, despite the "faintness" of the image. Neither seems to affect the other. In this sense, then, they seem to be in separate spaces, both of which seem to be "in front" of my point of view.






[1] By the “sensation in” your hand, I mean the feeling that one has simply of its “being there”, of a part of oneself as pervading that space. It is this sort of sensation one loses when a part of one’s body “falls asleep”.
[2] Brand Blanshard, The Nature of Thought, Volume One, p. 149
[3] Synesthetes are people who have something we can call “cross-modal activation”: Certain experiences in one perceptual modality (i.e., sight, touch, hearing, etc.) activate experiences in another. Let us assume for a moment that there is a synesthete who has cross-modal activation between the portions of their brain dealing with shape and sound. One question that I have not heard addressed is whether in such a case the shapes or textures are merely felt at the same time the sounds are, or whether they truly qualify the sounds themselves, the sound being apprehended as being triangular, say, in the same way that a color patch may be apprehended as being triangular.
[5] For clarity, I intend “visual field” to be taken in the sense of one’s subjective visual experience, not that portion of the physical world that visible to one. The question of whether and in what sense there is such a thing as the “visual field”, so conceived, will be addressed later [Or so it would have been, if I had finished the work].

Whither Fractional Objects?

To me,

(1) There is at most one half of an apple in the fruit bowl

sounds fine, but

(2) There is at most one half of an object[1] in the fruit bowl

sounds odd. (I trust that others will think the same, but feel free to correct me if I’m wrong!) Surely, if an apple is an object, half an apple is half an object? But if (1) makes sense and (2) doesn’t, does that mean a half of an apple is not half an object? Perhaps the thought which drives the sense of oddness is that nothing is a half simpliciter, it is always a half of some sort of thing: One mile is half of two miles, and if we dropped the term "mile" and started calling two mile intervals “stretches”, one mile could simply be called “half a stretch”. Yet this “halfness” is nothing ontically basic; one and the same thing is half a stretch, one mile, two half-miles, and five thousand two hundred and eighty feet.

Even so, why couldn’t we have at most half of an object in the fruit bowl if “object” picks out a genuine category? If we can eat half an apple and drive half a mile, what prevents us from throwing half an object across the room? We could certainly throw half a football. The answer to these queries might be that a given entity which is a fraction of one thing is always a whole (and thus one) of something else. E.g., one slice of a pizza is also one eighth of the whole pie. We can also note that if there is at most half of an object in the fruit bowl, it cannot be the case that there is at least one, and if the bowl is not empty that is impossible. Thus we cannot say there is at most half an object in the fruit bowl; wherever we have a fraction of one sort of object there is always at least one of different sort. All this goes to show that "object" picks out a very special category if it picks out any at all.

The above reflections seem to commit us to a Fregean view in which nothing is intrinsically one or many. This view is not without its problems: Does it make good metaphysical sense to hold that how many things there are depends on what category we apply to them? Aren’t we contradicting ourselves if we say that one thing can be identical to many? After all, one deck of cards cannot be identical to two decks, why should it be any more possible for it to be identical to fifty two cards? Yet if we do not embrace the Fregean view, how else might we explain (or explain away) the strangeness of (2)? These are difficult issues, but hopefully with your input we can get a clearer view of the matter.


[1] “Object” being construed broadly as covering anything that exists.