A theory of spacetime

I am not saying this theory is correct—it's too platonic for my taste. But it's suggestive. There are special properties called "locators". Moreover, as it happens, the collection of all locators forms a topological space (one can think of the open sets as corresponding to certain distinguished properties of locators). This space we can call the Receptacle. The Receptacle partitions into topologically connected subspaces. Each of these we can call a spacetime. Thus, a spacetime is a maximal connected set of locators. Some spacetimes have an additional structure, say a metric or manifold one.

The points of a spacetime are simply the locators that make it up. They are, thus, Platonic entities. An entity x occupies a point P if and only if x has the property P. Occupation, then, is simply exemplification. A spacetime is said to be actualized if and only if some point in it is occupied.

Question: Wherein do locators differ from other properties, like mass-properties (having mass x grams), that also have a topological (and even metric) structure?

A theory of personal identity with no counterexamples

This is likely equivalent to Merricks' proposal—I still need to think about whether it is—but I like it. Question: When is it the case that the same person is located at spatiotemporal location y and at spatiotemporal location z? Answer: When and only when there exists an x such that (a) x is a person, (b) x is located at y, and (c) x is located at z. Note that the answer does not use the concept of identity, and all the concepts it uses are ones that substantive theories of personal identity also presuppose.

Vagueness

A guiding intuition in much of my thinking in metaphysics is that no vague fact is to be taken metaphysically seriously. I don't have an account of the seriousness, though. Still, the intuition has some nice consequences. Psychological theories of personal identity make diachronic identity vague—but diachronic identity should be taken seriously, so the theories are false. Materialism makes it vague where there is intentionality (because it makes all interesting macroscopic properties vague), hence materialism is false.

The problem of animal pain

Supposedly intense pains that non-human animals undergo provide significant evidence against theism. Why? Well, the thought is that, if he existed, God could have done things better. But how?

Suggestion 1: He could have made something that has the same motivational effects that pain has but that doesn't hurt.

Response: It's not clear that this is possible—it may be that the qualia of pain reduce to motivational effects and cognitive content. But let's grant it's possible. Now we can ask: Do we have good reason to think God hadn't done this? After all, if the pain-replacement, call it shpain, had the same motivational effects, we would observe the same kinds of aversive responses to shpain as to pain. Maybe we wouldn't expect certain kinds of whimpering. But a dog's whimpering is not quite like human whimpering. I think the reason we see the two as species of the same behavior is because both are associated with similar triggers and similar motivational states. But if the objection to theism that we are evaluating is that God instead of creating pain in animals should have created shpain, then we need evidence that animals experience pain instead of shpain, and if I am right about why we see whimpering as a pain behavior, the whimpering does not provide such evidence.

Maybe we can get some evidence for animals having pain rather than shpain by looking at neurological similarities between humans and animals. This may, however, presuppose the supervenience of the mental on the physical, which is controversial. Furthermore, we do not know enough about how pain systems in the brain work. We know that in addition to similarities between human and non-human brains there are differences. Given that shpain and pain have similar triggers and similar motivational results, on the hypothesis that animals have pain rather than shpain, we would expect a lot of neurological similarity and some difference between animal brains and our brains—and that's exactly what we observe.

Suggestion 2: God could have miraculously prevented pain in those cases in which the motivational role of pain is not important to the animal's flourishing, say when the animal is certain to die.

Response: Let's consider the hypothesis that he has, in fact, done so, and see how strong the disconfirming evidence is. It is plausible that God's miracles would be calculated to produce a particular effect and would be in some way minimal as deviations from the ordinary operations of nature. The reason for that is that there is a great value in the ordinary operations of nature. If so, then what we would expect as a miraculous intervention would be a minimal deviation—one sufficient to relieve the pain. Now, the pain has certain neural correlates. A minimal miraculous intervention might well keep most (if materialism is true) or all (if dualism is true) of these correlates intact. And in particular it might very well be that pain behaviors continue because of the remaining correlates. Now, granted, the fact that we still observe the pain behavior is some evidence against the hypothesis that God has eliminated pain in these cases by being evidence against the hypothesis that God has eliminated pain in a way that eliminates pain behaviors. But unless it was very plausible that the latter is how God would eliminate pain, the evidence against the hypothesis that God has eliminated pain behaviors is not that strong.

Suggestion 3: God could have made a world where animals don't need pain or anything like it, because conscious non-human animals are never endangered by anything.

Response: To evaluate this would require the evaluation of a different argument from the argument from animal pain—the argument from the red-in-tooth-and-claw nature of our world, bracketing the question of pain. I think it is plausible that animal death is not an evil in itself—animals do not naturally have immortality. But death is an ultimate kind of danger, and if so, then the plausibility of the suggestion is decreased. Maybe we could imagine a world where nobody dies before reproducing, but that would be a world where it would be hard for evolution to work, and evolution is valuable.

Conclusions: The problem of animal pain only becomes a problem when one adds some reason to think that God could have done better here. There are three suggestions to that effect. On the first two, the theist can make the reasonable response that we do not have very strong reason to think God hadn't done that allegedly better thing. On the last one, we have a broader problem than that of animal pain.

Verificationism and idealism

I just realized (thinking about Quine's description of verificationist reductionism in "Two Dogmas") that there does not seem to be any difference between verificationism and idealism.

Real numbers

For a long time I've been puzzled—and I still am—by this. Our physics is based on the real numbers (complex numbers, vectors, Banach spaces—all that is built out of real numbers). After all, there are non-standard numbers that can do everything real numbers can. So what reason do we have to think that "the" real numbers are what the world's physics is in fact based on?

I think one can use this to make a nice little argument against the possibility of us coming up with a complete physics—we have no way of telling which of the number fields is the one our world is based on.

Color perception

Here's another data point towards a theory of perception. My son, 4, is colorblind (or color perception deficient or whatever the right term these days is). He was looking at the dark red flowers on his mom's blouse, and said they were black. He was told they were red, and he accepted that—he is very accepting of the fact that colors aren't what they seem to him as. I then asked him if they looked red to him after he was told they were red. He was very definite about an affirmative answer to this question.

Neonates' cries influenced by native language

This is rather neat.

Curry sentences

Curry sentences are of the form:

1. If (1) is true, then p,

where I shall stipulate the "If ... then ..." to be a material conditional, and where p abbreviates something not paradoxical. If p is false (in an unparadoxical way—maybe, p is "snow is red"), (1) is paradoxical because it provides an argument for p. Now, it is clear that whatever we say about (1) we should also say about:

2. If not-p, then (2) is not true.

Now, go back to my old favorite, the contingent liar paradox. There are many versions. One of them is this. Let D be some definite description of a sentence which picks out different sentences in different worlds. Then consider:

3. The sentence satisfying D is not true.

Paradox ensues in worlds where D picks out (3). Now, consider:

4. The contingent liar (3) is unparadoxical if D picks out a first-order sentence that is unproblematically true or unproblematically false, in which case (3) has the opposite truth value to that of that sentence.

Then, consider this:

5. The following sentence is not true: "1=1" if p and (5) if not-p.

By (4), sentence (5) is unparadoxically true if p. We ought to, however, say about (5) exactly whatever we say about:

6. "1=1" is true if p, and (6) is not true if not-p.

Thus, we ought to say that (6) is unparadoxically true if p. But we observe that the first conjunct in (6) is trivially true, at least if p is not itself paradoxical. So, surely, we ought to say about (6) exactly what we say about:

7. Sentence (7) is not true if not-p.

Thus, (7) is unparadoxically true if p.

But we ought to say the same thing about (2) as we say about (7), and about (1) as about (2). So, the Curry sentence (1) is unparadoxically true if p. And if p is false, it is a liar sentence, and a contingent liar sentence if p is contingently false. All this means that the Curry paradox is not very different from the contingent liar.

Sex solely for pleasure

Is there an intrinsic morally significant difference between having sex solely for one's pleasure and having sex solely for money? To sharpen the question, let's ask: Is there a morally significant difference between having sex solely for one's pleasure and having sex for money which one intends to use solely as a means to one's pleasure?

Both are cases where the sex is engaged in solely for hedonistic ends, but in the one case the pleasure is achieved more indirectly. Still, in both cases there is some indirectness. Sex, in and of itself, need not be pleasurable. In both cases, it seems to be engaged in as a mere means to pleasure. The difference, however, is that in the one case, the pleasure is the pleasure of this very sexual act, while in the other case, the pleasure is a different pleasure (e.g., the pleasure of driving a nice car, or the pleasure of sex with someone else whom one wishes to seduce in an expensive way). So, in the case of sex solely for one's pleasure, the pleasure is more closely tied to the sex, and it may even be a mistake to talk of the pleasure as a distinct end. If so, then there is a significant—and perhaps morally so—difference between the two cases: in the money case, sex is engaged in purely instrumentally, while in the pleasure-of-sex case, the end is too close to the sex to call the sex purely instrumental.

This distinction, however, imports into the original question something that wasn't there. Granted, there is a difference between sex solely for the pleasure of the sex, and sex for the sake of money which one wants for the sake of some other pleasure. But in the case I originally specified, I did not suppose a case of sex for the sake of the pleasure of the sex; I supposed a case of sex for the sake of pleasure simpliciter. And when one's end is pleasure simpliciter, then one's action plan involves a fungibility of means: one looks around for the ways to get a lot of pleasure, considering whether it is more convenient to get pleasure by proving a new theorem, or having sex, or eating cake, or volunteering at a shelter—or by having sex for money and then using the money to buy a pleasure. Insofar as one is having sex solely for the sake of pleasure, one is prima facie indifferent between these options except insofar as they produce different levels of pleasure with different degrees of convenience.

And if so, then it does not seem that there is a significant moral difference between sex solely for money solely for pleasure and sex directly solely for pleasure. In particular, it follows that if we think that non-marital sex for money is always wrong, we will conclude that non-marital sex solely for pleasure is always wrong; and if we think that marital sex for money is always wrong, we will likewise conclude that marital sex solely for pleasure is always wrong. (To be honest, I think some cases of marital sex for money—say, when one is starving and one's spouse refuses to provide food except on condition of sex—are more defensible than marital sex solely for pleasure.)

However, there is a difference between sex for the pleasure of the sex and sex for money. Sex for the pleasure of the sex is not solely hedonistic. The hedonist as such does not care what she is taking pleasure in, convenience, consequences and intensity being kept constant. Insofar as one cares about what one is taking pleasure in, one is not a pure hedonist. In a case of sex for the pleasure of the sex, the sex is not present purely instrumentally. Here, we also should distinguish sex for the pleasure of sex from sex for the pleasure of the sex. The pleasure of sex can be achieved apart from sex, say by direct neural input. The pleasure of the sex can only be achieved through the sex. It may be that there is little moral difference between sex for the sake of the pleasure of sex and sex for the sake of money. After all, one could have sex for the sake of money in order to get the pleasure of sex—perhaps one is saving up for a neural sexual pleasure implant. But there is a moral difference between sex for the sake of the pleasure of the sex and sex for the sake of money. Say that a sophisticated hedonist is someone for whom not only the intensity, convenience and consequences of a pleasure matters, but the kind of pleasure also matters. Maybe the sophisticated hedonist wants to have a variety of kinds of pleasure, or maybe she has arbitrarily chosen some pleasures over others. In any case, the person who has sex for the sake of the pleasure of the sex is neither a pure hedonist nor a sophisticated hedonist, for she not only cares for the kind of pleasure, but also that which it is had in.

One is unlikely—perhaps it is even an impossibility—to value the pleasure of the sex without non-instrumentally valuing the sex. There may well be people who have sex solely for pleasure. For instance, if Sally wants to have some pleasure and goes through all the options and chooses the one with the best balance of intensity and convenience, and that happens to be sex, she may be having sex solely for pleasure. But such cases are, I think, rare. The pure case of someone who wants to have sex for the sake of the pleasure of sex is less rare. Such a case would require the person to be indifferent as to the gender, age, appearance and species of the sexual partner, except insofar as this impacts convenience, consequences and the pleasure received. Maybe some people do have such an indifference—the only reason, for instance, why they prefer their partners to be of their own species is that they find bestiality to lack something of pleasure.

There is a further kind of distinction we should draw at this point, a distinction between having sex for the sake of the pleasure of the sex—of this particular sexual act with this person at this time—and having sex for the sake of the pleasure of this sort of sex. Thus, the person who cares about the appearance of their sexual partner (typically) seeks the pleasure of sex with a good-looking person. The number of people who have sex for the sake of pleasure is probably small, the number of people who have sex for the sake of the pleasure of sex is probably also small, but the number of people who have sex for the sake of the pleasure of sex of a certain sort (where the sort is either specified by specifying the kind of sexual act or the kind of partner or both) is probably larger. And this, too, I think is not very different morally from sex for money. After all, one might well be having sex for money for the sake of the pleasure of sex of the preferred sort. And I think this is morally objectionable, and apt to make an object of the partner.

On the other hand, sex for the sake of the pleasure of the sex requires or at least tends to require valuing the sex with this person at this time non-instrumentally (actions are individuated by agent, time, patient, etc.) And that's different.

The Christian tradition has unanimously condemned sex for the sake of one's own pleasure. But it is not clear that this condemnation of hedonistic sex applies in the case of sex for the sake of the pleasure of the sex—for in that case, the intended end, "the pleasure of the sex", is partly constituted by the sex itself, and hence the sex is engaged in for the sake of the pleasant good of the sex, rather than for the sake of pleasure alone. And if the sex is intrinsically unitive, this may well be sex for the sake of pleasant union, which is a species of sex for the sake of union, which in turn is taken to be permissible by the tradition. Of course, this is very speculative, and the tradition is authoritative while my interpretation of it is not.

The paradox of Shakespeare's last words

Let p be the proposition that the last thing asserted by Shakespeare in his life is not true. This is a perfectly good proposition, and it is one that we can easily assert. Moreover, it is a proposition that Shakespeare could easily have asserted many times—but only if these times weren't the last moment of his life. Suppose in our world, w₀, Shakespeare asserted p at time t₁. (For all we know, he did!) Surely there is a world, w₁, which is just like our world, but where Shakespeare is killed instantly after t₁. In w₁, then, Shakespeare did not assert p, since p is something that it is logically impossible for Shakespeare to assert as the last assertion of his life. But of course, in w₁, Shakespeare uses the exact same words at t₁ as he does in w₀, and seemingly with the same intention.

So, what are we to make of this? On pain of contradiction, we must hold that in w₁, Shakespeare fails to assert p in his last moment. If we think that words plus intention suffice to determine a proposition asserted (and even if we don't, we can perhaps stipulate a sense of "asserted" in which that is true, and make sure that that's the sense in p), it follows that what intentions one has can depend on what will happen later or that one's "words" include contextual features such as whether one dies shortly thereafter or when one utters them. In other words, we get a temporal externalism about intentions, or else a very weird notion of "words".

And we get an argument from this liar paradox against open futurism. For in w₀ at t₁, it is open whether Shakespeare will die right after t₁ or not. But if he dies right after t₁, he is not intending p. But it is true at t₁ that he is intending p. Hence, it is true at t₁ that he does not die after t₁, which contradicts open futurism. Or, to put it differently, according to the open futurist, there is no fact at t₁ as to what Shakespeare intends at t₁.

Let's make the open futurist even more uncomfortable. Suppose at t₁, you say:

1. One day, I will open my mouth and utter a noise that does not express a true proposition.

This is a perfectly ordinary locution, and one that all of us can reasonably make in light of our fallibility, unless we're expecting to die shortly. Surely you've said something, indeed something most likely true. But this is not the case if open futurism is true. For it is open for you next to say:

2. I just uttered a noise that did not express a true proposition

and then die. Our options are: (a) take (1) to be true and (2) to be either false or nonsense; (b) take (2) to be true and (1) to be either false or nonsense; and (c) take both (1) and (2) to be nonsense—i.e., to fail to express a proposition. There seems to be no reason to prefer (a) to (b) or (b) to (a). So we should go for (c). But if we take (c) as the right solution, and open futurism is true, then we have to say that whenever (1) is uttered, there is not yet a fact about whether it expresses a proposition. This is really weird. Not that it's not weird without open futurism. But it's less weird.

Fun with substitutional quantification

Stipulate that "x strongly believes p" iff x believes p and it is not the case that x believes not-p. Consider the argument:

1. For anything that Freddie believes, there is a possible world where Sally strongly believes it.
2. Freddie believes the negation of Sally's deepest held belief.
3. Therefore, there is a possible world where Sally strongly believes the negation of Sally's deepest held belief.

Isn't it fun to derive an impossibility from two propositions whose conjunction is possible?

We learn from this that if we are to read (1) substitutionally, we need a substitutional quantification in which we are only allowed to substitute names. In that case, (3) does not follow from (1) and (2), because if "Xyzzy" is the name of the negation of Sally's deepest held belief, then instead of (3) all we get to conclude is:

4. There is a possible world where Sally strongly believes Xyzzy.

But there is no contradiction here, because in the relevant possible world, Xyzzy isn't the negation of Sally's deepest held belief. But still, wasn't (1)-(3) fun?

Is quantification substitutional?

Consider:

1. Possibly, something exists which could not be referred to with a linguistic expression.

If quantification is at base substitutional, then (1) is false. But the negation of (1) is:

2. Necessarily, everything can be referred to with a linguistic expression.

Call this "referential universalism". Now, there presumably are worlds where there is no language. Could there be entities that could exist only in such worlds? If so, then, most likely (2) would be false (some such individuals could be referred to in a cross-worldly way by appropriate definite descriptions, but there is little reason to think they all could be). So, referential universalism is not particularly plausible.

The substitutionist could affirm that referential universalism is a trivial truth. In English, some names, like "Alex", ambiguously refer to multiple entities, and are disambiguated contextually. Presumably, there is an extension English* of English which has the name "Ting" that is much more ambiguous—it can refer to anything at all. Thus, "George loves Sally" is appropriately translated by "Ting loves Sally" as well as by "George loves Ting", in different contexts. But then (2) is a trivial truth—"Ting" can refer to anything at all.

It is a fine question how to allow for ambiguous reference and remain a substitutionist. One way is not open: take substituents to be pairs consisting of an ambiguous referring term and a referent. For if one did that, one is doing objectual quantification over referents. So, probably, what one needs to do is to substitutionally quantify over pairs <e,c> where e is an ambiguously referring expressing and c is a description of a context (it can't just be a context as then we'd be objectually quantifying over contexts). But then our substitutionist becomes committed to the highly non-trivial truth:

3. Necessarily, everything is such that in some context there is a linguistic expression that unambiguously refers to it.

Now, maybe it will be said that I haven't offered an argument against (2) or (3). True. But I now make this move. Look: (2) and (3) are trivially true when read substitutionally. Our understanding of (2) and (3) as non-trivial truths shows that we do not, in fact, read their quantifiers substitutionally, and hence substitutionism is false.

None of this affects the claim that there is a perfectly good substitutional quantifier--only the claim that all quantification is to be understood in terms of it.

Experiences and presentism

That x is having a certain kind of conscious experience at t is not just a claim about what is happening right at t. If mental processes are in some way correlated with physical processes, then this follows from the fact that it does not really make sense to talk of the instantaneous state of the physical process (think, for instance, of wave phenomena or classical momenta—these are defined in terms of what happens at other times). But even without this correlation, this is plausible. Thought experiment: imagine seeing a red circle for a tenth of a second with no after image and no memory (the memory is wiped instantly). You see an obvious flash. Shorten the amount of time you're seeing the red circle. Eventually, you don't see it at all.

But if presentism is true, isn't this really weird? It would be really weird if my present conscious state were partly constituted by past-tensed states of affairs. The eternalist (or even growing block theorist) can talk of a temporally extended conscious state. That's not a problem. But the presentist can only talk of the present conscious state together with some (dodgy) past-tensed states, like having seen a red circle a quarter of a second ago. Of course, folks who think that beings coming out of swamps at random couldn't be conscious even if they had souls will not be bothered by this.

Why can't the past change?

If you're a B-theorist, it is no puzzle that the past can't change. It can't change because we are always in the same world, and so neither the past, nor the present nor the future can change. Today, let us suppose (I think correctly) that it is the case that on Wednesday it was raining. Could it tomorrow be the case that it wasn't raining on Wednesday? Not at all—for the very same world, the very same events, that make propositions true today is the one that we evaluate against tomorrow. The fact that the past can't change, thus, is a matter of mere logic—it just follows from the truth conditions for sentences.

But what if you're an A-theorist? So, you think that things will be objectively different tomorrow. Indeed, you already do think that some things about Wednesday will objectively change. For instance, while today (Saturday) Wednesday is objectively three days in the past, tomorrow it will objectively recede one more day into the past. So in fact we already have a change, but a change that the A-theorist doesn't mind. (Though she should.)

In any case, logic alone doesn't do the job. One way to see this is that some A-theorists actually think the future changes. Thus, today, it is false that either I am at Mass on November 8 or that I am absent from Mass on November 8. But come November 8, this disjunction will be true. But the clever tricks that open futurists use to make sense of an open future could be used, equally well, to make sense of an open past. (The parallel holds for B-theory. The B-theorist is committed to the claim that the future cannot change. This sounds fatalistic, but we must distinguish the ability to change the future from the ability to affect the future.)

In the setting of my earlier post on A-theory, the claim that the past cannot change corresponds fairly closely (and in fact exactly, if we assume a closed past) to the claim that the earlier-than relation is transitive. If today, a world where it rains on Wednesday is is past, tomorrow that world will also be past. So in the setting of that post, the explanatory challenge to the A-theorist is why the earlier-than relation E is transitive. The A-theorist who takes E to be fundamental can only say that it is a brute fact that it is necessarily transitive.

There may be A-theorists who can meet the challenge, however. Suppose that you think that there is a TimeShift operator which shifts tensed propositions time-wise. Thus, if p is the proposition that it is sunny, TimeShift(+1 day, p) is the proposition that in a day it'll be sunny. Suppose, further, we take worlds to be maximal consistent collections of propositions, or maximally specific consistent propositions. Then the TimeShift operator can also operate on worlds, and we can define E(w₁,w₂) to hold iff there is a t<0 such that w₁=TimeShift(t,w₂). Then it really is a matter of simple logic that E is transitive, and we have a perfectly good explanation of why the past cannot change.

Note, however, that an open-futurist cannot take this explanation. For her, the fixeity of the past remains a surd.

If this is right, then Tom Crisp is mistaken in taking the earlier-than relation between abstract times (which are just worlds in my terminology) to be primitive. An A-theorist should not say it's primitive—it needs explaining. Or at least I remember him taking it to be primitive, but my memory isn't so good.