Relativity, simultaneity, minds and brains

This is very much a thinking-in-progress post rather than a finished argument. But I've been toying with this line of thought:

1. The simultaneity relations between conscious mental states of an ordinary human (e.g., "itching while feeling cold") are not relative to reference frame.
2. The simultaneity relations of spatially extended states of an object are relative to a reference frame.
3. If conscious mental states are identical with or wholly constituted by brain states, then they are spatially extended states.
4. So, conscious mental states of an ordinary human are neither identical with nor wholly constituted by brain states.

The restriction to ordinary people rules out cases where someone has two or more centers of consciousness at a given time (e.g., due to brain-splitting, time travel, or multiple personalities). In the case of such a non-ordinary person, we can run the argument for each center of consciousness and conclude that the center's states are not identical with or constituted by brain states.

What makes this argument tricky—and this is the part I need think more about—is that of course the relativistic effects between different bits of the brain are practically negligible. The kind of time difference that would be involved in trying to see whether I started itching before starting to feel cold or whether it was the other way around would be so minuscule that I couldn't tell the difference as to which state started earlier or whether they started simultaneously. Nonetheless, there is some plausibility in thinking that there is a fact of the matter as to which state started earlier or whether they started simultaneously. Moreover, maybe we could imagine beings with bigger and faster brains where the effects would be real--and (1) plausibly isn't just a fact about us, but about any discursive agents with a single center of consciousness.

Here's an interesting thing. Suppose that one responds to the argument by saying that there is an absolute reference frame, despite relativity theory, much as defenders of the A-theory of time hold. That response doesn't get one completely out of the argument. We can argue: the absolute frame is insignificant for physics; yet it is significant for mind; so mind doesn't reduce to physics.

I also think the argument (though perhaps not the absolute-frame variant) may lead to some problems for supervenience theories of mind. But that's for future research.

Living on in people's memories

There is a philosophical (in the popular sense of the word--professional philosophers don't tend to defend this) outlook on death that says that we live on in people's memories of us. I was discussing this view with students in my Death and Afterlife class, and one of them connected this to the memory theory of personal identity. My first reaction was that this was completely confused. But after reflection, I thought that there was a deep point about the memory theory of personal identity there.

Start by observing how unsatisfying this kind of "afterlife" in people's memories is--it's not really "living on". Now, the student's potential confusion was that on canonical versions of the memory theory of personal identity, we live on through a chain of first-person memories, while the memories through which we are said to live on are third-person ones. But does that point matter? Suppose one or more of the people through whose memories I was said to live on actually managed to acquire first-person (apparent) episodic memory of my life, say by thinking about me so much. That's a bit creepy, but it's no more satisfying as an afterlife than when the memories were third-person.

Of course the proponent of the memory theory can say I am unfair. The memory theory requires that there be only a single person with those memories, and it has restrictions on what sort of causal chain is allowed to pass the memories on. But these matters of detail do not, I think, affect whether I am living on in any robust sense through a person who has memories of my life.

Towards a counterexample to Weak Transitivity for subjunctives

Transitivity for a conditional → says that if A→B and B→C, then A→C. For subjunctive conditionals this rule is generally taken to be invalid. If I ate squash (B), I would be miserable eating squash (C). If I liked squash (A), I'd eat squash (B). But it doesn't follow that if I liked squash, I'd be miserable eating squash.

Weak Transitivity says that if A→B, B→A and A→C, then A→C. The squash counterexample fails, for it's false that if I were eating squash (B), I'd like squash (A).

I don't know whether Weak Transitivity is valid. But here's something that at least might be a counterexample. Suppose a heavy painting hangs on two strong nails. But if one nail were to fail, eventually--maybe several days later--the other would fail. The following seem to be all not unreasonable:

1. If the right nail failed (B), the left nail would fail because of the right's failure (C).
2. If the left nail failed (A), the right nail would fail because of the left's failure (D).

So, by Weakening (if P→Q and Q entails R, then P→R):

3. If the left nail failed (A), the right would fail (B).
4. If the right nail failed (B), the left would fail (A).

If Weak Transitivity holds, then:

5. If the left nail failed (A), the left nail would fail because of the right's failure (C).

But surely (2) and (5) aren't true together.

As I said, I am not sure if Weak Transitivity is valid. If it is, then there is something wrong with (1)-(4), probably with (1) and (2). Maybe there is. But the example should at least give one reason not to be very confident about Weak Transitivity. (There is another reason: Weak Transitivity is incompatible with the non-triviality of the Adams Thesis for subjunctives.)

That nasty oxygen

We think of gasoline, lighter fluid and hydrogen as dangerous flammable substances (in the ordinary, not philosophical, sense). But in the ordinary course of things, when they burn, they do so because of oxygen. So it seems more reasonable to think of oxygen as the dangerous inflamer here. This is of course a very standard example in philosophy of causation: we don't normally think of oxygen as the cause of a fire, but we could just as well, except for pragmatic stuff. I just didn't realize until recently how great the example is. Having oxygen about is having a fire about to happen. Thinking about this also makes it clear just how precarious our existence is, dependent on such a highly dangerous chemical as it is.

Coin placing algorithms

Consider algorithms for sequentially placing a coin each day either in a heads or a tails configuration depending on how coins were placed on past days. For instance, the rule might say that if you placed heads yesterday, today you place tails, and if yesterday you placed tails, this time you place heads. The algorithm might depend on the date, too: maybe on Wednesdays you place heads if and only if you placed tails last Wednesday, but on all other days of the week you place heads.

Here's an interesting question about a coin-placing algorithm: Is it mathematically coherent to suppose that the algorithm had been running from eternity? For some algorithms, the answer is positive. Both of the algorithms I described above have that property. But not all algorithms are like that. For instance, here's an algorithm based on a comment by Ian: if infinitely many heads have been placed, place tails; otherwise, place heads. This algorithm could not have been running from eternity. [Proof: For suppose it was. Then either it would have placed infinitely many heads or not. Suppose it placed infinitely many heads up to today. Suppose that on some day n the last of the heads was placed. Then prior to day n there would have been infinitely many heads (since from that day to today only one heads was placed, namely on day n, as day n was the latest heads day), and so on day n tails was placed, which is a contradiction. So the algorithm would have placed only finitely many heads. But then prior to each day there would have been only finitely many tails, and so each day a heads should have been placed, whereas only finitely many were placed, so again we have a contradiction.]

Now here's a fun fact:

Theorem: If the algorithm only needs to check a finite number of past placements to determine a given day's placement, then there is a sequence of coin placements that goes back infinitely many days that fits with the algorithm.

In Ian's algorithm, the placement on each day of course depends on infinitely many past placements. [I find it moderately surprising that the proof doesn't use the Axiom of Choice. Basically, you generate first a sequence of finite sequences of heads or tails with the property that the sequence could be generated by applying the algorithm a finite number of times to some pre-given backwards-infinite sequence, and that the sequence is the alphabetically the smallest sequence (heads=H and tails=T) if we write right-to-left that has this property. Then we're guaranteed convergence in at any particular distance from the end of this sequence as the length goes to infinity. The result generalizes to any finite alphabet, not just heads/tails.]

So what? Maybe nothing much. Still, it's an interesting difference between the finite and the infinite: it's always mathematically coherent to suppose algorithms with finite memory for history that ran for eternity but not always mathematically coherent to have algorithms ones that look infinitely far back that have done so. (Causal finitism, however, rules out both kinds. I wonder if that's a count against causal finitism? If so, not much of one, since metaphysical possibility implies mathematical coherence but not conversely.)

Unreleasable promises and the value of punishment

Alice and Bob are conscientious vegetarians. Alice gets Bob to promise her that if Alice ever considers ceasing to be vegetarian, Bob should offer her the most powerful arguments in favor of vegetarianism even if Alice doesn't want to hear them. Years pass, and Alice's vegetarian fervor fades, and she mentions to Bob that she is considering giving up vegetarianism. Alice then says: "Please don't try to convince me otherwise."

What should Bea do? As a rule, the promisee can release the promiser from a promise. So it seems that Alice's request that Bob not importune her with the arguments for vegetarianism overrides the promise. But Bob promised to offer the arguments even if Alice didn't want to hear them. It seems that this was a promise where the usual release rule makes no sense. Can a promise like that be valid?

As the case demonstrates, there are times when it would be useful to be able to make promises that one cannot be released from by the promisee. But one cannot infer the existence of an ability from its usefulness: it could be useful for a pig to be able to fly. Still, it seems pretty plausible that Bob's promise is valid.

But now compare another case. During a fight, Carlos spitefully promises Alice that he's not going to get Alice's birthday party even if she wants him to come. Carlos does not, I think, have any moral duty to keep his promise if Alice reaches out to mend fences, releases him from his promise and invites him to his party.

In fact, my sense is that the release from the promise is irrelevant in the case of Carlos. For suppose that Dan, also fighting with Alice, promises Alice not to get her a birthday present. Dan does not, I think, violate any moral duty by giving Alice a birthday present, even absent a release, as long as it's clear that Alice would enjoy the present.

So how does the Bob case differ from the Carlos and Dan cases? I think it's that what Carlos and Dan promise Alice isn't good, or if it has any value it's a value dependent on how Alice feels about it at the time. But what Bob promises Alice has a value independent of how Alice feels at the time.

But here is another kind of unreleasable promise: an authority might unconditionally promise Alice a fair punishment should Alice do a particular wrong. And it is clear that Alice's releasing of the authority is irrelevant. If what I said about Bob's, Carlos' and Dan's promises is a guide, then unreleasable promises must be valuable for the promisee independently of the promisee's views and desires. Hence, just punishment is good for the punishee.

Accretion of particles

There is good Aristotelian reason to think that when a particle accretes to a substance--say, when I eat it--the particle ceases to exist. For prior to being accreted, it seems the particle is an independent substance. But a substance can't have substances as parts. And it seems absurd to think that the particle would change from being a substance to a non-substance.

But the view that post-accretion the object that is now a part of the substance is distinct from the object that was accreted is counterintuitive. Here I want to run a partners in crime response to this by showing how a very different and yet fairly mainstream set of assumptions leads to the same counterintuitive conclusion. This should help make that conclusion a little less counterintuitive.

To that end, assume reality is four-dimensional, that objects have lots of temporal parts and that parthood is transitive. This is a fairly commonly accepted set of assumptions. Now suppose I ate a particle x. I will argue that the particle perished in the process. For suppose that x is still a part of me. Let u be a temporal part of x prior to the accretion. Then x is a part of me. But u is a part of x. So by transitivity of parthood, u is a part of me. But that's absurd. So we must deny that x is a part of me on this set of assumptions, too. Hence, this set of assumptions leads to the same conclusion that it is impossible for an object to exist as not a part of something and then continue to exist as a part of that object.

Experiencing present events and simultaneous causation

When I look at a rock, I see the rock and not just its outside surface. Of course, it is the outside layer that is causally responsible for my perception: a typical rock would look the same (except when intense light was shining through it) if suddenly all but the outer one millimeter of it disappeared. Similarly, when I see an event like a ball flying through the air, I see an event that includes the ball's presently flying through the air, even though it is only the temporal parts of the event fractions of a second prior to my perception that are causally responsible for my perception, since it takes light a few of nanoseconds to get to me from the ball and then it takes my visual apparatus rather longer to process it, and I need to process data from two different times in order to get the perception of motion. In both cases the data is processed without my being aware of it, and a rock or an event that includes the present is presented to me. If all goes well, this is veridical, though it could happen that there is no rock but a mere shell or that the ball was annihilated just before I had the perception.

So, in these experiences, when things go well, I have an experience of something extended through space and/or time caused by a very small proper part of the object of the experience. But veridical experiences must be caused by their objects (and in the right way). This means that a whole can count as causing something that is only caused by a proper part. (There are, of course, plenty of non-perceptual examples.) Moreover, notice that the case of the ball flying through the air, then, is a case of something like simultaneous causation when all goes well: a temporally extended event of the ball flying--including its flying now--causes my present perception, and the two events temporally overlap.

But this instance of simultaneous causation seems grounded in a case of non-simultaneous causation: a past temporal part of the ball's flight causing a present experience. That may be so. However, for all we know this non-simultaneous causation could be grounded in a finite sequence of fundamental simultaneous causations between temporally-extended temporally-simple events.

Is love a virtue?

An obvious way to harmonize Christianity with Aristotelian ethics is to say that love is the chief virtue. For a number of years I thought something like this, but now I am not so sure. Here's why.

First, courage and justice are simply courage and justice. But love is always love for someone. There is a habit of courage or justice that goes over and beyond the particular contexts or individuals: a courageous person would act bravely in counterfactual circumstances and a just person would justly towards counterfactual people. But love is love for these particular individuals, Tom, Dick and Harry, say.

Second, virtues are not even partly constituted by particular judgments or emotions, but rather dispose one towards judgments or emotions. But if I love you, then my appreciation of you is partly constitutive of the love. In the case of just action, we have something like this picture. Katherine has (1) the habit of justice. She comes across a case where justice is called for. She (2) makes some judgments about the case which lead to (3) certain cognitive and emotional attitudes about the case and a drive towards an action type in the case. This in turn results in (4) action. There are thus four ingredients:

1. the habit
2. the judgment
3. the particular complex of mental states, and
4. the action.

Of these four ingredients, love for another is most like (3). It already includes particular cognitive and emotional attitudes, say ones of appreciation, and a drive towards things like union and beneficence in the case of this individual.

These disanalogies between love and paradigmatic virtues also suggest a certain kind of problem for Christian ethics. According to the New Testament, love of God and neighbor suffices for moral perfection. But suppose that I were only one of five people in the world, and the other four were all friends of mine. It seems that I could love God and neighbor but have a disposition to hate (and not love) everyone else, should anyone else ever come into existence. That is far from moral perfection, just as it is far from courage if I never irrationally flee from danger because I am only ever in four dangers and none of which I happen to shrink from.

What to do about this problem? One option is to posit a virtue of lovingness that disposes one to come to love persons. A virtue gives rise to a cognitive, emotional and volitive context when one comes across a particular kind of entity or event. The virtue of lovingness gives rise to love for x whenever one comes across an entity x that is a person. We can now restore the parallel with other virtues. Francis has (1) the habit of lovingness. He comes across Clare. He (2) judges Clare to be a person. Thus, he (3) loves Clare. And so (4) he acts unitively and beneficently towards Clare, pursuing the kind of union that is appropriate between two people heels over heads in love with God.

The lovingness option is philosophically attractive. And perhaps one can claim that some of the New Testament usages of the word agapê refer not to love but to lovingness. Perhaps, but I think it is a bit of a stretch.

There is another option. What is central to Christian ethics is not just love for neighbor but love for God and neighbor. Love for God then gives rise to love for neighbor, both because God loves our neighbor and because our neighbor participates in God. We have the (1)-(4) structure, except that Francis's step (1) is not the virtue of lovingness but love for God. Thus, a theist can build ethics on love rather than lovingness, because love for God already includes something like lovingness towards neighbor.

Could we take this last option and say that love for God is a virtue? Love for God isn't just one love among many: it is the root of other loves in the good life. We still have a disanalogy with courage and justice, I think. Courage and justice, it seems, are not even partly constituted by cognitive and emotional attitudes: they are constituted by a disposition to form cognitive and emotional attitudes. But love for God is at least partly constituted by cognitive and emotional attitudes.

Maybe we should just say that love for God isn't a virtue, and so an ethics of love isn't a virtue ethics. But love for God is something akin to a virtue, something more vibrant and active (less dispositional) than a virtue. This solves another Aristotelian difficulty. Aristotle thought that human flourishing wasn't constituted by having virtues but by acting on them. But human flourishing is constituted in large part by loving God. Loving God has both dispositional and the active components. It is (1) and (3) taken together, and maybe (4) as well. It's a super-virtue.

Question: Am I describing the life of nature or the life of grace?

Answer: At least the life of grace. But perhaps also the life of nature. For there is a natural and a graced, infused love for God. Maybe then natural love of neighbor should flow from a natural love for God--a love that naturally responds to God's goodness as discernible to the life of reason--while supernatural love of neighbor flows from a supernatural love for God--a love that can only come by grace.

The magical

Magical things happen. The glorious glow of the sunset, the elegant glide of the turkey vulture or the delight of conversation with friends. Such experiences of the magical are what gives life its zest.

To experience these things as magical is to experience the events as going over and beyond the merely natural. Thus, if naturalism is true, such experiences are all deceptive. And that makes naturalism a very dour doctrine indeed.

Yet even if naturalism is false, how can these experiences be of events going beyond the merely natural? A sunset is, after all, just light refracted in the atmosphere as the part of the earth on which one stands turns away from the sun. So there is something more going on than the physics describes. This something more could be intrinsic or relational or both. Perhaps the sunset reflects something much deeper beyond it. Or perhaps there is more in the very sunset than the physics describes.

Universal beneficence and love

Take as true this plausible thesis:

1. If you love someone, you have moral reason to benefit that person.

This is curious: it means that if I brainwash you into loving me, you will have moral reason to benefit me. But surely you did not gain a moral reason to benefit me from my brainwashing you. So you must have already had that moral reason before I brainwashed you into loving me. Hence you always already had a moral reason to benefit me, and since I'm not special in this respect, you always already had a moral reason to benefit everyone.

Here's another thesis:

2. You should never try to stop loving.

But again suppose I brainwash you into loving me. If loving me was something optional, something you had no duty to, then it should be permissible for you to undo my imposition of love. But by (2) it's not permissible. So although I did wrong in forcing you to love me, loving me is indeed the right thing for you to do--it is your duty. But I'm not special. So you always already had a moral reason to love everyone.

But it is not in general wrong to try to stop having a particular form of love. We can find ourselves with the wrong form of love: we can love grown children as small children, for instance, or having a romantic love towards someone we ought not. In those cases, it is right to try to stop having that particular form of love, trying as much as one can to replace it with the right form.

Relative identity and relative shape

Take a classic case of relative-identity. At time 1, we have a lump of clay, Lumpy1, that is formed into a statue of a horse, a statue I will call "Bucephalus". At time 2, the lump continues to exist as Lumpy2, but is reformed into into a statue of a big man, a statue I will call "Goliath". Then Lumpy1 is the same lump as Lumpy2, Lumpy1 is the statue as Bucephalus, Lumpy2 is the same statue as Goliath, but it does not follow that Lumpy1 is the same statue as Lumpy2, since we only have transitivity of relative identity when we keep the kind fixed.

Now suppose a four-dimensionalism that says that ordinary objects are four-dimensional (no further commitments on temporal parts, etc.). Then it seems we have a very odd thing. Lumpy1 the lump has a different shape and size from Bucephalus the statue. For Lumpy1 the lump is extended temporally up to and including at least time 2, while Bucephalus the statue does not extend temporally up to time 2. So shape and size are kind-relative. As a lump, Lumpy1 has one four-dimensional shape and size. As a statue, it's Bucephalus and it has a different four-dimensional shape and size. The causal powers are different, too. Lumpy1 can still be seen at time 2, while Bucephalus can no longer be seen then (except in photographs). So the causal powers of a thing are kind-relative, too. Moreover, this kind of thing happens routinely--it's not a miracle as when Christ is omnipresent qua God but only in Jerusalem qua human. It seems implausible that we would have routine kind-relative variation of size and shape.

This makes relative identity not so plausible given four-dimensionalism. But four-dimensionalism (in the weak sense I'm using) is clearly true. :-)

Relative identity and relative parthood

Advocates of relative identity say that identity is always relative to a kind. This seems to have an interesting and underappreciated consequence: If there is such a thing as parthood, it's relative to a kind too. For:

1. Necessarily: x=y if and only if x is a part of y and y is a part of x.

This is very plausible and is a consequence of the antisymmetry of parthood axiom. So if we had an absolute parthood relation, we would automatically get an absolute identity relation out of it.

Is it crazy to think parthood is relative to a kind? Maybe not. Consider classic apparent counterexamples to the transitivity of parthood like: My right foot is a part of me and I am part of the Admissions Committee, but my right foot is not a part of the Admissions Committee. Well, we could say: my right foot is a part of me qua organism, while I am a part of the Admissions Committee qua organization. It's unsurprising that can't chain "___ is a part of ___ qua F" and "___ is a part of ___ qua G" together. On the other hand, perhaps we can say that my right foot is a part of me qua physical object and I am a part of the Admissions Committee qua physical object, so my right foot is a part of the Admissions Committee qua physical object. That sounds just right! So the kind-relativity of parthood seems to be a helpful thesis, at least in this regard.

Still, having to say that parthood is kind-relative is additional baggage for the relative identity theorist to take on board. Can she escape from the weight of that load? Maybe. She could say that diachronic identity is relative but synchronic identity is absolute. If she says that, then she could say that (1) holds but only for synchronic identity and synchronic (three-dimensionalist) parthood. (I think, though, that one shouldn't make diachronic identity be any different from synchronic identity. They are both, just, identity.)

Simplicity and beauty

Consider these two candidates for fundamental physical equations:

1. G=8πT
2. G=(8+π)T.

These two equations are equally simple. (The second has three extra characters in the above inscription. But that's just an artifact of the fact that we abbreviate "(8·π)" as "8π".) But the first equation is much more elegant. For it is elegant to multiply π by a power of two while it is inelegant to add a positive integer to π. The former just feels like a much natural expression.

There are other kinds of beauty of physical hypothesis that do not have much to do with simplicity. Sometimes, for instance, a given physical hypothesis can be characterized in two different ways: say, using a variational principle and a mechanistic story (Leibniz often talks about this). Physicists and mathematicians love this sort of thing. It definitely contributes to the felt beauty of the theory, and a theory that has such a dual characterization will, I think, be preferred to one that does not.

We like theories that tell a compelling story. There was something very compelling about Newton's idea that force is the rate of change of momentum and that the force of gravity drops off precisely in proportion to how "spread out" it is over a spherical shell at a given distance (i.e., the force of gravity is inversely proportional to the distance).

These are all aesthetic judgments, ones like those we employ when judging a piece of art or literature. "This really goes with that." "That's just a pointless plot twist."

This could lead us to non-realism about science. But I think it is better to see a tie between the physical world and our aesthetic judgments. It is, for instance, exactly the kind of tie we would expect if the world were the work of an artist whose tastes are not utterly alien to us.

Sewing fun: Climbing chalk bag

With the semester ended, I took a break from philosophizing and sewed a bag for climbing chalk from worn-out jeans and a microfiber cleaning cloth. I mostly followed this Instructable, but added some worn-out guitar string to keep the top nice and round. Sewing is fun!

Ineffability

Consider this argument against divine ineffability: Let p be the conjunction of all fundamental truths intrinsically about God (I'm thinking here of something like the Jon Jacobs account of ineffability, but the point should work on other similar accounts). Stipulate that the sentence "It divines" (a feature-placing sentence or zero-place predicate, like in "It rains") expresses p. It divines. It seems I have just said the conjunction of all fundamental truths intrinsically about God. Hence God is not ineffable.

But this argument cannot be sound, since God is in fact ineffable--divine ineffability is, for instance, part of the creed of the Fourth Lateran Council. So what goes wrong with the argument?

First, one might have technical worries about infinite conjunctions or arbitrary linguistic stipulations. I'll put those to one side, though they are worth thinking about.

More deeply, one might worry whether there are any fundamental truths intrinsically about God. Truths are true propositions. Perhaps the fundamental reality of God not only cannot be expressed in language, but cannot even be given propositional form. I am not sure about this, though it is a promising response to the argument. But, plausibly, propositions are divine thoughts. And God surely does express his fundamental reality in his thought (indeed, this is central to Augustine's Trinitarianism).

I want to try out a different response to the argument: question the last step in the argument, the inference "Hence God is not ineffable." This response allows that we can stipulate and assert a sentence that means the conjunction of all fundamental truths intrinsically about God, but denies that this is a problem for ineffability. Ineffability isn't a denial of the possibility of asserting a sentence whose semantic content is such-and-such truths about the divine nature. Rather, it is the denial of the possibility of linguistically communicating these truths. For me to linguistically communicate a truth to you it is required that my sentence give rise to your thinking that truth. But the truth expressed by "It divines" isn't a truth you can think. On this understanding, divine ineffability is an immediate consequence of divine incomprehensibility, and rather than being a doctrine about semantics, it's a doctrine about communication.

If this is right, then stipulation allows the semantics of our language to outrun communication and thought. You can think some deep philosophical truth that I don't know, and I can stipulate that "It xyzzes" means that truth, and I can sincerely assert "It xyzzes." But I don't thereby think that truth. I can, of course, think the second order thought that "It xyzzes" is true, but to do that is not the same as to think that it xyzzes. Similarly, I can think that "It divines" is true, but that's a thought about a piece of stipulated language rather than a thought about God. Indeed, it divines, but I don't understand the sentence "It divines" as I can't grasp the proposition it expresses.

Sometimes people are accused of a certain kind of insincerity like this: "You're just saying the words but don't really understand." This is a different kind of insincerity than when people are lying. A person who is "just saying the words" may believe that the sentence composed of the words is really true, and if so, then she isn't lying. (Corollary: One can say something one doesn't believe and yet not be a liar, as long as one believes that what one is saying is true.) The reason that there may be insincerity in "just saying the words" is that normally one implicates that one believes (and hence has a minimal understanding of) the content of what one says. But that's an implicature that can be canceled to avoid even this kind of insincerity: "I don't exactly know what 'God loves you' means, but I believe that it is true. God loves you." And when people are talking of a topic neither is close to being an expert on, the implicature of understanding one's words may be contextually canceled.

Quantifier and Predicate Variance

Suppose we decide to speak with a quantifier family (a quantifier family includes ∃ and ∀, but may also include things like "many" and "most" and "at least three", and maybe even two-place quantifiers, all ranging over the same domain) that makes arbitrary pluralities of things have a fusion, i.e., a mereologically universalist quantifier family. According to the Quantifier Variance thesis, this decision to extend quantifiers is a linguistic decision that needs merely pragmatic justification, a decision that introduces a quantifier perhaps different from the one most ordinarily used.

This sounds like a decision solely about quantifiers. Not so. For now we need to say something about the meaning of predicates applied to variables bound by these quantifiers. For instance, we need to be able to meaningfully say using the new "there is" whether there is something whose mass is 455 tons, i.e., whether ∃x(Mass(x, 455T)). (Using van Inwagen quantifiers which range over simples and organisms, unless there are alien organisms much larger than blue whales, there isn't anything of that mass.) We can give a semantics for the universalist quantifiers in terms of plural quantification, but we need to account for how much a plurality masses. Intuitively, the mass of a plurality is the sum total of the masses of the simples in the plurality (some technical problems: what if there is gunk? do we count the mass-equivalent of the energy of the bonds between the simples?), and so ∃x(Mass(x, 455T)) provided that there are ys which plurally mass 455T. I suppose extending mass in this way once one has extended the quantifiers is pretty obvious.

But not all predicates extend in an obvious way. For instance, consider the predicate that says that something is spatially extended. Does that predicate apply to the fusion of the number seven with the Empire State Building? Here we have a decision to make, roughly about what it is to be plurally extended: Do we say that for the ys to be plurally extended, each one of them must be extended, or is it enough that one of them is extended? The former decision will fit better with the intuition that extended objects are material. The latter with the intuition that occupying space is sufficient for extension. And either way, we will have some technicalities (can't a plurality of unextended points make up something extended?). Or take the causal relation. Did the people who built the Empire State Building cause the fusion of the number seven with the Empire State Building? It's hard to say. And aesthetic properties will be particularly hairy (is the fusion of Beethoven's Ninth with Michelangelo's David beautiful? is it a work of art?).

Thinking about such examples makes it clear that the linguistic decision to speak with a new quantifier family needs to come along with a correlate decision about the semantics of predicates extended to work with this new quantifier family (a decision that could, sometimes, be simply to leave a predicate underdefined or vague). This means that it is a bit misleading to talk of "Quantifier Variance". The relevant thesis is "Quantifier and Predicate Variance". (And we may also need to have "name variance", unless we consider names to be a kind of quantifier.)

Note that none of this is an issue if one creates a new quantifier merely by domain restriction. It's domain expansion that generates the problems.

Transit of Mercury

I'm taking a break from grading. See small dot right and up of center. Larger and more diffuse dot left of center is a sunspot.

An alternative to quantifier variance

According to quantifier variance (QV), there are many families of quantifiers, including the ordinary English family that quantifies over such things as dogs, chairs, holes and shadows, the abstemious ontologist's family that quantifies only over elementary particles, the organicist family that quantifies over elementary particles and living things, and so on. None of these is in any way primary or more fundamental than the others.

The main motivation of QV is to protect apparently reasonable people (whether ordinary or ontologist) against making lots of false statements. While the abstemious ontologist says "There are no chairs anywhere", she doesn't actually disagree with the ordinary person who says "There are five chairs in the room", as they use different quantifiers.

Here is an interesting alternative. Keep the QV story's claim that the ordinary person's "There are" and the ontologist's "There are" mean something different. But deny that they are both quantifiers. Only the ontologist is quantifying. The ordinary person is doing something else.

What about the plurality of ontologists? Are they all quantifying, or is only one camp quantifying? I suspect that most of ontologists are quantifying. And most are saying things that are false. So, unlike QV, I am only interested in saving the ordinary person from making lots of false statements. Ontologists doing ontology do so at their own risk.

Why is it 2016?

According to the A-theory, it's an objective but contingent fact about the world that it's the year 2016. What explains this contingent fact about the world? I've argued against the A-theory along these lines before, but I want to try a somewhat different tack right now. The most plausible explanation is:

1. It's 2016 because a year ago it was 2015.

But what kind of explanation is (1)? I know of three kinds of explanations of contingent facts. First, there are causal explanations, where we explain a fact by giving a cause of it. Second, there are grounding or constitutive explanations, where we explain a fact by giving a ground of it. Third, there are nomic explanations, where we explain a fact by giving a law of nature and initial conditions (I think this is a special case of causal explanations, but that's a different question).

Which of these is (1) an example of? It doesn't seem causal. Its having been yesterday a day ago doesn't cause it to be today. Events yesterday may have caused there to be a today, but they don't cause the A-theoretic fact of its being today. It also doesn't seem to be constitutive. Its being 2016 isn't constituted by its having been 2015 a year ago. Nor does the connection between its having having been 2015 a year ago and its being 2016 now seem to be merely nomic. It's both metaphysically necessary and a priori that if it was 2015 a year ago, then it's 2016.

Of course, the A-theorist can say that (1) is an instance of a sui generis kind of explanation. But types of explanation should not be multiplied beyond necessity, and a type of explanation that applies only in one narrow set of cases seems ad hoc.

From a certain A-theory of time to a countably infinite fair lottery

Suppose:

1. The past has to be finite.
2. The future has to be infinite.
3. The A-theory of time is true.

Then contingent reality appears to generate a countably infinite fair lottery: Simply let N be the number of days since the beginning of time, rounded down. Surely no one day is more likely to be objectively present than another, so N is the outcome of a fair lottery with tickets numbered 0,1,2,.... But such lotteries are well known to lead to many paradoxes (e..g, see chapter 4 of Infinity, Causation and Paradox). Thus, one shouldn't hold all of (1)-(3).

Not every A-theorist has this problem: only those who accept (1) and (2) as well.

Determinates vs. values

Spot has a mass of 10kg, while Felix has a mass of 8kg. The standard Platonic way to model the facts expressed by this is to say that Spot and Felix both have the determinable property of mass and they also have the determinate properties mass-of-10kg and mass-of-8kg, respectively. But there is another Platonic way to model these facts. Rephrase the beginning statement as: "Spot masses 10kg while Felix masses 8kg." The natural First Order Logic rendering of the English is now: Masses(spot, 10kg) and Masses(felix, 8kg). In other words, there is a relation between Spot and Felix, on the one hand, and the two respective values of 10kg and 8kg, on the other.

The determinate property approach multiplies properties: for each possible mass value, it requires a property of having mass of that value. The value approach, on the other hand, introduces a new class of entities, mass-values. So far, it looks like Ockham's razor favors the standard determinate property approach, since we don't want to multiply classes of entities.

However, the determinate property approach has some further ideology. It requires a determinable-determinate relation, which holds between having mass and having mass m. The mass-value approach doesn't require that. We can define having mass in terms of quantification: to have mass is to mass something (∃x Masses(spot, x)). Moreover, the value approach might be able to greatly reduce the number of values it posits. For instance, mass, length and charge values could all simply be real numbers in a natural unit system like Planck units. If one thinks that the Platonist needs mathematical objects like numbers anyway, the additional commitment to values comes for free. Further, the determinate property approach requires positing either a privileged bijection relation (or set of bijection relations) between mass values and non-negative real numbers or enough mathematical-type relations between mass determinates (e.g., a relation of one mass determinate being the sum of two or more mass determinates) to make sense of the mathematics in laws of physics like F=Gmm'/r².

There is also a potential major epistemological bonus for the value approach if the values are real numbers. Standing in a mass relation to a particular real number will be causally relevant. Thus, real numbers lose the inertness, the lack of connection to concrete beings like us, that is at the heart of the epistemological problems for mathematical Platonism.

All that said, I'm not enough of a Platonist to like the story. Is there a non-Platonic version of the story? Maybe. Here's one wacky possibility after all: Values are non-spatiotemporal contingent and concrete beings. They may even be numbers, contingent and concrete nonetheless.