Aristotle's optimism and pessimism

Aristotle seems to accept these three claims:

1. For the most part, things behave in a natural way.

2. Most people are bad.

3. To behave well is to behave in accordance with your nature.

I always thought there was a contradiction between (1) and (2) given (3). But actually whether there is a contradiction depends on the reference class of the “For the most part” operator in (1). Suppose the reference class is all behaviors of all things. Then it is quite likely that most of these behaviors are natural, bad human behaviors being far outnumbered by the natural behaviors of insects and elementary particles.

Back when I thought there was a contradiction, I assumed the reference class was the behaviors of a particular kind of thing, a sheep or a human, say. That may be correct exegetically, but even so it does not yield a contradiction. For morally significant activity is only a small fraction of the activity of a human being. Leibniz thought that about three quarters of the time we behaved as mere animals. That’s likely an underestimate. So even if all our morally significant activity is bad, it may be far outnumbered by non-moral activity, and hence it may well be that most activity of humans is good. But when we say that a human is good or bad, we only refer to their moral activity.

The only hope for a contradiction is to take the reference class of (1) to be all the activities of every subsystem type. Even so, I do not know that there is a contradiction. For to say that a person is bad is not to say that the majority of their morally significant actions are bad. Suppose that Monday in the morning Bob kicked a neighbor’s puppy. At noon, she sent a harsh and false email to a struggling student saying that he had never seen worse work than theirs. At three, he googled for articles in obscure Romanian journals that I could translate and plagiarize. And in the evening he cheated while playing chess with his daughter in order that she might never win. It would be fair to say that Bob am very bad person indeed, but that’s only on the strength of four morally significant actions. There were many other morally significant actions Bob engaged in. Each time he was asked a question, he had the possibility of lying. When driving, he had the possibility of murder. He did many things that were morally neutral and no doubt a number of things that were good. But the four bad things he did were enough to show that he was a bad person.

Our standards for moral okayness are much higher than the standards for a hard calculus exam where you just need to get more than half the questions right.

See also the quote from George MacDonald here.

The Need for Human Nature

A popular article of mine on “The Need for Human Nature” has just been posted on Sapientia. One can think of it as a precis of the main ideas in my in-progress Norms, Natures, and God book.

Progress on Norms, Natures and God

In the fall, I opened a github repository for my in-progress Norms, Natures and God book manuscript, but all I had was a table of contents. I’ve finally started to regularly contribute text to the book. You can monitor my progress here, and you’re welcome to submit suggestions and bug reports via the Issues page.

Don’t count on the repository being available permanently: it will disappear when it’s time to submit to a publisher. (My preferred way to write books is to write them and then submit the whole draft to a publisher.)

Vagueness and degrees of truth

Consider the non-bivalent logic solution to the problem of vagueness where we assign additional truth values between false and true. If the number of truth values is finite, then we immediately have a regress problem once we ask about the boundaries for the assignment of the finitely many truth values: for instance, if the truth values are False, 0.25, 0.50, 0.75 and True, then we will be able to ask where the boundary between “x is bald” having truth value 0.50 and having truth value 0.75 lies.

So, the number of truth values had better be infinite. But it seems to be worse than that. It seems there cannot be a set of truth values. Here is why. If x has any less hair than y, but neither is definitely bald or non-bald, then “x is bald” is more true than “y is bald”. But how much hair one has is quantified in our world with real numbers, say real numbers measuring something like a ratio between the volume of hair and the surface area of the scalp (the actual details will be horribly messy). But there will presumably be possible worlds with finer-grained distances than we have—distances measured using various hyperreals. Supposing that Alice is vaguely bald, there will be possible people y who are infinitesimally more or less bald than Alice. And as there is no set of all possible infinitesimals (because there is no set of all systems of hyperreal), there won’t be a set of all truth values.

Moreover, there will be vagueness as to comparisons between truth values. One way to be less bald is to have more hairs. Another way is to have longer hairs. And another is to have thicker hairs. And another is to have a more wrinkly scalp. Unless one adopts epistemicism, there are going to be many cases where it will be vague whether “x is bald” is more or less or equally or incommensurably true as “y is bald”.

We started with a simple problem: it is vague what is and isn’t bald. And the non-bivalent solution led us to a vast multiplication of such problems, and a vast system of truth values that cannot be contained in a set. This doesn’t seem like the best way to go.

Epistemicism and physicalism

1. There is a precise boundary for the application of “bald”.

2. If there is a precise boundary for the application of “bald”, that boundary is defined by a linguistic rule of infinite complexity.

3. If physicalism is true, then no linguistic rules have infinite complexity.

4. So, physicalism is not true.

The argument for (1) is classical logic. The argument for (2) depends on the many-species considerations at the end of my last post. And if (3) is true, then linguistic rules are defined by our practices, and our practices are finitary in nature.

Objection: We are analog beings, and every analog system has possible states of infinite complexity.

Response 1: Our computational states ignore small differences, so in practice we have only finite complexity.

Response 2: There is a cardinality limit on the complexity of states of analog systems (analog systems can only encode continuum-many states). But there is no cardinality limit on the number of humanoid species with hair, as there are possible such species in worlds whose spacetime is based on systems of hyperreals whose cardinality goes arbitrarily far beyond that of the reals.

The unknowability part of epistemicism about vagueness

One way to present epistemicism is to say that

1. vague concepts have precise boundaries, but

2. it is not possible for us to know these boundaries.

A theist should be suspicious of epistemicism thus formulated. For if there are precise boundaries, God knows them. And if God knows them, he can reveal them to us. So it is at least metaphysically possible for us to know them.

Perhaps the “possible” in (b) should be read as something stronger than metaphysical possibility. But whatever the modality in (b) is, it seems to imply:

3. none of us will ever know these boundaries.

But if epistemicism entails (c), then we don’t know epistemicism to be true. For if there are sharp boundaries, for all we know God will one day reveal them to a pious philosopher who prays really hard for an answer.

I think the best move would be to replace (b) with:

4. it is not possible for us to know these boundaries without reliance on the supernatural.

This is more plausible, but it seems hard to be all that confident about (d). Maybe there is some really elegant semantic theory that has yet to be discovered that yields the boundaries. Or maybe our mind has natural powers beyond those we know.

Let me try, however, to offer a bit of an argument for (d). Let’s imagine what the boundary between bald and non-bald would be like. As a first attempt, we might think it’s like this:

1. Necessarily, x is bald iff x has fewer than n hairs.

But there is no n for which (1) is true. For n would have to be at least two, since it is possible to be bald but have a hair. Now imagine Bill the Bald who has n − 1 hairs, and now imagine that these hairs grow in length until each one is so long that Bill can visibly and fully cover his scalp with them. At that point, Bill wouldn’t be bald, yet he would still have n − 1 hairs. So, the baldness boundary cannot be expressed numerically in terms of the number of hairs.

As a second attempt, we might hope for a total-length criterion.

2. Necessarily, x is bald iff the total length of x’s hairs is less than x centimeters.

But it is possible to have two people with the same total length of hairs, one of whom is bald and the other is not. For the thickness of hairs counts: if one just barely has the requisite total length but freakishly thin hairs, that won’t do. On the other hand, clearly x would have to be at least four centimeters, since a single ordinary hair of four centimeters is not enough to render one non-bald, but one could have a total hair length of four centimeters and yet be non-bald, if one has four hairs, each one centimeter long and 10 centimeters in diameter, covering one’s scalp with a thick keratinous layer.

So, we really should be measuring total volume, not length. But there are other problems. Shape probably matters. Suppose Helga has a single hair, of normal diameter, but it is freakishly rigid and long, long enough to provide the requisite volume, but immovably sticking up away from the scalp and providing no coverage. Moreover, whatever we are measuring has to be relative to the size of the scalp. A baby needs less hair to cease to be bald than an adult. But it’s not just relative to the size of the scalp, but also the shape of the scalp. If one has a very large surface area of scalp but that is solely due to many tiny wrinkles, one doesn’t need an amount of hair proportional to that large surface area. To a first approximation, what matters is the surface area of the upper part of the convex hull of one’s scalp. But even that’s not right if we imagine a scalp that has very large wrinkles.

So, in fact, we have good reason to think the real boundary wouldn’t be simply numerical. It would involve some function of hair shape, volume and rigidity, as well as of scalp shape and size. And if we think about cases, we realize that it will be a very complex function, and we are nowhere close to being able to state the function. Moreover, to be honest, there are likely to be other variables that matter.

At this point, we start to see the immense amount of complexity that would be involved in any plausible statement of the precise boundary of baldness, and that gives us positive reason to doubt that short of something supernatural we could know where the boundary lies.

But suppose our confidence has not yet been quashed. We still have other serious problems. What we are looking for is a perfectly precise necessary and sufficient condition for someone to be bald. In that definition, we cannot use other vague terms. That would be cheating. What the epistemicist meant by saying that we don’t know where the boundaries lie was that we do not know any transparently precise statements of the boundaries, statements not involving other vague terms. But “hair” itself is a vague term. Both hair and horns are made of keratin. Where does the boundary between hair and horns lie? Similarly, “scalp” is vague, too. And it’s only the volume of the part of the hairs sticking out of the scalp that counts—the size of the root is irrelevant. But “sticking out” is vague, as is obvious when we Google for microscopic photography of scalps. And which particles are in the hair or in the scalp is going to be vague. Next, any volume and surface area measurements suffer from vagueness even if we fix the particles, because for quantum reasons particles will have spread out wavefunctions. And then Relativity Theory comes in: volume and surface area depend on reference frame, and so we need a fully precise definition of the relevant reference frame.

Once we see all the complexity needed in giving a transparently precise statement of the boundary of baldness, it becomes very plausible that we can’t know it by natural means, just as it is very plausible that no human can know the first million digits of π by natural means.

And things get even worse. For humans are not the only things that can be bald. Klingons can be bald, too. Probably, though, only humanoid things are bald in the same sense of the word, but even when restricted to humanoid things, a precise statement of the boundary of baldness will have to apply to beings from an infinite number of possible species. And the norms of baldness will clearly be species-relative. Not to mention the difficulty of defining what hair and scalp are, once we are dealing with beings whose biochemistry is different from ours. It is now starting to look like a transparently precise statement of the boundary of baldness might actually have infinite complexity.

Mystery and religion

Given what we have learned from science and philosophy, fundamental aspects of the world are mysterious and verge on contradiction: photons are waves and particles; light from the headlamp on a fast train goes at the same speed relative to the train and relative to the ground; objects persist while changing; we should not murder but we should redirect trolleys; etc. Basically, when we think deeper, things start looking strange, and that’s not a sign of us going right. There are two explanations of this, both of which are likely a part of the truth: reality is strange and our minds are weak.

It seems not unreasonable to expect that if there were a definitive revelation of God, that revelation would also be mysterious and verge on contradiction. Of the three great monotheistic religions, Christianity with the mystery of the Trinity is the one that fits best with this expectation. At the same time, I doubt that this provides much of an argument for Christianity. For while it is not unreasonable to expect that God’s revelation would be paradoxical, it is a priori a serious possibility that God’s revelation might be so limited that what was revealed would not be paradoxical. And it would also be a priori a serious possibility that while creation is paradoxical, God is not, though this last option is a posteriori unlikely given what we learn from the mystical experience traditions found in all the three monotheistic religions.

So, I am not convinced that there is a strong argument for Christianity and against the other two great monotheistic religions on the grounds that Christianity is more mysterious. But at least there is no argument against Christianity on the basis of its embodying mysteries.

Three levels of theological models

There are three kinds of metaphysical models of a theological mystery—say, Trinity, Incarnation or Transubstantiation:

• realistic model: a metaphysical story that is meant to be a true account of what makes the mysterious doctrine be true

• potential model: a metaphysical story that is meant to be an epistemically possible account of what makes the mysterious doctrine be true

• analogical model: a story that is meant to be an epistemically possible account of what makes something analogous to the mysterious doctrine be true.

For instance, Aquinas’s accounts of the Trinity, Incarnation and Transubstantiation are realistic models: they are meant to be accounts of what indeed makes the doctrines true. Van Inwagen’s relative identity account of the Trinity or his body-snatching account of the resurrection, on the other hand, are only potential models: van Inwagen does not affirm they are true. And the history of the Church is filled with analogical models.

A crucial test of any of these models is this: Imagine that you believe the story to be true, and see if the traditional things that one says about the mystery (in the case of a realistic or potential model), or analogues of them (in the case of an analogical model), sound like reasonable things to say given what one believes.

For instance, consider a time-travel model of the Incarnation. Alice, currently a successful ultramarathoner and brilliant geologist, will live a long and fruitful life. Near the end of her life, she has lost most of her physical and mental powers, and all her knowledge of geology. She uses a time machine to go back to 2020 when she is in her prime. If we thought this story was true, it would be reasonable to find ourselves saying things like:

• Alice is a successful ultramarathoner and barely able to walk

• Alice understands continental drift and does not not know what magma is

• Alice is young and old

• Alice is in the pink of health and dying.

These things would sound like a contradiction, but the time-travel story shows they are not. However, these claims are also analogous to claims that constitute an especially mysterious part of the mystery of the Incarnation (and I suppose a mysterious part of a mystery is itself a mystery): Christ suffers and is impassible; Christ is omniscient and does not know everything; Christ is timeless and born around 4 BC.

Of course nobody should think that it’s literally true that the Incarnation is to be accounted for in terms of time travel. But what the analogical model does show is that there are contexts in which it is reasonable to describe a non-contradictory reality in terms that are very similar to the apparently contradictory incarnational claims.

Slowing down pleasures and pains, once again

If suddenly everything in game and in my brain slowed down while I was having a good time playing Asteroids, my conscious sequence wouldn’t be subjectively affected, and the hedonic value of the game would not change in any way. It would just take proportionately longer to get the same overall hedonic value.

But this leads to a paradox. Suppose that I am experiencing an approximately constant moderate pleasure for five minutes, and you experience that pleasure for ten minutes. Then, obviously, you get approximately twice the hedonic value. But one way to make it be the case that you experience the same pleasure for ten minutes is just to slow down all of your life by a factor of two. And yet such a slowdown should not affect hedonic value.

I think I previously thought that one way out of this paradox was to suppose that time is discrete. But I don’t think so any more. In fact, it seems to me that making time be discrete makes the paradox worse. For in your slowed-down ten minutes of pleasure, there will be twice as many pleasurable moments of time, which should predict, contrary to the intuition I began with, that you will have twice the hedonic value. Granted, if time is discrete, there will be some technical difficulties with how the slowdown happens at very short time-scales. But that doesn’t matter for us, since if time is discrete, it is discrete on a Planck scale, which is way below any time-scales relevant to my enjoying a game of Asteroids. And we need not imagine any weird “microphysics slowing down” for the thought experiment: it suffices that the computer software slow down by a factor of two and that you be given drugs that make your brain work more sluggishly than mine.

A different way to try to solve the problem is to suppose that there is some kind of a clock in my brain, and that only states at a clock tick are pleasurable. Thus, if your life is slowed down by a favor of two, then that clock will slow down, and in ten minutes of your enjoying Asteroids there will be the same number of pleasurable ticks as in me, and so you will get the same total pleasure.

But this is tricky. Whatever process is generating the clock ticks in our brains is presumably a fairly continuous analog process. Thus, there will be no such thing as an instantaneous tick of the clock. Rather, there will be an extended period of time (on a time-scale many orders of magnitude above the Planck scale, so any discreteness of physical time will be irrelevant) at which the tick occurs. (Think of a physical clock ticking. The tick is a sound that occurs every second for a fraction of a second—but that fraction is non-zero.) So if I am having pleasure during the tick and you’re having pleasure during the tick, since your tick takes twice as long, it seems you have twice as much pleasure.

I can think of only one way out of the paradox right now, and that is to deny that it makes sense to talk of there being a pleasure or a pain at an instantaneous physical time. Rather, pleasures and pains (and presumably other qualia) always occur over an interval of times. The clock toy model can now be rescued. For we could say that what counts is a pleasurable or painful tick, but if the tick itself is shortened or extended, the hedonic value does not actually change. Let’s imagine that the clock works like some processor clocks. There is an electric square wave generated somewhere, and the ticks are the transitions from a high to a low voltage. Since real-life “square wave” isn’t actually square, but has transitions with wobbly smooth edges, the ticking—i.e., the transition from high to low—takes time. What makes it be the case that one has experienced a pleasure or pain during an interval of times is that this interval contained a clock transition from high to low together with some further state that is not itself pleasurable or painful but that, when combined with the clock transition, constitutes the pleasure or pain. The number of pains or pleasures during a period of time is the number of such transitions.

If one slows down the system, the clock transitions become slower. But the number of clock transitions is unchanged, as is the number of pleasurable or painful clock transitions. Thus there is no change in overall hedonic value.

But notice that on this toy model it is never true that one is experiencing a pleasure or pain at an instant. For there is no transition from high to low clock state at an instant. Transitions happen over an interval of times. This will bother presentists.

The above line of thought assumed supervenience of the mental on the physical. But a robust dualism faces the same problems of slowing down and speeding up, and the fundamental idea of the solution, that pleasures and pains are constituted by essentially temporally extended processes and that there are no instantaneous pleasures or pains, is still available.

Swapping ones and zeroes

Decimal addition can be done by a computer using infinitely many algorithms. Here are two:

1. Convert decimal to binary. Add the binary. Convert binary to decimal.

2. Convert decimal to inverted binary. Inv-add the binary. Convert inverted binary to decimal.

By conversion between decimal and inverted binary, I mean this conversion (in the 8-bit case):

• 0↔11111111, 1↔11111110, 2↔11111101, …, 255↔00000000.

By inv-add, I mean an odd operation that is equivalent to bitwise inverting, adding, and bitwise inverting again.

You probably thought (or would have thought had you thought about it) that your computer does decimal addition using algorithm (1).

Now, here’s the fun. We can reinterpret all the physical functioning of a digital computer in a way that reverses the 0s and 1s. Let’s say that normally 0.63V or less counts as zero and 1.17V or higher counts as one. But “zero” or “one” are our interpretation of analog physical states that in themselves do not have such meanings. So, we could deem 0.63V or less to be one and 1.17V or higher to be zero. With such a reinterpretation, logic gates change their semantics: OR and AND swap, NAND and NOR swap, while NOT remains NOT. Arithmetical operations change more weirdly: for instance, the circuit that we thought of as implementing an add should now be thought of as implementing what I earlier called an inv-add. (I am inspired here by Gerry Massey’s variant on Putnam reinterpretation arguments.)

And if before the reinterpretation your computer counted as doing decimal addition using algorithm (1), after the reinterpretation your computer uses algorithm (2).

So which algorithm is being used by a computer depends on the interpretation of the computer’s functioning. This is a kind of flip side to multiple realizability: multiple realizability talks of how the same algorithm can be implemented in physically very different ways; here, the same physical system implements many algorithms.

There is nothing really new here, though I think much of the time in the past when people have discussed the interpretation problem for a computer’s functioning, they talked of how the inputs and outputs can be variously interpreted. But the above example shows that we can keep fixed our interpretation of the inputs and outputs, and still have a lot of flexibility as to what algorithm is running “below the hood”.

Note that normally in practice we resolve the question of which algorithm is running by adverting to the programmers’ intentions. But we can imagine a case where an eccentric engineer builds a simple calculator without ever settling in her own mind how to interpret the voltages and whether the relevant circuit is an add or an inv-add, and hence without settling in her own mind whether algorithm (1) or (2) is used, knowing well that either one (as well as many others!) is a possible interpretation of the system’s functioning.

Another really weird thought experiment

Suppose we accept a memory theory of personal identity and accept that people can be moved from one set of hardware to another. Now suppose Alice is an internally determinstic person, currently without inputs from the outside world, whose mental state is constantly backed up to a hard drive. Suppose now that Alice is a person who in hardware AliceOne has experiences E₀, E₁, E₂, E₃ at times 0,1,2,3, respectively. Then the initial hardware is destroyed, and the backup from just before time 2 is restored into another piece of hardware, AliceTwo, who goes on to have experience E₂. Then AliceTwo is destroyed, and a backup from just before time 1 is restored into AliceThree, who goes on to have experience E₁, after which all the hardware and the backups are destroyed by a natural disaster.

What is the order of Alice’s experiences? The obvious answer is:

• E₀, E₁, E₂, E₃, E₂, E₁ at times 0−5, respectively.

In particular, when Alice is experiencing E₂ for the second time, if she were informed of what is going to happen, she would be rationally dreading E₁ if E₁ is unpleasant. For E₁ would be in her future.

What makes it be the case that the second E₁ is experienced after the second E₂? It is the order of external time, according to which the second E₁ comes after the second E₂. It is not the order of causal connections in Alice (since the second E₂ comes from first E₁ while the second E₁ comes from the first E₀, and since there need be no causal connection between the hardware AliceTwo and AliceThree).

I think this is all a bit odd. To make it odder, let’s imagine that AliceTwo and AliceThree are in a room that time-travels in such a way that it is first at time 5 and then at time 4. Now, perhaps, Alice experiences the final E₁ before she experiences the final E₂. That’s really unclear, though.

The more I think about various combinations of time-traveling backups and time-traveling hardware, the more indeterminate it looks to me whether the final E₂ comes before the final E₁.

This is not much of an argument. But the above lines of thought lead me to think that one or more of the following is true:

1. Time travel is impossible.

2. People cannot be moved from one piece of hardware to another.

3. One does not survive restoration from a backup.

4. The order of experience does not have tight connections to rationality of attitudes.

5. The order of experience can be quite indeterminate.

Timeless flow of consciousness?

We could imagine that all the computation a deterministic brain does being done by an incredibly complex system of gears operated by a single turn of the crank to generate all the different intermediate computational results in different gears. Now, imagine a Newtonian world with frictionless, perfectly rigid and perfectly meshing gears, and suppose that the computations are done by that system. Perfectly rigid and perfectly meshing gears compute instantly. So, all the computation of a life can be done with a single turn of a crank. Note that the computational states will then have an explanatory order but need not have a temporal order: all the computations happen simultaneously. So:

1. On a computational theory of mind, it is possible to live a conscious mental life of many years of subjective flow of consciousness without any real temporal succession.

It follows that:

2. Either computational theories of mind are false, or the subjective flow of consciousness does not require any real time.

I think there is a potential problem in (1) and (2), namely a potential confusion between real time and external time. For it could be that internal time is just as real as (or more real than!) external time, and is simply constituted by the causal order of interactions within a substance. If so, then if the system of gears were to be a substance (which I think it could only be if it had a unified form), its causal order could actually constitute a temporal order.

This and other recent posts could fit into a neat research project—perhaps a paper or even a dissertation or a monograph—exploring the costs of physicalism in accounting for the temporality of our lives. As usual, I am happy to collaborate if someone wants to do the heavy hitting.

Digital and analog states, consciousness and clock skew

In a computer, we have multiple layers of abstraction. There is an underlying analog hardware level (which itself may be an approximation to a discrete quantum world, for all we know)—all our electronic hardware is, technically, analog hardware. Then there is a digital hardware level which abstracts from the analog hardware level, by counting voltages above a certain threshold as a one, below another—lower—threshold as a zero. And then there are higher layers defined by the software. But it is interesting that there is already semantics present at the digital level: three volts (say) means a one while half a volt (say) means a zero.

At the (single-threaded) software level, we think of the computer as being in a sequence of well-defined discrete states. This sequence unfolds in time. However, it is interesting to note that the time with respect to which this sequence unfolds is not actually real physical time. One reason is this. At the analog hardware level, during state transitions there will be times when the voltage levels are in an area that does not define a digital state. For instance, in 3.3V TTL logic, a voltage below 0.8V is considered a zero, a voltage above 2.0V is considered a one, but in between what we have is “undefined and results in an invalid state”. Since physical changes at the analog hardware level are continuous, whenever there is a change between a zero and a one, there will be a period of physical time at which the voltage is in the “undefined” range.

It seems then that the well-defined software state thus can only occur at a proper subset of the physical times. Between these physical times are physical times at which the digital states, and hence the software states that are abstractions from them, are undefined. This is interesting to think about in connection with the hypothesis of a conscious computer. Would a conscious computer be conscious “all the time” or only during the times when software states are well defined?

But things are more complicated than that. The technical means by which undefined states are dealt with is the system clock, which sends a periodic signal to the various parts of the processor. The system is normally so designed that when the clock signal reaches a component of the processor (say, a flip-flop), that component’s electrical states have a well-defined digital value (i.e., are not in the undefined range). There is thus an official time at which a given component’s digital values are defined. But at the analog hardware level, that official time is slightly different for different components, because of “clock skew”, the physical phenomenon that clock signals reach different components at different times. Thus, when we say that component A is in state 1 and component B is in state 0 at the same time, the “at the same time” is not technically defined by a single physical time, but rather by the (normally) different times at which the same clock signal reaches A and B.

In other words, it may not be technically correct to say that the well-defined software state occurs at a proper subset of the physical times. For the software state is defined by the digital state of multiple components, and the physical times at which these digital state “count” is going to be different for different components because of clock skew. In fact, I assume that the following can and does sometimes happen: component B is designed so that the clock signal reaches it after it has reached component A, and by the time component B is reached by the clock signal, component A has started processing new data and no longer has a well-defined digital state. Thus at least in principle (and I don’t know enough about the engineering to know if this happens in practice) it could be that there is no single physical time at which all the digital states that correspond to a software state are defined.

If this is right, then when we go back to our thought experiment of conscious computer, we should say this: The times of the flow of consciousness in that computer are not even a subset of the physical times. They are, rather, an abstraction, what we might call “software time”. If this is right, the question of whether the computer is presently conscious will be literally nonsense. The computer’s software time, which its consciousness is strung out along, has a rather complex relationship to real time.

So what?

I don’t know exactly. But I think there are a few directions one could take this line of thought:

1. Consciousness has to be strung out in a well-defined way along real time, and so computers cannot be conscious.

2. It is likely that similar phenomena occur in our brains, and so either our consciousness is not based on our brains or else it is not strung out along real time. The latter makes the A-theory of time less plausible, because the main motive for the A-theory is to do justice to our experience of temporality. But if our experience of temporality is tied to an abstracted software time rather than real time, then doing justice to our experience of temporality is unlikely to reach the truth about real time. This in turn suggests to me the conditional: If the A-theory of time is true, then some sort of dualism is true.

3. The problem that transitions between meaningful states (say, the ones and zeros of the digital hardware level) involve non-meaningful states between them is likely to afflict any plausible theory on which our mental functioning supervenes on a physical system. In digital computers, the way a sequence of meaningful states is reconstructed is by means of a clock signal. This leads to an empirical prediction: If the mental supervenes on the physical, then our brains have something analogous to a clock signal. Otherwise, the well-defined unity of our consciousness cannot be saved.

Relativity, brains and the unity of consciousness

I was grading undergraduate metaphysics papers last night and came across a very interesting observation in a really smart student’s paper on Special Relativity and time (I have the student’s permission to share the observation): different parts of the brain have different reference frames, and so must experience time slightly differently.

Of course, the deviation in reference frames is very, very small. It comes from such facts as that

• the lower parts of the brain are closer to a massive object—the earth—which causes a slight amount of time dilation, and

• we are constantly wobbling our heads in a way that makes different parts of the brain move at different speeds relative to the earth.

Does such a small difference matter? As I understand their argument, my student thought it would make the A-theory less plausible. For it makes it questionable whether we can say that we really perceive the true objective now in the way that A-theorists would want to say we do. That’s an interesting thought.

I also think the line of thought might create a problem for someone who thinks that mental states supervene on physical states. For consider the unity of consciousness whereby we are aware of multiple things at once. If the consciousness of these different things is partly constituted by different chunks of the brain, then it seems that what precise stream of consciousness we have will depend on what reference frame we choose. For instance, I might hear a sound and feel a pinch at exactly the same moment in one reference frame, but in another reference frame the sound comes before the feeling, and in other the feeling comes before the sound. But that seems wrong: the precise stream of consciousness should not depend on the reference frame.

This shows that if the order of succession within the stream of consciousness does not depend on the reference frame (and it is plausible that it does not), then the precise stream of conciousness cannot supervene on physical states. This is clear if there is no privileged reference frame in the physical world. But even if there is a metaphysically privileged reference frame as A-theorists have to say, it seems reasonable to say that this frame is “metaphysical” rather than “physical”, and hence a dependence of consciousness on this frame is not a case of supervenience of mind on the physical.

Here is what I think we should say: If the A-theory is true, then the mind somehow catches on to the absolute now. If the B-theory is true, then the mind has its own subjective timeline, which is not the timeline of the brain or any part of it.

I think a really careful materialist might be able to affirm the latter option, by analogy to how in a modern digital computer, even though at the electronic hardware level there is analog time (perhaps itself an approximation to some frothy weird quantum time), synchronization of computation to clock ticks results in the possibility of abstracting a precisely defined discrete time that “pretends” that all combinatorial logic happens instantaneously. Roughly speaking, the assembly language programmer works with respect to the discrete time, while the FPGA programmer works primarily with respect to the discrete time but has to constantly bear in mind the constraints that come from the underlying analog time. However, the correspondence between the two levels of time is only vague. Similarly, I think that it is likely that the connection between the mind’s timeline and the physical timelines is going to suffer from vagueness (though perhaps only epistemic). How philosophically happy a materialist would be with such a view is unclear, and there is a serious empirical assumption here for the materialist, namely that the brain has a global synchronizing process similar to a microprocessor’s or FPGA’s synchronizing clock. I doubt that there is, but I know very little of neuroscience.

Simultaneity, A-Theory and Relativity

Here is a standard story about Special Relativity and the A-theory of time:

• There is an objective metaphysical simultaneity, but

• this metaphysical simultaneity does not affect physical events and is unobservable.

Let’s assume the A-theory is correct and this story is also correct.

Now, when people talk about this metaphysical simultaneity, they normally think they it aligns with the frame-relative simultaneity of Special Relativity for some privileged reference frame. This seems reasonable. But it is an interesting question to ask for an explanation of this alignment.

Causation may put some constraints on metaphysical simultaneity. For instance, perhaps, there shouldn’t be any possibility of future to past causation. But a metaphysical simultaneity relation can satisfy such constraints without coinciding with any frame-relative simultaneity.

If God exists, I guess we might suppose that metaphysical simultaneity coincides with a frame-relative simultaneity because it’s more elegant if it does.