Monday, June 1, 2020

A variant of the at-at theory of change

It’s occurred to me that some of the difficulties with the at-at theory of change nicely disappear if the theory is expressed in terms of the internal time of an object: x changes provided that it is F at internal time t1 and not-F at internal time t2 such that t1 < t2 or t2 < t1.

For instance, consider this difficulty: Fred is bilocated and is sitting all day today and he is standing all day today. So at 10 he is not standing (and standing!) and at noon he is standing (and not standing!). On an external-time at-at theory of change, Fred has changed: at one time he is standing and and at another he isn’t. But that doesn’t seem right.

On an internal-time account of bilocation, we need to ask: is an internal time at which Fred is standing earlier or later than an internal time at which Fred is sitting? And what the answer is depends on how the bilocation was arranged. Suppose Fred was sitting all day, and at the end of the day he activated a time machine and went back to the beginning of the day and stood all day. Then he was sitting internally-earlier than he was standing, and so we do have change—just as we should. But suppose that Fred is just leading two parallel bilocated lives, without any time travel involved. Then his internal time splits into two streams when the bilocation begins and rejoins when they reunite. And plauusibly there are no earlier-than or later-than relations between the two parallel streams. And so there is no change.


Michael Gonzalez said...

Pruss: I'm sorry, but bilocation seems meaningless on its face. Surely, if it is possible to destroy a substance, A, while leaving substance B unscathed, it follows that substance A and substance B are not the same substance (bi-located or otherwise). If anything counts as differentiating one substance from another, then surely to goodness this does!

Your examples in the other post are not compelling, though most of them would require a strong appeal to Biblical authority for me to deal with. I'll just say that the Greek word "estin" can be used to say "means" or "represents" instead of "is" in the right contexts (e.g. Matt. 12:7 is usually translated "means"), and there is, I think, zero chance that the disciples looking at Jesus' intact body would have believed him to mean "this piece of bread is my body". At worst, we could imagine they thought "this is a piece of my body" (consumption of which was illegal under a Law that was still in force in God's eyes)... but, even then, bilocation is nowhere in the neighborhood.

Leaving that aside, time travel is separately meaningless, as anyone can show by attempting to make a sentence about it without misusing tenses (the misuse of which renders the sentence meaningless).

All that aside, I'm interested in this concept of "internal time". Do you mean "inside his body", "his subjective perception of time", or "time for him subject to the Lorentz contraction when he moves"? I don't think you can mean the first, and the second can be illusory/hallucinatory/self-deceiving/etc. The final one, I worded that way because STR takes change from one frame to another to be a mere "boost" (a geometrical priming; nothing more), when in fact there is a physical change (the Lorentz contraction) without which the identity of frames of reference would not hold (just consider Bell's "rocket ships with a thread connecting them" thought experiment). Besides, GTR certainly does not take acceleration from one inertial frame into another to be a mere mathematical convenience; it involves physical change during acceleration. So, the "internal time" in this case would simply be a deformed measuring of time (where "measuring" includes the rate of aging and other physical processes which can be used to mark time).

Does that make any sense? What do you mean by "internal time", if not something like that?

Alexander R Pruss said...

Elizabeth II is Queen of England and Australia. If Australia becomes a republic, she doesn't cease to exist or be Queen: she just ceases to be Queen of Australia. Similarly, if you are bilocated in England and Australia, and the Australians destroy you, then you don't cease to exist or be located, you just cease to be located in Australia.

I don't think of internal time as subjective or in connection with Relativity. My view is Leibnizian: time is primarily a feature of individual substances which have an internal causal history. This internal causal history is strung out along what I call "internal time". If all we had were a bunch of non-interacting substances, then all we would have is a different internal time for each substance, and it would make no sense to ask questions like: "When I was washing my hair, what were you doing?", because there would be no correlations between internal times. But in fact we have interacting substances which induces some correlations between internal times. External time, then, is then constituted by the nexus of correlations between internal times. Relativity Theory ensures that the correlations are sometimes insufficiently rich to allow one to say which two of two events is the earlier (namely, when the two events are spacelike), though sometimes they are rich enough for that.

In Twin Paradox kinds of cases, the internal times of different substances flow at different rates.

As for consumption of Christ's body, Christ is the telos of the Law, and just as God can command Abraham to kill Isaac, so Christ can command his disciples to eat his flesh. That said, what is your source for the claim that the Law prohibits eating human flesh? See also:

Michael Gonzalez said...

1) Are you really saying that a mere social status (like Queenhood) is on an existential and substantive par with where my physical body is located?

2) Does a living organism really have a purely "internal causal history"? We are constantly embedded in the world around us, and any causal history we would give of ourselves would be quite incomplete and explanatorily deficient if it lacked reference to "external" causes, no? Indeed, for the Aristotelian, our nutritive psyche has direct reference to the taking in of nutrients from the world....

3) I take back the bit about cannibalism being illegal (though the example of Abraham doesn't help because it precedes the Law, and Jesus (because he is its telos) always kept the Law, and moreover the Law was against murder not killing simpliciter (otherwise judges and other such agencies couldn't carry out the death penalty) so an example of a divinely commanded killing doesn't help....). All that to say I was quite mistaken. There is nothing in the Law expressly forbidding cannibalism. I mean, humans don't fit the descriptions of "clean" animals either, and the idea of eating humans was used as a repugnant and shocking reference by God (like when a siege would cause them to eat children).

That said, do you really think the disciples, seeing his intact body there with them, would ever have understood "this {estin} my flesh" as "is" rather than "means" or "signifies"? Also, if we consider the other token of his blood, that indeed WOULD be a violation of the Law and of God's pre-Law statements to Noah. Acts 15:20, 29 expressly shows that the prohibition on blood was still in force for Christians.... How does one deal with that?

Alexander R Pruss said...

1: All I mean is that to be in a location is to stand in a certain relation to that location. You can lose the relation and still exist. It's true that my example was a social status. But one can make the example work with non-social statuses. For instance, I can stand in the touching relationship to two different rocks. You can annihilate my touching relationship with one of the rocks (or both rocks) and I will still exist.

2. The history does have inputs from the outside, of course. But there are also internal relations in it.

3. I suspect the disciples were puzzled and didn't know what to make of this, just as they were puzzled and didn't know what to make of Jesus's speech about how one has to eat his flesh to have life. Eventually, the Holy Spirit enlightened them, and that is why as far back as we can trace it, Christians took this literally.

As for blood, in the Old Testament arguably the concern is with animal blood. In any case, it is reasonable to say that the Torah concerns have to do with the accidents of blood. When the blood lacks its usual accidents, it's rather different.

Michael Gonzalez said...

1) That's still not even close to the existential content of "where I am". Besides, how about the matter of there being two distinct, living, breathing organisms, one of which you can kill and destroy without affecting the other?

2) I'm not trying to be disagreeable, but I think it's much more intertwined than that. If my causal history includes a perception, becoming aware of things, nutritive activity like breathing or eating, even movement (subject to fluid dynamics in this atmosphere, etc)... I don't see how to draw the line for a distinct "time".

3) God's original command about blood was to Noah, and he directly mentions human and animal blood both being "asked back" by Him. The ratification into the Mosaic Law contains similar comparisons between human and animal blood (because the nephesh is in the blood in both cases). When the apostles and elders in Jerusalem were deciding which parts of the Law still applied, they did not add an extra distinction. God still "asks back" human and animal blood alike.

In any case, I'm sure there are ways of understanding even your theological position without robust bilocation... Maybe?

Alexander R Pruss said...

1: One can deny that in bilocation cases there are two distinct organisms. There may be but one organism.

3: Remember that one of the rabbinical arguments is that humans aren't meat. If so, then the prohibition on eating meat with blood wouldn't apply. I add that taking in the Eucharist is a bit different from ordinary eating. For one, the presence of Christ's body and blood ends at the time of digestion: as soon as the bread and wine are sufficiently digested not to count as bread and wine, the presence of body and blood ends. So it's not correct to say that we are digesting Christ's body and blood.

Also, the prohibition on blood was a temporary prudential rule to allow Jews and gentile Christians to live together in peace. It is clear from Paul, and from Church tradition, that eventually this prohibition was removed.

Michael Gonzalez said...

1) Imagine that one of the locations had poisoned air or extreme heat or some other harmful circumstance. Clearly only one body would experience the effects. Indeed, it's hard to see why anything at all would happen to the body in Rhode Island just because the body in South Africa is being poisoned or even vaporized in a nuclear explosion. I really think this whole concept is misguided.... But I could be wrong.

3) I'm not sure what you see in Paul (who carried the letter I mentioned from the Apostles around to the various congregations himself) that indicates this rule ever came to an end. God, from when He first permitted meat eating (in Noah's day) expresses that the soul/life is in the blood and that it thus belongs to Him. It predated the Jews and the Mosaic Law by centuries. Then it was considered one of the few things that had to remain (even singling out "things strangled" as well, just because they would contain the blood) even when the Mosaic Law was removed (while Sabbaths and other such hot issues were utterly left out).

You make an interesting point about digestion, but I don't think God has ever distinguished digesting when giving His many statements about the sacredness of blood in the Scriptures. In any case, I guess it's something that folks disagree about theologically.

Alexander R Pruss said...

1. Let's say that in 2040 I die from cancer. Then in 2040 I am dying and in 2020 I am thriving. And it's the numerically same body that is dying and thriving. This is no different from my dying in one spatial location and my living in another. OK, I know you won't like this because you're not an eternalist. :-)

3. It seems quite reasonable to take Romans 14 to acknowledge the completion of all dietary law. I realize that this dietary law preceded Judaism. But it wasn't a part of the natural law (for if it were, then it would have been in place before Noah).

Michael Gonzalez said...

1) You know me so well! Haha. I have to say a few things (I can't help myself):

1a) If you go for any version in which we're continuous 4-d objects, then it isn't really "bi-location", is it? It's more like being extended in space (like my body taking up various parts of the couch).

1b) If it's discontinuous then I think we'd all agree that the 2040 human isn't me, and that the successive Michaels cease to exist moment by moment and are replaced by new ones.

Either option actually strengthens my point about bi-location: either I'm just huge and extended between Rhode Island and South Africa, in which case a piece of me gets vaporized while the other parts persist... or else we are just manifestly discontinuous, distinct beings -- one in Rhode Island and one in South Africa.

This is, of course, leaving aside the glaring fact that 4d (or even 10d) objects still either change or they don't. So, making us 4d-shaped is just orthogonal (pun intended) to the question of "time".... But that's not important right now. I think the analogy actually does strengthen my case against the meaningfulness of bi-location.

3) First off, nobody ate anything that had blood until Noah, so the law wouldn't have made any sense prior to then. Besides, it's not a mere "dietary law". God doesn't just command us not to eat it, He says to spill it out on the ground because the soul is in it and He asks it back from every dead animal or human (Genesis 9; Leviticus 17). And the reaffirmation of that particular thing by the Apostles and Elders, while they did not reaffirm any other dietary law (indeed saying to "abstain" from blood, and listing it along with fornication) really seems to put it in a special category.

It's like the command for Adam and Eve not to partake of the fruit of the tree. Not a natural law, not really "dietary", just something He has the right to grant special significance to and to hold back from us.