Wednesday, June 18, 2014

Spatializing time

Would it not be strange to accuse biologists of equinizing sharks because they say that horses and sharks are organisms ontologically on par with each other. Of course, both sharks and horses are organisms. Of course, they are ontologically on par. (If biological reductionism holds, they both reduce to particles. If biological anti-reductionism holds, neither reduces to particles.) And the similarities don't end there. They both have DNA, they reproduce sexually, they are both chordates, and so on. Nonetheless, they are obviously different in ways that do not mark an ontological difference, and the biologist is interested in such differences as well as in the similarities.

Eternalists get accused of spatializing time, because they are claimed to hold that time is a dimension ontologically on par with and akin to spatial dimensions. Now, first of all, an eternalist need not think time is a dimension ontologically on par with spatial dimensions. She could, for instance, be an absolutist about spatial relations and a relationalist about temporal ones, or vice versa. She could think that spatial relations are constituted by degrees of interaction (things that tend to interact more are therefore closer together), while temporal relations are primitive. Or she could think that spatial relations are primitive, while temporality is constituted by facts about the causal nexus. All if this is compatible with eternalism. So eternalists certainly do not need to take time to be ontologically on par with space. Of course, they will take time to be akin to space insofar as they hold that being now rather than then no more marks an ontological difference in an object than being here rather than there. But that's just one similarity, a similarity compatible with much ontological dissimilarity.

But let's even grant that we are dealing with an eternalist who thinks the temporal dimension is ontologically on par with the spatial ones. Still, as the case of horses and sharks shows, being ontologically on par is compatible with much significant difference. The biologist doesn't equinize sharks or sharkify equines. Likewise, an oscilloscope and a hammer are ontologically on par, and they are both kinds of tools, but saying that neither oscilloscopifies hammers nor hammerizes oscilloscopes. The differences are important and hard to miss.

The same is true for space and time. Persons' lives are strung out through time in a way that they are not strung out through space: they show significant temporal development but no analogous spatial development, and we are vastly thinner spatially than temporally. Time has a direction connected both with the increase of entropy and causation, while space is isotropic. Even in Relativity Theory, which treats space and time as a unified manifold, the temporal component gets counted completely differently in the metric: the square of the distance between two spacetime points in a flat space is equal to dx2+dy2+dz2dt2: the time difference crucially gets a minus sign in the signature, a fact that has vast physical consequences. These are vast differences.

A standard four-dimensionalist analysis of change is that change consists of being one way at one time and another way at another. (It's hard to deny that this is necessary and sufficient for change1) This account is accused of making change be too much like the variation in landscape along a spatial axis. But that accusation assumes that on the four-dimensionalist analysis there is no significant difference between temporal and spatial variation. But if there is a significant difference between time and space, something that we saw is quite compatible with eternalism (and very hard to deny!), the accusation falls flat. Saying that temporal and spatial variation on eternalism is the same is like saying that there is no difference between imprisoning an innocent and a guilty person, because both are imprisonments. They are both imprisonments, but one is of an innocent and the other of a guilty person. Likewise, both temporal and spatial variation are variations, but one is a temporal variation and the other a spatial variation. Change is temporal variation.


Michael Gonzalez said...

"Of course, they will take time to be akin to space insofar as they hold that being now rather than then no more marks an ontological difference in an object than being here rather than there. But that's just one similarity..."

Is it not a rather crucial similarity, since it is completely different from our intuitions about temporal becoming? Is it not the case that (like the "worm" in your "How Fat Am I?" post) the eternalist picture of me is of a 4-d object that never stops being exactly the same 4-d shape?

"they show significant temporal development but no analogous spatial development"

It's easy enough to imagine an object which showed the same spatial development as temporal. We worms might not be that way, but something could be. And its bizarre, 4-d cone shape is eternally, statically, unchangingly its shape.

"Time has a direction connected both with the increase of entropy and causation, while space is isotropic."

Arbitrary distinctions if the block theory is really true. Saying that entropy increase is "later" is exactly as justified as calling it "earlier", since such distinctions are nonexistent in the physics. Moreover, even if I granted a directionality, it would only mean that there is eternally, unchangingly more entropy on this side of the static block than on that side, no?

As for causality, it seems to me that causation is a primitive, and so the order of temporal becoming is beholden to causation. But temporal becoming doesn't exist on the eternalist view. Whatever causes the 4-d block to be as it is, causes each piece of it to be the way it is simultaneously. It is the cause of everything all at once. While I'm not denying that there can be causally explanatory relations within the block, it is actually still always the case that x is the way it is because the Cause of the Block makes it so simultaneously with making y and z and everything else so. It's honestly a lot like Leibniz's "Pre-Established Harmony", so far as I can see, and the Pre-Established Harmony view doesn't really have any causation except God's.

"But that accusation assumes that on the four-dimensionalist analysis there is no significant difference between temporal and spatial variation."

Does it? I don't think so. I think there could be many difference between the temporal axis and the spatial one and yet the presentist would still object that your 4-d analysis of "change" is "too much like the variation in landscape along a spatial axis". Why? Because of the one way that the eternalist insists space and time are the same: "being then rather than now is like being there rather than here". That similarity seems to me to be all that is needed to make "change" meaningless. So this 4-d object is shaped differently over here than over there... so what? It is eternally shaped that way! Nothing changes. And if I replace "over here" with "now" and "over there" with "then", why is that different in any relevant way?

Michael Gonzalez said...

Just as a consideration: What if the 4-d block were to change? What if the spatiotemporal shapes of things were to undergo a morphing (I know this can't actually happen on an eternalist model, but I don't see any metaphysical impossibility in it). If it happened, then that would not be an extension along some 5th axis, would it? Surely we would simply acknowledge this change as ceasing to be one way and becoming another way... an A-theoretical way of looking at change (pun intended, since I think this is the "atheoretical" or commonsense view).

Even consider your example of "imprisonments". Only pieces of me are guilty. And pieces of me are totally innocent. I never changed from being innocent to guilty. It has always, eternally (hence "eternalist") been true that those parts of me are guilty and these parts are innocent. It just isn't intuitively what we mean when we say that "he used to be an innocent person, but now he has changed and become a murderer".

Alexander R Pruss said...

"Only pieces of me are guilty. And pieces of me are totally innocent."

This comes up on anybody's view on which we have proper parts. If I think an unkind thought about my neighbor, my big toe is not at all guilty. :-)

Guilt and innocence are attributed to a person in certain respects. I am guilty in *this* action, and innocent in *that* action.

As for eternal shape, the presentist who isn't an open futurist also thinks it's eternally true that I am sitting at t1, and eternally true that I am standing at t2.

Michael Gonzalez said...

My point was that, as a moral agent, I have not committed any crimes. If I change in my character and become a criminal, this seems dramatically different from just saying that parts of my body are guilty and other parts are not. We condemn people as wholes, do we not?

Doesn't the idea that I am both eternally sitting peacefully at t1 and eternally punching someone in the face at t2 cause a problem for causality? Or, at least, for causal allocation? Doesn't it seem very much like Monadism, where God has simply created the whole picture at once, and is really the cause of everything in it?

On the topic of "spatializing time", does it really not seem to you that, when we say "X changed", we don't mean that it is shaped differently at different points along an axis? I don't mean to press the issue unnecessarily, but I don't see how this has been addressed at all. "Change" is supposed to mean that "x stopped being one way and became another way". On the eternalist picture this never happens.

Alexander R Pruss said...

Few people are wholly good and few if any are wholly corrupt. We praise people in some respects and castigate them in others.

As for causation, unless one takes an open future version of presentism, the presentist will agree that it's eternally true that event A at t1 causes event B at t2.

Michael Gonzalez said...

Respects and body parts are not really the same thing, are they? Pruss, I have to say, I am rather bewildered the more I think about moral accountability on the eternalist view. Each segment of me, which is having different beliefs, different desires, and different actions, should really be regarded as a different person, shouldn't it?? Heck, even if I were one head out of several on some many-headed being, it would be clear that my thoughts and desires and beliefs have nothing to do with those of the other heads!

I guess I've always taken an open future view. I think it's currently true that A was the cause of B. "It is true" is already in the present tense, so I'm not sure I can even accommodate a statement of the form "it is eternally true that...". That's something I need to work on some more. It just seems to me that the counterfactual analysis of the causal relation doesn't make much sense if God created all the points in time simultaneously. The only counterfactual causal relation seems to be "if God had not created it this way, it wouldn't all be this way!"

Alexander R Pruss said...

I don't think a segment of me is a person. It's too temporally short to do anything. Even consciousness takes time. (Because of this, I am not sure that there could be consciousness on presentism.) Rather, I am one person, either a four-dimensional entity or a multiply located three-dimensional entity. But just as this person would synchronically exhibit multiple (well, two) centers of consciousness in a split-brain experiment (which I hope isn't going to happen to me), he diachronically exhibits multiple centers of consciousness. In the split brain case, I could be guilty in one respect (the left brain, say) and innocent in another (the right brain, say). Likewise, I can be guilty in respect of one time and innocent in respect of another.

You seem to write as if on eternalism all the points of time are simultaneous.

Michael Gonzalez said...

You seem to contradict yourself in that last post. Perhaps I'm not reading it correctly. It seemed like you said that a segment is too small to do anything (even think), but then went on to say that a segment could be guilty while the other could be innocent. Perhaps you mean that some collection or cluster of segments can collectively be guilty of an action, but then they can likewise have a thought (indeed, perhaps the thing their guilty of is a sinful thought). And, if a cluster or collection of segments can have a thoughts, beliefs, desires, etc, then by the typical definition of "person", I would have to regard that as another person. Indeed, if I'm understanding your split-brain analogy, and there are separate streams of consciousness going on, then I would say there are two people, not one. They may both think they are the same person, and perhaps they were both formed from the same person, but then so are twin daughters ;-) Seriously, I don't see how a segment or collection of segments which is having different thoughts, beliefs, desires, etc than I am can be me. It falls under the opposite of the principle of identity of indiscernables, doesn't it? Much like on a many-headed beast, only some of the heads may be having wicked thoughts; others might be having virtuous thoughts. By virtue of their separate streams of consciousness, we would regard them as different people with different moral standing.

They do seem to be rather simultaneous from a 4-d standpoint. God certainly doesn't create one piece and then create the other. He just eternally sustains all of it in being. As you said "I am eternally sitting at t1 and eternally standing at t2". So that one, eternal moment is all there is. And God is eternally causing each piece of it, just like in Monadism.

Alexander R Pruss said...

An instantaneous segment is too short for consciousness, while guilt and innocence can be localized to persons over an interval of time, of non-trivial length.

Ontologically, all the thoughts are had by me. But they are had by me differently: some are had at t1, some at t2, and so on. Likewise, in a split brain experiment, all the thoughts would be my thoughts, but some would be had in respect of the left half brain and some in respect of the right half brain. Compare how a watermelon is green in respect of the outside and red in respect of the inside.

Alexander R Pruss said...

"God certainly doesn't create one piece and then create the other."

Creation can be considered on the side of the agent and on the side of the effect. On the side of God, God's creating A and God's creating B can be simultaneous actions, but their effects are not simultaneous.

This happens with us. We do two things at one time, but their effects are at different times.

Michael Gonzalez said...

"An instantaneous segment is too short for consciousness, while guilt and innocence can be localized to persons over an interval of time, of non-trivial length."

To be guilty, some collection of segments must be able to commit a particular sin. That sin may itself be a wicked thought. Therefore a collection of segments can have a thought. And, if the collection has it's own thoughts, then it is its own person. If the green part of a watermelon had a stream of consciousness, beliefs, desires, etc, and such was different from the stream of consciousness, etc, had by the red part, then I would say there are two people in the watermelon. Imagine my many-headed being for a moment, please. Let's say that each of the heads has different beliefs, desires, etc (and obviously is experiencing different things than each other head, since, at the very least, it experiences the other heads as being in certain locations relative to it). This is sufficient to make each head its own person. Indeed, perhaps this is a hydra, and some of the heads are going to try to kill me; but it's conceivable that some of the other heads might try to save me. By the indiscernibility of identicals, I can't consider those to be the same person. What difference does it make if the many-headed beast is a four-dimensional object, and so some of the heads extend in that direction rather than one of the usual 3?

"We do two things at one time, but their effects are at different times."

That seems to miss the point that God is not just doing two causes simultaneously; He is also doing all of the so-called effects. He is doing each thing. He is as much the cause of the things that seem to be causes as He is the cause of the things that seem to be effects. In other words, just as God can cause a snowflake here and a supernova elsewhere, He can also cause a punch here and a hurt cheek nearby! It's Monadism. It's just a pre-established harmony, in which God is the cause of each thing rather than starting a Universe off and then dynamically interacting with it as it evolves and changes.

Wesley C. said...

I've always wondered what extra dimensions of time were supposed to be. Like what does it even mean for there to be a 2nd or 3rd dimension of time? What even is a temporal dimension exactly, and how do extra temporal dimensions relate to causality as a feature of time?

Alexander R Pruss said...

My view is that a dimension is temporal provided that it has the right kind of correlation with causation---that there is a directionality along that dimension which is sufficiently correlated with a mostly unidirectional causal nexus.

Now imagine a spacetime with five dimensions, x,y,z,w and t. Suppose that there are exactly two kinds of physical objects, the alphas and the betas. Alphas interact with alphas and betas interact with betas, but alphas and betas don't interact with one another. Alpha-causal interaction is strung out unidirectionally along the w-axis. Beta-causal interaction is strung out unidirectionally along the t-axis. I think if the causal structure of the world were like that, it would be reasonable to say that there are two time dimensions.

Could one have a two temporal dimensions without such a division into two different types of physical objects that do not mutually interact? I think so. Our world's having a temporal dimension would not be threatened by the existence of simultaneous causation, as long as there was enough non-simultaneous causation to yield a directedness in the causal nexus. So if sometimes an alpha causes a beta or vice versa, as long as there are two clearly discernible directednesses to the causal nexus, I think it is reasonable to say that there are two temporal dimensions.

A related and even harder question is what makes a dimension be a spatial dimension. There are dimensions that are neither spatial nor temporal. For instance, any colored object in the world occupies a region of RGB color "space", but being purple -- i.e., occupying some place near the point (1,0,1) in color "space" -- isn't really a form of spatiality. My best answer is that some dimensions are spatial provided that two objects' having closeness with respect to those dimensions correlates with an increase in the causal powers that they have to affect one another. Purplish objects aren't more apt to affect purplish objects than greenish ones, and so color "space" is not really space.

I'm also fond of, but do not endorse, the early Kant's reduction of space to gravitational force. One might say (I am not sure that this was *exactly* what the early Kant said) that the distance between two objects is nothing but the square root of G m1 m2 / F where F is the gravitational force.

Heavenly Philosophy said...

Since God is causally active everywhere, does this view of space entail omnipresence?

Alexander R Pruss said...

Or at least infinitely close to everything? Nice observation!