Tuesday, February 5, 2013

An argument against the possibility of instantaneous causation

Instantaneous causation is causation where the cause and effect both occur at the same instant. It's a species of simultaneous causation, with the added condition that the events are instantaneous.

Suppose that instantaneous causation is possible. Then the following are compossible characters: the Judge, who instantaneously stamps death warrants, and the Executioner, who executes the person listed on the warrant in such a way that the very instant that the death warrant is stamped, the person is dead. Moreover, the Executioner takes no orders from dead people: she only executes people if the Judge was alive at the instant the warrant was stamped, and she executes no one else.

There is no metaphysical absurdity if the Judge stamps a warrant for your death—there is "merely" an injustice. But what if the Judge stamps a warrant for his own death?

Then, instantaneously, the Executioner executes the Judge. But then the Judge wasn't alive to stamp the warrant (and if he stamped it posthumously, then that doesn't count). But with no warrant stamped, the Executioner didn't do anything. And so the Judge both is and is not executed, which is absurd.

Now, we might conclude from this just that it's not possible for the Judge to stamp a warrant for his own death. And we could tell stories similar to banana-peel stories from the Grandfather Paradox: if the Judge were to go to stamp his own death warrant, he'd slip on a banana peel, or the stamp would be out of ink, or some other such thing would happen. But many philosophers are unsatisfied with such stories. It sure seems like it's no harder in principle (though it may be psychologically harder, though only if he knows it's his) for the Judge to stamp his own warrant than anyone else's.

It seems that a particularly good way to explain the impossibility of the setup, without any banana peels, is that instantaneous causation is not possible. In any case, people who think the Grandfather Paradox establishes the impossibility of time travel should think that this argument establishes the impossibility of instantaneous causation.

But what about the intuition one might have that instantaneous causation is possible? Here is a suggestion. Let the date of an event E be the temporal duration between the beginning of the universe and the event. (If the universe has no beginning, choose some other base for dates, with dates before it being negative.) Then our intuition that instantaneous causation is possible can have some justice done to it by saying that it is possible to have causation where the cause and effect have the same date, even though they are at different instants. These instants, then, have no duration between them. Thus, we could have the Judge and Executioner story work like this. There is a duration T (say, in seconds) from the beginning of the universe at which there is an instant, a, at which the Judge stamps his death warrant. And with no temporal gap, no duration in between, there is another instant b, at which the Judge is dead, also duration T after the beginning of the universe. (And between a and b there will be other instants, such as the instant when the Executioner sees the stamping and the instant when she initiates the causal process that kills the Judge. Quite possibly, in this story time is not dense.)

This does some justice to our intuition that there can be instantaneous causation. It's not quite instantaneous causation, but it's causation with no temporal extension, no temporal gap.

Acknowledgment: I got the warrant-stamping from Jon Kvanvig. It works better rhetorically than the instantaneous writing of the warrant that I initially had in mind.


Richard A. Christian said...

I’m not sure your argument works, let S= the Judge, F= the warrant, G= the executioner.
(1) If at an instant t S stamps F, then G executes S at t.
(2)If G executes S at t, then S is dead at t.
(3) If S is dead at t, then it is not the case that G executes S at t.
But you tell us to suppose the antecedent of (1), but that has the logical consequence that (4) If at an instant t S stamps F, then it is not the case that G executes S at t. And (1) and (4) can’t both be true. Does this undermine your argument? I take (3) from “Moreover, the Executioner takes no orders from dead people: she only executes people if the Judge was alive at the instant the warrant was stamped, and she executes no one else.”

Alexander R Pruss said...

Exactly, there is a contradiction. But if instantaneous causation is possible, the situation should be possible. After all, it's possible for the Judge to stamp someone else's warrant, so why not his own?

Richard A. Christian said...
This comment has been removed by the author.
Richard A. Christian said...

Can we use a similar argument for non-instantaneous causation?
(1) If at an instant t S stamps F, then G executes S one second after t.
(2)If G executes S one second after t, then S is dead one second after t.
(3) If S is dead one second after t, then it is not the case that G executes S one second after t. (since in my scenario she only executes people who are alive at exactly one second after t)
But if non-instantaneous causation is possible, the situation should be possible. After all, it's possible for the Judge to stamp someone else's warrant, so why not his own?
Just wondering how you would reply to that.
“if instantaneous causation is possible, the situation should be possible” why? The Judge can stamp his own warrant but the executioner wouldn’t be able to deliver because he is faced with an impossible task, I can image the executioner saying to the Judge “hey, I can’t execute you at T since you have to be alive at T to stamp the warrant, I can’t make it such that you’re dead and not dead at the same time”. Also, (2) and (3) entails that if the executioner executes the Judge at T, then she does not execute the Judge at T.It doesn't matter if the argument has these contradictions independent of (1)?

Alexander R Pruss said...

Your story still has instantaneous causation. To execute only people who aren't dead at t, one has to notice that the person isn't dead at t. And that noticing is a causal process presumably, which is instantaneous.

Anonymous said...


I think this argument only applies to certain kinds of instantaneous causation. After all, I think we have at least one bona fide example of instantaneous causation in the EPR paradox, and it doesn't seem to me as if this argument would be applicable in that case.

Alexander R Pruss said...

Whether in EPR cases you have instantaneous causation will depend on what you think happens in those cases. You might think the causal story is this. I initiate an observation of the spin of one of the particles. This non-instantaneously causes two simultaneous effects: (1) my observing of the spin and (2) the collapse of the wavefunction (at both spatially isolated locations, of course). There is no instantaneous causation here.

Now you might think that one particle's acquiring of definite spin instantaneously causes the other particle's acquiring of definite spin. If so then you may have instantaneous causation. But it seems to me to be much more natural to think of your observation as interacting with a non-local reality, the entangled wavefunction.

There is still a possible instantaneous causation in quantum collapse, even apart from EPR, on the traditional interpretation. For on the traditional interpretation, the observation triggers collapse. But now it seems we have three simultaneous and instantaneous events:
1. The observing.
2. The collapse to a pure state.
3. The observing of the pure state.
And it seems that 1 causes 2 and 2 causes 3.

This could be true instantaneous causation. For there need be no observing prior to the observing of the pure state.

But it is very weird to think of 1 as causing 3. On plausible coarse-grained accounts of events, 1 and 3 are the very same event. My seeing right now is the same event as my seeing of this computer screen.

It seems preferable instead to take the sequence: There is some cause C of my observing. This cause then causes the collapse to a pure state. And the collapse to a pure state makes the observing be an observing of the pure state. All of these events might happen on the same date, but at different instants.

Anonymous said...


Those are all interesting points...

Here's another possible scenario of "instantaneous causation" for you to consider: if you think the past is finite then it seems to me that the kalam cosmological argument (KCA) plausibly gives you an instance of instantaneous causation.

Alexander R Pruss said...


Anonymous said...

My understanding is that KCA wants to say that the temporal world was brought into being by some external cause. However, that cause (for obvious reasons) could scarcely have temporarily preceded the effect that is the temporal world. So, the cause must be simultaneous with the effect in this case.

Do you see a problem with this line of reasoning?

Alexander R Pruss said...

The cause could be outside of time. Probably, that's the best way to take it, no?

Anonymous said...

"The cause could be outside of time. Probably, that's the best way to take it, no?"

In light of your recent argument against instantaneous causation I suppose it might have to be an atemporal cause. :)

I am not sure why, but at some point I developed an allergy to the idea of an atemporal cause having a temporal effect. However, that's starting to look like rank prejudice right now.

Alexander R Pruss said...

I think a take in the spirit of Bill Craig would be that God exists in an undifferentiated moment that has infinite duration prior to creating. God at that moment then creates a universe-at-the-first-differentiated-moment. So there are two moments: God's undifferentiated eternally long moment and the first moment of creation.

I don't like this on theological grounds--it seems to make God change. Metaphysically, can a moment have duration? I don't know.

Anonymous said...

"I don't like this on theological grounds--it seems to make God change. Metaphysically, can a moment have duration? I don't know."

I don't either. It's deeply perplexing stuff.

David Gordon said...

A weakness of this example is that it depends for its force on the stipulation "the Executioner takes no orders from dead people: she only executes people if the Judge was alive at the instant the warrant was stamped, and she executes no one else."
The argument doesn't show that instantaneous causation is intrinsically metaphysically or physically impossible; instead, it only shows that instantaneous causation can't be combined with a particular legal arrangement.

Alexander R Pruss said...

Or one could suppose that there can't be uncaused events and there is nothing else that can cause the stamping.

Scott said...

I think the problem with Pruss’ example is not instantaneous causation, but rather circular causation. Now some forms of circular causation are acceptable, like if I throw a ball against a wall and the ball bounces back and hits me. But these circular causal chains always seems to be accidentally ordered series and this not dependent on the first cause. What Pruss idea is describing is an essentially ordered circular causal series. It is tricky because it is roundabout. There is a sense in which both the Judge and Executioner are the first causes of the series. The judge requires life to stamp. The judge is essentially dependent for his life (and stamping authority) on the executioner not killing him. The judge however is the essentially ordered cause of the execution (by stamping. So you have a case of A depends on B and B depends on A in the exact same way.

Examples could be multiplied. When a small piece of metal gets to 0 degrees Celsius a robotic heating device instantaneously senses it and heats it to 100 degrees Celsius. The piece of metal is now 0 degrees Celsius and 100 degrees Celsius at the same time. The reason this seems logically possible for other objects but not the object at the beginning of the causal chain is because of the circularity introduced. The instantaneous nature is somewhat tangential to the issue.

Wesley C. said...

Another thing about the example is that it's an ONLY IF structure, and it could be argued that instantaneous causation can't have such a structure but that it's still logically possible. So actions like destroying a glass ONLY IF it also exists at instant t1 are impossible because causal reactions with that structure can't work like that and produce a contradiction. But other possible instantaneous causations could work.

For example, someone could instantly act and change something in an instant without that depending on the thing being presently unchanged in that instant as well.

Alexander R Pruss said...


I think what is central to the argument is the intuition that it is *no harder* for the Judge to stamp the warrant for his own death than for anyone else's. If instant warrant-signing of someone else's warrant is possible, why not of the Judge's?

Here's another way to look at it. If the Executioner takes a coffee break, there is no difficulty with the Judge stamping the warrant. But why should whether the Executioner took a coffee break affect whether the Judge can stamp the warrant?

Scott said...

The Executioner taking a coffee break would break the circularity. Now you would have A causing B and then the causal chain would stop. It does not seem intuitive, but I feel like this example extends beyond our intuitions.

Maybe this example would help. Suppose you have a square on a screen (like an old 80’s video game). It seems fairly intuitive to say that if you move left, that simultaneously moves the square down. Therefore any move to the left actually will be a move diagonally down and to the left.

But it seems absurd to say that moving to the left could simultaneously move the square to the right. Such a move would really be no move at all. And motion and non-motion are contradictions. But that the fact that some types of simultaneous movements are impossible does not entail that all simultaneous movements are possible. And I think if you want to extend the argument to the general case (rather than the specific circular case), you are going to need further argumentation.

Mariel. C said...

Mr Pruss, you don't believe in simultaneous causation? Isn't it considered in general an important point for Classical Theism?

Alexander R Pruss said...


Why? God isn't in time, so God's causation won't be simultaneous with anything. I suppose one might use simultaneous causation to counter the principle that all causation requires temporal priority, but one might just say that that principle is not itself justified.

Alexander R Pruss said...

I should also add that it's not accurate to say that I don't believe in simultaneous causation. It's true that eight years ago I made up this argument. But I promptly forgot it. In fact, I used the possibility of simultaneous causation in various arguments since then. :-)

Now that I see the argument again, I do find it fairly persuasive, especially since it has some nice parallels to what I say in my causal finitism book.

Unknown said...

Just thinking out loud, but could we make a distinction between instantaneous and simultaneous causation? Take me pushing a chair around (the example is Garrigou-Lagrange's, I think). If we were to view time as continuous (and hence, deny the reality of instants), it still seems quite plausible to say that my pushing the chair is simultaneous with the chair being pushed. In fact, both would be two different descriptions (from the point of view of the cause and from the point of view of the effect) of the same temporally extended causation event.

It seems to me that denying simultaneous causation severely damages many of the classical theist's arguments for God, which rely on there being hierarchical or per se causal series. If simultaneous causation is not a thing, then it seems that all purportedly hierarchical series collapse into linear or per accidens series (from instant to instant).

Alternatively, do you think the judge-argument leaves room for denying the possibility of only some kinds of instantaneous causation, but not others? Maybe those which, like the example given, involve two distinct causal events (the judge stamping the death warrant + the executioner executing). It seems weird to say that, if time is indeed made up of instants, something like thinking could not possibly be an instance of instantaneous causation. We would need to say that I think in t1 but that my thought comes into existence in t2. Anyway, I'm probably just rambling :)

Thanks for your work, Dr. Pruss!

Alexander R Pruss said...

I do not think one needs to rely on per se causal series in cosmological arguments.

But one limitation of the argument is that it only applies to event causation. That might help with the thinking case.

Wesley C. said...


I think your Judge-Executioner problem is a specific example of a more general principle - for example, imagine instead that the Executioner acted alone and wanted to execute the Judge without the Judge's permission at instant t1 IF the Judge was alive at instant t1. But in that case the Judge would be dead at t1 and so the Executioner wouldn't act, which means the Judge wouldn't be dead etc etc - leading to a contradiction.

So what this means is that the nature of instants is such that "if X obtains, then Y causally acts against X" is impossible in an instant, but this doesn't in any way at all imply that all instant causation as such is impossible.

For example, you already mentioned how the Exec killing someone else that the Judge writes a warrant about and how it doesn't seem inherently contradictory - such a structure of "if X obtains, then Y does Z" doesn't seem inherently contradictory since it's not Y acting against a presupposed X.

Of course, you could say that such a linear structure is also incoherent because there is still a jump from one thing to another - only one X can obtain in one instant, and/or the idea of THEN contradicts the nature of instants since it's a carrying-over-modifier which can't obtain in one instant even if it's viewed as a logical relation rather than a temporal one.

But even in that case, instant causation could still be possible since instant events are still a coherent concept - even if structures like "if X obtains, then Y does something" are impossible in a single instant, one could divide this into 2 or 3 instants whereby in the first instant X obtains then in the second one Y does something, or in the second one Y chooses to do something, and then in the third one something is finally done.

Wesley C. said...


Also, now that I think about it, there are some other considerations here. For one, the relation "Intact-Coffee-Cup AND broken-wine-glass" is a simple logical conjunction of states of affairs that can clearly apply in a single instant. So the question is whether or not the relation between them could be causal or even conditional - namely, if the Coffee Cup is intact then the Wine Glass will be broken, all in a single instant.

And there doesn't seem any reason as to why causal relations can't apply to instants - in fact, it seems that the reason why the structure "if X, then Y causes Z" seems weird or absurd in a single instant is because of subconscious associations with linear temporal causation; we ordinarily think of an agent noticing something, then deciding to do something and then causing something to happen when thinking of causal relations.

But this would be misleading in the case of instants - by definition instant causation isn't linearly temporal, and any agents acting during instants don't function in linear temporal steps either. So since we can coherently talk about causality applied to instants, it seems that instant causation isn't completely incoherent either.

Unknown said...

Dr. Pruss, could you clarify what you mean by "one limitation of the argument is that it only applies to event causation. That might help with the thinking case". I'm not sure I get it. Thanks!

Mariel. C said...

Well, principally because God would sustain existence at every moment or is existence itself (though maybe this is more related to the essence/existence distinction). That is kind of the Classical Theist view. Otherwise, wouldn't be a kind of neo-classical Theism?

Unknown said...

that paradox only eliminates certain cases of instantaneous causes, but I don't think it eliminates all possible cases of instantaneuos causes.

Alexander R Pruss said...

Right, but there is a general strategy of arguing from paradoxes which goes as follows: We have a paradox in case A; but it would be weird if case A were impossible and case B were possible; so case B is impossible.

For instance, in the Grim Reaper paradox, the strategy goes as follows. It is impossible for the GRs to have their alarms set for 30 minutes after noon, 15 minutes after noon, 7.5 minutes after noon, and so on. But it would be weird if that was impossible, while it was possible for their alarms to be set for 30 minutes before noon, 15 minutes before noon, 7.5 minutes before noon, and so on. After all, imagine that they are set the second way. What would prevent each of them from flipping to the other time? So, it's impossible both ways.

Now, go back to the judge and executioner paradox. Imagine the Judge is named Wilhelm and has two warrants on her table, one for Wilhelm and one for Wilhelmina. She can't stamp the Wilhelm one. But it would be really weird if she could stamp the Wilhemina one and not the Wilhelm one. So she can't stamp either. So we can generalize. And so on.