Tuesday, September 29, 2015

Infinite causal histories and causal loops

As I was thinking about causal finitism, the view that nothing can have an infinite causal past, I realized that there were structural similarities between the arguments for it on the basis of paradoxes like the Grim Reaper and Grandfather-like arguments against causal loops. And that led me to thinking whether there wasn't some way to generalize causal finitism so as to rule out both infinite causal pasts and causal loops.

There is. Here is one way. Say that a causal nexus is a network of nodes with partial-causation arrows between them, such that there is an arrow A→B if and only if A is a partial cause of B (or causally prior to? I think that's the same thing, but I'm not sure; or, if there is such a thing, directly causally prior to). Say that a monotonic sequence in a causal nexus is a finite sequence A1,A2,...,An of nodes such that each node is joined with an arrow to the next: A1→A2→...→An. The sequence culminates in An. Note that if there are causal loops, then a monotonic sequence can contain the same node multiple times.

The generalization of causal finitism now says:

  • No metaphysically possible causal nexus contains a node that is the culmination of infinitely many monotonic sequences.
This rules out three kinds of causal nexuses:
  1. Infinite regresses: longer and longer monotonic sequences of distinct nodes culminating in a given node.
  2. Infinite cooperation: infinitely many arrows pointing to a single node (and hence infinitely many monotonic sequences of length two culminating in it).
  3. Causal loops: longer and longer repeating monotonic sequences culminate in a given node (e.g., A→B, B→A→B, A→B→A→B, ...).

The possibility of handling infinite causal histories and causal loops--which I've long thought absurd--in the same framework makes me even more confident in causal finitism.


Anonymous said...

The problem with this is that it is not true in general. An efficient cause can be the efficient cause of the final cause, and the final cause is the final cause of the efficient cause. So you have a causal loop. The same thing happens with material and formal causality.

I agree that you cannot have a loop or an infinite sequence if your chain of causality is all of the same type.

Alexander R Pruss said...

The "final cause" understood in this way isn't really a cause. When A acts to achieve B, so that B is the "final cause" of A, then the existence of B doesn't do anything to explain A's activity. To see this, consider a case of final causation: a dog drinks to hydrate the body. The hydration of the body is the final cause. But suppose that the dog is sick and it vomits before the drink hydrates the body. It is still true that the hydration of the body was the final cause of its drinking. But in this case the hydration of the body never occurs. So the "final cause" in this sense need not even exist to explain the activity. But real causation is a relation between real relata. A final cause understood like this is a cause only in a manner of speaking.

It is better to understand final causation where the final cause is something like a representation of the effect the causation is directed towards, a representation found in the efficient cause.

Heath White said...

Alex, have you given any thought to what a node is? If it is a substance, then two substances can interact with each other easily (two-body gravitation problem, for example) and you will get loops quite easily. The natural thing to say is that nodes are events. But that indicates that you should believe in event-causation, not substance-causation.

I have no brief for infinite causal chains or loops, I'm just wondering how this squares with other things.

Alexander R Pruss said...


Interesting, but I don't think interaction is partial causation. But you did inspire me to add this to the relevant part of the book:

In the above, I took the directed lines to be partial causation relations. We do
need to, however, be cautious. If two spouses cook meals for each other, then
each is a cause of a part (some cells, say) of the other. If $x$'s being a cause
of a part of $y$ is sufficient for $x$'s being a partial cause of $y$, then this
is a loop violating \dref{unified}. And when you eat, you become a cause of a part
of yourself, which would seem to be a case of partial self-causation.
However, we should not take being a cause of a part of to be sufficient for being a
partial cause of. We wouldn't say, for instance, that the D-Day Invasion was a partial
cause of World War II, though it was a cause of many battles that are a part of
World War II. There are cases where by being a cause of a part of something one is a
partial cause of it, but they are cases where one is a cause of something like one of
the initiating parts. For instance, a sperm is a partial cause of an organism by
being a cause of part of the first cell, and each German officer who ordered an initial part
of the invasion of Poland was a partial cause of World War II. To be a partial cause of
a substance- or event-like node is to be a partial cause of the existence or occurrence of
the node.

Heath White said...

I didn't realize you were confining your point to causation-of-existence. What about causation-of-change? (Maybe that's "interaction.") Infinite chains and loops don't seem any less counterintuitive in those cases. Is there a similar principle ruling them out? (And then: what are the nodes?)

Alexander R Pruss said...

In causation of change, one thing causes a new attribute of another thing.

The nodes are whatever the relata of causation are. That may include substances, events (especially on the right hand side), tropes, etc. :-)

Unknown said...

I'm wondering if there isn't a relevant difference between infinite cooperation and the other types of causal nexuses. Here's what I'm thinking: it seems to me that the problem with (1) and (3) is that in each case you never get an explanation of the given node, and you never get an explanation because the causality of each of the contributing causes is itself explained by another cause, ad infinitum. Thus, there is neither a first cause nor a totality of causality that could explain the given node. But (2) seems a little different: in that case, each cause does have its own causality (either by being a first cause, or by having a first cause) independent of the other causes with which it cooperates. So it seems like there is a sense in which there is a totality of causality in the case of infinite cooperation that is impossible in the cases of an infinite regress or loop.

Alexander R Pruss said...

Yes, there is a relevant difference. But both sorts of violations of causal finitism make for paradoxes.

Unknown said...

I guess I just don't see that paradoxes that result from infinite cooperation. Are you thinking that the Grim Reaper argument is a case of this?