Friday, February 13, 2015

Grounding overdetermination


  1. The sky is blue or snow is white.
This is grounded by:
  1. The sky is blue.
But's it's also grounded by:
  1. Snow is white.
This is a case of grounding overdetermination. I was tempted to characterize this as follows:
  1. p is grounding overdetermined iff p is grounded by q and grounded by r, and qr, and neither q grounds r nor r grounds q.
The proviso at the end ensures that grounding chains do not count as cases of overdetermination. But (4) isn't good enough. Consider this:
  1. The sky is blue or the sky has a color.
This seems to be grounding overdetermined by:
  1. The sky is blue.
  2. The sky has a color.
But (6) grounds (7), so the proviso in (4) kicks in. Oops!

This odd phenomenon is related to a deficiency of the causal analogue of (4):

  1. E is causally overdetermined iff there are C1 and C2, with C1C2, and each of them is a full cause of E and neither of which is a full cause of the other.
But counterexamples akin to (5) are easy to manufacture. Boff is a trainee exterminator and Biff is his boss. Biff tells Boff to imitate everyting he does. Biff pours a lethal dose of crocodile poison into the customer's pond. Boff imitates him and pours another lethal dose. While Biff poured first, Boff poured closer to the crocodile, and as a result both doses arrived at the crocodile simultaneously, each sufficient to kill it. The alligator's death was overdetermined by the pouring of the two doses, even though one pouring caused the other.

We could try this:

  1. p is directly grounding overdetermined iff p is directly grounded by q and directly grounded by r and qr.
And then we could say that:
  1. p is grounding overdetermined iff it is either directly grounding overdetermined or it is grounded in something directly grounding overdetermined.
(And there is an obvious analogue for causation.) But this is only plausible if grounding is transitive. Maybe what we need to add to (10) something like "in a way that doesn't generate a relevant failure of the transitivity of grounding"?

Another difficulty with (9) is that the notion of direct grounding is not so easy to define. The tempting definition of direct grounding is, after all:

  1. p is directly grounded by q iff p is grounded by q and there is no r such that p is grounded by r and r is grounded by q.
But cases of overdetermination like (5) are counterexamples to (11), since (5) is directly grounded by its first disjunct, even though the first disjunct grounds the second and the second grounds all of (5). So one wants to say:
  1. p is directly grounded by q iff p is grounded by q and there is no r such that p is grounded by r and r is grounded by q and this is not a case of grounding overdetermination.
But of course then we have circularity.

All this suggests to me that we need a notion not reducible to grounding to make the above distinctions. We might, for instance, take direct grounding to be primitive. Or overdetermination. Or maybe we could use some version of my grounding graph approach.


Michael Gonzalez said...

I've not seen the grounding graph yet, and I'm not too well-versed on this business of grounding, but, for some reason, I've never found the examples of overdetermination particularly perplexing or compelling. If the poison from Biff and Boff arrives at the same time, then they both killed the crocodile. It would be false to say that Biff killed the crocodile alone, and false to say that Boff did. The cause of the crocodile's death is poison. The cause of there being sufficient poison in the water at that moment to kill the crocodile is both Biff and Boff. Indeed, if one imagines them holding the same bucket of poison, and tipping it in together, one is not surprised that the cause is both of them, even if it would have been possible for Biff to tip the bucket in by himself.

Perhaps my nonchalance is due to not fully grasping the issues. But, for example, (5) is not problematic to me, nor is it a case of overdetermination, since the first disjunct (fully spelled out) CONTAINS the second one. The first disjunct, spelled out, is "the sky has a color which is blue".

As for the first statement, which got this whole ball rolling, I don't think it's overdetermined. I mean, sure, it would be true even if one of the disjuncts failed to be true, but the grounding of a disjunctive statement p∨q is that p, q, or both are true. So, since in this case both disjuncts are true, the grounding is the third option. If only one of them had been true, then the grounding would have been just that one.

I think the "overdetermination" question is much more interesting in terms of causality (especially when moral accountability is involved), but I've still never found a compelling example. If I stab someone in the heart while you simultaneously shoot them in the heart, and the person dies of blood loss, we are both together the cause of the person's death, even if one of us would have been sufficient. I mean, the proximal cause was that the heart was pierced and therefore not able to function. Proximal causes screen off distal causes, and it seems that our guilt for the murder comes from our having pierced the heart with the intent to kill, but his death was caused by having a non-functioning, pierced heart. If he'd been Wolverine, from the X-Men, his heart might have healed itself and death would not have happened despite both of our piercings. So, rather than considering it a case of causal overdetermination, you have one cause of death (pierced heart leading to blood loss) and you have two people guilty of murder (because we both, with intent, did something to cause pierced heart and blood loss.

What am I missing?

Dagmara Lizlovs said...

"Consider: The sky is blue or snow is white. This is grounded by: The sky is blue. But's it's also grounded by: Snow is white. This is a case of grounding overdetermination." Very good thing I'm not in Boston where there is a very real overdetermination of snow!