Suppose we have an infinite regress of chickens and eggs, with no first item, and suppose that if there is any last item, it’s not a chicken.
Plausibly, then:
- The plurality of the chickens explains the eggs.
But also plausibly:
- If x has an explanation, then x has a fundamental explanation.
However:
No plurality of chickens and eggs fundamentally explains the eggs.
So, something that is other than a plurality of chickens and eggs fundamentally explains the eggs.
Why is (3) true? Well, there are two kinds of chicken and egg pluralities.
- Pluralities with an earliest item.
- Pluralities with no earliest item.
A Type I plurality does not explain the chickens and eggs, because it does not explain any chickens and eggs earlier than the earliest item in the plurality.
A Type II plurality at best non-fundamentally explains the eggs. For given a Type II plurality, choose any item x in the plurality. Item x is a chicken or egg, and there is an earlier chicken or egg y in the plurality. Since y explains x, by a plausible case of transitivity, the subplurality where we drop x also explains the eggs. So the initial Type II plurality did not fundamentally explain the eggs.
Since every plurality of chickens and eggs is of Type I or Type II, we have (3).
The argument above applies beyond chickens and eggs. Suppose:
- Every physical item in the world is caused.
Then:
- Either there is a physical item with a non-physical cause or every physical item has a physical cause.
Add:
There are no loops of physical causes.
Physical causation is transitive.
As I show in my 1999 paper using Zorn’s Lemma, if every physical item has a physical cause, it is then possible to partition the physical items into an “even” and an “odd” subset, where every item in the even subset causes an item in the odd subset, and every item in the odd subset causes an item in the even subset. Call the odd items “eggs”. Call the non-final even items “chickens” (a non-final item is one that causes a further physical item). Then, plausibly, the chickens explain the eggs. By the argument above, something non-physical thus explains the eggs. Anything non-physical that explains the eggs explains all of physical reality (because for any physical item, it is either an egg or there is an egg prior to it). So:
- There is a non-physical item that explains all of physical reality.
I think the thing that needs the most defense is premise (2). It’s somewhat close to causal finitism.
3 comments:
The Type II step concludes non-fundamentality from the dispensability of any single member. But doesn't that presuppose that a fundamental explanation must be irredundant, that no proper part of it could do the same explanatory work? The Hume-Edwards defender denies exactly this: he holds that the infinite collection explains as a whole, and its members' individual dispensability is a feature of regresses, not a defect in their explanatory standing. So is the Type II argument establishing that no infinite plurality is fundamental, or is it building irredundancy into 'fundamental', in which case the weight isn't on (2) but on a fundamentality-standard that the regress-defender has independent reason to reject?
To be clear, I do not endorse that view, I am just worried that could be a valid critique.
Yeah, that step is hard. Here's a thought. Take a finite collection, consisting of A causing B causing C causing D. Then the subcollection consisting of A and B and C explains D. But it clearly doesn't explain it fundamentally. Why not? Because A and B is a *more* fundamental explanation of D than A and B and C. (I am assuming that if X is more fundamental than Y, then Y isn't fundamental. One might challenge that. Maybe there are degrees of fundamentality among fundamentals. I think this is a red herring, but it requires more thought.) The dispensibility of C seems to be a good explanation of why A and B and C is not a fundamental explanation of D. And why should the infinite case be different?
Thanks, that finite case is clarifying, and I think it actually sharpens where my worry lives. You're right that in A→B→C→D the dispensability of C is a good reason {A,B,C} isn't fundamental: dropping C moves you toward A, the ground, so "more fundamental" has a clear sense there. But that seems to be exactly because the chain has a least element. In the Type II case there's no ground to move toward, pruning a member just yields another groundless tail, order-isomorphic to the original, no nearer any bottom, so I'm not sure "a proper part is more fundamental" even has content there. So my hesitation isn't about the conclusion; it's about the route.
And I should be clear where I actually stand: I'm not defending the groundless regress, I'm quite sympathetic to the view that Type II collections fail to explain, for the sort of reasons you'd press. My worry is only that the dispensability argument might be borrowing its force from the finite, well-founded case, when the real work against Type II is being done by groundlessness itself rather than by minimality. If that's right, (3) is still true, but perhaps for the reason you'd give directly rather than via dispensability. Does that seem like a distinction that matters, or am I over-separating them?
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