Monday, February 14, 2022

A cosmological argument from the Hume-Edwards Principle

The Hume-Edwards Principle (HEP) says:

  1. If you’ve explained every item in a collection, you’ve explained the whole collection of items.

This sounds very plausible, but powerful counterexamples have been given. For instance, suppose that exactly at noon, cannonball is shot out of a cannon. The collection C of cannonball states after noon has the property that each state in C is explained by an earlier state in C (e.g., a state at 12:01:00 is explained by a state at 12:00:30). By the Hume-Edwards Principle, this would imply that C is self-explanatory. But it plainly is not: it requires the cannon being fired at noon to be explained.

But I just realized something. All of the effective counterexamples to the Hume-Edwards Principle involve either circular causation or infinite causal regresses. We can now argue:

  1. HEP is necessarily true.

  2. If circular causation is possible, counterexamples to HEP are possible.

  3. If infinite causal regresses are possible, counterexamples to HEP are possible.

  4. So, neither circular causation nor infinite causal regresses are possible.

  5. If there is no first cause, there is a causal circle or an infinite causal regress.

  6. So, there is a first cause.

Similarly, it is very plausible that if infinite causal regresses are impossible, then causal finitism, the thesis that nothing can have an infinite causal history, is true. So, we get an argument from HEP to causal finitism.

Dialectically, the above is very odd indeed. HEP was used by Hume and Edwards to oppose cosmological arguments. But the above turns the tables on Hume and Edwards!

Objection: Not every instance of causal regress yields a counterexample to HEP. So it could be that HEP is true, but some causal regresses are still possible.

Response: It’s hard to see how there is sufficient structural difference between the cannonball story and other regresses to allow one to deny the cannonball story, and its relatives, while allowing the kind of regresses that are involved in Hume’s response to cosmological arguments.

Final remark: What led me to the above line of thought was reflecting on scenarios like the following. Imagine a lamp with a terrible user interface: you need to press the button infinitely many times to turn the lamp on, and once you do, it stays on despite further presses. Suppose now that in an infinite past, Alice was pressing the button once a day. Then the lamp was always on. Now I find myself with two intuitions. On the one hand, it seems to me that there is no explanation in the story as to why the lamp was always on: “It’s always been like that” just isn’t an explanation. On the other hand, we have a perfectly good explanation why the lamp was on n days ago: because it was on n + 1 days ago, and another button press doesn’t turn it off. And I found the second intuition pushing back against the first one, because if every day’s light-on state has an explanation, then there should be an explanation of why the lamp was always on. And then I realized this intuition was based on somehow finding HEP plausible—despite having argued against HEP over much of my philosophical career. And then I realized that one could reconcile HEP with these arguments by embracing causal finitism.


swaggerswaggmann said...
This comment has been removed by a blog administrator.
swaggerswaggmann said...

And in the first case of course, you didn't take the firing moment into account, so you never actually explained every item in the collection... Quite sad.
Quite funny that you try to use circular causation and infinity to attack the principle, as then you already
6 is wrong there can be multiples simultaneous causes (assuming PSR for the sake), but no first.

ASBB said...

Didn't you already offer this argument in Infinity, Causation and Paradox pp.29-30? Did you just (re-)discover this argument?

Alexander R Pruss said...

One comment removed due to sarcasm.

Alexander R Pruss said...


Once I write something, it is transfered from my mind to the new medium, and so of course it doesn't remain in the mind. :-)

Alexander R Pruss said...

Might be worth noting what I said in the book: "Thus we have an argument, from HEP plus the fact that infinite regresses are not explanatory, for the impossibility of infinite regresses. But this argument is not very compelling, as HEP is not very compelling in infinite cases."

I now think that I may have underestimated how compelling HEP is in full generality. I'm kind of feeling that some of the force of the Bill Craig style arguments against forming actual infinites by successive addition might have something to do with HEP, but I can't quite my finger on it.

cmfox said...

This might not be entirely related, but I’m curious how you would answer the problem of divine simplicity entailing modal collapse (and entailing that God is not really free in the libertarian sense). And, on the other hand, if divine simplicity is not true, then I’m troubled with the idea of God really being necessary after all. If God possesses “parts” in a metaphysical sense, then how come God happens the being which is distributed across all possible worlds, rather than any other being which too possesses parts? This has probably been the most troubling dilemma for me regarding God’s existence.

Alexander R Pruss said...

A user given to sarcasm and other language that lacks the proper tone for academic discussion has been banned. New comments from that user will be automatically and periodically deleted by a bot. If the user wishes to be reinstated, they should email me about their plans to improve their manners.

Alexander R Pruss said...


I have a number of posts on free will and divine simplicity, and an extended discussion in this paper: (if you don't have access, I can email it).

RunDec said...

Do you have any intention to write more on the Gap Problem any time soon?

I get the feeling that at this point a lot of progress has already been made on Stage 1 and more and more atheists have been trying to block the argument by focusing resistance on Stage 2.

Caio said...

Dr. Pruss, do you find the versions of the Littlewood-Ross and Thomson lamp paradoxes formulated by Joe Schmid in his article on causal finitism convincing?

Alexander R Pruss said...


Not so much...


I should at some point.

Dominik Kowalski said...

Do I understand you correctly that the HEC-Principle isn't able to answer all possible/reasonable why-questions? Applying your argument on another example (Anthony Kenny's eternally moving Atom), I assume that you would then say that the collection of moments lacks the sufficient explanation for why the atom has a specific direction rather than another?

Sam Harper said...

I'm really curious what think about whether arguments for causal finitism can be applied to the future. Do they mean the future is also finite? And I don't mean finite in the sense that it will always be the case that only a finite number of days will have passed between "now" and some arbitrary point in the past. I'm talking about the actual future. Are there an infinite number of days that WILL happen?