I wish one could formulate and defend a version of explanatory finitism, roughly saying that nothing has infinitely many explanations or an infinite chain of explanations, even if these explanations are not causal (causal finitism of course rules out the causal case). But it seems hard to do so. There do seem to be counterexamples to explanatory finitism. Here some I’m thinking about right now:
Why are there infinitely many primes? Because there are infinitely many primes bigger than two. Why are there infinitely many primes bigger than two? Because there are infinitely many primes bigger than three. And so on.
Alice has just gone to heaven. Why is she going to experience a day of bliss? Because she will have a day of bliss tomorrow. And also because she will have a day of bliss the day after tomorrow. And also because she will have a day of bliss the day after that. And so on.
Alice has just gone to heaven. Why is she going to experience bliss on every future day? Partly because she will have bliss tomorrow. And partly because she will have bliss the day after tomorrow. And so on.
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If we assume that either infinities (whether causal or explanatory) are impossible, then what would happen if God attempted to create a universe containing an infinite number of secondary causes or explanations?
Probable response: such an act is impossible. Like the creation of a square circle, it involves a logical contradiction and therefore falls outside the scope of divine omnipotence.
However, doesn't this limitation imply the existence of an arbitrary finite maximum? I mean, does it mean there is a specific finite number of secondary causes or explanations that God's creative power cannot surpass?
Why do you want to be able to formulate a defensible version of explanatory finitism? Why do you want it to be true?
No it doesn't imply the existence of an abritrary finite maximum. Say we have a being that has a power to create any natural number of stones, but not infinity stones, than there is no finite maximum (let's assume for the sake of contradiction that there is maximum natural number n, but than n+1 is a natural number also, so it can create n+1 stones, so we have contradiction so there is no maximum).
Also act/thing with certain properties may be metaphysically impossible, even if these properties don't imply logical contradiction.
A formalist could probably ground mathematical truths in finitely many propositions. Too bad formalism is false.
Actually, I think that there's a pretty straightforward strategy of defending this view. Humans have finitely many beliefs. And the structure of justification usually looks quite similar to the structure of explanation. So, whenever someone claims that they know p is true, and that p has an infinite explanatory chain, an explanatory finitist could say the *true* explanatory chain looks like the structure of their beliefs. So, what's the explanation Alice will experience infinite days of bliss? Because God has a perfectly good nature and therefore will ensure this good obtains.
It would help establish stage 1 of a contingency argument.
That there are an infinitely many primes (strictly, that there is no largest prime) is a tautology, proved in Euclid. As such, it needs no explanation; it is implied by the defining properties of the natural numbers and the usual rules of reasoning.
An explanation must be prior (I.e. ‘more explanatory’) in some relevant sense to the thing explained. That there are infinitely many primes greater that two etc., are true statements, but I’m not seeing that they have the required priority. As I see it, that statement A implies statement B does not by itself give statement A the required priority. The priority based on human reasoning goes: Euclid’s proof > infinitely many primes > Infinitely primes greater than two etc.
Similarly for Alice in heaven. Heaven is by definition or assumption a place (or state) of eternal bliss. So the conceptual priority goes: bliss every day > bliss on first day. ‘Bliss tomorrow’ etc. are true but add nothing explanatory.
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