I will give an argument for causal finitism from a premise I don’t accept:
- Necessary Arithmetical Alethic Incompleteness (NAAI): Necessarily, there is an arithmetical sentence that is neither true nor false.
While I don’t accept NAAI, some thinkers (e.g., likely all intuitionists) accept it.
Here’s the argument:
If infinite causal histories are possible, supertasks are possible.
If supertasks are possible, for every arithmetical sentence, there is a possible world where someone knows whether the sentence is true or false by means of a supertask.
If for every arithmetical sentence there is a possible world where someone knows whether the sentence is true or false by means of a supertask, there is a possible world where for every arithmetical sentence someone knows whether it is true or false.
Necessarily, if someone knows whether p is true or false, then p is true or false.
So, if infinite causal histories are possibly, possibly all arithmetical sentences are true or false. (2-5)
So, infinite causal histories are impossible. (1, 6)
The thought behind (3) is that if for every n it is possible to check the truth value of ϕ(n) by a finite task or supertask, then by an iterated supertask it is possible to check the truth values of ∀xϕ(x) (and equivalently ∃xϕ(x)). Since every arithmetical sequence can be written in the form Q1x1...Qkxkϕ(x1,...,xk), where the truth value of ϕ(n1,...,nk) is finitely checkable, it follows that every arithmetical sequence can have its truth value checked by a supertask.
The thought behind (4) is that one can imagine an infinite world (say, a multiverse) where for every arithmetical sentence ϕ the relevant supertask is run and hence the truth value of the sentence is known.
6 comments:
Hello, Dr. Pruss. On a different note, do you think that creation ex nihilo violates the material causal principle?
I don't believe in any material causal principle. :-)
I don't know if you know Felipe Léon's article against creation ex nihilo, where he argues that creation ex nihilo is incompatible with this. But I think I expressed myself badly in the previous text.
My last question to you, Pruss: do you support the thesis of existential inertia or do you reject it? If you reject it, could you explain the argument you use or point out some objection to inertia? I'm asking this because, in contemporary literature, I only see Thomistic objections to inertia."
The negative inductive argument does not work for the material causal principle because for classical theists, only an omnipotent being (God) has the power to create things ex nihilo. (I think Scotus argued for this.) So, the reason nothing appears ex nihilo is simple: God decided to creating everything ex nihilo at the very beginning. However, the negative inductive argument works for a general causal principle because you can't say that things happen for no reason because the thing that needs to cause it to happen didn't, because the whole point is that it doesn't need a cause. So, denying everything contingent needs a material cause is different in that the person can argue for a restraining factor as an explanation, like the one I described, but with denying everything contingent needs a cause/explanation simpliciter, you can't appeal to an external explanation for why we don't observe uncaused contingent things, because by definition there can be nothing that explains the difference.
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