, Volume 190, Issue 14, pp 2749-2772
Date: 19 May 2012

A Church-Fitch proof for the universality of causation

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In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga’s, Actualism and possible worlds, reprinted in: Davidson (ed.) Essays in the metaphysics of modality, 2003), and the idea that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic B. Fitch’s work (J Symb Logic 28(2):135–142, 1963) [with credit to who we now know was Alonzo church’s, Referee Reports on Fitch’s Definition of value, in: (Salerno (ed.), New essays on the knowability paradox, 2009)] that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church–Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument.

An earlier version of this paper was presented at the Rutgers University philosophy department Grad-talk series. I’m indebted to the many comments I received there. I also owe many thanks to Andrew Bailey, Tom Donaldson, Robert Koons, Jonathan Kvanvig, Tim Maudlin, Graham Oppy, Graham Priest, Alexander Pruss, Joshua Rasmussen, Joe Salerno, Jonathan Schaffer, Alexander Skiles, Dean Zimmerman, and two anonymous referees with Synthese for their comments and/or correspondence on earlier drafts of this paper. Any errors that remain are due to my incompetence.
I owe special thanks to Joe Salerno for not only some kind comments about Weaver (2012), but for also turning my attention to an argument akin to the one in Sect. 4.2 of this paper. I should also point out that Sect. 4.2 of this paper has a conceptual ancestor in Oppy (2000, pp. 347–348). Graham Oppy provided a Church–Fitch-like proof with explanation content, although he used that proof in an attempt to show that a certain cosmological argument begs the question (with this I disagree, see Gale and pruss). Oppy credited Lloyd Humberstone (Oppy 2000, p. 347) with pointing out the similarity of his argumentation to Fitch’s reasoning. It was not known at the time of the publication of Oppy’s article that Alonzo Church was the anonymous referee credited in Fitch’s paper with the knowability result (represented by Proposition (1) below).