Abstract
Trivialism is the doctrine that everything is true. Almost nobody believes it, but, as Priest (2000) shows, finding a non-question-begging argument against it turns out to be a difficult task. In this paper, I propose a statistical argument against trivialism, developing a strategy different from those presented in Priest (1999, 2000, 2006).
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Notes
I am following Van Inwagen in taking the lowest possible degree of probability to be zero. Alternatively one could say that the probability of living in an empty world is infinitesimal. Nothing important hinges upon that. See Van Inwagen (1996, fn. 5).
Of course, just as there is only one empty world, there is only one actual world: “For the sake of balanced reporting, van Inwagen should acknowledge that, by his reasoning, the actual world is also as improbable as anything can be. What really counts here is the probability of ‘There is something’ as opposed to ‘There is nothing’.” (Sorensen 2012).
I will return on this point at the end of the paper.
This is a version of Plantingian realism. Other versions take possible worlds to be maximal consistent sets of propositions (sentences, etc.).
Even if we consider worlds as pairs of sets, the set of the true and that of the false proposition, still there is just one trivial world: the one individuated by the pair {V, V}.
This is true even if Kabay (2010) makes his case for trivialism arguing that everything is necessary true. My point is just that in the dialectical context we are considering the trivialist is not entitled to presuppose Spinozism: there is no reason why the neutral arbiter should think that arguing against Spinozism we are in any way begging the question against the trivialist.
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Acknowledgments
Many thanks to an anonymous referee and to audiencies at NIP and the University of Padua, in particular Francesco Berto, Graham Priest and Stephan Torre. This paper is dedicated to the memory of Lorenzo Bernardi.
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Plebani, M. Could Everything Be True? Probably Not. Philosophia 43, 499–504 (2015). https://doi.org/10.1007/s11406-015-9584-8
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DOI: https://doi.org/10.1007/s11406-015-9584-8