Abstract
This paper introduces a new infinite paradox. The main novelty is that it poses problems of causality in a very different form from to the one in use until now. By means of a probabilistic generalization, the paradox shows that the disposition to act according to a specific plan is not always necessary to derive causal effects in Benardete-type contexts involving infinity. It also suggests that, in such cases, the explanation for those causal effects requires a propensity interpretation of probability.
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Notes
If no Olympic rule prohibited the magic potion then the Gauls would have taken it before starting the game. No an would ever have been stopped by the corresponding a*n+1 player and the Gauls would assuredly have won the competition.
Consider one of such triumphs. Was it caused by Asterix’s disposition to act according to the (AS) strategy? It is not clear, because, as we saw in section 1, there is a non-null probability of a Gaulish triumph even without following any special strategy (and, of course, without the magic potion). This is a new and interesting problem of causality posed by the magic potion paradox.
Could we not say that there is in Cacofonix the disposition to act in accordance with the (AS) plan with a certain probability? This is, at the very least, obscure because we may suppose that the inattentive, distracted Cacofonix has never even heard of the (AS) plan and has certainly never thought about it. This way the causal role of the dispositions is safeguarded by a mere stipulation, by introducing them wherever convenient. This is not a philosophically illuminating strategy.
References
Benardete, J. A. (1964). Infinity. An essay in Metaphysics. Oxford: Clarendon Press.
Hájek, Alan, "Interpretations of Probability", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2012/entries/probability-interpret/>.
Laraudogoitia, J. P. (2014). Dispositions and the Trojan Fly. Nous, 48(4), 773–780.
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The authors declare that they have no conflict of interest.
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For Amaia Corral Villate, who inspired the writing of this article
Research for this work is part of the research project FFI2015–69792-R (funded by the Spanish Ministry of Economy and Competitiveness, Government of Spain)
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Laraudogoitia, J.P. The Magic Potion Paradox. Philosophia 45, 1227–1234 (2017). https://doi.org/10.1007/s11406-017-9879-z
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DOI: https://doi.org/10.1007/s11406-017-9879-z