Abstract
The lottery paradox shows that the following three individually highly plausible theses are jointly incompatible: (i) highly probable propositions are justifiably believable, (ii) justified believability is closed under conjunction introduction, (iii) known contradictions are not justifiably believable. This paper argues that a satisfactory solution to the lottery paradox must reject (i) as versions of the paradox can be generated without appeal to either (ii) or (iii) and proposes a new solution to the paradox in terms of a novel account of justified believability.
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Notes
In fairness to deniers of NC, it should be noted that this argument might turn out dialectically ineffective against those who reject NC. After all, if you are willing to reject NC, you will likely not be too attached to NMP either. At the same time, for the many who do not want to give up NC, it does provide an additional reason for not so doing: they would have to give up a further plausible principle governing justified believability. Thus, even if these considerations do not move foes of NC, I take them to provide some reason to think that NC is not the culprit of the paradox. Of course, if NC is not the culprit, it’ll have to be either CC or ST.
Notice that, besides receiving support by the plausible MCH and NC, MCN is independently plausible. After all, it captures the epistemic force of reductio arguments (Kaplan 1981).
See Kelp ang Ghijsen (forthcoming) and Kelp (forthcoming b) for some such comparisons.
I do not mean to suggest that there is nothing of philosophical substance to be said about the nature of knowledge. In fact, I am inclined to think that the nature of knowledge is given by the thesis that knowledge is the goal of inquiry.
There may be cases in which one has other ways of forming beliefs about lottery propositions available to one. For instance, one may have been told by a reliable informant that a certain ticket will lose the lottery because the lottery is rigged against it. Since, at least in certain conditions, believing lottery propositions on the basis of the informant’s say-so disposes one to acquire knowledgeable beliefs about lottery propositions, in this situation one is in a position to believe the lottery proposition via an exercise of an ability to know. By JBY, the lottery proposition is justifiably believable for one. I take this to be the right result.
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Acknowledgments
Thanks to the audiences of the following conferences for helpful feedback on the material of this paper: 2012 EEN Meeting, Universities of Bologna and Modena (2012); CCPEA, Academia Sinica, Taipei (2012); 2013 Bled Philosophical Conferences, Bled (2013); Epistemic Justification and Reasons, University of Luxembourg (2013); Neue Perspektiven der Epistemischen Rechtfertigung, University of Dresden (2013), Saving Safety, Bonn (2013), Yonsei Philosophy Summer Conference, Yonsei University (2014); Normative Epistemic Reasons, University of Luxembourg (2014), The Virtue Turn, University of Taipei (2014); 2015 Bled Philosophical Conferences, Bled (2015). Thanks also to the Leuven Epistemology Group and two anonymous referees of this journal for their feedback on the paper. Special thanks to Harmen Ghijsen and Mona Simionescu for commenting on various versions of the paper. This work was funded by grants from KU Leuven’s Special Research Fund (BOF) and Research Foundation Flanders (FWO).
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Kelp, C. Lotteries and justification. Synthese 194, 1233–1244 (2017). https://doi.org/10.1007/s11229-015-0989-5
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DOI: https://doi.org/10.1007/s11229-015-0989-5