Abstract
According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes (Synthese 196(9):3773–3787, 2019a) and Praolini (Australas J Philos 97(4):715–726, 2019). This paradox synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes (Philos Stud 176(11):2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory.
Highlights
BackgroundConsider the following principle: If one has justification for believing each of P1, P2, ... , Pn , one has justification for believing P1 ∧ P2 ∧ ... ∧ Pn
The normic theory predicts that I lack justification for believing that the book contains a falsehood—I lack justification for believingP1 ∨ ̃P2 ∨ ... ∨ ̃P100.9 does the normic theory offer a way of preserving Closure in the face of the lottery and preface paradoxes—it would appear to deliver a general validation of the principle: Suppose one has justification for believing P1, justification for believing P2, ..., justification for believing Pn
The lottery and the preface paradoxes both highlight certain commitments that any defender of Closure must be prepared to undertake—and so it is with the new hybrid paradox described by Praolini and Backes
Summary
Consider the following principle: If one has justification for believing each of P1, P2, ... , Pn , one has justification for believing P1 ∧ P2 ∧ ... ∧ Pn. The only way to preserve Closure, in the face of this paradox, is to insist that I lack justification for believing some of P1, P2, ..., P100. The only way to preserve Closure, in the face of this paradox, is to insist that I lack justification for believingP1 ∨ ̃P2 ∨ ... Believing that some of the claims in the book are false) These stipulations should be acceptable to all non-sceptics, but the assumptions provide an avenue of response for the defenders of Closure. A new Closure-challenging paradox has been set out, in somewhat different forms, by Backes (2019a) and Praolini (2019) This paradox, which combines elements of the lottery and the preface, relies on no obvious assumptions about epistemic justification and appears to resist the familiar Closure-preserving strategies
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