2015
DOI: 10.1111/phc3.12267
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Iteration Principles in Epistemology I: Arguments For

Abstract: Epistemic iteration principles are principles according to which some or another epistemic operator automatically iterates---e.g., if it is known that P, then it is known that P, or there is evidence that P, then there is evidence that there is evidence that P. This article provides a survey of various arguments for and against epistemic iteration principles, with a focus on arguments relevant to a wide range of such principles.

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Cited by 22 publications
(13 citation statements)
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“…This contextualist version of safety, in which iterations of safety can follow trivially from first-order safety, fits in nicely with extant contextualist accounts of knowledge. As I argue in Greco (2014), a broadly Lewisian contextualist framework can be used to defend the KK principle-the thesis that if a subject knows that P, then she knows that she knows that P. 15 And the reasons why it can be defended in this framework are structurally very similar to the reasons why iterations of robustness and safety can come for free in the contextualist picture we've been exploring-on the view I defend in my (2014), knowing requires avoiding error in a contextually determined set of cases, but which cases those are doesn't itself systematically vary with the case, but only with the context. And as we've seen, when the set of relevant cases (whether relevant for attributions of robustness, safety, or knowledge) doesn't itself vary from case to case, but only from context to context, second-order robustness/safety/knowledge isn't more demanding than its first-order cousin.…”
Section: Iterationmentioning
confidence: 92%
See 1 more Smart Citation
“…This contextualist version of safety, in which iterations of safety can follow trivially from first-order safety, fits in nicely with extant contextualist accounts of knowledge. As I argue in Greco (2014), a broadly Lewisian contextualist framework can be used to defend the KK principle-the thesis that if a subject knows that P, then she knows that she knows that P. 15 And the reasons why it can be defended in this framework are structurally very similar to the reasons why iterations of robustness and safety can come for free in the contextualist picture we've been exploring-on the view I defend in my (2014), knowing requires avoiding error in a contextually determined set of cases, but which cases those are doesn't itself systematically vary with the case, but only with the context. And as we've seen, when the set of relevant cases (whether relevant for attributions of robustness, safety, or knowledge) doesn't itself vary from case to case, but only from context to context, second-order robustness/safety/knowledge isn't more demanding than its first-order cousin.…”
Section: Iterationmentioning
confidence: 92%
“…See Greco () for some discussion of the connection between common knowledge on the one hand, and iteration principles in epistemology on the other.…”
mentioning
confidence: 99%
“…Accordingly, we are only justified in 30 A version of the JJ-principle for idealized inferential justification is defended by Fumerton (1995Fumerton ( , 2015. For discussions on iteration principles, see Greco (2014Greco ( , 2015a. 31 Here it is tacitly assumed that self-referring higher-level beliefs are not justified.…”
Section: Kk-principlementioning
confidence: 99%
“…The reply also threatens to undermine some of the most prominent arguments for the importance of common knowledge (Heal () (now elegantly presented by Greco ()), Clark & Marshall (), Fagin et al . (), among many others): if one attempted to save common knowledge assumptions from their paradoxical consequences by blaming the message‐passing setup, one would thereby lose some important motivations for the importance of common knowledge in the first place.…”
mentioning
confidence: 99%