Sensitivity, safety, and impossible worlds

Abstract

Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan (Notre Dame J Formal Logic 38:535-572, 1997), on which we also consider impossible worlds. Nolan's account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S's belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities.

Knowledge from Falsehood, Ignorance of Necessary Truths, and Safety

“…According to Pritchard's solution, the set of propositions is constrained by the basis of the belief. We should only consider beliefs that are formed on the same basis while beliefs formed on a different basis 7 For similar arguments, see Becker (2007), Blome-Tillmann (2017), Collin (2018), Dietz and Hawthorne (forthcoming), Hales (2016), Levy (2011), Melchior (2017Melchior ( , 2021, Miščević (2007), Zhao (2021, forthcoming). Bernecker (2011), Broncano-Berrocal (2019, Freitag (2014), Greco (2016), Hiller and Neta (2007), Hirvelä (2017Hirvelä ( , 2019, Kripke (2011), Paterson (2020), Stone (2013), and Zhao (2021) also argue that in addition to necessary truths, modally robust contingent truths, which are true in all nearby possible worlds, incur the same problem for SAFETY.…”

Realism, reliability, and epistemic possibility: on modally interpreting the Benacerraf–Field challenge

“…As I suggested above, then, if we adopt a conception based on Safety, we'll be able to return the verdict that orthodox realism renders our mathematical reliability inexplicable only if we can motivate the claim that certain metaphysically impossible worlds where the mathematical facts are different-namely, those where the natural facts are the same as they are in the actual world-count as similar to the actual world. For more on the status of Safety in a semantics that includes impossible worlds, see Melchior (2020), which appeared while this paper was under review. 17 Liggins, to take just one example, asks us to consider the case of Pierre, a mathematician who devotes his life to proving some mathematical conjecture C and is disappointed when its negation is proved insteadin this case, says Liggins, "The question 'How would Pierre have felt were he to have proved C?'…”

A Dilemma for Globalized Safety

“…For similar arguments, seeBecker (2007),Blome-Tillmann (2017),Collin (2018),Melchior (2017Melchior ( , 2021,Miščević (2007), andRoland and Cogburn (2011) Bernecker (2011), Broncano-Berrocal (2019,Freitag (2014),Greco (2016),Hiller and Neta (2007),Hirvelä (2019),Kripke (2011), Paterson (2020), and Stone (2013. also argue that in addition to necessary truths, modally robust contingent truths which are true in all nearby possible worlds cause the same problem for SAFETY.…”