Philosophy of language

Mathematical economics

Polymer chemistry

Mathematics

Epistemic modal logic

Counterfactual thinking

Epistemology

Possible world

Mathematical analysis

Philosophy

Political science

Philosophy of mind

Metaphysics

Semantics (computer science)

Chemistry

Programming language

Modal logic

Impossibility

Face (sociological concept)

Closeness

Common knowledge (logic)

Computer science

Linguistics

Modal

Counterfactual conditional

Philosophical Studies

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.

Sensitivity, safety, and impossible worlds