Insensitive and unsafe knowledge

Sensitivity and safety are modal concepts of knowledge. A person’s belief that p is sensitive if and only if in the closest possible world where p is false S does not believe that p. A person’s belief that p is safe if and only if in most near-by possible worlds in which S continues to form her belief that p in the same way as in the actual world the belief continues to be true. Robert Nozick claims that sensitivity is a necessary condition for knowledge. Ernest Sosa, Timothy Williamson and Duncan Pritchard argue among others that safety is necessary for knowledge. I shall contest both views by offering counterexamples of persons, to whom it is highly plausible to ascribe knowledge although their beliefs are neither sensitive nor safe. I conclude that neither sensitivity nor safety is a necessary condition for knowledge and that insensitive and unsafe knowledge exists.