Offering a solution to the skeptical puzzle is a central aim of Nozick's sensitivity account of knowledge. It is well-known that this account faces serious problems. However, because of its simplicity and its explanatory power, the sensitivity principle has remained attractive and has been subject to numerous modifications, leading to a 'second wave' of sensitivity accounts. I will object to these accounts, arguing that sensitivity accounts of knowledge face two problems. First, they deliver a far too heterogeneous picture of higherlevel beliefs about the truth or falsity of one's own beliefs. Second, this problem carries over to bootstrapping and Moorean reasoning. Some beliefs formed via bootstrapping or Moorean reasoning are insensitive, but some closely related beliefs in even stronger propositions are sensitive. These heterogeneous results regarding sensitivity do not fit with our intuitions about bootstrapping and Moorean reasoning. Thus, neither Nozick's sensitivity account of knowledge nor any of its modified versions can provide the basis for an argument that bootstrapping and Moorean reasoning are flawed or for an explanation why they seem to be flawed.

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.

Keith DeRose's solution to the skeptical problem is based on his indirect sensitivity account.Sensitivity is not a necessary condition for any kind of knowledge, as direct sensitivity accounts claim, but the insensitivity of our beliefs that the skeptical hypotheses are false explains why we tend to judge that we do not know them. The orthodox objection line against any kind of sensitivity account of knowledge is to present instances of insensitive beliefs that we still judge to constitute knowledge. This objection line offers counterexamples against the claim of direct sensitivity accounts that sensitivity is necessary for any kind of knowledge.These examples raise an easy problem for indirect sensitivity accounts that claim that there is only a tendency to judge that insensitive beliefs do not constitute knowledge, which still applies to our beliefs that the skeptical hypotheses are false. However, a careful analysis reveals that some of our beliefs that the skeptical hypotheses are false are sensitive; nevertheless, we still judge that we do not know them. Therefore, the fact that some of our beliefs that the skeptical hypotheses are false are insensitive cannot explain why we tend to judge that we do not know them. Hence, indirect sensitivity accounts cannot fulfill their purpose of explaining our intuitions about skepticism. This is the hard problem for indirect sensitivity accounts.

I will compare Lehrer's anti-skeptical strategy from a coherentist point of view with the anti-skeptical strategy of the Mooreans. I will argue that there are strong similarities between them: Neither can present a persuasive argument to the skeptic and both face the problem of easy knowledge in one way or another. However, both can offer a complete and self-explanatory explanation of knowledge although Mooreanism can offer the more natural one. Hence, one has good reasons to prefer Mooreanism to Lehrer's anti-skeptical approach, if one does not prefer coherentism to foundationalism for other reasons.