He defines armchair knowledge as knowledge that is eitherstrictly a priori knowledge or not strictly a priorior a posteriori. In the latter case, the knowledge is suchthat experience plays no strictly evidential role, but at the sametime the role of experience does not fit the model of apriori knowledge, since far too much experience played a role inenabling concept possession and reliable use. Given Williamson’sacknowledgement of armchair knowledge as a domain into which manyinstances of modal knowledge fall, it is best to describe his view asbeing an armchair account of modal knowledge, as opposed to astrictly rationalist or non-rationalist account.
It is important to note that Nozick’s argument depends on theclaim that if there is no reliable module or faculty for detectingnecessity, then none of our beliefs about necessity arejustified. With respect to this assumption one might argue thatalthough there is no specific faculty for detectingnecessity, we are capable of reasoning our way to necessity by way ofother faculties that we do have. Counterfactual theories of theepistemology of modality typically take this approach (see for discussion)
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Van Inwagen (1998), taking note of Yablo’s (1993) account ofwhat it is to conceive something, discusses what has come to be afundamental challenge for theories involving conceivability andimaginability. The problem presented by van Inwagen is related to theproblem of a posteriori necessities. Van Inwagen’s goalis to present a limited form of skepticism about modal knowledge. Heis not a skeptic about all modal knowledge. His position is that wehave a lot of ordinary modal knowledge concerning practical,scientific, and mathematical matters, but perhaps limitedextraordinary modal knowledge. Extraordinary modal knowledgeconcerns matters on the periphery of scientific investigation or inthe realm of metaphysical debate. He argues for his skepticism aboutextraordinary modal knowledge on the basis of an analogy withjudgments of distance by the naked eye. He maintains that in a rangeof cases, naked-eye judgments of distance are reliable, thoughfallible; and likewise in a range of cases, modal judgments aboutordinary practical matters and scientific matters are also reliable,though fallible. However, he argues that just as judgments of distanceby the naked eye break down in certain cases, judgments aboutextraordinary modal claims based on conceiving or imagining asituation that appears to verify a statement equally break down. Themain issue concerns how we can be confident that we have conceivedthings to the relevant level of depth required for the scenario toactually be a presentation or manifestation of a genuinepossibility.
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Cambridge Bilingual English-Spanish dictionary; Oxford dictionary
The first premise in the deduction of an a posteriorinecessity involves some necessity-generating principle, a principlethat moves from some sort of fact, typically a non-modal fact, to theclaim that the fact is necessary. Kripke thought that these principleswere usually arrived at through a priori philosophicalreflection. Plausible, and often discussed, examples ofnecessity-generating principles are:
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Now a modal argument is one in which either a premise or theconclusion is an ordinary or an extraordinary modal judgment. Thus, inmodal arguments, we reason about what is necessary, possible, orimpossible, or about what might, must, or could not be the case. Modalarguments can therefore be found both inside and outside of philosophy(within philosophy many important philosophical positions are in factmodal positions). Assuming that a modal argument is valid (i.e., thepremises validly imply the conclusion), then the evaluation of a modalargument focuses on whether the premises are justified. The questionthen arises: how does one show that a modal premise of a modalargument is justified?