Knowability

Knowability is the concept that figures in epistemic theories true---for instance semantic anti-realism claims, necessarily, every truth is knowable in principle.  Michael Dummett argues for the position along the following lines.  Given that meaning is fully manifestable in use and that grasp of meaning involves knowing truth conditions, the fully competent user of the language is in principle able to recognize that a proposition is true when it is.   The most important alleged consequence of the position is that classical logic is not unrestrictedly valid.  For the unrestricted principle of excluded middle together with semantic anti-realism (and some modest auxiliary assumptions) entails strong decidability---i.e., that, unrestrictedly, every proposition or it’s negation is knowable in principle.  And that conclusion is false, not known apriori, and unacceptably immodest. Therefore, exclusively classical principles are false, not known apriori and unacceptably immodest. 

Most recent discussion centers around  Fitch’s paradox of knowability.  The paradox threatens to collapse semantic anti-realism into an implausible idealism----the theory that, necessarily, every truth is (at some time) known.  Since an important selling point of moderate anti-realism is that it distances itself from naïve idealism, the collapse is unwelcome to the anti-realist.  But the paradox is not just a problem for anti-realists, because the result threatens to erase the very logical distinction between semantic anti-realism and naïve idealism. Even those of us who have not been seduced by anti-realism may still want to distinguish it from (and treat it as logically weaker than) idealism.  

Influential variations on the thesis that truth is an epistemic notion are articulated in Berkeley & Turbayne 1907, Dummett 1975, Kant 1991, Peirce 1940, Putnam 1981, and Tennant 1997, et. al. The connections between anti-realism and a rejection of classical logic are found in Dummett 1975, Wright 1992, Tennant 1997, and Salerno 2000.   The first publication of Fitch's paradox is Fitch 1963.  The result there was conveyed anonymously to Fitch in a pair of referee reports in 1945, which were later published in Church 2009.  An overview of the key points of debate regarding Fitch’s paradox is found in Brogaard & Salerno 2010.  Two volumes of essays, which center around the key points of contention in that debate are Salerno 2008 and Salerno 2010.  The only monograph on the paradox is L. Kvanvig 2006.  The last of chapter of Williamson 2000 also has exerted much influence on recent discussion.