Sundholm’s Paradox of Knowability: A Novel Paradox?

In this paper I take a closer look at a recently published paradox by Göran Sundholm involving the notion of knowability. I point out that this paradox is not a novel, genuine paradox, but rather an important variant of the Knower Paradox. I briefly discuss further variations of the Knower Paradox, and in a final section I try to show that it is not unproblematic to assume that knowability is factive. There are several different notions and conceptions of knowability. The most straightforward ones are non-factive. Anti-realists as Sundholm and Tennant obviously use a different notion of knowability which they assume to be factive. But this notion has not yet been made sufficiently clear to rely on it as common ground in debates between realists and antirealists. 1 Another Knowability Paradox The modern debates between realists and anti-realists are often centred on the notion of knowability. Typical anti-realists defend an equivalence claim between truth and knowability, whereas realists deny such a thesis. In recent years one focus of this debate has been the so-called Knowability Paradox or Church-Fitch Paradox,1 and the literature on it has exploded.2 This paradox consists in a formal derivation that seems to show that the anti-realistic knowability principle ‘Every truth is knowable’ implies the seemingly much stronger claim that every truth is actually known, a thesis unacceptable even for all but the hardest anti-realists. Now, in a short note Göran Sundholm (2008) has presented another paradox 1Originally the argument was published in a paper by Frederic Fitch (1963), who attributed it to an anonymous referee. So, for a long time the paradox was named after Fitch, until Joe Salerno recently found out that the anonymous referee was Alonzo Church and proposed the name Church-Fitch Paradox. Cf. Salerno (2009b). 2For an overview see the online entry in the Stanford Encyclopledia of Philosophy by Berit Brogaard and Joe Salerno, and for a recent collection of papers see Salerno (2009a). Even a monograph has been written on this subject: Kvanvig (2006). I have contributed to this debate also myself, Rückert (2004).