The Paradox of Knowability and Semantic Anti-Realism

ing away from its implications for knowledge and knowability, at least to begin with. He thinks that once this is done, Fitch’s result is only initially surprising; for it is clear that the result is derived simply because truth-entailing operators can be used to construct self-refuting expressions. Mackie gives the following example to illustrate this: Let J be an operator variable that has any number of “innocent interpretations” (which is to say that for any p, it is possible that Jp and it is also possible that ¬Jp), including the interpretation, “it is written in green ink at t1 that”. Let W be the truthentailing counterpart of J such that Wp is defined as (Jp ∧ p). At this point, Mackie notes that it is tempting to say that, for any p, it is possible that Jp and thus for any p that is true it is possible that Wp. Mackie calls this latter claim inference rule R. He also notes one proviso: W distributes over conjunction. Mackie then proves that this inference rule is inconsistent with a statement of the form, (p ∧ ¬Wp) in a similar fashion to the proofs presented in chapter one of this paper. Thus, though it may be true that “p but it is not written in green ink at t1 that p”, it does not follow from this that it can be truly written in green ink at t1 that “p, but it is not written in green ink at t1 that p”. Mackie thinks that this should be no more surprising than the fact that while I may be saying nothing at t1, I cannot truly say at t1 that I am saying nothing at t1. So inference rule R is unsound. Not everything that is true can be truly written in green ink at t1; for there may be things that are true, and can be written in green in at t1, but which if they were written in green ink at t1, would not be true. So, how does this help one to better understand the reasoning employed by Fitch? 32 Mackie, J.L. "Truth and Knowability," Analysis 40, (1980), 90 33 Ibid., 91 34 Ibid., 91