A Solution to Fitch' Paradox of Knowability

There is an argument (first presented by Fitch), which tries to show by formal means that the anti-realistic thesis that every truth might possibly be known, is equivalent to the unacceptable thesis that every truth actually is known (at some time in the past, present or future). First, the argument is presented and some proposals for the solution of Fitch’s Paradox are briefly discussed. Then, by using Wehmeier’s modal logic with subjunctive marker (S5∗), it is shown how the derivation can be blocked if one respects adequately the distinction between the indicative and the subjunctive mood. Essentially, this proposal amounts to the one by Edgington which was formulated with the help of the actuality-operator. Finally it is shown how the criticisms by Williamson against Edgington can be answered by the formulation of a new conception of possible knowledge that α (thereby α being in the indicative mood and thus referring to the actual world). This conception is based on the concept of same de re knowledge in different possible worlds. Anti-realists such as Dummett and Wright claim that linguistic meaning is intimately related to the use of relevant expressions by the human linguistic community. What is expressed by a certain sentence thus depends essentially on how it is used. According to this position it is not possible that the states of affairs that are expressed might be in principle independent from the corresponding contexts of use that may arise in the linguistic community: The meaning of a mathematical statement determines and is exhaustively determined by its use. The meaning of such a statement cannot be, or contain as an ingredient, anything which is not manifest in the use made of it, lying solely in the mind of the individual who apprehends that meaning: if two individuals agree completely about the use to be made of the statement, then they agree about its meaning. (Dummett 1978, 216)1 Thus, it is plausible to accept the thesis that there are no states of affairs that may be expressed by linguistic means and that are nevertheless in principle inaccessible to the members of the linguistic community. This means for the anti-realistic concept of truth that it is epistemically constrained: Truths have to be epistemically accessible to the members of the linguistic community in principle. In its strongest reading this condition says that every truth might under certain (possibly counterfactual) circumstances also be known.2 Now, an ordinary language formulation of the anti-realistic thesis (ART) can be given: (ART) Every truth might possibly be known.