Knowability, possible knowledge, and the Church-Fitch paradox

This essay is concerned with the logical structure of the concept of knowability in the context of a specific debate. For the last four decades, philosophers have been discussing a peculiar logical result, known as the Church-Fitch paradox, which is standardly interpreted as saying that if every truth is knowable, then every truth is known. Whereas the antecedent of this claim is not obviously false, the consequent is philosophically indefensible. On the interpretation just given, the result is mainly referred to as the knowability paradox. Not only this labelling, but also the common construal of the logical result as a paradox concerning knowability is based on the tacitly accepted but curiously underdiscussed presupposition that the logical structure of knowability is the same as the logical structure of possible knowledge, where possible knowledge is considered to be the straightforward composition (or concatenation, on the syntactic level) of possibility and knowledge. Against this discursive background, two theses will be defended in this essay, one negative and one positive. The negative thesis is that the decompositional analysis of knowability, i.e. the analysis of knowability as the simplest composition of possibility and knowledge, is not compatible with some attractive principles about knowability. Various arguments and intuitive evidence show that the decompositional concept of knowability is in tension with some independently motivated principles governing knowability, possibility, and knowledge. The positive thesis is that a proper concept of knowability can be motivated philosophically such that it involves the concepts of possibility and knowledge as its components, but in a non-decompositional, more complex way than postulated by the tacit presupposition indicated above. Apart from being in accordance with the principles that seem to govern knowability, the main merit of this new explication of knowability is that it evades the difficulties that make the plain decompositional concept problematic and, more particularly, that it solves the aforementioned knowability paradox.