The Bishop’s Church: Berkeley’s Master Argument and the Paradox of Knowability

We can find in the passages that set out the Master Argument a precursor to the paradox of knowability. That paradox shows that if all truths are knowable, all truths are known. Similarly, Berkeley might be read as proposing that if all sensible objects are (distinctly) conceivable, then all sensible objects are conceived.

Conditionals, Paradox, and Probability

This is a volume of essays in philosophy and linguistics in tribute to Dorothy Edgington, the first woman to hold a chair in philosophy in the University of Oxford. The volume focuses on topics to which Edgington has made many important contributions including conditionals, vagueness, the paradox of knowability, and probability. The volume will be of interest to philosophers, linguists, and psychologists with an interest in philosophical logic, natural language semantics, and reasoning.

When Protagoras Made Aristotle His Fitch

While defending the principle of non-contradiction in Metaphysics 4, Aristotle argues that the Measure Doctrine of Protagoras is equivalent to the claim that all contradictions are true; given all appearances are true (as the Protagorean maintains), anytime people disagree we get a true contradiction. This argument seems clearly invalid: nothing guarantees that actual disagreement occurs over every matter of fact. The argument in fact works perfectly, I propose, because the Protagorean view falls prey to a version of Fitch's “paradox” of knowability. The proposed reading shows how Aristotle treats the Protagorean view at issue as an epistemic theory of truth distinct from the mere claim that all appearances are true (which other opponents put forward on different grounds) and reveals Aristotle's underlying concern with the modal collapse of possibility into actuality. The revised Protagorean view Aristotle confronts in a subsequent chapter is furthermore best understood as an attempt to avoid this Fitch-style result.

Analytic and synthetic based on the paradox of knowability

The purpose of this paper is to show how the paradox of knowability loses its paradoxical character when we correctly interpret one of its premises. It is then shown how this new interpretation can be used to logically define analytical and synthetic truths. In this way, the paradox of knowability is traced back to the harmless affirmation that, in order to know every proposition with certainty, there must be no propositions whose truth is synthetic.

Truth, Demonstration and Knowledge. A Classical Solution to the Paradox of Knowability

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from the theory of understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that the principle fails to imply the problematic instances of the original unrestricted knowability principle but that the overall view still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against BHK semantics, for the non-constructive character of the demonstrations envisaged by anti-realists, and contends that, in such a setting, one of the most natural arguments in favour of a revision of classical logic loses all its force.