We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)

Propositions are central to at least most theorizing about the connection between our mental lives and the world: we use them in our theories of an array of attitudes including belief, desire, hope, fear, knowledge, and understanding. Unfortunately, when we press on these theories, we encounter a relatively neglected family of paradoxes first studied by Arthur Prior. I argue that these paradoxes present a fatal problem for most familiar resolutions of paradoxes. In particular, I argue that truth-value gap, contextualist, situation (...) theoretic, revision theoretic, ramified, and dialetheist approaches to the paradoxes must deny us the conceptual resources that they themselves make use of, on pain of contradiction. I then detail the costs of the extant strategies that avoid this issue: Hartry Field’s paracomplete approach; Andrew Bacon’s classical treatment of indeterminacy; a generalization of ideas from Prior, Nicholas J.J. Smith, and Hartley Slater; and free logics as recently explored by Bacon, John Hawthorne, and Gabriel Uzquiano. I argue that none of these is perfect, and that each restricts the theories we can endorse in a variety of areas of philosophy. I spell these restrictions out, showing, I hope, that the further investigation of these paradoxes must be a part of future research on propositional attitudes. (shrink)

About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of them have. Most papers on the Liar Paradox offer (...) some explanation of the behavior of paradoxical sentences, and most also offer some extension for the predicate ‘true’ that they think is adequate, at least in some restricted setting. But if this is a solution, then the problem we face is far from a lack of solutions; rather, we have an overabundance of conflicting ones. Kripke’s work alone provides us with uncountably many different extensions for the truth predicate. Even if it so happens that one of these is a conclusive solution, we do not seem to know which one, or why. We should also ask, given that we are faced with many technically elegant but contradictory views, if they are really all addressing the same problem. What we lack is not solutions, but a way to compare and evaluate the many ones we have. (shrink)