Stephen Yablo

Knowledge is closed under implication, according to standard theories. Orthodoxy can allow, though, that apparent counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility which they seek to explain away. Should not everyone, orthodox or not, want to make sense of “intimations of openness”? This paper compares two styles of explanation: evidence that boosts P’s probability need not boost that of its consequence Q; evidence bearing on P’s subject matter may not bear on the subject matter of Q.

….it [is] wholly irrational to regard as doubtful matters that are perceived clearly and distinctly by the understanding in its purity, on account of mere prejudices of the senses and hypotheses in which there is an element of the unknown.Descartes, Geometrical Exposition of the MeditationsSubstance dualism, once a main preoccupation of Western metaphysics, has fallen strangely out of view; today’s mental/physical dualisms are dualisms of fact, property, or event. So if someone claims to find a difference between minds and bodies per se, it is not initially clear what he is maintaining. Maybe this is because one no longer recognizes ‘minds’ as entities in their own right, or ‘substances.’ However, selves - the things we refer to by use of ‘I’ - are surely substances, and it does little violence to the intention behind mind/body dualism to interpret it as a dualism of bodies and selves. If the substance dualist’s meaning remains obscure, that is because it can mean several different things to say that selves are not bodies.

Many topics have not been covered, in most cases because I don't know quite what to say about them. Would it be possible to add a decidability predicate to the language? What about stronger connectives, like exclusion negation or Lukasiewicz implication? Would an expanded language do better at expressing its own semantics? Would it contain new and more terrible paradoxes? Can the account be supplemented with a workable notion of inherent truth (see note 36)? In what sense does stage semantics lie “between” fixed point and stability semantics? In what sense, exactly, are our semantical rules inconsistent? In what sense, if any, does their inconsistency resolve the problem of the paradoxes?The ideals of strength, grounding, and closure together define an intuitively appealing conception of truth. Nothing would be gained by insisting that it was the intuitive conception of truth, and in fact recent developments make me wonder whether such a thing exists. However that may be, until the alternatives are better understood it would be foolish to attempt to decide between them. Truth gives up her secrets slowly and grudgingly, and loves to confound our presumptions

David Lewis in ‘A Problem About Permission’ asks about the effect on context of permitting the previously forbidden. The set of permissible worlds expands, but how? One can ask in a similar vein about the effects of calling a circumstance possible which had previously been ruled out. This chapter proposes a unified rule. Permission to take the day off adds in world _W_ if the reasons _W_ was initially ruled out all imply taking the day off. _W_ remains impermissible if the reasons it was initially ruled out include some that could still have obtained even if one had remained at work. Similarly, ‘It might rain’ adds a world to the context set if and only if was ruled out for rain-implying reasons. These rules turn out to have non-trivial effects even if the new possibility was not previously ruled out. This runs counter to Lewis, but is arguably the right result.

This chapter explores the prospects for a unified theory of deontic and (so-called) epistemic modality. A theory of deontic modality needs to solve the puzzles raised by David Lewis in ‘A Puzzle About Permission’. In particular, it needs to say what the effect is of making something permissible, and what consequences a permission has in terms of what else is thereby permitted. It is argued that when _p_ is made permissible, then a world _w_ is still impermissible if, antecedently, _w_ was impermissible for a reason not implying _p_. This model is extended to (so-called) epistemic modality. What should happen to the conversational context when it is accepted that it might be that _p_? The chapter suggests that three things happen. Most obviously, the common ground of the conversation now includes at least one world where _p_. Further, the common ground now includes worlds that were previously only ruled out for reasons that entailed ~_p_. Finally, once it is accepted that it might be that _p_, this _cancels_ any assertion that ~_p_, even one that has not been explicitly made in this conversation.

Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains

….it [is] wholly irrational to regard as doubtful matters that are perceived clearly and distinctly by the understanding in its purity, on account of mere prejudices of the senses and hypotheses in which there is an element of the unknown.Descartes, Geometrical Exposition of the MeditationsSubstance dualism, once a main preoccupation of Western metaphysics, has fallen strangely out of view; today’s mental/physical dualisms are dualisms of fact, property, or event. So if someone claims to find a difference between minds and bodies per se, it is not initially clear what he is maintaining. Maybe this is because one no longer recognizes ‘minds’ as entities in their own right, or ‘substances.’ However, selves - the things we refer to by use of ‘I’ - are surely substances, and it does little violence to the intention behind mind/body dualism to interpret it as a dualism of bodies and selves. If the substance dualist’s meaning remains obscure, that is because it can mean several different things to say that selves are not bodies.