Paradox without self-reference

Why are some sentences paradoxical while others are not? Since Russell the universal answer has been: circularity, and more especially self-reference. 1 Not that self-reference suffices for paradox. Such a view is refuted by the work of Gödel and Tarski, and by various commonsense examples, such as “For the last time, stop that racket! ” and “So dear Lord to Thee we raise, this our hymn of grateful praise.” What many do seem to think is that some sort of self-reference, be it direct or mediated, is necessary for paradox. So one often hears that the surest way of keeping a language paradox-free is to impose an absolute ban on all self-reference. “This may be using a cannon against a fly, ” it is said, “but at least it stops the fly.” Except that it does not stop the fly: paradoxes like the Liar are possible in the complete absence of self-reference. Imagine an infinite sequence of sentences S1, S2, S3,....., each to the effect that every subsequent sentence is untrue: (S1) for all k>1, Sk is untrue (S2) for all k>2, Sk is untrue (S3) for all k>3, Sk is untru

The real distinction between mind and body

Descartes's "conceivability argument" for substance-dualism is defended against Arnauld's criticism that, for all he knows, Descartes can conceive himself without a body only because he underestimates his true essence; one could suggest with equal plausibility that it is only for ignorance of his essential hairiness that Descartes can conceive himself as bald. Conceivability intuitions are defeasible but special reasons are required; a model for such defeat is offered, and various potential defeaters of Descartes's intuition are considered and rejected. At best though Descartes shows the separability of mind from body, not (as he claims) their actual separatenes

Almog on Descartes’s Mind and Body

Descartes thought his mind and body could exist apart, and that this attested to a real distinction between them. The challenge as Almog initially describes it is to find a reading of “can exist apart” that is strong enough to establish a real distinction, yet weak enough to be justified by what Descartes offers as evidence: that DM and DB can be conceived apart

Ifs, Ands, and Buts: An Incremental Truthmaker Semantics for Indicative Conditionals

Indicative conditionals appear to lie on a continuum, with the subjective and information-based on one side, and the objective and fact-based on the other. Attempts to bring them all under the same theoretical umbrella usually start at the subjective end; conditionals get more objective as they come to be based in higher-quality, less parochial, information. I propose to go in the other direction, looking first for a class of “absolute” conditionals, then bringing in other conditionals by relaxing the constraints defining that class. (A plan of action is laid out at the end of section 4. The final footnote of each section sketches the contents of the next.

Wide Causation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73061/1/0029-4624.31.s11.12.pd

How in the world?

....the final proof of God's omnipotence [is] that he need not exist in order to save us. Peter DeVries, The Mackerel Plaza Is it just me, or do philosophers have a way of bringing existence in where it is not wanted? All of the most popular analyses, it seems, take notions that are not overtly existence-involving and connect them up with notions that are existence-involving up to their teeth. An inference is valid or invalid according to whether or not there exists a countermodel to it; the Fs are equinumerous with the Gs iff there exists a one-to-one function between them; it will rain iff there exists a future time at which it does rain; and, of course, such and such is possible iff there exists a world at which such and such is the case. The problem with these analyses is not just the unwelcome ontology; it is more the ontology's intuitive irrelevance to the notions being analyzed. Even someone not especially opposed to functions, to-1- take that example, is still liable to feel uneasy about putting facts o

Explanation, Extrapolation, and Existence

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

A Problem about Permission and Possibility

This chapter explores the prospects for a unified theory of deontic and (socalled) 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