Skepticism and the principle of sufficient reason

Philosophical Studies - The Principle of Sufficient Reason must be justified dialectically: by showing the disastrous consequences of denying it. We formulate a version of the Principle that is...     

Conjunctions,Disjunctions and Lewisian Semantics for Counterfactuals

Consider the reasonable axioms of subjunctive conditionals (1) if p q ₁ and p q ₂ at some world, then p (q ₁ & q ₂) at that world, and (2) if p ₁ q and p ₂ q at some world, then (p ₁ ∨ p ₂) q at that world, where p q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.     

The A-theory of time and induction

The A-theory of time says that it is an objective, non-perspectival fact about the world that some events are present, while others were present or will be present. I shall argue that the A-theory has some implausible consequences for inductive reasoning. In particular, the presentist version of the A-theory, which holds that the difference between the present and the non-present consists in the present events being the only ones that exist, is very much in trouble.     

Regular probability comparisons imply the Banach–Tarski Paradox

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: (a) there can be nonmeasurable events that have no probability at all and (b) on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice (AC). We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory.     

Sincerely Asserting What You Do Not Believe

I offer examples showing that, pace G. E. Moore, it is possible to assert ‘Q and I don't believe that Q’ sincerely, truly, and without any absurdity. The examples also refute the following principles: (a) justification to assert p entails justification to assert that one believes p (Gareth Evans); (b) the sincerity condition on assertion is that one believes what one says (John Searle); and (c) to assert (to someone) something that one believes to be false is to lie (Don Fallis).     

The accomplishment of plans: a new version of the principle of double effect

The classical principle of double effect offers permissibility conditions for actions foreseen to lead to evil outcomes. I shall argue that certain kinds of closeness cases, as well as general heuristic considerations about the order of explanation, lead us to replace the intensional concept of intention with the extensional concept of accomplishment in double effect.