This paper argues that the most famous objection to backward time travel can carry no weight. In its classic form, the objection is that backward time travel entails the occurrence of impossible things, such as auto-infanticide-and hence is itself impossible. David Lewis has rebutted the classic version of the objection: auto-infanticide is prevented by coincidences, such as time travellers slipping on banana peels as they attempt to murder their younger selves. I focus on Paul Horwich's more recent version of the objection, according to which backward time travel entails not impossible things, but improbable ones-such as the string of slips on banana peels that would be required to stop a determined auto-infanticidal maniac from murdering her younger self-and hence is itself highly improbable. I argue that backward time travel does not entail unusual numbers of coincidences; and that, even if it did, that would not render its occurrence unlikely.

This book argues that an adequate account of vagueness must involve degrees of truth. The basic idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. This idea is immediately appealing in the context of vagueness — yet it has fallen on hard times in the philosophical literature, with existing degree-theoretic treatments of vagueness facing apparently insuperable objections. The book seeks to turn the tide in favour of a degree-theoretic treatment of vagueness, by motivating and defending the basic idea that truth can come in degrees, by arguing that no theory of vagueness that does not countenance degrees of truth can be correct, and by developing a new degree-theoretic treatment of vagueness — fuzzy plurivaluationism — that solves the problems plaguing earlier degree theories.

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This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities assigned to them)? The paper first outlines a certain simple response to the Pasadena game and identifies two problems with this response, the second of which is that it leads to a wholesale violation of evaluative compositionality.I then argue that rationality does not require decision makers to factor in outcomes of arbitrarily low probability. A method for making decisions which flows from this basic idea is then developed, and it is shown that this decision method (Truncation) leads to a limited-as opposed to wholesale-violation of evaluative compositionality. The paper then argues that the truncation method yields solutions to the problems posed by the Pasadena game and its relatives that are both attractive in themselves and superior to those yielded by alternative proposals in the literature.