Juhani Yli-Vakkuri

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of LF, lays out some notational conventions, and states some basic technical facts about the system.

In general, a given object could have been different in certain respects. For example, the Great Pyramid could have been somewhat shorter or taller; the Mona Lisa could have had a somewhat different pattern of colours; an ordinary table could have been made of a somewhat different quantity of wood. But there seem to be limits. It would be odd to suppose that the Great Pyramid could have been thimble-sized; that the Mona Lisa could have had the pattern of colours that actually characterizes The Scream; or that the table could have been made of the very quantity of wood that in fact made some other table. However, there are puzzling arguments that purport to show that so long as an object is capable of being somewhat different in some respect, it is capable of being radically different in that respect. These arguments rely on two tempting thoughts: first, that an object’s capacity for moderate variation is a non-contingent matter, and second, that what is possibly possible is simply possible. This book systematically investigates competing strategies for resolving these puzzles, and defends one of them. Along the way it engages with foundational questions about the metaphysics of modality.

Timothy Williamson is one of the most influential living philosophers working in the areas of logic and metaphysics. His work in these areas has been particularly influential in shaping debates about metaphysical modality, which is the topic of his recent provocative and closely-argued book *Modal Logic as Metaphysics* (2013). The present book comprises ten essays by metaphysicians and logicians responding to Williamson’s work on metaphysical modality. The authors include some of the most distinguished philosophers of modality in the world, as well as several rising stars. Each essay is followed by a reply by Williamson. In addition, the book contains a major new essay by Williamson, ‘Modal science,’ concerning the role of modal claims in natural science. This book was originally published as a special issue of the *Canadian Journal of Philosophy.*