This book is about the idea that some true statements would have been true no matter how the world had turned out, while others could have been false. It develops and defends a version of the idea that we tell the difference between these two types of truths in part by reflecting on the meanings of words. It has often been thought that modal issues—issues about possibility and necessity—are related to issues about meaning. In this book, the author defends the (...) view that the analysis of meaning is not just a preliminary to answering modal questions in philosophy; it is not merely that before we can find out whether something is possible, we need to get clear on what we are talking about. Rather, clarity about meaning often brings with it answers to modal questions. In service of this view, the author analyzes the notion of necessity and develops ideas about linguistic meaning, applying them to several puzzles and problems in philosophy of language. Meaning and Metaphysical Necessity will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and philosophical logic. [See my homepage for a sample chapter.]. (shrink)

Gödel’s first incompleteness theorem is sometimes said to refute mechanism about the mind. §1 contains a discussion of mechanism. We look into its origins, motivations and commitments, both in general and with regard to the human mind, and ask about the place of modern computers and modern cognitive science within the general mechanistic paradigm. In §2 we give a sharp formulation of a mechanistic thesis about the mind in terms of the mathematical notion of computability. We present the argument from (...) Gödel’s theorem against mechanism in terms of this formulation and raise two objections, one of which is known but is here given a more precise formulation, and the other is new and based on the discussion in §1. (shrink)

Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles (...) and principles of mathematical and transfinite induction as well as the status of the latter with respect to various foundational characterizations of number theory. (shrink)