This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does (...) is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency. (shrink)

Naturalistic teleological accounts of mental content rely on an etiological theory of function. Nanay has raised a new objection to an etiological theory, and proposed an alternative theory of function that attributes modal force to claims about function. The aim of this paper is both to defend and to cast a new light on an etiological theory of function. I argue against Nanay’s “trait type individuation objection,” suggesting that an etiological theory also attributes modal force to claims about function. An (...) etiological theory of function can be thought to analyze claims about function with modal force, not relying on any theory of counterfactuals. (shrink)

I clarify some of the details of the modal theory of function I outlined in Nanay (2010): (a) I explicate what it means that the function of a token biological trait is fixed by modal facts; (b) I address an objection to my trait type individuation argument against etiological function and (c) I examine the consequences of replacing the etiological theory of function with a modal theory for the prospects of using the concept of biological function to explain mental content.