Quine and Boolos on second-order logic : an examination of the debate

Abstract

The aim of this thesis is to examine the debate between Quine and Boolos over the logical status of higher-order logic-with Quine taking the position that higher-logic is more properly understood as set theory and Boolos arguing in opposition that higher-order logic is of a genuinely logical character. My purpose here then will be to stay as neutral as possible over the question of whether or not higher-order logic counts as logic and to instead focus on the exposition of the debate itself as exemplified in the work of Quine and Boolos. Chapter I will be a detailed consideration of Quine's conception of logic and its place within the wider context of his philosophy. Only once this backdrop is in place will I then examine his views on higher-order logic. In Chapter II, I turn to Boolos's response to Quine-his attempt to examine the extent to which we may want to count higher-order logic as logic and the extent to which we may want to count it as set theory. With each point Boolos raises, I attempt to give what I think would have been Quine's reply. Finally, in Chapter III, I consider Boolos's attempt to show that monadic second-order logic (MSOL) should be understood as pure logic as it does not commit us to the existence of classes, as we may take the standard interpretation of MSOL to do. I discuss here some of the major reactions to Boolos's plural interpretation (Resnik, Parsons, and Linnebo), and conclude with more speculative remarks on what Quine's own response might have been. Throughout this thesis, my primary method has been one of close textual analysis.