In this letter to Quine Lewis discusses Quine’s contribution to the appendix of Lewis’s set theory book, Parts of Classes.
Summary of Letter
Lewis argued, in Parts of Classes, for the equation: set theory = mereology + plural quantification + the singleton function. He then went on to argue that what’s puzzling about classes is traceable to what’s puzzling about the singleton function. Lewis raised the possibility of “ramsifying out” the singleton function, i.e. going structuralist about classes. But he couldn’t see how to do this without quantifying over relations. Lewis took relations to be ordered pairs, too. So this would mean either resorting to set theory, or a primitive as mysterious as the singleton function itself.
Hazen showed how to avoid appealing to set theory or primitive pairing via simulated quantification over n-tuples of atoms. Then Quine showed how to simulate quantification covering n-tuples of fusions of atoms. In this letter to Quine, Lewis retells these developments. He also invites Quine to be a co-author with Hazen, Burgess and Lewis of an appendix to Parts of Classes on these results. (Quine declined.)
Quine-Lewis correspondence and our project research
As part of our project research, we are writing research papers an a monograph about Lewis’s influence and influences. His correspondence provides evidence for the lines of influence we uncover and discuss. In a forthcoming joint paper, MacBride and Janssen-Lauret argue that Quine’s influence on Lewis was more significant than most philosophers think. Their paper focuses on Quine’s version of structuralism and its influence on Lewis’s later work. This letter forms part of the evidence for Quine’s influence on Parts of Classes. Lewis here credits Quine, which supports the interpretation. The paper also argues that Lewis’s ‘Ramseyan Humility’ has a strong Quinean influence.
Frederique Janssen-Lauret and Fraser MacBride (forthcoming) `W.V. Quine and David Lewis: Structural (Epistemological) Humility’ in Quine: Structure and Ontology (ed. F. Janssen-Lauret), Oxford University Press.