ONE of the insufficiently recognized pleasures of philosophy is the
chance it gives to enter into conversations that last over years.
Carried on face to face, or by letter, telephone, and the exchange of
papers, these conversations occupy a middle ground that touches on
both friendship and professional civility. It's lucky that no one can
have the last word in these sometimes dispassionate, sometimes
heated exchanges, so that they can run on and on, even beyond our
lifetimes. I am grateful to the people and conversations that have
sustained, enriched, and revised the writing of this book.

The dedication acknowledges my first debt of gratitude, to Jules
Vuillemin. He has been not only a careful and serious reader of my
work, but has provided an exemplary combination of speculative
philosopher and meticulous historian. His reflective assessment of
important episodes in the history of logic, mathematics, and meta-
physics so as to question assumptions and revive possibilities in
contemporary philosophy, is an unfailing source of inspiration. I
would also like to thank him and his wife Gudrun for their hospitality
on a number of occasions.

I have profited immensely from the important work of Henk Bos in
the history of seventeenth-century mathematics, as well as from his
conversation and criticism. Daniel Garber's articles on Descartes's
physics and metaphysics, and his lively and instructive talk, have
likewise served as important sources for this book. The criticism,
books, and translations of Marjorie Grene and Roger Ariew, my
friends at VPI, have left their imprint, especially on the last chapter.
Discussions with Michael Resnik and Philip Kitcher have taught me
a great deal about the nature of reduction and mathematical know-
ledge. And John Yolton's broad understanding of seventeenth-
century philosophy, enriched by his enthusiastic bibliophilia, has
formed an important part of this book's background.

A rolling stone gathers no moss, but a travelling philosopher
picks up lots of useful information. Edith Sylia's essays on proportion
were a revelation to me when I was down in North Carolina. And in
Rome, Guiseppa Battisti's work on proportion and her conversa-
tions about Descartes were invaluable. Off and on throughout the
last decade in Paris, I have profited from the philosophical and

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