 Given the magnitude of our topic, we clearly cannot cover all aspects of it, or even a sizable proportion of them. For example, we do not engage much with the many roles infinitude plays in science and the social sciences (except in section   8), retaining our focus on its roles in philosophy. We limit our discussion to what can be understood without highly advanced mathematics, but provide links to a number of supplementary documents that discuss further issues: infinite idealizations, quadratures of the circle, overviews of two recent developments in mathematics that promise to make the infinite realm more tractable (numerosity theories and surreal numbers), further paradoxes (God’s lottery, two envelopes), and proofs of theorems. We ask for the forbearance of readers whose favorite topics have been left out. We hope to mitigate this somewhat with our large set of pointers to further topics, the references in our extensive bibliography, and other internet resources.