## Philosophical Perspectives on InfinityThis book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. |

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Achilles alternatives argument assemblages of points assumption axioms believe C-ordering cardinal number claim classical mathematics consider contingent countable additivity days in Heaven decision theory discussion divergent domain elements envelope example existence explanation finite finitist function fusion given Gršunbaum Ifwe Ifwe suppose infinite collections infinite number infinite regress infinite series infinite utility streams infinitesimal infinitist instant interval kind large and small least Lebesgue measure line segment machine magnitudes Malament-Hogarth spacetime measure mereological mereological atoms metres modal Moreover natural numbers nonstandard objects ontological ordinal paradox particle perhaps philosophy of mathematics physical infinities plausible possible worlds principles of sufficient probability properties quantities quantum field theory quantum mechanical question rational numbers real numbers realm reasonable belief regions relation seems sentences set theory small denumerable someone space spacetime spatial subset sufficient reason suggestion supervenient things tion Tristram Shandy true two-envelope paradox uncountably zero