Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

index 303Euclidean space, 5, 177, 197–98, 200, 202–3,214Eudoxos of Knidos, 22–23Euler, Leonhard, 59n4, 62–64Eunomian controversy/Eunomius, 28–30,28n62, 266, 278everlasting/eternal inflation, 180, 183, 185,187–88, 190–91ex nihilo (out of nothing) concept, 236, 238,252, 267, 288, 294–95exponentiation, 82, 84–85, 280extenders (Inner Model Program), 113–15fear of infinity, 4–5, 76Fermat, Pierre de, 56, 62, 96Fichte, Johann Gottlieb, 272finite set theory, 92–96finite vs. infinite number of states, 7, 188–91finitismin Aristotle, 22–23, 64, 73–74Cauchy and, 64and God, 22–23, 249–50, 253, 272, 274and language, 243in mathematics, 83Nelson advocating, 5in Peano arithmetic, 60–61and potential infinity, 22tand P vs. NP, 73–74serial, 297and set theory, 94First Vatican Council, 226FLRW. SeeFriedmann-Lemaître-Robinson-Walkermetricfluctuations, 7, 179–80, 183, 188–90, 189n11,196n10, 198, 200–203four-dimensional space, 68, 197n12, 244Fourth Lateran Council, 265Fraenkel, Abraham, 77frame bundles, 222Frege, Gottlob, 66, 77, 139Friedman, Harvey M., 4, 12, 121, 123–24,130–64Friedman isomorphism theorem, 121–24Friedmann-Lemaître-Robinson-Walker (FLWR)metric, 176–78, 181, 183, 196–97, 201–3,222Friedmann singularities, 223Friedrich, Caspar David, 208friends and strangers theorem, 60–61, 61fGalileo Galilei, 9, 37–39, 278n12, 279–80Gamow, George, 55, 65–66, 74Gardner, Martin, 57Gauss, Carl Friedrich, 39, 279Gaussian perturbations, 179general relativity theory (GR) (Einstein)curvature of space in, 38, 69failure of, 196n10and FLRW, 176gravity theories in, 223–24and homogeneous and isotropic space, 178n3,196and infinity, 176, 194and light propagation, 220–21points at infinity in, 219and quantum theory, 168spacetime in, 8, 168, 176, 219–22, 224success of, 168vs. theology, 251generic multiverse, 3, 102–12Gentzen, Gerhard, 38, 47, 79geodesics, 8, 219–22, 222n9Geroch, Robert, 222God. Seealsodivine infinity; God and infinityas the Absolute, 9, 11as Absolute Mystery, 275–76, 283and actual infinity, 29–30, 32–33, 285, 288alienation from, 45arguments for existence of, 250Aristotle’s views of, 22–23, 42as axiom of choice, 235n2Cantor on, 31, 41, 47, 282–83n22as Creator, 7, 11–12, 211, 283n22, 295Dionysius the Areopagite on, 34Eunomius on, 28and finitism, 22–23, 249–50, 253, 272, 274as Great Designer, 7, 228vs. Greek metaphysics, 47Gregory of Nyssa on, 11–12, 28–31as incomprehensible, 275–76, 283, 285,298as infinite perfection, 290and the Logos, 12and the multiverse, 7ontological infinity of, 37Origenes on, 27Pannenberg on, 285–87Plato on, 277and positive infinity, 12, 293as potential infinity, 9predicates/properties of, 42, 236–48, 252,275–76, 278, 285–87as present vs. transcendent, 8and Pseudo-Dionysius, 296–97R. J. Russell on, 11simplicity of, 293–94sparse theories of, 237–39transcendence of, 8, 23, 212, 228, 263–72,292, 297–98