Infinity and the Mind: The Science and Philosophy of the Infinite

Absolute Infinite actually infinite alef-one argument atoms axioms basic Berry paradox billion words called cardinal number code numbers conceivable property concept consistent countable decimal expansion defined definite describe digits discussed exist extendible cardinals fact Figure finite description formal system Georg Cantor given Gödel's Incompleteness Theorem Hilbert human idea inaccessible inaccessible cardinals infinite number infinite regress infinite sets infinitesimal infinity Kurt Gödel language large cardinals Liar paradox logical mathematical mathematicians meaningful formulas means mind Mindscape multiplicity mystical nameable natural numbers never notion object one-to-one One/Many problem ordinals less particles philosophy physical proof provable prove Pythagoreans question rational real number Reflection Principle robots Rudy Rucker rules sense sentence sequence set theory sort space space-time statement strings of symbols subsets tetration thing tion transfinite numbers true truth machine Wheelie Willie X₁ York zero