In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he (...) maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism. (shrink)

Three premises set the stage for a Peirce based notion of resemblance, which, as Firstness, cannot be more than vaguely distinguished from Secondnessand Thirdness. Inclusion of Firstness with, and within, Secondness and Thirdness, calls for a nonbivalent, nonlinear, context dependent mode of thinkingcharacteristic of semiosis — that is, the process by which everything is always becoming something other than what it was becoming — and at the same time itincludes linear, bivalent classical logic as a subset. Certain aspects of the (...) Dao, Buddhist philosophy, and Donald Davidson’s ‘radical interpretation’ affordadditional, and perhaps unexpected, support for the initial set of three premises. (shrink)

This authoritative study explores the scientific and mathematical cultural milieu that patterns much of the Argentine writer Jorge Luis Borges's narrative design. Although criticism of Borges's fiction and essays has long emphasized philosophical traditions, Merrell expands the context of this interrogation of traditions by revealing how early twentieth-century and contemporary mathematics and physics also participated in a similar exploration. Topics treated include the semiotic flows of paradox and contradiction, the patterns of infinities, the limits of natural and mathematical languages, and (...) the narrative function in scientific theory. Against this, background, Merrell provides incisive readings of Borges's complex fiction and essays. (shrink)