Godel

Mathematician, logician and philosopher Kurt Gödel (1906-1978) is, without a doubt, one of the greatest minds of our times. His answers to the radical questions posed by the 20th century in the fields of language, mathematics and rational thought decisively altered the foundations of contemporary knowledge: Does a language exist that can be used to isolate true statements applicable to all possible worlds? Can we prove or disprove each of the statements that we can formulate therein? Or do undecidable propositions exist in any given language? In broader terms, do absolutely undecidable propositions exist that cannot be proved or disproved within any plausible language? Are we machines? If we think correctly, our thought should be able to be stated in univocal language-yet, by using a definite language, we write as though we were machines. Are there machines capable of transcribing all of our thoughts? Do objects exist that are neither in space nor in time, and which we can only perceive with our minds? Are numbers such objects? Mathematics apparently constitutes the model of rational activity, while arithmetic serves as the model of mathematical certainty. But can we identify a basis for elementary arithmetic? In this book, the author presents Gödel's answers to such questions while tracing the progress of his logical and philosophical work, from his proof of the semantic completeness of first-order predicate calculus (1929), to his thoughts on continuity in the work of Cantor (1947), not to mention his so-called "Incompleteness Theorem" (1931)-one which made Gödel famous beyond his own field, and even influenced the psychoanalyst Jacques Lacan. Pierre Cassou-Noguès, who holds an agrégation in Mathematics and a Doctorate in Philosophy, is a researcher with the CNRS. His other published works notably include Hilbert and De l'expérience mathématique.