Stretching the point, it might be argued that self-reflexiveness is related to Goedel
's Theorem, a proof that in any mathematical system involving transfinite induction there must be propositions that cannot (within the system) be proved to be either true or false.
, CCRA, serves as Senior Clinical Research Scientist, and Bernard Cook, PhD, DABCC, FACB, serves as Manager, Global Scientific Affairs, for Beckman Coulter Diagnostics.
While Robert was concerned also with the Lucas/Penrose adaptation of Goedel
and Bernard Lonergan's classical analysis in "insight", it is his delivery of another bombshell, the problem of fine-tuning in the cosmos, with which we will concern ourselves.
Infinity Mathematical Physical Absolute Abraham Robinson 0 0 0 Thomas Aquinas 0 0 1 Plato 0 1 0 Luitzen Brouwer 0 1 1 David Hilbert 1 0 0 Kurt Goedel
1 0 1 Bertrand Russell 1 1 0 Georg Cantor 1 1 1
Hilbert's program has been widely discredited and made irrelevant by Goedel
's incompleteness theorem.
book, L'infanzia di Goedel
(Godel's childhood), in 1999.
Of special note is the recognition of important but often overlooked contributors to the field like Post and Gentzen, often overshadowed by such luminaries as Cantor and Goedel
. Featuring chapters dedicated to the diagonal argument, ordinals, computability and proof, logic, arithmetic, natural unprovable sentences; and axioms, as well as being enhanced with the inclusion of a lengthy bibliography and a comprehensive index, "Roads to Infinity: The Mathematics of Truth and Proof" is highly recommended reading for students, scholars, and non-specialist general readers with an interest in the history and contemporary issues of mathematics today.
Here are the original formulations of Goedel
published in the years 1935-1937: