KURT GÖDEL (1906-1978)

Kurt Gödel made it clear that certainty of any kind is impossible and initiated the twentieth-century retreat from an almost dogmatic belief in science to renewed spiritual questioning. Like Albert Einstein he was a pure scientist unable to refrain from commenting on God, consciousness and eternity, although he allowed his more personal comments to be published only after his death.

EXTRACT FROM THE EXPLORATORIUM

In 1931 the mathematician and logician Kurt Gödel proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms that define the system. This is known as Gödel's Undecidability Theorem. He also showed that in a sufficiently rich formal system in which decidability of all questions is required, there will be contradictory statements. This is known as his Incompleteness Theorem.
    In establishing these theorems Gödel showed that there are problems that cannot be solved by any set of rules or procedures; instead for these problems one must always extend the set of axioms. This disproved a common belief at the time that the different branches of mathematics could be integrated and placed on a single logical foundation.
    Alan Turing later provided a constructive interpretation of Gödel's results by placing them on an algorithmic foundation: There are numbers and functions that cannot be computed by any logical machine.
    More recently, Gregory Chaitin, a mathematician working at IBM, has stressed that Gödel's and Turing's results set fundamental limits on mathematics.
    These results, along with quantum uncertainty and the unpredictability of deterministic (chaotic) systems, form a core set of limitations to scientific knowledge that have only come to be appreciated in recent years.

POSTHUMOUS QUOTES

"Consciousness is connected with one unity. A machine is composed of parts."

"The brain is a computing machine connected with a spirit."

"Materialism is false."

"Our total reality and total existence are beautiful and meaningful ... We should judge reality by the little which we truly know of it. Since that part which conceptually we know fully turns out to be so beautiful, the real world of which we know so little should also be beautiful. Life may be miserable for seventy years and happy for a million years: the short period of misery may even be necessary for the whole."