Yourgrau P. A world without time.. the forgotten legacy of Goedel and Einstein (Basic Books, 2005)(ISBN 0465092934)(176s)_PPop_

functions, it was an inescapable consequence of the second theorem that it directly
refuted Hilbert's program of establishing a finitary proof of consistency for formal
arithmetic. Through the work of Church and Turing, then, the full force of Godel's theorem
began to be appreciated.
The Formal and the Intuitive
God's mercy preserves mathematics from being drowned in mere technique
SIMONE WEIL
But it was not always so. The mathematical shot heard round the world began as a
whisper. Godel may have been a spy in the house of logic, a revolutionary, an intellectual
bomb thrower, but he was also a
citizen of Vienna, the city of coffeehouses. So he first communicated his momentous
discoveries to Rudolf Carnap in the Cafe Reichsrat, shortly before they both left for a
conference on the foundations of mathematics in Konigsberg (today, Kaliningrad, in which
both Kant and Hilbert were born), where Godel would announce his results publicly. The
first to be apprised of what the young man had done, however, seems to have been the
first to fail to appreciate it. At the Konigsberg conference a few days later, Carnap
proceeded, in good positivist style, to recommend consistency once again as the
touchstone of formal mathematical theories.
Carnap had been a student of Frege and of the philosopher Edmund Husserl and by 1931
was an established logician. If Frege can with justice be called the father of modern
"analytical" philosophy, Husserl can be considered the father of the "continental" branch.
The two reviewed each other's books and corresponded, but their followers assembled into
armed camps that exchanged intellectual gunfire. The influence Husserl came to have on
Godel late in his life was an anomaly; to his colleagues, it was an embarrassment. In 1931,
however, it was not an embarrassment for Carnap to have studied with Husserl. That such
a man as Carnap failed to grasp the force of GodePs accomplishment is an indication of the
break with tradition that Godel was inaugurating (a phenomenon his future friend Einstein
had already encountered with relativity theory). Even a year later, Carnap confided that
he still found Godel's results hard to understand.
Von Neumann alone immediately grasped the force of the discovery. He was present at the
meeting as one of the principal speakers, and after this encounter he would become a
lifelong friend and admirer of Godel. But Von Neumann, as was so often the case, was the
exception. So little impact did GodePs announcement have on his immediate listenersóthe
cream of the foundationalist mathematicians and formal logiciansóthat when Hans
Reichenbach, another prominent member of the Vienna Circle, wrote up an account of the
conference for the journal Erkenntnis, he did not even mention Godel. The mathematical
community, however, was quick to recover from this