But every error is due to extraneous factors (such as emotion and education); reason itself does not err Kurt Gödel
Kurt Friedrich Gödel was born on April 28, 1906, in the Czech Republic. His father, Rudolf Gödel, originally was from Vienna; his mother, Marianne Handschuh, belonged to German Rhineland. The young Gödel was known by the nickname, der Herr Warum (Mr. Why) because of his inquisitive inclination of asking questions. In Logical Dilemmas: The Life and Work of Kurt Gödel, biographer John W. Dawson, Jr., regards him as “an earnestly serious, bright, and inquisitive child who was sensitive, often withdrawn and pre-occupied, and who, already at an early age, exhibited certain signs of emotional instability.” Kurt Gödel was one of the most influential mathematical logicians of the twentieth century. In 1999, when Time magazine conducted a poll for determining the 20 most influential thinkers of the 20th century (a survey crowned by Einstein), Gödel, who has often been pronounced as “the most important logician since Aristotle,” was ninth in the list—ahead of Watson Keynes, and Crick of DNA eminence and Tim Berners-Lee (world wide web pioneer). Fond of Disney movies and hiding under the furnace, Godel was rightly seen as ‘eccentric genius’ who casted everything in the mould of logic even the sanity itself .
Incompleteness, Inconsistency and Limits to ‘Truth’
In 1931, Gödel published his results in formal mathematical logic that are considered as breakthrough of 20th-century mathematics. Gödel demonstrated in his own bohemian way, in effect, that efforts in reductionism of mathematics to an axiomatic(formal) system, as imagined by mathematicians and philosophers at the start of the 20th century, were lacking in many respects in proving every mathematical truth. His trailblazing findings ended the logicist ‘project’ of Bertrand Russell and Alfred North Whitehead while demonstrating the stark limits of David Hilbert’s formalist vision for mathematics. Godel at first turned to Physics and then found his true metier in mathematics, as he was fascinated by the rigour of developments of mathematical methods and the certainty of mathematical truth during the 1920s
By the age of 25 Kurt Gödel had produced his famous “Incompleteness Theorems.” His fundamental results showed that in any defined/consistent mathematical (axiomatic) system there are propositions having the intrinsic provability/disprovability within this system and that the consistency of the axioms too themselves cannot be proved ).
While being mostly influenced by Platonism, Gödel knew there was no consistency in human reason, and his ‘incompleteness’ has been put in with three important discoveries of 20th century mainly that of Einstein’s Relativity, Heisenberg’s Uncertainty which had their basis on expounding our limits of expounding the architecture of absolute truths in universe. Gödel’s thought was indicative of Enlightenment mode of ‘arriving at truth’ through observations and logic, were not possible in the cannot mathematical system too . Gödel proved by terming out the ‘propositions’ that are beyond the formal axiomatic logic, that transcendental/higher truths are beyond the reach of reason. Roger Penrose,theoretical physicist and philosopher of Science was influenced by Gödel as a graduate student at Cambridge. Gödel’s while recalling the revelatory imprint that had left on him as certain claims in mathematics are true but cannot be proven and related this mathematical elixir into his work on consciousness ( Emperor’s New Mind) which was through famous Minsky-Penrose debate. Gödel proved that the mathematical methods since Euclid’s (around 300 BC) were not enough for discovering all that is true about the numbers. His discovery literally shook mathematical foundations on which they were built upto the 20th century, stirred new wave of inconsistency and indecidability among thinkers and spawned a lively debate about the nature and form of truth. Incompleteness theorems have a far-reaching implications from the foundation of mathematics to Gödel’s innovative techniques, which could be applied to computational algorithms, also laying the foundation for modern computer science. His findings strongly influenced the (later) discovery that a computer can never be programmed to answer all mathematical questions with his ‘Gödel numbering’ and worked on the ‘halting’ principle with Alan Turing which determined the limits of computer systems in its ‘computability’ . Incompleteness theorem-“the most significant mathematical truth of the century,” as it would soon be described in a ceremony at Harvard University-set a permanent limit on our knowledge of the basic truths of mathematics.
Thus, while the man may not be found in the popular culture as the likes of Einstein and Russell, his work has rich legacy—in philosophy, science, literature and even theology (he gave ontological proof for the existence of God) too; he has also been celebrated in poetry (“Homage to Gödel” by Hans Magnus Enzensberger) and adapted to music too (Hans Werner Henze’s Second Violin Concerto contains a setting of Enzensberger’s poem). Douglas Hofstadter’s 1979 book Gödel, Escher, Bach: An Eternal Golden Braid, a 800 page masterpiece of finding beauty in mathematics through music, linguistics and abstract fields which got a Pulitzer and became a surprising bestseller while describing the philosophical profundity of Gödel.
Einstein, Gödel and Shadows of Coming Dictator
Einstein commented that his own work no longer meant much to him and that he now went to his office “just to have the privilege of walking home with Kurt Gödel.” Freemon Dyson, their colleague notes that ” Gödel was the only one of our colleagues who walked and talked on equal terms with Einstein.” Reigniting his taste for physics with this stroll down the Institute of Advanced Studies Princeton, where Einstein had succeeded in transforming time into space, Gödel would perform a trick yet more magical making the time disappear. Rocking the mathematical world to its foundations with his incompleteness theorem, Gödel now stepped into the world of Einstein and relativity. He surprised everyone with his discovery of cosmological solutions to the field equations of general relativity, solutions being transformed itself with so called Gödel Universe’s where we could travel back in time, (imagine Mr.Peabody’s WABAC). Gödel was the amalgam of Einstein and Kafka, had for the first time in human history proved, from the equations of relativity, that time travel was not a philosopher’s fantasy but a scientific possibility. Yet again he had somehow contrived, from within the very heart of mathematics to drop a bomb into the laps of the philosopher. When in 1947 he received US citizenship the hearing was the one test in his life that he waltzed with unparalleled brilliance. He had discovered how the US could legally be turned into a dictatorship, by logically examining the propositions and of its Constitution. Well, not so wrong..!!
Tailpiece
Remaining ill in his last 20 years Gödel turned thin, frail, and mostly disturbed. He was very concerned about his health and turned sceptical of everything including his doctors as he thought they were going to kill him. He refused to eat, even after he had been admitted to hospital. He died of malnutrition and inanition caused by personality disturbance, as his death certificate recorded. Gödel had once beautifully remarked that “We live in a world in which ninety-nine per cent of all beautiful things are destroyed in the bud” We should preserve the legacy of Gödellian ‘mathematical intuition’ and it is clear enough in a deep sense, that we all do live in Gödel’s universe.