Citado no livro: Incompleteness (2005) de Rebecca Goldstein
Frases de Kurt Gödel
Data de nascimento: 28. Abril 1906
Data de falecimento: 14. Janeiro 1978
Kurt Friedrich Gödel foi um matemático austríaco, naturalizado norte-americano.
O trabalho mais conhecido de Gödel é seu teorema da incompletude, no qual afirma que qualquer sistema axiomático suficiente para incluir a aritmética dos números inteiros não pode ser simultaneamente completo e consistente.
Isto significa que se o sistema é auto-consistente, então existirão proposições que não poderão ser nem comprovadas nem negadas por este sistema axiomático. E se o sistema for completo, então ele não poderá validar a si mesmo — seria inconsistente.
Citações Kurt Gödel
„A complexidade dos seres viventes tem que estar presente no material ao qual eles são derivados ou nas leis que governam sua formação.“
Citado no livro: Nature’s Imagination (1995)
„Noventa por cento dos [filósofos contemporâneos] tem como principal tarefa extirpar a religião da cabeça dos homens. Estamos muito longe de sermos capazes de fornecer uma base científica para a visão teológica do mundo.“
Citado no livro: Vida e Trabalho de Kurt Gödel (1997) por John W. Dawson Jr.
Publicado no livro: "Topoi : The Categorial Analysis of Logic" (1979)
„The meaning of the world is the separation of wish and fact. Wish is a force as applied to thinking beings, to realize something. A fulfilled wish is a union of wish and fact. The meaning of the whole world is the separation and the union of fact and wish.“
As quoted in The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us (MIT Press) 2013 by Yanofsky, Noson S
„Ninety percent of [contemporary philosophers] see their principal task as that of beating religion out of men's heads. … We are far from being able to provide scientific basis for the theological world view.“
As quoted in Logical Dilemmas : The Life and Work of Kurt Gödel (1997) by John W. Dawson Jr.
As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13
„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.“
„Only someone who (like the Intuitionist) denies that the concepts and axioms of classical set theory have any meaning could be satisfied with such a solution, not someone who believes them to describe some well-determined reality. For in reality Cantor's conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of reality.“
„To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r).“
Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931); Informally, recursive systems of axioms cannot be complete.
As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang
„But every error is due to extraneous factors (such as emotion and education); reason itself does not err.“
Attributed as a remark of 29th November 1972, in Incompleteness (2005) by Rebecca Goldstein
„The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material [from which they are derived] or in the laws“
governing their formation
As quoted in "On 'computabilism’ and physicalism: Some Problems" by Hao Wang, in Nature’s Imagination (1995), edited by J. Cornwall, p.161-189