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An Incompleteness Theorem for the Natural World

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Irreducibility and Computational Equivalence

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 2))

Abstract

The philosopher Gottfried Wilhelm von Leibniz is perhaps best known for the fierce controversy that arose between him and Sir Isaac Newton over the invention of calculus. The S-like integral sign that we use to this day is in fact a notation invented by Leibniz.

When Leibniz was a youth of nineteen, he wrote a paper called “De Arte Combinatorica”, in which he tried to formulate a universal algebra for reasoning, in the hope that human thought might some day be reducible to mathematical calculations, with symbols or characters standing for thoughts.

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References

  1. Chaitin, G.J.: The Unknowable. Springer, New York (1999)

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  2. Leibniz, G.W., Gerhardt, C.I. (eds.): Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Georg Olms Verlag, Hildesheim (1978)

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  3. Rucker, R.: Infinity and the Mind. Birkhäuser, Boston (1982)

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  4. Rucker, R.: The Lifebox, the Seashell, and the Soul. Thunder’s Mouth Press, New York (2005)

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  5. Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)

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Correspondence to Rudy Rucker .

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Rucker, R. (2013). An Incompleteness Theorem for the Natural World. In: Zenil, H. (eds) Irreducibility and Computational Equivalence. Emergence, Complexity and Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35482-3_14

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  • DOI: https://doi.org/10.1007/978-3-642-35482-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35481-6

  • Online ISBN: 978-3-642-35482-3

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