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On a logical paradox implicit in the notion of a self-reproducing automation

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Abstract

The notion of automaton as used by J. von Neumann is formalized according to methods previously described (Rosen, 1958,Bull. Math. Biophysics 20, 245–60; 317–41). It is observed that a logical paradox arises when one attempts to describe the notion of self-reproducing automaton in this formalism. This paradox is discussed, together with some of the recent attempts to construct automata which exhibit self-reproduction. The relation of these results to biological problems is then investigated.

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Literature

  • Delbruck, M. and G. S. Stent. 1957. “On the Mechanism of DNA Replication” inA Symposium on the Chemical Basis of Heredity (W. McElroy and B. Glass, eds.). Baltimore: Johns Hopkins Press.

    Google Scholar 

  • Jacobson, H. 1958. “On Models of Reproduction.”Amer. Scientist,46, 255–84.

    Google Scholar 

  • Meselson, M. and F. W. Stahl. 1958. “The Replication of DNA inEscherichia coli.”Proc. Nat. Acad. Sci.,44, 671–82.

    Article  Google Scholar 

  • von Neumann, J. 1951. “The General and Logical Theory of Automata” inCerebral Mechanisms in Behavior. New York: John Wiley & Sons.

    Google Scholar 

  • Penrose, L. S. 1958. “Mechanics of Self-Reproduction.”Annals Human Genetics,23, 59–72.

    Google Scholar 

  • Rashevsky, N. 1959. “Suggestion for a Possible Approach to Molecular Biology.”Bull. Math. Biophysics,21, 309–26.

    MathSciNet  Google Scholar 

  • Rosen, R. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–60.

    Article  Google Scholar 

  • — 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”,20, 317–41.

    Article  Google Scholar 

  • — 1959. “A Relational Theory of Biological Systems II.”,21, 109–128.

    Article  Google Scholar 

  • Turing, A. M. 1937. “On Computable Numbers.”Proc. London Math. Soc. (2)42, 230–65.

    Google Scholar 

  • Watson, J. D. and F. H. Crick. 1953.Cold Spring Harbor Symp. Quant. Biol.,18, 123–31.

    Google Scholar 

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Authors and Affiliations

  1. Committee on Mathematical Biology, The University of Chicago, Chicago, USA

    Robert Rosen

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  1. Robert Rosen
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Rosen, R. On a logical paradox implicit in the notion of a self-reproducing automation. Bulletin of Mathematical Biophysics 21, 387–394 (1959). https://doi.org/10.1007/BF02477897

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  • DOI: https://doi.org/10.1007/BF02477897

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