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ANY MATERIAL REALIZATION OF THE (M,R)-SYSTEMS MUST HAVE NONCOMPUTABLE MODELS

    Robert Rosen's (M,R)-systems are a class of relational models with a structure that defines a necessary distinguishing feature of organisms. That feature is an impredicative hierarchy of constraint on the properties of the model that correspond to the closure of an organism's entailment relations with respect to efficient cause. As a consequence, a computable model cannot be an (M,R)-system. This has been mathematically proven, and hence indisputable. Nevertheless, "computable" implementations of the mappings in an (M,R)-system have been reported. This paper explains the logical impossibility of the existence of these "counterexamples." In particular, it examines the errors in the construction of one of the most interesting among them. The relevance of this result to neuroscientists is that the same structure of closure to efficient cause is observed in brain dynamics.

    References

    • C. F.   Gauss , Disquisitiones Arithmeticae (1801) ( Yale University Press , New Haven CT , 1966 ) . Google Scholar
    • B.   Goertzel , Creating Internet Intelligence , ed. B.   Goertzel ( Kluwer Academic/Plenum Publishers , New York , 2002 ) . CrossrefGoogle Scholar
    • C. R.   Hadlock , Field Theory and its Classical Problems ( The Mathematical Association of America , Washington DC , 1978 ) . Google Scholar
    • A.   Jones , S. A.   Morris and K. R.   Pearson , Abstract Algebra and Famous Impossibilities ( Springer-Verlag , New York , 1991 ) . CrossrefGoogle Scholar
    • S. W. Kercel, J. Integr. Neurosci. 3, 7 (2004). LinkGoogle Scholar
    • S. W. Kercel, J. Integr. Neurosci. 3, 61 (2004). LinkGoogle Scholar
    • R. Rosen, B. Math. Biophys. 26, 103 (1964). Crossref, MedlineGoogle Scholar
    • R. Rosen, B. Math. Biophys. 26, 239 (1964). Crossref, MedlineGoogle Scholar
    • R. Rosen, B. Math. Biophys. 28, 141 (1966). Crossref, MedlineGoogle Scholar
    • R. Rosen, Bull. Math. Biophys. 33, 303 (1971). Crossref, MedlineGoogle Scholar
    • R. Rosen, Foundations of Mathematical Biology 2, ed. R. Rosen (Academic Press, New York, 1972) pp. 217–253. CrossrefGoogle Scholar
    • R.   Rosen , Life Itself ( Columbia University Press , New York , 1991 ) . Google Scholar
    • R.   Rosen , Essays on Life Itself ( Columbia University Press , New York , 2000 ) . Google Scholar
    • A. Silberschatz and P. B. Galvin, Operating System Concepts, 5th edn. (Addison-Wesley, Reading MA, 1998). Google Scholar
    • P. L. Wantzel, J. Math. Pures Appl. 2, 366 (1837). Google Scholar