TY - JOUR

T1 - Autonomic life as the proof of incompleteness and Lawvere's theorem of fixed point

AU - Gunji, Yukio Pegio

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1994/3/15

Y1 - 1994/3/15

N2 - If finite velocity of observation propagation is taken into consideration, one is faced with a paradox or infinite regression in his own logic. It is the same as Goedel's theorem of incompleteness or Wittgenstein's paradox, and in general it can be formally replaced by Lawvere's theorem of a fixed point. To describe time evolution under finite velocity of observation propagation is not to construct a new logic in which the paradox can be removed or improved, but to accept the paradox itself. Given a system in which a paradox is deduced by taking the finite velocity of observation propagation, we can regard the whole formal description, which consists of the system and a proof sequence, toward the paradox, as an evolutionary system. A formal evolutionary system defined here is one demonstration of autonomic life.

AB - If finite velocity of observation propagation is taken into consideration, one is faced with a paradox or infinite regression in his own logic. It is the same as Goedel's theorem of incompleteness or Wittgenstein's paradox, and in general it can be formally replaced by Lawvere's theorem of a fixed point. To describe time evolution under finite velocity of observation propagation is not to construct a new logic in which the paradox can be removed or improved, but to accept the paradox itself. Given a system in which a paradox is deduced by taking the finite velocity of observation propagation, we can regard the whole formal description, which consists of the system and a proof sequence, toward the paradox, as an evolutionary system. A formal evolutionary system defined here is one demonstration of autonomic life.

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U2 - 10.1016/0096-3003(94)90049-3

DO - 10.1016/0096-3003(94)90049-3

M3 - Article

AN - SCOPUS:0000687430

VL - 61

SP - 231

EP - 267

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2-3

ER -