### Abstract

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.

Original language | English |
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Pages (from-to) | 231-267 |

Number of pages | 37 |

Journal | Applied Mathematics and Computation |

Volume | 61 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1994 Mar 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

**Autonomic life as the proof of incompleteness and Lawvere's theorem of fixed point.** / Gunji, Yukio.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 61, no. 2-3, pp. 231-267. https://doi.org/10.1016/0096-3003(94)90049-3

}

TY - JOUR

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

AU - Gunji, Yukio

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.

UR - http://www.scopus.com/inward/record.url?scp=0000687430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000687430&partnerID=8YFLogxK

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 -