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 |
|---|---|
| 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.
In: Applied Mathematics and Computation, Vol. 61, No. 2-3, 15.03.1994, p. 231-267.Research output: Contribution to journal › Article
}
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.
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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 -