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An axiomatic explanation of complete self-reproduction

Löfgren, Lars LU (1968) In Bulletin of Mathematical Biophysics 30(3). p.415-425
Abstract
A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions... (More)
A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions indeed are independent from ordinary logical-mathematical reasoning, but that they need not imply any inconsistencies. Instead such functions can be axiomatized, and in this sense they really do exist. Finally, the introduced notion of complete self-reproduction is compared with “self-reproduction” of ordinary biological language. It is pointed out that complete self-reproduction is primarily of interest in connection with formal theories of evolution. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Bulletin of Mathematical Biophysics
volume
30
issue
3
pages
415 - 425
publisher
Springer
external identifiers
  • scopus:51249189718
ISSN
0007-4985
DOI
10.1007/BF02476604
language
English
LU publication?
yes
id
99583479-5d57-4fa2-bee0-279ab2ef0ce8 (old id 1744364)
date added to LUP
2010-12-13 11:41:00
date last changed
2017-08-06 04:31:20
@article{99583479-5d57-4fa2-bee0-279ab2ef0ce8,
  abstract     = {A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions indeed are independent from ordinary logical-mathematical reasoning, but that they need not imply any inconsistencies. Instead such functions can be axiomatized, and in this sense they really do exist. Finally, the introduced notion of complete self-reproduction is compared with “self-reproduction” of ordinary biological language. It is pointed out that complete self-reproduction is primarily of interest in connection with formal theories of evolution.},
  author       = {Löfgren, Lars},
  issn         = {0007-4985},
  language     = {eng},
  number       = {3},
  pages        = {415--425},
  publisher    = {Springer},
  series       = {Bulletin of Mathematical Biophysics},
  title        = {An axiomatic explanation of complete self-reproduction},
  url          = {http://dx.doi.org/10.1007/BF02476604},
  volume       = {30},
  year         = {1968},
}