An axiomatic explanation of complete selfreproduction
(1968) In Bulletin of Mathematical Biophysics 30(3). p.415425 Abstract
 A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete selfreproduction and complete selfexplanation. These latter concepts are shown to be independent from ordinary logicalmathematicalbiological reasoning, and a special form of complete selfreproduction 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 selfreproduction and complete selfexplanation. These latter concepts are shown to be independent from ordinary logicalmathematicalbiological reasoning, and a special form of complete selfreproduction 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 logicalmathematical 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 selfreproduction is compared with “selfreproduction” of ordinary biological language. It is pointed out that complete selfreproduction is primarily of interest in connection with formal theories of evolution. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1744364
 author
 Löfgren, Lars ^{LU}
 organization
 publishing date
 1968
 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
 00074985
 DOI
 10.1007/BF02476604
 language
 English
 LU publication?
 yes
 id
 995834795d574fa2bee0279ab2ef0ce8 (old id 1744364)
 date added to LUP
 20160401 16:11:37
 date last changed
 20210314 04:39:12
@article{995834795d574fa2bee0279ab2ef0ce8, abstract = {{A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete selfreproduction and complete selfexplanation. These latter concepts are shown to be independent from ordinary logicalmathematicalbiological reasoning, and a special form of complete selfreproduction 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 logicalmathematical 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 selfreproduction is compared with “selfreproduction” of ordinary biological language. It is pointed out that complete selfreproduction is primarily of interest in connection with formal theories of evolution.}}, author = {{Löfgren, Lars}}, issn = {{00074985}}, language = {{eng}}, number = {{3}}, pages = {{415425}}, publisher = {{Springer}}, series = {{Bulletin of Mathematical Biophysics}}, title = {{An axiomatic explanation of complete selfreproduction}}, url = {{http://dx.doi.org/10.1007/BF02476604}}, doi = {{10.1007/BF02476604}}, volume = {{30}}, year = {{1968}}, }