An axiomatic explanation of complete selfreproduction
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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.
Details
Authors  

Organisations  
Research areas and keywords  Subject classification (UKÄ) – MANDATORY

Original language  English 

Pages (fromto)  415425 
Journal  Bulletin of Mathematical Biophysics 
Volume  30 
Issue number  3 
Publication status  Published  1968 
Publication category  Research 
Peerreviewed  Yes 