An axiomatic explanation of complete self-reproduction

Research output: Contribution to journalArticle

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.

Details

Authors
  • Lars Löfgren
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Electrical Engineering, Electronic Engineering, Information Engineering
Original languageEnglish
Pages (from-to)415-425
JournalBulletin of Mathematical Biophysics
Volume30
Issue number3
Publication statusPublished - 1968
Publication categoryResearch
Peer-reviewedYes