To:  "[ontologforum]" <ontologforum@xxxxxxxxxxxxxxxx> 

From:  Alex Shkotin <alex.shkotin@xxxxxxxxx> 
Date:  Tue, 21 Sep 2010 11:00:16 +0400 
Messageid:  <AANLkTim9kXLf81ZBKWE_tyKV7Bf38Ji_rr8VWuuW=Bw@xxxxxxxxxxxxxx> 
Chris, you are right:  I should be more careful using FOL term abbreviation. It should be "In First order language to get definition..." or even "In First order language with definition feature to get definition...".  and we do need theorem of existence and uniqueness. This is why I have mentioned transitive closure: If we keep in mind that systems we describe are algebraic systems, then in set theory (as you mentioned) we may prove that for that kind of models we do have definition.  and in FOL we do can only introduce an axiom R_(x,y) <> R(x,y) or there_exists z such_that R_(x,z) and R(z,y) as representative of our definition. and anyway may I summarize that definition is more then just axiom;) Even context of "definition" may be beyond just language (and logic)  may be we need to keep in mind referent itself or at least class of models (math speaking). For ex if an infinite in one direction, properly directed chain (node > node >...) is an existing thing for us then "+", "*" arithmetic operations has recursive definition on it. Alex 2010/9/20 Christopher Menzel <cmenzel@xxxxxxxx>
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