About existence-as-consistency

[sambin at math.unipd.it]

Dear Fomers,
   

  I am deeply interested in the historical origin and explanation of  
the principle by which consistency of an axiomatic theory T (typically  
ZFC) is sufficient to  justify it and derive that what it speaks about  
exists (in the case of ZFC, sets satisfying the properties described  
by its axioms). I call this principle: existence-as-consistency,  
shortly EaC.

  I am thinking for instance of the appearance of EaC in Hilbert's  
program in the 1920s. I suspect that the standard model theoretic  
explanation of EaC (by which T is consistent iff it has a model) came  
later. 

   

  A related question is: is there a way to avoid assuming EaC while  
keeping classical logic (and hence validity of LEM)?

   

  I thank in advance for any information and comments.

  Giovanni Sambin
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20210627/74bf6550/attachment.html>