About existence-as-consistency

sambin at math.unipd.it sambin at math.unipd.it
Sun Jun 27 14:57:33 EDT 2021

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  


  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
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