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
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>
More information about the FOM
mailing list