FOM: reply to Detlefson on vagueness

Neil Tennant neilt at
Wed Dec 3 13:52:33 EST 1997

Mic Detlefson suggests that some applications of the term-forming operator
"set of..." might be on vague formulae, and thereby produce vague set terms;
while others not, and therefore not.
In response, I would point out that we only have to apply my original objection
recursively. What makes those formulae (to which "set of..." is being applied)
vague? If it's because of yet further containeed set-terms being vague, re-pose
the question ... Eventually we have to bottom out with epsilon and the identity
Also, Mic says that '{x|...x...}' has to be understood contextually. But actually that is not so; it can be taken as a primitive operator, and on can lay down
rules of natural deduction for it (introduction and elimination rules for set
terms in identity contexts) that specify a lovely "logic of sets" that is
existentially non-committal but pins down the essential connections between
set-existence, defining conditions and membership of sets. Extensionality and
Church's conversion schema (suitably formulated in a free logic) drop out as
logical results. The rest (existence of omega; etc.) is mathematical.
Neil Tennant

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