[FOM] On definitions of terms, and free logic---a quick follow-up
Tennant, Neil
tennant.9 at osu.edu
Tue Oct 27 22:55:36 EDT 2015
Harvey proposes indefinite-ary (but presumably finitary?) braces as functions or operators: {blah blah blah}.
Looking forward to the details. Presumably he will lay down first principles that will enable one to prove the following sequent:
Ft1 , ... , Ftn, (x)(Fx -> (x=t1 v ... v x=tn)) : {x|Fx}={t1,...,tn} ?
---and to prove such things as
{x|x=t} = {t} = {t,t} = {t,t,t,} ... ;
{x|x=t v x=u} = {t,u} = {u,t} = {t,t,u} = {t,u,t} = {u,t,t} = ... = {t,u,t, t,u,t, t,u,t} = ... ?
What advantages will the complication of adding indefinite-ary braces have, for the formalization of mathematical reasoning, over the definitional abbreviation strategy of simply reading {t1,...,tn} as short for {x|x=t1 v ... v x=tn}?
Neil Tennant
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