[FOM] Leibnizian principles
f.a.muller at fwb.eur.nl
Wed Nov 12 02:17:44 EST 2014
> Message: 1
> Date: Tue, 11 Nov 2014 18:39:33 +1300
> From: W.Taylor at math.canterbury.ac.nz
> To: W.Taylor at math.canterbury.ac.nz
> If one doesn't wish to go to a hierarchy of predicate variables,
> and is prepared (largely ignoring 1st/2nd-order distinctions)
> to treat objects and properties on the same footing, then
> Leibnitz' law has an interesting "dual" form, which might be useful.
> IDENTITY OF INDISCERNABLES: (Leibnitz)
> [all x,y] x = y <=> [all P] Px <=> Py
If true, a line has only one point, because all points share their properties.
> IDENTITY OF INDISCRIMINABLES: (dual)
> [all P,Q] P = Q <=> [all x] Px <=> Qx
If true, "having a unique successor" is
identical to "having a unique prime decomposition" (when x is a natural number variable).
--> F.A. Muller
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