[FOM] Leibnizian principles

[F.A. Muller]

> 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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