[FOM] Leibnizian principles
S. S. Kutateladze
sskut at math.nsc.ru
Fri Nov 14 22:38:42 EST 2014
Foundations of Mathematics wrote :
A points position on a line is an essential property of a point despite it being relational, hence it must be counted a property.
-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of F.A. Muller
Sent: Wednesday, November 12, 2014 9:18 AM
To: <fom at cs.nyu.edu>
Subject: [FOM] Leibnizian principles
> 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
Sent from my iPhone
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Sobolev Institute of Mathematics
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