[FOM] Leibnizian principles

[S. S. Kutateladze]

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

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