[FOM] Leibnizian principles

[Harry Deutsch]

On 11/14/14, 2:16 PM, Charlie wrote:
> 	   It’s always seemed to me that Leibniz had to have packed relations into his properties.   How else would one object having only properties, be able to reflect all properties about all other objects in the same world.   For L., everything is relational.  So, more or less as Blum says, I think it’s right that if point x is in position A, and there’s a point y on the same line to the left of x, they are different points, for I think Leibniz would consider it a “property” that
> “Point y is to the left of point x”.  I should add the qualification that I’m no Leibnizian scholar and that I’m sure I’ve oversimplified (or misinterpreted) much.
>
> On Nov 13, 2014, at 1:32 AM, Alex Blum <Alex.Blum at biu.ac.il> 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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Years ago, I asked Dan Gallin a question concerning which relations were 
definable in terms of boolean combinations of monadic formulas.  I had 
Leibniz in mind.  The algebraist Steve Comer answered the question in 
print model theoretically.  Sorry, I don't have the reference.

Harry