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RE: [ontac-forum] Theories, Models, Reasoning, Language, and Truth

To: "ONTAC-WG General Discussion" <ontac-forum@xxxxxxxxxxxxxx>
From: "Paul S Prueitt" <psp@xxxxxxxxxxxxxxxxxx>
Date: Tue, 20 Dec 2005 13:39:37 -0700
Message-id: <CBEELNOPAHIKDGBGICBGMEGGHAAA.psp@xxxxxxxxxxxxxxxxxx>

The lattice that you are refering to is a construction, or potential
construction.  In this way it is similar to the set of counting numbers.
The set of positive integers can be regarded as existing only as a
potential... given that there is no way to get the entire construction put
somewhere.  But this is a mute point, as you point out.    (01)

In the counting numbers one has a total, sometimes called linear, order.
This order extends to the real numbers but not the complex numbers.    (02)

The lattice can be a structure with a partial order having a minimal element
and a maximal element.    (03)

An example of this is the set of subsets can be organized in such a fashion.
John, is your , and Tarski's, notion of a lattice of theories such a
structure?  This is what I just do not see.  How do you or Tarski compare to
theories?  Suppose that all theories are the special ones that are
formalized to a degree necessary.    (04)

Lattice geometries are discussed at    (05)

http://www.hermetic.ch/compsci/lattgeom.htm    (06)

and I may say that in 1987 I published a paper on spin glass lattices in the
journal "Complex Systems".  I recognize how really interesting it is to say
that there is a relationship ....    (07)

In my recent work I develop the notion of a non specific relationship
(without order) as a means of mapping data structure into computer memory.    (08)

But ...  I do not understand this notion of a lattice of theories.    (09)

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