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Topic: LOGIC & MATHEMATICS
Replies: 96   Last Post: Jun 6, 2013 5:19 AM

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fom

Posts: 1,969
Registered: 12/4/12
Re: LOGIC & MATHEMATICS
Posted: May 29, 2013 10:24 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 5/29/2013 7:13 AM, Julio Di Egidio wrote:
>
> (By the way, your news: links do not work, at least not for me.)
>


I almost forgot that I put these
in the thread. Assuming this is
to what you had been referring,
I have taken the time to find the
hypertext links.


======================================

> I understand certain basic relations
> geometrically,
>
> news://news.giganews.com:119/Jr2dnbdYvtfPdlrNnZ2dnUVZ_t->

dnZ2d@giganews.com
>

https://groups.google.com/forum/?fromgroups#!msg/sci.logic/V41XKFS9zSU/4vcFbzXcyRMJ

the "corrected" version reflects a name change

THIS -> NOT


> and I understand compositionality through an
> intensional axiomatized equational theory,
>
> news://news.giganews.com:119/IqudndogJ8->

VB1zNnZ2dnUVZ_qydnZ2d@giganews.com
>

https://groups.google.com/group/sci.logic/msg/362a82b11fe77f70?dmode=source




> Truth table semantics begins with geometric
> forms instantiating all possibilities for
> logical equivalence,
>
>

news://news.giganews.com:119/zsCdnW9U7v4BOlzNnZ2dnUVZ_hmdnZ2d@giganews.com

https://groups.google.com/group/sci.logic/msg/446ad325630ae309?dmode=source

the diagrams are not really readable in the web
page.

There are incidence tables. The column headings are 4-tuple
column vectors of '-' and '|' delimited by columns of '|'.
The row labels are triples of 4-tuple column vectors.

Each locus in the tables has a 'T' or 'F' positioned to
be coherently matched with the column headings.

In the first table,

T -> |
F -> -

In the second table,

T -> -
F -> |

Fix a column heading to fix representation of
Logical Equivalence (biconditional), LEQ.

Fix a row to fix truth table components.

Ordering is still an issue, it will depend
on a specific representation that you may
not choose. The point with the first
selection is that LEQ is the initial
representation that decides the form of
a truth table. A truth table is needed
for the semantics of a complete connective.
The ordering in the next step fixes a truth
table for a complete connective...


> and ends with a canonical ordering that
> fixes a representation for a complete
> connective,
>
>

news://news.giganews.com:119/AuqdnYcXm8eaLVzNnZ2dnUVZ_h-dnZ2d@giganews.com
>
> These particular constructions actually
> become quite complex. Certain group theoretic
> constructions reflecting the choice of
> representation provide a syntactic labeling
> of the free orthomodular lattice on two generators.


https://groups.google.com/group/sci.logic/msg/75ca0a179004e0e6?dmode=source

The ordering is based on an Euler trail
and a palindromic symmetry for the 15
symbols different from LEQ. The center
is XOR. The last three form a truth
table for NOR.

To understand this emphasis on LEQ, note
that Tarski wrote a paper treating LEQ as
the primitive connective of "logistic".
This had been important to Lesniewski's
deliberations. These analyses had been
second-order. But, I am concerned with
demarcations that ground a system of
connectives with a classical bivalence.
I am not trying to "purport" a logical
system as much as I am trying to
represent an analysis of it.


> My understanding of propositions is
> based on a free DeMorgan algebra,
>
>

news://news.giganews.com:119/Jr2dnbNYvtf9cFrNnZ2dnUVZ_t-dnZ2d@giganews.com

https://groups.google.com/forum/?fromgroups#!msg/sci.logic/IFbunFH1vJ8/o5eUKxD2Nv0J

The "corrected" version has the name change

THIS -> NOT


> and, in fact, I view DeMorgan algebra
> as foundational rather than Boolean
> algebra,
>
>

news://news.giganews.com:119/Jr2dnbBYvtedcFrNnZ2dnUVZ_t-dnZ2d@giganews.com
>

https://groups.google.com/forum/?fromgroups#!msg/sci.logic/3nLe4eMRpgU/40irzsxhEUgJ

The "corrected" version has the name change

THIS -> NOT


> The ortholattice O_6 which appears in these
> constructions is fundamental to models of
> logic as discerned by Pavicic and Megill in
>
> http://arxiv.org/pdf/quant-ph/9906101v3.pdf





> Although I have nothing to show for my efforts,
> I have taken the issue of demarcation very
> seriously. After all, what exactly is meant
> by "foundational" if one is starting somewhere
> in the middle?



There are other posts in this initial sequence.
Look for 'fom' 02 - 10

https://groups.google.com/group/sci.logic/index/browse_frm/month/2012-12?_done=%2Fgroup%2Fsci.logic%2Fbrowse_frm%2Fmonth%2F2012-12%3F&

https://groups.google.com/group/sci.logic/browse_frm/month/2012-12?start=250&sa=N


However you come to view these posts, please
try to keep in mind that it is hard to see
things differently from others. And, since
I received no inquiries, there is little to
no explanation.





Date Subject Author
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