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

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: LOGIC & MATHEMATICS
Posted: May 29, 2013 10:24 PM

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

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

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

dnZ2d@giganews.com
>

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
>

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

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

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.

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
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

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
>

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

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
5/26/13 Zaljohar@gmail.com
5/26/13 namducnguyen
5/26/13 Zaljohar@gmail.com
5/26/13 namducnguyen
5/26/13 Peter Percival
5/26/13 namducnguyen
5/26/13 Peter Percival
5/26/13 namducnguyen
5/26/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/28/13 Charlie-Boo
5/26/13 Zaljohar@gmail.com
5/27/13 zuhair
5/27/13 fom
5/27/13 Zaljohar@gmail.com
5/27/13 fom
5/28/13 namducnguyen
5/28/13 Zaljohar@gmail.com
5/28/13 namducnguyen
5/29/13 Peter Percival
5/30/13 namducnguyen
5/30/13 Peter Percival
5/30/13 Peter Percival
5/30/13 namducnguyen
5/31/13 Peter Percival
5/30/13 Bill Taylor
5/30/13 Peter Percival
5/30/13 Zaljohar@gmail.com
5/30/13 Zaljohar@gmail.com
5/30/13 namducnguyen
5/31/13 Peter Percival
5/31/13 Zaljohar@gmail.com
5/31/13 LudovicoVan
5/31/13 fom
5/28/13 Peter Percival
5/28/13 namducnguyen
5/27/13 Charlie-Boo
5/27/13 fom
5/28/13 Charlie-Boo
5/28/13 fom
6/4/13 Charlie-Boo
6/4/13 fom
6/5/13 Zaljohar@gmail.com
5/28/13 Zaljohar@gmail.com
5/28/13 LudovicoVan
5/28/13 ross.finlayson@gmail.com
5/28/13 LudovicoVan
5/28/13 LudovicoVan
5/28/13 fom
5/29/13 LudovicoVan
5/29/13 fom
5/30/13 LudovicoVan
5/29/13 fom
5/30/13 LudovicoVan
5/30/13 fom
5/31/13 LudovicoVan
5/31/13 Zaljohar@gmail.com
5/31/13 LudovicoVan
5/31/13 ross.finlayson@gmail.com
6/1/13 LudovicoVan
6/1/13 namducnguyen
6/1/13 ross.finlayson@gmail.com
6/2/13 LudovicoVan
6/2/13 ross.finlayson@gmail.com
6/3/13 Shmuel (Seymour J.) Metz
6/3/13 ross.finlayson@gmail.com
6/4/13 LudovicoVan
6/4/13 namducnguyen
6/4/13 Peter Percival
6/5/13 Shmuel (Seymour J.) Metz
6/5/13 fom
6/6/13 Peter Percival
5/31/13 fom
6/1/13 LudovicoVan
6/1/13 fom
6/2/13 ross.finlayson@gmail.com
6/2/13 fom
6/2/13 Herman Rubin
6/2/13 fom
6/2/13 LudovicoVan
6/3/13 Herman Rubin
6/3/13 Peter Percival
6/4/13 Herman Rubin
6/4/13 Peter Percival
6/4/13 Peter Percival
6/1/13 fom
6/1/13 LudovicoVan
6/1/13 namducnguyen
6/5/13 Peter Percival
6/1/13 fom
6/2/13 LudovicoVan
6/2/13 fom
5/28/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/27/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/30/13 Zaljohar@gmail.com