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 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
> 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