Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

ONT Re: Apposite Purposes Of Logical Languages Objectified (APOLLO)




¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

What does that mean, 'sharing experience'?
Does it mean that 'some original pathema' (SOP),
some impression of the 'world as a whole' (WAAW),
is apportioned into lots and distributed to our
several rations, here, on this earthly sphere?
Something to muse on while I drone.

Having the incidence matrix of -- what shall I name it for short? -- "Lot(2^2^2)"
before me, I am emboldened to try and sketch its lattice diagram in Asciiischean.
In the diagram, the name "j", coded in Hexadecimal, will denote the function f_j.
By way of laying out the lattice of Lot(16) a bit more elegantly in the frame of
the plane, let me exploit a trick of Peirce, known as the "teridentity relation",
in order to identify the scattered avatars of entities in the order whose tokens
are required to be distributed throughout a host of different sites in the plane,
all the more facilely to meet the demands of their various and sundry incidents.

             ____________F____________
            /           / \           \
           /           /   \           \
          /           /     \           \
         /           /       \           \
        /           /         \           \
     __7__       __B__       __D__       __E__
    /  |  \     /  |  \     /  |  \     /  |  \
   3   5   6   3   9   A   5   9   C   6   A   C
    \   \   \ /     \   \ /   /     \ /   /   /
     \   \   /       \   /   /       /   /   /
      \   \ / \       \ / \ /       / \ /   /
       \   /   \       /   /       /   /   /
        \ / \   \     / \ / \     /   / \ /
         3   \   \   /   9   \   /   /   C
         |    \   \ /   / \   \ /   /    |
         |     \   /   /   \   /   /     |
         |      \ / \ /     \ / \ /      |
         |       5   \       /   A       |
         |      / \ / \     / \ / \      |
         |     /   \   \   /   \   \     |
         |    /   / \   \ /   / \   \    |
         3   /   /   \   6   /   \   \   C
        / \ /   /     \ / \ /     \   \ / \
       /   \   /       \   \       \   \   \
      /   / \ /       / \ / \       \ / \   \
     /   /   \       /   \   \       \   \   \
    /   /   / \     /   / \   \     / \   \   \
   3   5   9   3   6   A   5   6   C   9   A   C
    \__|__/     \__|__/     \__|__/     \__|__/
       1           2           4           8
        \           \         /           /
         \           \       /           /
          \           \     /           /
           \           \   /           /
            \___________\ /___________/
                         0

Table.  Incidence Matrix of the Implication Ordering <f_i => f_j>
o-----o------o----------o---------------------------------------------------------------o
|     |      |   f_i    |                              f_j                              |
|   p | 1100 |          o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o
|   q | 1010 |          | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
o-----o------o----------o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o---o
|     |      |          |                                                               |
| f_0 | 0000 |    ()    | 1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 |
|     |      |          |                                                               |
| f_1 | 0001 |  (p)(q)  |     1       1       1       1       1       1       1       1 |
|     |      |          |                                                               |
| f_2 | 0010 |  (p) q   |         1   1           1   1           1   1           1   1 |
|     |      |          |                                                               |
| f_3 | 0011 |  (p)     |             1               1               1               1 |
|     |      |          |                                                               |
| f_4 | 0100 |   p (q)  |                 1   1   1   1                   1   1   1   1 |
|     |      |          |                                                               |
| f_5 | 0101 |     (q)  |                     1       1                       1       1 |
|     |      |          |                                                               |
| f_6 | 0110 |  (p, q)  |                         1   1                           1   1 |
|     |      |          |                                                               |
| f_7 | 0111 |  (p  q)  |                             1                               1 |
|     |      |          |                                                               |
| f_8 | 1000 |   p  q   |                                 1   1   1   1   1   1   1   1 |
|     |      |          |                                                               |
| f_9 | 1001 | ((p, q)) |                                     1       1       1       1 |
|     |      |          |                                                               |
| f_A | 1010 |      q   |                                         1   1           1   1 |
|     |      |          |                                                               |
| f_B | 1011 |  (p (q)) |                                             1               1 |
|     |      |          |                                                               |
| f_C | 1100 |   p      |                                                 1   1   1   1 |
|     |      |          |                                                               |
| f_D | 1101 | ((p) q)  |                                                     1       1 |
|     |      |          |                                                               |
| f_E | 1110 | ((p)(q)) |                                                         1   1 |
|     |      |          |                                                               |
| f_F | 1111 |   (())   |                                                             1 |
|     |      |          |                                                               |
o-----o------o----------o---------------------------------------------------------------o

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤