[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 44

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Arisbe List, Cybernetics List,

The following Table will suffice to suggest the syntactic correspondences among
the "streamer-cross" forms that Peirce used in his essay on "Qualitative Logic"
and Spencer Brown used in his book 'Laws of Form', as they become extended by
successive steps of controlled reflection, the plaintext string syntax, and
the rooted cactus graphs:

o-----------------------------o-----------------o-----------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
| ` ----------o ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` a ` ` |
| ` ` ` ` ` ` | ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` o ` ` |
| ` ` ` a ` ` | ` ` ` ` ` ` ` | ` (a) ` ` ` ` ` | ` ` | ` ` |
| ` ` ` ` ` ` | ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` O ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
o-----------------------------o-----------------o-----------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
| ` ----------o---o ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` a ` b ` |
| ` ` ` ` ` ` | ` | ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` o---o ` |
| ` ` ` a ` ` | b | ` ` ` ` ` | ` (a , b)`  ` ` | ` `\`/` ` |
| ` ` ` ` ` ` | ` | ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` O ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
o-----------------------------o-----------------o-----------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
| ` ----------o---o---o ` ` ` | ` ` ` ` ` ` ` ` | ` a b c ` |
| ` ` ` ` ` ` | ` | ` | ` ` ` | ` ` ` ` ` ` ` ` | ` o-o-o ` |
| ` ` ` a ` ` | b | c | ` ` ` | ` (a , b , c) ` | ` `\`/` ` |
| ` ` ` ` ` ` | ` | ` | ` ` ` | ` ` ` ` ` ` ` ` | ` ` O ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` | ` ` ` ` ` |
o-----------------------------o-----------------o-----------o

| Reference:
|
| C.S. Peirce, "Qualitative Logic", MS 736, pp. 101-115 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. C.S. Peirce, "Qualitative Logic", MS 582 (Fall-Winter 1886), pp. 323-371 in:
|'Writings of Charles S. Peirce:  A Chronological Edition, Volume 5, 1884-1886',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1993.
|
| QUAL.  Qualitative Logic
| QUAL.  http://stderr.org/pipermail/inquiry/2005-May/thread.html#2697
| QUAL.  http://stderr.org/pipermail/inquiry/2005-June/thread.html#2776

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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