Date: Tue, 7 Oct 2003 15:51:43 -0400 (EDT)
From: Alan Sondheim <sondheim@panix.com>
To: 7-11@mail.ljudmila.org
Subject: Scheme for a General Literature
Scheme for a General Literature
Wittgenstein, TLP:
[P, E, N(E)] :
P = all propositions
E = any set of proportions
N(E) = negation of E
Russell: 'The whole symbol means whatever can be
obtained by taking any selection of atomic
propositions, negating them all, then taking any
selection of the set of propositions now obtained,
together with any of the originals--and so on
indefinitely. This is, he [Wittgenstein] says, the
general truth-function and also the general form of
proposition.' (Introduction, TLP.)
Now the negation is necessary to produce the Sheffer
stroke and its dual; atomic propositions, however, are
illusory - show me one.
Nevertheless, one can write P, where
P = generalized alphabetics; and E, where
E = a finite subset methodology (axiom of choice)
in any order of P. Note that P is a reasonably
small integer < 40,000. (Of course further reduction
is possible by virtue of binary or unary mapping.)
We have in addition S({E}), where
S = the substructure or ordering-site (Peirce's
"sheet of assertion"); {E} (a set of finite subsets
of P) is mapped onto S.
Then clearly [P, E, S({E})] is the general form of
literature - in particular, religious or other
traditional or exemplary texts (including their
diacritical and extra-alphabetic graphemes) - issues
of practicality, decidability, etc. notwithstanding.
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