ONT Re: De In Esse Predication
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
CSP = Charles Peirce
JA = Jon Awbrey
BM = Bernard Morand
CSP: | [A Boolian Algebra With One Constant] (cont.)
|
| To express the proposition: "If S then P",
| first write:
|
| A
|
| for this proposition. But the proposition
| is that a certain conceivable state of things
| is absent from the universe of possibility.
| Hence instead of A we write:
|
| B B
BM: All was going right till there for me
CSP: | Then B expresses the possibility of S being true and P false.
BM: Now, I am stopped. May be there is an intermediary
implicit proposition that I am not seeing? If yes
which one? This could be of interest to Gary too:
I guess that for the whole passage the elements
of the demonstration count more than the
conclusion in itself.
CSP: | Since, therefore, SS denies S, it follows
| that (SS, P) expresses B. Hence we write:
|
| SS, P; SS, P.
|
| C.S. Peirce, CP 4.14, untitled paper circa 1880.
Bernard,
Peirce is working analytically here -- I mean that in the good sense of the word --
in the manner that Bentham called "paraphrasis", Boole "development", or most math
folks "expansion", if I remember right. But he already knows the answer he wants,
so the whole analysis will have that "pulling a rabbit out of the hat" quality of
such performances.
The basic operation is unmarked, or you could think of the blank space as a symbol
for the "joint denial", that Peirce called one of the "amphecks" (cutting both ways),
Sheffer called a "stroke", and comp sci folk call NNOR (neither nor). The punctuation
marks are not really operators, they just group terms, much like the "puncts" or "dots"
of Peano that Russell so butchered to the point of unintelligibility, like so much else.
In saying "S => P" one is saying "that a certain conceivable state of things
is absent from the universe of possibility" -- sounds awfully "intensional",
does it not? -- but anyway, the conceivable states of things that one is
excluding from the universe of possibility are any states of things that
would form a counterexample to "S => P", namely, those states of things
that are described by "S and not P".
That denial would take the form:
S and not P. S and not P.
Let's call that the Lady Macbeth denial.
It remains to analyze the metalanguage phrase "S and not P"
using only "S", "P", and the tacit joint denial connective.
If I wrote "S P", this would be saying "not S and not P",
so all I need to do is change the sign on the S part of it,
which I can do by doubling the S. As we have stipulated,
doubling is a way of putting things in doubt. Therefore,
"SS, P" says "S and not P", which is the thing we want
to deny, and which final denial we can make by writing:
SS, P; SS, P.
Voila!
Jon
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o