Thank you very much John for a most enlightening post.
Recto/verso issue (in other forms, of course) was taken up & became
somewhat popular within feminist philosophy 1980's and 1990's. I felt
uncomfortable with it. But could not pinpoint the locical (in the narrow
sense) errors.
A pseudograp is always false, you wrote. If and when probabilies are
taken seriously. Just as the prefix in naming the concept implies.
In other contexts CSP uses "quasi-", denoting an "as if.." prefix.
Something, anything in priciple, may be taken as if it were true. - E.g.
beliefs no one present (in any sense) doubts.
N-valued logic, in abtracto, does not involve time. So I gather? - So,
even if the possible truth values are unnumerable, innumerable, as soon
as events and successions of events are involved, (logical) anything
just vanishes. Then there always (already) is something.
With empereia, there always is something.
To all I know, CSP never used the term 'semantics'. It was introduced &
became popular after CSP. (If anyone proves me wrong, I'll be glad to
know better).
I attended Hintikka's lectures on game theory in early 1970's. No shade
of Peirce. I found them boring. No discussion invited nor wellcomed.
Later on he got more mellow. And very interested on Peirce. - I greatly
appreciate his latest work, remarkable indeed. Especially from a
representative of analytical philosophy, to which he remained true. -
Still, it hurts my heart and soul to read a suggestion that Peirce's
endoporeutic may have or could have been a version of Hintikka's game
theoretical semantics. - Must have been a slip.
Is it so that Peirce never gave up his project on developing a genuinely
triadic formal logic? Even though Part II, existential graphs were the
only part he completed in a satisfactory way (to his own mind)?
Thanks again,
Kirsti
John F Sowa kirjoitti 29.10.2017 19:16:
Jon A and Gary F,
Peirce's way of presenting EGs in his Lowell lectures and his
publications of 1906 is horrendously complex. The best I could
say for it is "interesting". But I would never teach it, use it,
or even mention it in an introduction to EGs. I would only present
it as a side issue for advanced students.
The version I recommend is the 8-page summary that he wrote in a
long letter (52 pages) in 1911. The primary topic of that letter
is "probability and induction" (NEM v 3, pp 158 to 210).
When he got to 3-valued logic and probabilities, the recto/verso
idea is untenable. Instead of talking about cuts, seps, and scrolls,
he just talks about *areas* on the sheet of assertion. To represent
negation, he uses a shaded oval, which he calls an area, not a cut.
The shading makes his notation much more readable. An implication
(the old scroll) becomes a shaded area that encloses an unshaded area.
His rules of inference are much clearer, simpler, and more symmetric:
just 3 pairs, each of which has an exact inverse. See the attached
NEM3p166.png. (URLs below)
Jon
Peirce's introduction of the “blot” at this point is
I would continue that sentence with the word 'confusing'.
Peirce said that a blank sheet of assertion is a graph. Since
it's a graph, you can draw a double negation around it. The blank
is Peirce's only axiom, which is always true. If you draw just
one oval around it, you get a graph that negates the truth.
Therefore, it is always false. Peirce called it the pseudograph.
In a two-valued logic, the pseudograph implies everything.
But when you get to probabilities or N-valued logic, you can't
make that assumption. I believe that's why Peirce dropped his
earlier explanations. For the semantics, he adopted endoporeutic,
which is a version of Hintikka's Game Theoretical Semantics.
Gary
At this point the “experiment” resorts to a kind of magic trick:
Peirce makes the blot disappear (gradually but completely) — yet
falsity remains
Yes. But it's just another confusing way of explaining something
very simple: The pseudograph is always false. If you draw it in
any area, it makes the entire area false.
John
___________________________________________________________________
I first came across this version of Peirce's EGs from a copy of a
transcription of MS514 by Michel Balat. (By the way, I thank Jon
for sending me the copy. I still have his email from 14 Dec 2000.)
For my website, I added a commentary with additional explanation
and posted it at http://jfsowa.com/peirce/ms514.htm
In 2010, I published a more detailed analysis with further
extensions: http://jfsowa.com/pubs/egtut.pdf
For the published version in NEM (v3 pp 162-169), see
https://books.google.com/books?id=KGhbDAAAQBAJ&pg=PA163&lpg=PA163&dq=%22false+that+there+is+a+phoenix%22&source=bl&ots=LKYw9nZEKh&sig=LEaTyTSTGiEuT-P_-9a6XHEVwWQ&hl=en&sa=X&ved=0ahUKEwi509vA9pPXAhWEOSYKHcDQBZQQ6AEIJjAA#v=onepage&q=%22false%20that%20there%20is%20a%20phoenix%22&f=false
Note: I found that volume of NEM by searching for the quoted phrase
"false that there is a phoenix" -- which Peirce used as an example.
The attached excerpt is from a screen shot.
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