List,
I Googled around to see whether anybody had commented on Peirce's 1913
remark to F.A. Wood, and found that Gary Fuhrman at his website had
incorporated the remark as a note to 4.569
http://www.gnusystems.ca/ProlegomPrag.htm#4569 (once there, scroll down
a little).
I didn't know about Peirce's concern with the "strange rule" etc., when
I first saw the remark to F.A. Woods years ago, and since then I had
just a hazy memory of a late correction.
To be clear, if I'm correct in my reading of the graphs, then Peirce
merely suffered a late glitch and the Collected Papers editors (and
later, Zeman and others) saw that and were correct not to try to
incorporate the correction. (Gary F. doesn't incorporate it either, he
just presents it in a footnote at the paragraph's end. I really need to
explore Gary F.'s site more!)
I have noticed a tendency of Peirce to regard the indefinite particular
in terms of, for example, "a man whom I could name," "a certain man".
According to the Century Dictionary, where Peirce had charge (see
http://web.archive.org/web/20120324152520/http://www.pep.uqam.ca/listsofwords.pep?l=C)
of the definition of 'certain', 'a certain...' means something or
someone _/known but unspecified/_ by the speaker (when it doesn't mean
'a sure...' or the like). So Peirce knew the difference between 'a
certain' and 'some' which just means 'one or another'. 'A certain' is
more a veiled constant than a true variable like 'some'. (I would say
'masked constant' but it's hard to say aloud with the consonantal
pile-up in it.) But, according to Peirce,
[CP 3.94.] The old logics distinguish between _/individuum
signatum/_ and _/individuum vagum/_. "Julius Cæsar" is an example of
the former; "a certain man," of the latter.[....]
[From "Description of a Notation for the Logic of Relatives" (1870)]
When I first read that years ago, I wasn't familiar enough with Peirce's
precision or the Century Dictionary, and I wondered, did the old logics
really say "a certain" rather than "some"? (Note, Peirce goes on to
discuss allowing the phrase 'any individual man' as an example of an
_/individuum vagum/_) But later I did happen to run into a Latin old
logic on Google Books and indeed it used forms of _/quidam/_ ('a
certain') rather than _/aliqui/_ ('some') in examples of the particular.
I'm wondering whether Peirce's concern against the "strange rule"
(equivalence of 'something is blue or round' with 'something is blue or
something is round') can be seen as involving a half-conscious notion
that any of us might have of capturing something from the sense of 'a
certain' and using it in 'some'.
A year or two ago, when I first read "On an Improvement on the Gamma
Graphs" where Peirce mentions the "strange rule", at first I thought he
must be wrong; somehow I was interpreting 'some' as if it meant 'a
certain', even though I had only the slightest acquaintance with old
logics. I was well aware of difference of meaning between the English
words 'some' and 'a certain', but as unaware of how the sense of 'a
certain' can creep into one's sense of 'some'. It took a while for me to
strip the example down till I saw a 'rule of passage,' of which I had
read 15 or more years earlier.
The "strange rule" expresses the fact that, with the variable, an
alternative among predicates gets 'mixed into the general population',
so to speak, of the alternative among variable's possible values. But if
one takes 'a certain' as a veiled constant, then the "strange rule" does
not apply to '_/A certain/_ woman commits suicide if her husband fails
in business'.
Anyway, onward to the example of "a man whom I could name".
[CP 5.447.]
[....] _/Example:/_ "A man whom I could mention seems to be a little
conceited." The _/suggestion/_ here is that the man in view is the
person addressed; but the utterer does not authorize such an
interpretation or _/any/_ other application of what she says.
[....] Every utterance naturally leaves the right of further
exposition in the utterer; and therefore, in so far as a sign is
indeterminate, it is vague, unless it is expressly or by a
well-understood convention rendered general. [....]
["Issues of Pragmaticism" (1905)].
This involves Peirce's idea of logical quantification as involving a
dialogue between an utterer and an interpreter. If the uttered
proposition is universal, then the interpreter has the right to select
any example. But I had thought, the interpreter has just as much power
to verify the particular proposition, even if it involves a different
example. If the utterer says, "somebody walks", the interpreter can
verify it with a different example than the one in the utterer's mind.
But if the utterer coyly says, 'a certain person walks', the interpreter
can't verify it until the utterer candidly says who it is who walks; 'a
certain person walks' is like a schema using not a variable expressed by
letter 'x' or the like, but a constant expressed by a letter such as 'c'
masking the walker's identity. All of that is overcome in Peirce's
endoporeutic, if not earlier. In "Existential Graphs: MS 514 by Charles
Sanders Peirce" http://www.jfsowa.com/peirce/ms514.htm, John Sowa comments:
In the game of endoporeutic, one player, called the _/proposer/_,
tries to show that a given EG is true, and another player, called
the _/skeptic/_, tries to show that it is false.
[End quote]
Sowa discusses how proposer and skeptic switch roles as negations are
peeled away:
If the current EG consists of just a single negation (shaded oval),
the negation is removed by unshading the outermost oval and
reversing the shading of any nested areas. Then the two players
switch sides: the current proposer becomes the new skeptic, and the
current skeptic becomes the new proposer.
[End quote]
Clearly formulating the distinct roles of proving an affirmation and
disproving a denial brings a lot of clarity to the situation. Now we no
longer have an interpreter who lacks the information to prove the
utterer's particular (or really veiled-singular) affirmation and has a
universe to exhaust in order to disprove the utterer's affirmation.
Instead, in this game, the proposer needs to prove the proposed
affirmation and thus will need to unmask the 'a certain'; and then the
skeptic will have the opportunity to disprove the affirmation.
I should add that Sowa says that Peirce's endoporeutic is logically
equivalent to Tarski's Model Theory and that it "can be defined as a
two-person zero-sum perfect-information game, of the same genre as board
games like chess, checkers, and tic-tac-toe". Now that I've learned more
about existential graphs, I've found Sowa's article very much worth
re-reading http://www.jfsowa.com/peirce/ms514.htm .
Best, Ben
On 2/12/2015 5:17 PM, Benjamin Udell wrote:
List,
While we're waiting for the Natural Propositions seminar to
recommence, I thought I'd send this on an oddity that I've found. I
think I've mentioned at peirce-l in the past that I couldn't track
down a certain correction that Peirce made to a graph in "Prolegomena"
- I don't mean Peirce's corrections in a subsequent issue of the
Monist. In one of the digressions of my effort to reply to Jeff
Downard's recent post, some key words occurred to me for a Collected
Papers search, and I found Peirce's correction, mostly by luck as it
turned out. Here it is. It's from a letter written by Peirce Oct.-Nov.
1913 and sent by him to F. A. Woods (scholarly details appear in this
post's appendix).
[CP 8 Bibliography: I. General: 1905 (pages 298-299)
With brackets in the original, and Zeman-style renditions by me of
the graphs appearing there,
*Quote* :]
In a letter to F. A. Woods, [Bibliography]M-22, Peirce says that
the material in [CP] 4.569, from "For the sake of illustrating
this . . ." up to the statement of the Fourth Permission, is
wrong. He says: "Instead of scribing
as I did, I should have scribed
". . . [This fallacy] cost me the trouble of my nonsensical
'tinctures' and heraldry.
"I am also sceptical as to the universal validity of my '4th
permission.'"
[*End quote* ]
I noticed that Zeman himself doesn't include this on his site (at
least where I can find it). I take it that Peirce thinks he's solved
the problem of the "strange rule" (now known as a "rule of passage"),
that "There is something round or blue" is equivalent to "There is
something round or there is something blue."
Now, please, please correct me if I'm wrong, but the second graph
seems to me to boil down to:
There is a suicide *or* non-failure's wife.
and, equivalently, by the "strange rule", to
There is a suicide *or* there is a non-failure's wife.
If I'm interpreting the graph correctly, he hasn't escaped the
"strange rule". Said in longer way, the graph says,
There is /x/ such that
( /x/ commits suicide *or* there is non-failure /y/ to whom /x/ is
wife) .
and, equivalently,
(There is /x/ such that /x/ commits suicide) *or* (there is /z/
such that there is non-failure /w/ to whom /z/ is wife)
If I'm right in my reading of the graph, then Peirce seems to have had
an off day or two. 1913 was very late in his life. This would explain
why it seems to have received little attention (but I'm far from
well-read in the existential graphs literature). Does the letter at
least show that Peirce's interest in the tinctures, the modal gamma
graphs, was indeed driven mainly by his concern about the "strange
rule"? I'm not even sure of that. And I don't think that that it would
pertain to his interest in graphs of 'second intentions', i.e.,
second-order graphs, which are also gamma graphs, and are reason
enough to motivate the gamma graph effort.
Any comments?
Appendix below concerns identifying the letter, its period of
composition, and that it was actually sent. - Best, Ben
APPENDIX
The passage is in CP 8 Bibliography: I. General: 1905 (pages 298-298),
and begins: "In a letter to F. A. Woods, [Bibliography]M-22, [....]".
The letter is from 1913 and mentions something in the 1906
"Prolegomena" but the quote appears under "1905" because the series of
three pragmatism papers began in 1905.
"M-22" means Item 22 under "III. Miscellaneous" in the Bibliography.
It says:
22. Woods, Frederick A. A letter, written during Oct and Nov 1913
in Widener VB2a. [CP] 8.380-388, except 380n4, are from it. See
also [Bibliography] G-1905-1c for a quotation from this letter.
Did Peirce actually send the letter? End note to 8.380-388's title "To
F.A. Woods, On 'Would Be'":
(Ed.) From a long letter to "My dear Dr. Woods," written over a
period between 14 October 1913 and 19 November 1913, with an added
quotation in 380n4. The letter was sent to Woods, but it is now in
Widener VB2a.
End of appendix.
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