John, List:
JAS: how would you scribe the graph for "A thinks that B is *possibly *
true"?
JFS: For my recommended version of metalevel EGs, I would first replace the
dotted line of your EG with a solid line. That would express the sentence
"A is thinking the proposition that there exists a B."
Thanks for the attempt, but this incorrectly treats B as denoting the *subject
*of a proposition ("there exists a B") instead of a *complete *proposition
(e.g., B = "C is a good girl"). Moreover, as Roberts explains (1973, pp.
76-77), the dotted line and oval are necessary to signify that what A is
thinking is an *abstraction*--in this case, a proposition--not a concrete
individual as denoted by a heavy (solid) line of identity. Accordingly,
here is the Gamma EG for "A is thinking the proposition that there exists a
B" or simply "A thinks that there exists a B."
[image: image.png]
It is almost identical to the Delta EG that I posted last night--the only
difference is that within the dotted oval, the heavy line is attached to
the left side of the B instead of its top side, but this is a *crucial
*notational
distinction. The horizontal heavy line is a Beta line of *identity*,
denoting an indefinite individual to which the general concept denoted by
the name B is being attributed; in English, "there exists a B" or simply
"something is B." The vertical heavy line is a Delta line of
*compossibility*, denoting a possible state of things in which the
proposition denoted by the letter B would be true; in English, "there
exists a possible state of things in which the proposition B would be true"
or simply "proposition B is possibly true."
JFS: Then I would connect that solid line by a ligature to the word
'possible'. Literally, that new EG could be read "A is thinking the
possible proposition that there exists a B." But it could be read more
simply "A thinks it's possible that there is a B."
Not exactly--the English translation of what you describe would be "A
thinks something that is possible and is the proposition that there exists
a B." What you need to represent is not "A thinks that the *proposition '*there
exists a B' is possible," but "A thinks that the *existence *of something
that is B is possible," i.e., "A thinks that the proposition 'there exists
a B' is *possibly true*." Can you see the difference? With that in mind, I
suggest this Gamma EG instead.
[image: image.png]
Its English translation is "A thinks *that *it is possible *that *there
exists a B"--the two instances of "that" correspond to the two dotted
line/oval combinations. Returning now to Helmut's original example in which
B denotes a complete proposition (e.g., "C is a good girl"), not a name for
a general concept, the Gamma EG for "A thinks that proposition B is
possibly true" is exactly the same, except with no line of identity
attached to B. Alternatively, substitute the Beta EG for proposition B
inside the innermost dotted oval--"A thinks *that *it is possible *that *C
is a good girl."
[image: image.png]
Or another option--"C is a girl, and A thinks *that *it is possible *that *she
is good."
[image: image.png]
These examples demonstrate conclusively that Gamma EGs could *already
*represent
modal propositions using metalanguage with the dotted line/oval notation
that Peirce anticipated in 1898 and introduced in 1903. He did not need a
new Delta part for *that *purpose in 1911.
JFS: Exactly the same procedure can be used to attach any other adjective
or phrase, such as 'necessary', 'impossible', 'probable', 'useful',
'desirable', 'feared', 'doubted', 'lawful', 'illegal' or 'written in Holy
Scriptures". That is the reason why the version of modality that C. I.
Lewis specified in 1932 is a dead end. Anything you can express with it can
be expressed more clearly and generally with metalanguage.
The goal here is not only to *express *modal propositions, but also to *reason
*about them. Another question that I keep asking but you (so far) have not
answered is, How would your approach facilitate this? What transformation
rules would there be for dotted lines/ovals? How would iterated modalities
be represented--perhaps with nested dotted lines/ovals attached to "is
possible" and/or "is necessary"? What permissions would correspond to the
standard modal axioms--perhaps explicit stipulations like a dotted
line/oval attached to "is necessary" can always be erased and a dotted
line/oval attached to "is possible" can always be added (axiom T)? What
could we validly deduce from the assertion that something is "probable,"
"useful," "desirable," "feared," or "written in Holy Scriptures"? How
exactly would that *inference *be carried out by a series of erasures,
insertions, iterations, and/or deiterations?
JFS: I believe that Peirce recognized the need for more expressive power.
And metalanguage adds that power without losing anything that might be
expressed with the 1903 EGs.
Again, the 1903 Gamma EGs *already *included the dotted oval/line notation
for metalanguage, so there was no need for Peirce to invent something new
for *that *purpose in 1911. In order to represent *modal *propositions with
EGs, his *only *stated reason for adding a Delta part, he needed a better
notation to replace the unsatisfying broken cuts of 1903 and nonsensical
tinctures of 1906. The vertical heavy lines of R 339:[340r] fit the bill,
and as spelled out in my forthcoming paper, they provide *graphical *solutions
for iterated modalities, modal axioms, etc.
JFS: And we should all remember that Peirce List is a collaboration, not a
competition. If somebody corrects one of our mistakes, we should thank them
for the correction. (
https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00089.html)
I continue to agree wholeheartedly with these sentiments and hope that you
will give serious consideration to my feedback accordingly. I am sincerely
trying to help you as I work through all this myself.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
On Thu, Mar 14, 2024 at 1:54 PM John F Sowa <s...@bestweb.net> wrote:
> Jon,
>
> Every statement about a thought expresses a possibility. Every statement
> about a claim, a wish, a fear, etc, expresses a possibility. That is why
> metalanguage is a more explicit method for expressing and reasoning about
> possibility. Quine said that in the 1960s, and other logicians have been
> developing methods for doing that since the 1970s. Today, nobody uses the
> Lewis-style of modal logic for any practical purpose.
>
> JAS: how would you scribe the graph for "A thinks that B is *possibly *
> true"?
>
> I'm sorry that I forgot to answer that question. I was commenting on
> other points, and I forgot to state the translation for the EG you drew.
> For my recommended version of metalevel EGs, I would first replace the
> dotted line of your EG with a solid line. That would express the sentence
> "A is thinking the proposition that there exists a B." Then I would
> connect that solid line by a ligature to the word 'possible'.
>
> Literally, that new EG could be read "A is thinking the possible
> proposition that there exists a B." But it could be read more simply "A
> thinks it's possible that there is a B."
>
> Exactly the same procedure can be used to attach any other adjective or
> phrase, such as 'necessary', 'impossible', 'probable', 'useful',
> 'desirable', 'feared', 'doubted', 'lawful', 'illegal' or 'written in Holy
> Scriptures". That is the reason why the version of modality that C. I.
> Lewis specified in 1932 is a dead end. Anything you can express with it can
> be expressed more clearly and generally with metalanguage.
>
> I believe that Peirce recognized the need for more expressive power. And
> metalanguage adds that power without losing anything that might be
> expressed with the 1903 EGs. Some people dabbled with methods for
> computing with a Lewis-style of reasoning, but they have never been used
> for any practical applications. Metalanguage is simpler and more general.
>
> John
>
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