John, Gary F., List:
I am replying under this thread topic for reasons that will become
apparent. I agree with John that "every EG expresses a
proposition"--including "a line of identity, by itself"--and therefore is a
medad in the sense of *having no blanks*.
CSP: In a complete proposition there are no blanks. It may be called a *medad
*... (CP 3.465; 1897)
CSP: A rhema with no blank is called a *medad*, and is a complete
proposition. (CP 4.438; c. 1903)
CSP: A Graph is a Pheme, and in my use hitherto, at least, a Proposition.
(CP 4.538; 1906)
However, Peirce's 1909 "tutorial" on EGs (R 514)--reproduced in his June
22, 1911 letter to Mr. Kehler (NEM 3:162-169)--includes these statements
that paint a different picture.
CSP: Indivisible graphs usually carry 'pegs' which are places on their
periphery appropriated to denote, each of them, one of the subjects of the
graph. A graph like "thunders" is called a "*medad*" as having no peg
(though one might have made it mean "*some time* it thunders" when it would
require a peg). A graph or graph instance having 0 peg is a *Medad*. A
graph or graph instance having 1 peg is a *Monad*. A graph or graph
instance having 2 pegs is a *dyad*. A graph or graph instance having 3 pegs
is a *triad* ... The line of identity can be regarded as a graph composed
of any number of dyads "---is---," or as a single dyad. (NEM 3:164)
If every Graph is a Proposition, and every Proposition is a medad, how can
there be Graphs that are monads, dyads, and triads? The answer is that
Peirce *changed his usage*--by 1909, such terms no longer corresponded to
the number of *blanks *in a Rheme; instead, they corresponded to the number
of *subjects *connected by a predicate to form a Proposition.
CSP: Yet I consider my theories of scientific reasoning to be of high
importance, and also my idea (obtained by logical analysis), that the
division of all logical terms into those of valencies 1, 2, and >2, where
'valency' refers to the fact that, in existential graphs, every predicate
has either a single connexion with one subject (as in "it rains" where the
predicate is the present phenomenon and the subject is *rain *or
*pluviation*); or secondly, it is a dyadic relative between two subjects
and has valency= 2, as Napoleon was mortal, where Napoleon and Mortality
are the two subjects, or finally, it connects more than two subjects, as
the word *and *does when expressing as is usual *coidentity*, as in
'Napoleon was mortal and mendacious.' (NEM 3:885; 1908 Dec 5)
Peirce's examples here are all Propositions *with no blanks*; but rather
than all of them being medads, "it rains" is a monad (one subject),
"Napoleon was mortal" is a dyad (two subjects), and "Napoleon was mortal
and mendacious" is a triad (three subjects). Consistent with what I quoted
above, the Graphs for these Propositions have the same number of Pegs as
subjects. Similarly, a Line of Identity *by itself* is a Graph--a medad in
the earlier sense, because it has no blanks; but "a single dyad" in the
later sense, because it has two subjects, one at each end.
CSP: Now we have only to stretch such a heavy dot into a heavy line, and
it automatically becomes an assertion of the identity of the two
graph-subjects denoted by its two extremities. (R 670:9; 1911 June 9)
On the other hand, a Spot *by itself*, with no heavy dot(s) or Line(s) of
Identity attached to its Peg(s), would be a *Rheme*--i.e., an
*incomplete* Proposition--and
thus a monad, dyad, or triad in the earlier sense, based on the number of
blanks (unattached Pegs).
CSP: An ordinary predicate of which no analysis is intended to be
represented will usually be *written *in abbreviated form, but having a
particular point on the periphery of the written form appropriated to each
of the blanks that might be filled with a proper name. Such written form
with the appropriated points shall be termed a *Spot*; and each
appropriated point of its periphery shall be called a *Peg *of the Spot. If
a heavy dot is placed at each Peg, the Spot will become a Graph expressing
a proposition in which every blank is filled by a word (or concept)
denoting an indefinite individual object, "something." (CP 4.560; 1906)
Notice that such a Spot is *written*, rather than *scribed*, and it does
not become a Graph--i.e., a *complete *Proposition--unless and until "a
heavy dot is placed at each Peg" to serve as an indefinite subject
("something"). The two notions of valency are thus not *inconsistent *with
each other; the difference is simply that the earlier sense is tied to the
number of *actual *blanks (unattached Pegs), while the later sense tied to
the number of *potential *blanks (total Pegs).
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Thu, Mar 21, 2019 at 10:07 AM John F Sowa <[email protected]> wrote:
> On 3/20/2019 5:44 PM, [email protected] wrote:
> > what I asked for, “any Peirce text on EGs where he refers to a
> > Spot with one Tail, or a Line of Identity by itself, as a "Medad".
>
> Peirce's terminology for EGs evolved over the years from 1897 to 1911.
> See below for some excerpts from CP 4.394 to 560. Convention Zero
> (4.394) gives permission for revising certain features "at will".
>
> Peirce used Convention Zero to make his 1911 version the simplest and
> clearest of all. I believe that's a justification for adopting it with
> some borrowing of terminology from earlier versions, if needed.
>
> > in the 1906 Welby letter http://gnusystems.ca/PeirceWelbyMarch1906.htm
> > ... a Spot with one peg (i.e. one line of identity attached) is
> > labelled a “monad.” Your calling it a “medad” therefore requires some
> > explanation as does your statement that a particular graph is “a medad
> > because it has no unattached peg.” I can’t make sense of the term
> > “unattached peg.”
>
> CP 4.560 defines a peg as a "point" on a spot, not a line. CP 4.403
> defines 'hook' with nearly the same meaning. Don Roberts defined
> 'peg' as "Same as hook." Since eg1911 uses the word 'peg', but
> not 'hook', I'll use the word 'peg'. The word "unattached' means
> that there is no line of identity attached to that peg/hook.
>
> In talking about the ambiguity of the word 'subject', I needed some
> phrase to relate parts of an EG to an English sentence in which some
> words were replaced by blanks. Some of those parts are well-formed
> EGs, but other parts have pegs were some line was ripped out.
>
> > I asked for, “any Peirce text on EGs where he refers to a Spot with
> > one Tail, or a Line of Identity by itself, as a "Medad".
>
> CP 4.406 says that a line of identity shall be "a graph, subject to
> all the conventions relating to graphs". That point together with
> the definition "A graph or graph instance having 0 peg is a Medad"
> (NEM 3.164) implies that a line of identity, by itself, is a Medad.
>
> In any case, CP 4.406 is sufficient to imply that a line, by itself,
> is a Pheme because every EG expresses a proposition.
>
> > I raise the matter because it has implications for phaneroscopy
> > as well as EGs.
>
> I agree. And when we're talking about phaneroscopy, the issues
> about going to "stereoscopic moving pictures" become very important.
> For the context of that phrase, see the attached nem3_191a.png.
>
> An even more important context than page 191 is the entire letter to
> Mr. Kehler (NEM 3.159 to 212), which begins with the tutorial on EGs.
>
> I suspect that's the reason why Peirce simplified the EG definitions.
> He wanted to make them more general so that they could be applied
> to diagrams of stereoscopic moving images.
>
> John
> _____________________________________________________________________
>
> CP 4.394. Convention No. Zero. Any feature of these diagrams that is
> not expressly or by previous conventions of languages required by the
> conventions to have a given character may be varied at will. This
> "convention" is numbered zero, because it is understood in all agreements
>
> 403. Convention No. IV. The expression of a rheme in the system of
> existential graphs, as simple, that is without any expression, according
> to these conventions, of the analysis of its signification, and such as
> to occupy a superficial portion of the sheet or of any area shall be
> termed a spot. The word "spot" is to be used in the sense of a replica;
> and when it is desired to speak of the symbol of which it is the
> replica, this shall be termed a spot-graph. On the periphery of every
> spot, a certain place shall be appropriated to each blank of the
> rheme; and such a place shall be called a hook of the spot. No spot
> can be scribed except wholly in some area.
>
> 404. A heavy dot scribed at the hook of a spot shall be understood
> as filling the corresponding blank of the rheme of the spot with an
> indefinite sign of an individual, so that when there is a dot attached
> to every hook, the result shall be a proposition which is particular
> in respect to every subject.
>
> 405. Convention No. V. Every heavily marked point, whether isolated,
> the extremity of a heavy line, or at a furcation of a heavy line,
> shall denote a single individual, without in itself indicating what
> individual it is.
>
> 406. A heavily marked line without any sort of interruption (though
> its extremity may coincide with a point otherwise marked) shall,
> under the name of a line of identity, be a graph, subject to all
> the conventions relating to graphs, and asserting precisely the
> identity of the individuals denoted by its extremities.
>
> 560. By a rheme, or predicate, will here be meant a blank form of
> proposition which might have resulted by striking out certain parts
> of a proposition, and leaving a blank in the place of each, the parts
> stricken out being such that if each blank were filled with a proper
> name, a proposition (however nonsensical) would thereby be recomposed.
> An ordinary predicate of which no analysis is intended to be represented
> will usually be written in abbreviated form, but having a particular
> point on the periphery of the written form appropriated to each of the
> blanks that might be filled with a proper name. Such written form with
> the appropriated points shall be termed a Spot; and each appropriated
> point of its periphery shall be called a Peg of the Spot. If a heavy dot
> is placed at each Peg, the Spot will become a Graph expressing a
> proposition in which every blank is filled by a word (or concept)
> denoting an indefinite individual object, "something."
>
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