Kirsti, you asked why my post about 2.14 put “categories” in
quotation marks. It’s because that is the term Peirce used for
Firstness, Secondness and Thirdness in the Cambridge Lectures of 1898.
In the Lowell Lectures (and the Syllabus) of 1903, he mostly used the
term “elements” instead, as we’ll see in Lecture 3, for
instance. I’m drawing attention to the shift in terminology because
I think it reflects to a conceptual shift that becomes increasingly
evident in Peirce’s phenomenology from this point on.
As for SPOT, DOT and BLOT, if you’ve been following Lowell 2 it
should be clear enough how they are related; anyway, I don’t think I
can add anything to my last two posts that will clarify their usage in
the terminology of EGs.
Gary f.
-----Original Message-----
From: [email protected] [mailto:[email protected]]
Sent: 25-Nov-17 15:38
To: [email protected]
Cc: 'Peirce List' <[email protected]>
Subject: RE: [PEIRCE-L] Lowell Lecture 2.14
Gary f.,
I cannot understand your use of quotation marks. Why say: ... his
"categories"??? Insted of... his categories???
Also, instead or warning against confusing SPOT, DOT and BLOT, it
would have been most interesting to hear how they are related. This is
all about relational logic, is it not. In your opinion too?
Not about just classification.
Kirsti
[email protected] kirjoitti 25.11.2017 21:52:
List, Mary,
Lowell 2.14 introduces the SPOT (which must not be confused with
either the DOT or the BLOT!), and in this connection is worth
comparing with MS 439, the third of the Cambridge Lectures of 1898
(RLT 146-164, NEM4 331-46). In this lecture given five years before
Lowell 2, Peirce began with a sketch of his "categories" (Firstness,
Secondness and Thirdness), then applied them to formal logic (more
specifically to the "Logic of Relatives"), which he then explained
"by
means of Existential Graphs, which is the easiest method for the
unmathematical" (or so he claimed -- RLT 151). In this post I'll
include two paragraphs from that 1898 lecture. First, from RLT 154:
Any part of a graph which only needs to have lines of identity
attached to it to become a complete graph, signifying an assertion,
I
call a _verb_. The places at which lines of identity can be attached
to the verb I call its _blank subjects_. I distinguish verbs
according
to the numbers of their subject blanks, as _medads, monads, dyads,
triads_, etc. A _medad_, or impersonal verb, is a complete
assertion,
like "It rains," "you are a good girl." A _monad_, or neuter verb,
needs only one subject to make it a complete assertion, as
--obeys mamma
you obey--
A _dyad_, or simple active verb, needs just two subjects to complete
the assertion as
—OBEYS—
or —IS IDENTICAL WITH—
A _triad_ needs just three subjects as
--gives--to--
--obeys both--and--
The main difference between this and Lowell 2 is the terminology:
what
Peirce calls a "verb" here is called a "spot," "rheme" or
"predicate"
in the Lowell lectures. (Compare the usage of "rheme" in the
semiotic
trichotomy _rheme/dicisign/argument_ as given in the Syllabus,
EP2:292
or CP 2.250.) The "subject blank" or "line of identity" here
represents the individual "subject of force," as does the "heavy
dot"
in Lowell 2, where the sheet of assertion represents "the aggregate"
of those "subjects of the complexus of experience-forces
well-understood between the graphist, or he who scribes the graph,
and
the interpreter of it."
The other paragraph which I'll quote from the Cambridge lecture (RLT
155-6) relates the existential graph system both to semiotics and to
the Peircean "categories" -- and I think these relations also hold
in
the Lowell presentation of the graphs. Notice here that the _line of
identity_ is classed among "verbs" here, although the _ends_ of the
line (the "dots" of Lowell 2) represent "individual objects" which
would be the "subjects" of the "verbs" in the graph. As a verb,
though, all the line of identity can mean is "is identical with,"
its
subjects being those ends, which in Lowell 2 occupy the "hooks" of
the
"spots."
In the system of graphs may be remarked three kinds of signs of very
different natures. First, there are the verbs, of endless variety.
Among these is the line signifying identity. But, second, the ends
of
the line of identity (and every verb ought to [be] conceived as
having
such loose ends) are signs of a totally different kind. They are
demonstrative pronouns, indicating existing objects, not necessarily
material things, for they may be _events_, or even _qualities_, but
still objects, merely designated as _this_ or _that_. In the third
place the writing of verbs side by side, and the ovals enclosing
graphs not asserted but subjects of assertion, which last is
continually used in mathematics and makes one of the great
difficulties of mathematics, constitute a third, entirely different
kind of sign. Signs of the first kind represent objects in their
firstness, and give the significations of the terms. Signs of the
second kind represent objects as existing,-- and therefore as
reacting,-- and also in their reactions. They contribute the
_assertive_ character to the graph. Signs of the third kind
represent
objects as representative, that is in their Thirdness, and upon them
turn all the inferential processes. In point of fact, it was
considerations about the categories which taught me how to construct
the system of graphs.
One last comment: the usage of the word "individual" in logic can be
confusing, but Peirce's definition of the term in _Baldwin's
Dictionary_ -- http://gnusystems.ca/BaldwinPeirce.htm#Individual [1]
[1]
--is helpful for understanding Peirce's usage.
Gary f.
SENT: 23-Nov-17 16:38
Continuing from Lowell 2.13,
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-19
[2]
03-lowell-lecture-ii/display/13620
[2]
You will ask me what use I propose to make of this sign that
_something exists_, a fact that graphist and interpreter took for
granted at the outset. I will show you that the sign will be useful
as
long as we agree that _although different points on the sheet may
denote the same individual, yet different individuals cannot be
denoted by the same point on the sheet_.
If we take any proposition, say
A SINNER KILLS A SAINT
and if we erase portions of it, so as to leave it a _blank form_ of
proposition, the _blanks_ being such that if every one of them is
filled with a proper name, a proposition will result, such as
______ kills a saint
A sinner kills ______
______ kills ______
where _Cain_ and _Abel_ might for example fill the blanks, then such
a
blank form, as well as the complete proposition, is called a _rheme_
(provided it be neither [by] logical necessity true of everything
nor
true of nothing, but this limitation may be disregarded). If it has
one blank it is called a _monad_ rheme, if two a _dyad_, if three a
_triad_, if none a _medad_ (from μηδέν).
Now such a _rheme_ being neither logically necessary nor logically
impossible, as a [part of ?] a graph without being represented as a
combination by any of the signs of the system, is called a _lexis_
and
each replica of the lexis is called a _spot_. (_Lexis_ is the Greek
for a single word and a lexis in this system corresponds to a single
verb in speech. The plural of _lexis_ is preferably _lexeis_ rather
than _lexises_.)
Such a spot has a particular point on its periphery appropriated to
each and every one of its blanks. Those points, which, you will
observe, are mere places, and are not marked, are called the _hooks_
of the spot. But if a _marked point_, which we have agreed shall
assert the existence of an individual, be put in that place which is
a
hook of a graph, it must assert that some thing is the corresponding
individual whose name might fill the blank of the rheme.
Thus
• GIVES • TO • IN EXCHANGE FOR •
will mean "something gives something to something in exchange for
something."
http://gnusystems.ca/Lowell2.htm [3] [3] }{ Peirce's Lowell Lectures
of
1903
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-19
[2]
03-lowell-lecture-ii
[4]
Links:
------
[1] http://gnusystems.ca/BaldwinPeirce.htm#Individual [1]
[2]
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-19
[2]
03-lowell-lecture-ii/display/13620
[3] http://gnusystems.ca/Lowell2.htm [3]
[4]
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-19
[2]
03-lowell-lecture-ii
Links:
------
[1] http://gnusystems.ca/BaldwinPeirce.htm#Individual
[2]
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-19
[3] http://gnusystems.ca/Lowell2.htm
