Jeff,
As we'll see later in Lowell 2, Peirce does work toward more formal
definitions of the EG conventions in that lecture. But he starts "from
scratch," appealing to the imagination of his audience to follow what he's
doing and thus get a sense of what these diagrams are supposed to represent
("the course of thought.") It is interesting to compare what he says in
Lowell 2 with his more detailed presentations of EGs, several of which are
in CP 4. The quote you supply here is from "New Elements" (EP2:302 as well
as NEM), which is closely related to the Lowell Lectures in several ways. In
Lowell 2, though, Peirce makes no mention of axioms or postulates; instead,
he derives all his "permissions" from definitions, making use of both
"branches." And that comes later in the lecture.
Don Roberts' book is a valuable resource, indispensable really, for studying
EGs, but it's eclectic in its use of sources, and I think it's equally
valuable to follow Peirce's lead as he introduces these concepts to an
'innocent' audience, assuming as little as possible about their prior
knowledge of logic and mathematics. From the manuscripts I get the
impression that Peirce is thinking through (or rethinking) these concepts as
he writes, and (for me anyway) this brings EGs to life in a way that
textbook summaries rarely do. I find it rewarding to follow the course of
Peirce's thought instead of trying to summarize it all the time.
By the way, his use of the word "word" to explain the graph/replica
distinction (i.e. the type/token distinction) reappears in the 1906
"Prolegomena" (CP 4.537).
Gary f.
From: Jeffrey Brian Downard [mailto:[email protected]]
Sent: 22-Oct-17 01:42
To: [email protected]
Subject: Re: [PEIRCE-L] Lowell Lecture 2.3
Gary F, John S, List,
In this second Lecture, Peirce is providing informal explanations of the
starting points for setting up the EG. If these explanations were to be cast
in a more rigorous way, how might we characterize each of these assumptions
or conventions?
In his monograph, Don Roberts characterizes the first three conventions in
the following way:
Conventions
CI. The sheet of assertion in all of its parts is a graph. 4.396, 397.
C2. Whatever is scribed on the sheet of assertion is asserted to be true of
the universe represented by that sheet. 4.397.
C3. Graphs scribed on different parts of the sheet of assertion are all
asserted to be true. 4.433.
The logical system is being developed as a part of pure mathematics. As
such, we should be able to characterize each as a definition, postulate or
axiom.
Peirce provides the following
[CP 2.219-26].
1. A definition is the logical analysis of a predicate in general terms.
It has two branches, the one asserting that the definitum is applicable to
whatever there may be to which the definition is applicable, the other
(which ordinarily has several clauses), that the definition is applicable to
whatever there may be to which the definitum is applicable. A definition
does not assert that anything exists.
2. A postulate is an initial hypothesis in general terms. It may be
arbitrarily assumed provided that (the definitions being accepted) it does
not conflict with any principle of substantive possibility or with any
already adopted postulate. By a principle of substantive possibility, I
mean, for example, that it would not be admissible to postulate that there
was no relation whatever between two points, or to lay down the proposition
that nothing whatever shall be true without exception. For though what this
means involves no contradiction it is in contradiction with the fact that it
is itself asserted.
3. An axiom is a self-evident truth, the statement of which is
superfluous to the conclusiveness of the reasoning, and which only serves to
show a principle involved in the reasoning. It is generally a truth of
observation, such as the assertion that something is true.
4. A diagram is an icon or schematic image embodying the meaning of a
general predicate; and from the observation of this icon we are supposed to
construct a new general predicate [NEM 2.7].
2.
3.
Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354
_____
From: [email protected] <mailto:[email protected]> <[email protected]
<mailto:[email protected]> >
Sent: Saturday, October 21, 2017 6:45:12 AM
To: 'Peirce-L'
Subject: [PEIRCE-L] Lowell Lecture 2.3
Continuing from Lowell 2.2:
.The board itself is a graph, since it represents the universe as consisting
of single imaginary things. The board and what is written on it together
make up another graph.
It is quite important, however, to distinguish between a graph and a graph
replica. Suppose an editor writes to me and asks for an article of 4000
words. You know what he means by words in that case. In what I write the
single word "the" may occur twenty times on every page. Every time it will
count as a separate word. Yet in another sense, it is the same word. In this
latter sense, the word the consists in the sum total of general conditions
to which ink-marks or voice-sounds must conform in order to be understood in
a certain way.
In this sense the word the is, strictly speaking, never written; but what is
written conforms to it, or, as we say, embodies it. In the other sense a
written word is written once and only once, since every act of writing makes
a new word. Now when I speak of a graph, I mean the general type of whatever
means the same thing and expresses that meaning in the same way so far as
the conventions of this system take cognizance of the ways; while that which
is scribed once and only once and embodies the graph, I call a
graph-replica. For brevity, however, I speak of "scribing a graph" just as
we speak of writing the word the. The phrase may be defended as employing
the word "scribe" in a special sense. I will now put an additional replica
upon the board, or the sheet of assertion
Let us agree to understand that each of those replicas has the same meaning
as if it stood alone; and that it shall be the same with any other two
replicas on the sheet, so that I now assert not only that there is a ripe
pear, but also that it rains.
By calling this system a system of existential graphs, my meaning is that
two graphs at different points of the board, whether far or near, are both
asserted, each just as much as if the other were not there.
Manuscript and transcription:
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13600
<https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lo
well-lecture-ii/display/13600> 7 (C. S. Peirce Manuscripts, MS 455-456
(1903) - Lowell Lecture II) | FromThePage
fromthepage.com
7 (C. S. Peirce Manuscripts, MS 455-456 (1903) - Lowell Lecture II) - page
overview. 5 since existential graphs will be the only ones dealt with, I
shall call it a graph, simply. For example, what I have just written scribed
is ...
<http://gnusystems.ca/Lowells.htm> http://gnusystems.ca/Lowell2.htm }{
Peirce's Lowell Lectures of 1903
https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii
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