Jon AS,
I'm sorry for any condescension. But I was frustrated that you didn't
find the evidence convincing. Therefore, I'll add more.
CSP: Do not block the way of inquiry ... The last philosophical
obstacle to the advance of knowledge which I intend to mention is the
holding that this or that law or truth has found its last and perfect
formulation ... (CP 1.135-140, EP 2:48-49; 1898)
Peirce would never block the way of inquiry. But he wrote sharp
criticisms of people who went astray, even friends or prominent
philosophers whom he admired for other reasons. For example,
The more I studied [logic] the more and more deeply I felt the
shocking levity and looseness of thought with which these basic
questions had been treated. (NEM 3:159)
JAS
NEM 3:162-169 serves as an excellent "tutorial," although it omits
a few helpful clarifications, such as the fact that a Line of
Identity can always be branched at a Spot of Teridentity and then
extended inward through a Cut.
I copied NEM 3:159 and 162-169 in http://jfsowa.com/peirce/eg1911.pdf ,
and I added commentary that explains why he omitted certain words:
He reduced the jargon to a minimum by avoiding the words cut, sep,
dot, spot, recto, verso, and scroll, which refer to features on
a two-dimensional sheet of paper. Unlike the two-dimensional cut,
the new shaded ovals for negation can be generalized to shading
segments of a one-dimensional line or closed regions in three or
more dimensions. On page 191 of this letter, he regrets his lack
of funds for developing "stereoscopic moving images".
That comment is a hint that Peirce was already thinking about such
extensions. On page 166 (page 6 of eg1911.pdf), the "1st permission"
avoids the two-dimensional terms 'spot' and 'cut'. It has a simpler
and clearer explanation that can be generalized to diagrams or images
in any number of dimensions -- including "stereoscopic moving images".
Note that every definition and rule of inference in eg1911 can be
generalized to any number of dimensions just by changing the word 'area'
to 'region', 'shaded oval' to 'shaded region', and 'sheet of assertion'
to 'assertion space'. In three dimensions, there are no crossing
lines and no need for "selectives". But in one-dimension, all lines
of identity must be replaced by selectives (AKA variables in algebra).
I don't know whether MSS exist in which Peirce placed arbitrary images
or diagrams in EGs. But his comment about stereoscopic images gives
a hint about his thinking. I suspect that is why his 1911 version
avoided terminology that was limited to just two dimensions.
I have freely (and repeatedly) acknowledged that "proper" and
"ultimate" are relative to a purpose, and that mine is different
from yours.
Peirce considered EGs to be proper to the infinity of all imaginable
purposes, and so do I. That would include whatever you're assuming.
Right now I am focusing on Peirce's concept of Experience as
reflected in this careful distinction between Subjects as whatever
requires Collateral Experience and the Continuous Predicate as
whatever the Proposition itself conveys.
That sentence is inconsistent with what Peirce wrote in NEM 3:885 in
several important ways.
First, note the words 'term' and 'predicate' near the beginning
of the paragraph: "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..."
Only predicates have valence. If logical terms have valence,
then those terms must be predicates.
Second, that use of the word 'term' is derived from syllogisms, which
Peirce mentioned frequently. The Latin word 'terminus' and the English
'term' refer to the two "ends" (subject and predicate) of each sentence.
For example, the syllogism named Barbara, as Peirce stated and proved
it in eg1911.pdf: Any S is M. Any M is P. Therefore, any S is P.
To make 'is' the verb, both Peirce and Aristotle would transform
"Some man owns a red car" to "Some man is an owner of a red car."
For both of them,'man' and 'owner of a red car' are terms. But Peirce
made another distinction: the terms are monads, which become logical
subjects when they are attached to some word that indicates a line of
identity, such as 'any', 'some', or 'a'.
This analysis confirms the point that terms are monadic predicates.
They may be represented by single words such as 'car' or 'red' or by
arbitrarily large expressions in ordinary language, which are then
translated to more complex EGs with exactly one unattached peg.
If you don't trust my analysis, note the footnote by Weiss and
Hartshorne to CP 4.538: 'rheme' and 'dicisign' are synonyms for
'term' and 'predicate'. If you doubt their interpretation, you
have an obligation to present solid evidence to the contrary.
Re collateral experience: Note the exact wording of the sentence
in NEM 3:885: "take as the subject whatever there is of which
sufficient knowledge cannot be conveyed in the proposition itself,
but collateral experience on the part of its interpreter is requisite."
This sentence is about the requirements for reliable communication
between a speaker and an interpreter. In the following sentence,
Peirce wrote "Thus, if you say 'This rose is red' a color-blind
person will not apprehend your meaning."
Peirce's point: The speaker makes an assumption about the listener's
experience. The speaker uses that assumption (in language or logic)
to determine how much information to include in the subject term.
The listener is the one who has the experience. The speaker uses
symbolic reasoning, not phaneroscopy.
Re continuous predicate: Aristotle and his followers in the 19th c
considered only one subject per sentence, and their *proper form*
used only one continuous predicate: -is- .
Peirce's discussion about other continuous predicates begins with
the sentence "The result is that everything that can should be
thrown into the subjects, leaving the /pure/ predicate a mere form
of connection, such as..."
But note that the word 'predicate' is singular: Peirce and Aristotle
would rewrite the following sentence in exactly the same way::
"A rich young man owns a shiny red car." =>
"A rich young man is an owner of a shiny red car."
But Aristotle would make one division, and Peirce would make two:
Aristotle: "A rich young man" | "is an owner of a shiny red car"
Peirce: "A rich young man" | "is" | "an owner of a shiny red car"
Aristotle's analysis corresponds to a subject with a line of identity
and a predicate with one unattached peg. Peirce's analysis produces
two logical subjects, each with a line of identity, and one dyadic
predicate that is also a pure predicate.
JAS
the fundamental difference between MEGs and EGs is that Points
for Subjects replace Spots for predicates, while a single Line
of Relation for the Continuous Predicate replaces multiple Lines
of Identity for different individuals.
No. That's wrong for several reasons.
First, that "single line of relations" has multiple occurrences
of the relation which I named Rel and which you represent with the
same notation Peirce used for teridentity. That variation in syntax
has no semantic meaning whatsoever.
Second, it does not replace multiple lines of identity. The symbol
Rel or the MEG convention for connecting lines are the points that
separate lines of identity. How else would a MEG determine the
number of distinct individuals? By counting the monads?
But consider the example of "a shiny red car": there are three
monads (shiny- red- car-) all attached to a teridentity for a
single individual. How does MEG represent teridentity? If it
can represent teridentity, it must have lines of identity.
Third, the relation Rel, as Peirce defined it, replaces something
X that brings some Y and Z into relation. If X is ownership,
then Y is the owner and Z is the thing that Y owns. But he did
not say how a triad such as 'gives' should be represented.
The attached giving.png shows an EG for "Sue gives a book to a child."
That EG has a triad named 'Gives' with three attached lines of identity
for Sue, a book, and a child. A nominalization of 'gives' to the
gerund 'giving' would require two copies of Rel, which I show in
the second EG in giving.png.
If I read that EG in English, I would say "Giving relates Sue to a
transfer relation that relates a book to a child." I added the
label 'Transfer' to explain the role of the second relation. If you
prefer to ignore that label, you could say "Giving relates Sue to
an unnamed relation that relates a book to a child." But I believe
that naming the relation clarifies the intended meaning.
MEGs are intended primarily to provide a more Iconic representation
of a Proposition as consisting of (1) multiple Subjects that are
(2) "married" by one Continuous Predicate, or "divorced" where there
are Cuts.
No. That is another claim that is wrong for multiple reasons.
First, ambiguity does not improve iconicity. At the bottom of NEM 3:885,
Peirce lists four kinds of pure predicates: -is-, -possesses-, -Rel-,
and teridentity. A line of identity represents -is-, and a ligature
represents teridentity. The label -has- could be used for possession.
If you don't like the label 'Rel', you could select a special symbol
such as Ř or ⊕. Each pure predicate must have a distinct symbol.
Second, the "proper way" on page 3:885 puts *more* information into
the subject term in order to help the interpreter determine the
topic of the sentence. But reducing every subject to a single monad
does the exact opposite. It converts the proposition to a collection
of multiple subjects, each with a single monad. The listener would
have no way to determine which one of those many subjects is the
focus of the sentence. That is not what Peirce recommended.
Third, Peirce spent many years in developing and using the EG rules
of inference. To be used in such inferences, MEGs must support
equivalent rules: Every EG rule must be applicable to MEGs with
at most a minor change in wording. That implies a minor change in
syntax. Mathematicians have a word for syntactic changes: 'trivial'.
Finally, Peirce frequently mapped English or other symbolic forms
to EGs with predicates that map directly to the world or the phaneron.
On page NEM 3:886, he emphasized the importance of those predicates.
The subject specifies the matter, and the predicate specifies the form.
The pure predicates, which have no content, show interconnections:
The function of reason is to trace out in the real world analogues of
logical relations. Thus, corresponding to subject and predicate, or
that to which a predication refers, and the *predicate* the substance
of the predication, reason supposes there is an element of *matter*
which gives being, i.e. is that which is, and an element of *form*
which is *how* it is.
Conclusion: The evidence for the following points is overwhelming,
and there is no evidence against them:
1. The word 'term', as Peirce used it, is a synonym for 'rheme'
or 'predicate'. For modern usage, I checked the Merriam-
Webster Dictionary. Definition 1b of 'predicate' is "a term
designating a property or relation."
2. Continuous predicates correspond to structural features of EGs,
and they can support hypostatic abstractions of predicates for
various purposes.
3. The "proper way" to split a sentence into a subject and a predicate
is to transfer enough information to the subject term to determine
the intended referent. This transfer requires the speaker to make
some assumptions about what the listener knows.
4. It's possible to transform every predicate in an EG that has real-
world content to a monadic nominalization (hypostatic abstraction).
But Peirce never said or implied that such a total transformation
of an EG would be proper, useful, or desirable for any purpose.
5. As Peirce said in NEM 3:886, the "function of reason" is to
trace out "analogues of logical relations" in the real world.
That implies a combination of logic and phaneroscopy. The
pure predicates, as purely logical connectors, are more remote
from experience than predicates that map to the real world.
6. Either MEGs are trivial syntactic variants of EGs, or they cannot
express Peirce's rules of inference as effectively as EGs. In any
case, points #4 and #5 imply that MEGs are not as useful as EGs
for analyzing or representing experience in the phaneron.
There is nothing more to say about this overly long thread.
See below for more comments about eg1911.pdf.
John
______________________________________________________________________
See http://jfsowa.com/peirce/eg1911.pdf
This excerpt is the beginning of a long letter on probability and
induction (NEM 3:158 to 210). Peirce had written a first draft
in 1909 (R 514). In 1911, he wrote a clean copy, which he sent
to J. H. Kehler, a member of Lady Welby's Significs group.
CSP: Much of my work never will be published. If I can, before
I die, get so much made accessible as others may have a difficulty
in discovering, I shall feel that I can be excused from more.
(SS 44, 1904)
Since Lady Welby's group was his most receptive audience, this 53-page
letter sent to that group should be considered the equivalent of a
publication. The fact that he wrote the first draft in 1909 and copied
it without change in 1911 is significant. This version doesn't obsolete
his previous work on existential graphs, but it represents his final
preference for the choice of notation and terminology.
Although Peirce devoted most of the letter to probability, the excerpt
below (pp. 162 to 169) is Peirce's shortest and clearest presentation
of existential graphs. The semantics is equivalent to earlier versions,
but his new definitions and rules of inference are simpler, more
elegant, and easier to generalize to an open-ended variety of notations.
In this version, Peirce dropped the distinction between Alpha graphs
for propositional logic and Beta graphs for first-order logic, because
his revised rules of inference are identical for both. He reduced the
jargon to a minimum by avoiding the words cut, sep, dot, spot, recto,
verso, and scroll, which refer to features on a two-dimensional sheet
of paper. Unlike the two-dimensional cut, the new shaded ovals for
negation can be generalized to shading segments of a one-dimensional
line or closed regions in three or more dimensions.
For more examples of EGs and more detailed commentary on that tutorial,
see http://jfsowa.com/peirce/ms514.htm
By he way, whoever drew the EG in Fig. 16 of NEM 3:168 made a mistake.
The letter in the shaded area of Fig. 16 should be S, not M.
Michel Balat, who transcribed the text I used in ms514.pdf, correctly
transcribed Fig. 16. I redrew his version for ms514.htm.
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
