[PEIRCE-L] Re: Lowell Lecture 2.13 and 2.14

[Jon Awbrey]

John, List ...

JFS:
> This is less restrictive than the definition in the Lowell lectures.
> For example, it would allow a logician to use a sheet of paper to
> write a proof by contradiction.  In that case, there would be no
> universe about which the statements on the paper could be true.

In that case we may say that a sign's set of denoted objects is empty.
I think this tactic probably goes back to my earliest algebra courses,
where our teachers cautioned us to remember that the “solution set”
of a formula could be the empty set.  By apt analogy, then, we may
well call “a sign's set of denoted objects” its “denotation set”.
Of course an empty set is a subset of every set, but nothing
about this requires the universe of discourse to be empty,
much less not to exist.

By the way, to assert “Every word makes an assertion”
is either word magic, word animism (?), or nomimalism,
the very ilk of ills that Peirce's theory of signs is
prescribed against which to cure us.  In Peirce's case
I'll chalk it up to simple sloppy pedagogical rhetoric.

Regards,

Jon


On 11/27/2017 12:00 PM, John F Sowa wrote:

On 11/27/2017 10:30 AM, Jon Awbrey wrote:

JFS:

In 1911, Peirce clarified the issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.


There is a difference between *being* a universe of discourse
and *representing* a universe of discourse...


I agree.

In the Lowell lectures, Peirce defined the Sheet of Assertion
as the representation of a universe that was constructed during
a discourse between Graphist and Grapheus.

But that is just one of many ways of using logic.  In 1911,
he wrote about "whatever universe" and "the whole sheet":

Every word makes an assertion.  Thus ——man means
"There is a man" in whatever universe the whole sheet refers to.


This is less restrictive than the definition in the Lowell lectures.
For example, it would allow a logician to use a sheet of paper to
write a proof by contradiction.  In that case, there would be no
universe about which the statements on the paper could be true.

John



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[PEIRCE-L] Re: Lowell Lecture 2.13 and 2.14

[Jon Awbrey]

John, List ...

JFS:

This is less restrictive than the definition in the Lowell lectures.
For example, it would allow a logician to use a sheet of paper to
write a proof by contradiction.  In that case, there would be no
universe about which the statements on the paper could be true.


In that case we may say that a sign's set of denoted objects is empty.
I think this tactic probably goes back to my earliest algebra courses,
where our teachers cautioned us to remember that the “solution set”
of a formula could be the empty set.  By apt analogy, then, we may
well call “a sign's set of denoted objects” its “denotation set”.
Of course an empty set is a subset of every set, but nothing
about this requires the universe of discourse to be empty,
much less not to exist.

By the way, to assert “Every word makes an assertion”
is either word magic, word animism (?), or nomimalism,
the very ilk of ills that Peirce's theory of signs is
prescribed to cure us against.  In Peirce's case I'll
chalk it up to simple sloppy pedagogical rhetoric.

Regards,

Jon


On 11/27/2017 12:00 PM, John F Sowa wrote:

On 11/27/2017 10:30 AM, Jon Awbrey wrote:

JFS:

In 1911, Peirce clarified the issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.


There is a difference between *being* a universe of discourse
and *representing* a universe of discourse...


I agree.

In the Lowell lectures, Peirce defined the Sheet of Assertion
as the representation of a universe that was constructed during
a discourse between Graphist and Grapheus.

But that is just one of many ways of using logic.  In 1911,
he wrote about "whatever universe" and "the whole sheet":

Every word makes an assertion.  Thus ——man means
"There is a man" in whatever universe the whole sheet refers to.


This is less restrictive than the definition in the Lowell lectures.
For example, it would allow a logician to use a sheet of paper to
write a proof by contradiction.  In that case, there would be no
universe about which the statements on the paper could be true.

John



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Aw: [PEIRCE-L] RE: Categories vs. Elements (was Lowell Lecture 2.14)

[Helmut Raulien]

 
 

I wrote both, "a sign consists of sign, object, and interpretant", and: "A sign consists of sign relation, object relation, and interpretant relation". To me (in my theory) the first kind of consisting is functional composition, and the latter is composition from traits. I just wanted to add this, because by close reading one might have been confused.

 




Gary, Jon, List,

To the question, whether "categories" are "elements" or "universes" I can say little how Peirce has answered to this, but I would say, based on my contemporary dealing with the difference between composition and classification:

I think, that "universes" sounds like classification, and "elements" like composition. E.g. compositional categories: The sign consists of representamen (or sign), object, interpretant. They are categorial elements of the sign. Primisense, altersense, medisense are (compositional) elements of the consciousness.

Classification: A sign is either a quali-, sin-, or legisign. This is categorial classification. But to call classes universes seems a bit far fetched to me. But universes being classes sounds senseful to me. Though I find "universes" a bit confusing, and dont know, why one should use the universe for a metaphor. To me it seems too big and to all-encompassing to serve as a metaphor for something else.

"Kinds of elements" to me is a combination of composition and classification, like with the ten sign classes: A sign is composed of its sign relation, object relation, interpretant relation, so e.g. "rhematic indexical legisign" is a composition of classes, three kinds (classes) of three (composed) elements.

Best,

Helmut

 

 26. November 2017 um 23:58 Uhr
Von: g...@gnusystems.ca
 




Jon A.S.,

 

Thanks very much for posting here some of the Peirce passages which demonstrate that, as you put it, “"categories" and "elements" were effectively interchangeable for Peirce, precisely at the time of the Lowell Lectures” (and, I would add, afterwards, depending on Peirce’s context and audience).

 

The specifically logical usage of the term “categories” was virtually inherited by Peirce from Aristotle, Kant, and Hegel, and logicians and metaphysicians could be expected to be familiar with this terminology, so it was convenient in that sense for Peirce to use it in his phenomenology/phaneroscopy. But it was also misleading, because Peirce’s “categories” were quite different from those of his predecessors, and I think that after 1902 especially, he increasingly used the term “elements” because it was less familiar in this context, and better suited to his phenomenology, i.e. to his way of arriving at the three conceptions as “indecomposable elements.” But he continued to use both; in Lowell 3, for instance, which is mostly about Firstness/Secondness/Thirdness, he referred to them 16 times as “categories” and 35 times as “elements”, beginning with this:

“Phenomenology is the science which describes the different kinds of elements that are always present in the Phenomenon, meaning by the Phenomenon whatever is before the mind in any kind of thought, fancy, or cognition of any kind. Everything that you can possibly think involves three kinds of elements.”

 

You are right that the phrase “kinds of elements” is ambiguous in a way, and when he refers to (for instance) Thirdness as an “element”, we could regard that as a mere abbreviation for “kind of element.” But he does this so often that “element” becomes in these texts interchangeable with “category” in their technical senses, as you said. Anyway, we should get back to this discussion when we have Lowell 3 in front of us. 

 

Gary f.

 

 

From: Jon Alan Schmidt [mailto:jonalanschm...@gmail.com]
Sent: 26-Nov-17 17:06
To: Gary Fuhrman 
Cc: Peirce List 
Subject: Categories vs. Elements (was Lowell Lecture 2.14)

 


Gary F., List:


 



As you may recall, I offered the hypothesis over a year ago that late in his life, Peirce shifted his terminology from "categories" to "universes," or perhaps confined "categories" to phenomenology/phaneroscopy and employed "universes" for metaphysics, or at least suggested that predicates/relations are assigned to "categories" while subjects belong to "universes."  Back then, Gary R. cited a passage from one of the drafts of "Pragmatism" that finally convinced me to abandon this conjecture, and it would seem to stand equally against the suggestion that Peirce definitively shifted from "categories" to "elements."



 




CSP:  To assert a predicate of certain subjects (taking these all in the sense of forms of words) means,—intends,—only to create a belief that the real things denoted by those subjects possess the real character or relation signified by that predicate. The word "real," pace the metaphysicians, whose phrases are sometimes empty, means, and can mean, nothing more nor less. Consequently, to the three forms of predicates there must correspond three conceptions 

Aw: [PEIRCE-L] RE: Categories vs. Elements (was Lowell Lecture 2.14)

[Helmut Raulien]

Gary, Jon, List,

To the question, whether "categories" are "elements" or "universes" I can say little how Peirce has answered to this, but I would say, based on my contemporary dealing with the difference between composition and classification:

I think, that "universes" sounds like classification, and "elements" like composition. E.g. compositional categories: The sign consists of representamen (or sign), object, interpretant. They are categorial elements of the sign. Primisense, altersense, medisense are (compositional) elements of the consciousness.

Classification: A sign is either a quali-, sin-, or legisign. This is categorial classification. But to call classes universes seems a bit far fetched to me. But universes being classes sounds senseful to me. Though I find "universes" a bit confusing, and dont know, why one should use the universe for a metaphor. To me it seems too big and to all-encompassing to serve as a metaphor for something else.

"Kinds of elements" to me is a combination of composition and classification, like with the ten sign classes: A sign is composed of its sign relation, object relation, interpretant relation, so e.g. "rhematic indexical legisign" is a composition of classes, three kinds (classes) of three (composed) elements.

Best,

Helmut

 

 26. November 2017 um 23:58 Uhr
Von: g...@gnusystems.ca
 




Jon A.S.,

 

Thanks very much for posting here some of the Peirce passages which demonstrate that, as you put it, “"categories" and "elements" were effectively interchangeable for Peirce, precisely at the time of the Lowell Lectures” (and, I would add, afterwards, depending on Peirce’s context and audience).

 

The specifically logical usage of the term “categories” was virtually inherited by Peirce from Aristotle, Kant, and Hegel, and logicians and metaphysicians could be expected to be familiar with this terminology, so it was convenient in that sense for Peirce to use it in his phenomenology/phaneroscopy. But it was also misleading, because Peirce’s “categories” were quite different from those of his predecessors, and I think that after 1902 especially, he increasingly used the term “elements” because it was less familiar in this context, and better suited to his phenomenology, i.e. to his way of arriving at the three conceptions as “indecomposable elements.” But he continued to use both; in Lowell 3, for instance, which is mostly about Firstness/Secondness/Thirdness, he referred to them 16 times as “categories” and 35 times as “elements”, beginning with this:

“Phenomenology is the science which describes the different kinds of elements that are always present in the Phenomenon, meaning by the Phenomenon whatever is before the mind in any kind of thought, fancy, or cognition of any kind. Everything that you can possibly think involves three kinds of elements.”

 

You are right that the phrase “kinds of elements” is ambiguous in a way, and when he refers to (for instance) Thirdness as an “element”, we could regard that as a mere abbreviation for “kind of element.” But he does this so often that “element” becomes in these texts interchangeable with “category” in their technical senses, as you said. Anyway, we should get back to this discussion when we have Lowell 3 in front of us. 

 

Gary f.

 

 

From: Jon Alan Schmidt [mailto:jonalanschm...@gmail.com]
Sent: 26-Nov-17 17:06
To: Gary Fuhrman 
Cc: Peirce List 
Subject: Categories vs. Elements (was Lowell Lecture 2.14)

 


Gary F., List:


 



As you may recall, I offered the hypothesis over a year ago that late in his life, Peirce shifted his terminology from "categories" to "universes," or perhaps confined "categories" to phenomenology/phaneroscopy and employed "universes" for metaphysics, or at least suggested that predicates/relations are assigned to "categories" while subjects belong to "universes."  Back then, Gary R. cited a passage from one of the drafts of "Pragmatism" that finally convinced me to abandon this conjecture, and it would seem to stand equally against the suggestion that Peirce definitively shifted from "categories" to "elements."



 




CSP:  To assert a predicate of certain subjects (taking these all in the sense of forms of words) means,—intends,—only to create a belief that the real things denoted by those subjects possess the real character or relation signified by that predicate. The word "real," pace the metaphysicians, whose phrases are sometimes empty, means, and can mean, nothing more nor less. Consequently, to the three forms of predicates there must correspond three conceptions of different categories of characters: namely, of a character which attaches to its subject regardless of anything else such as that of being hard, massive, or persistent; of a character which belongs to a thing relatively to a second regardless of any third, such as an act of making an effort against a resistance; and of a character which belongs to a thing as 

[PEIRCE-L] Lowell Lecture 2.15

[gnox]

Continuing from Lowell Lecture 2.14,

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13623:

 

 

Now let us further agree that a heavily marked line 

*   , 

all whose points are ipso facto heavily marked and therefore denote
individuals, shall be a graph asserting the identity of all the individuals
denoted by its points. Then 



will mean that there is a ripe pear, that is, something is a pear and that
very same thing is ripe. 

We call such a heavy line a line of identity. A point from which three lines
of identity proceed has the force of the conjunction 'and.' 



There is no need of a point from which four lines of identity proceed; for
two triple points answer the same purpose. 



Therefore a figure like this 



is to be understood as two distinct lines of identity crossing one another.
Nevertheless, in order to avoid possible mistake a bridge may be represented
thus: 



One line passes under the bridge, the other upon it. 

 

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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[PEIRCE-L] Re: Lowell Lecture 2.13 and 2.14

[John F Sowa]

On 11/27/2017 10:30 AM, Jon Awbrey wrote:

JFS:

In 1911, Peirce clarified the issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.


There is a difference between *being* a universe of discourse
and *representing* a universe of discourse...


I agree.

In the Lowell lectures, Peirce defined the Sheet of Assertion
as the representation of a universe that was constructed during
a discourse between Graphist and Grapheus.

But that is just one of many ways of using logic.  In 1911,
he wrote about "whatever universe" and "the whole sheet":

Every word makes an assertion.  Thus ——man means "There is a man"
in whatever universe the whole sheet refers to.


This is less restrictive than the definition in the Lowell lectures.
For example, it would allow a logician to use a sheet of paper to
write a proof by contradiction.  In that case, there would be no
universe about which the statements on the paper could be true.

John

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RE: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[gnox]

John,

 

Unfortunately you've added to the rampant confusion by saying that "a spot is 
just a very short line of identity.” This is not true of Peirce’s “final 
preferred version” of EGs because, as you point out yourself, he does not use 
the term “spot” in that version. And it is not true of Lowell 2, because in 
that text, a “line of identity” (however short) is not a “spot”: rather the end 
of that line must be attached to a “spot” (rheme, predicate) at one of its 
“hooks” or “pegs” in order to form a complete graph representing the 
subject-and-predicate (-and-copula, if you like).

 

See the new commentary on 2.14 which I posted just now. 

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 27-Nov-17 02:06
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof 
Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

 

Gary F, Mary L, Kirsti, Jerry LRC, and list,

 

In 1911, Peirce presented his clearest and simplest version of EGs.

He explained the essentials in just 8 pages of NEM (3:162 to 169).

I believe that it is his final preferred version, and I'll use it for 
explaining issues about the more complex 1903 version.

 

Gary

> [Mary's] question about the “blot” has me thinking again about “the 

> two peculiar graphs” which are “the blank place which asserts only 

> what is already well-understood between us to be true, and the blot 

> which asserts something well understood to be false”

 

Kirsti,

> instead of warning against confusing SPOT, DOT and BLOT, it would have 

> been most interesting to hear how they are related.

 

In his 1911 terminology, Peirce did not use the words 'spot', 'dot', or 'blot'. 
 Instead, a spot is just a very short line of identity.

The line represents an existential quantifier, and there is no reason to 
distinguish long lines from short lines (spots).

 

He used the word 'peg' instead of 'dot'.   Each relation has zero

or more pegs, to which lines of identity may be attached.

 

He also shaded negative areas (nested in an odd number of negations) and left 
positive areas unshaded (nested in an even number, zero or more, negations).  A 
blot is just a shaded area that contains nothing but a blank.

 

Gary

> [The blank place and the blot] are peculiar in several ways, and each 

> is in some sense the opposite of the other.

 

Each is the negation of the other.  The blank place is unshaded, and the blot 
is a shaded blank.

 

Gary

> For instance, the blank cannot be erased, but any graph can be added 

> to it on the sheet of assertion; while the blot can be erased, but 

> nothing can be added to it, because it “fills up its area.”

 

One reason why the "the blank place" is "peculiar" is that Peirce had talked 
about it in two different ways.  He called the sheet of assertion the universe 
of discourse when it contains all the EGs that Graphist and Grapheus agree is 
true.

 

But the blank, by itself, is true before anything is asserted.

In modern terminology, the blank is Peirce's only axiom.  Any EG that can be 
proved without any other assumptions is a theorem.

 

In 1911, Peirce clarified that issues by using two distinct terms:

'the universe' and 'a sheet of paper'.  The sheet is no longer identified with 
the universe, and there is no reason why one couldn't or shouldn't shade a 
blank area of a sheet.

 

Gary, quoting Peirce

> [A blot] "fills up its area."

 

In 1911, Peirce no longer used this metaphor.  With the rules of 1903 or 1911, 
a blot or a shaded blank implies every graph.

To prove that any graph g can be proved from it:

 

  1. Start with a sheet of paper that contains a shaded blank.

 

  2. By the rule of insertion in a shaded area, insert the graph

 for not-g inside the shaded area.  All the shaded areas of not-g

 then become unshaded, and the unshaded areas become shaded.

 

  3. The resulting graph consists of g in an unshaded area that is

 surrounded by a shaded ring that represents a double negation.

 

  4. Finally, erase the double negation to derive g.

 

Another important point:  In 1911, Peirce allowed any word, not just verbs, to 
be the name of a relation.  From NEM, page 3.162:

> Every word makes an assertion.  Thus ——man means "There is a man" 

> in whatever universe the whole sheet refers to.  The dash before "man" 

> is the "line of identity."

 

This EG is Peirce's first example in 1911.  And note that he begins with a Beta 
graph.  In fact, he does not even mention the distinction between Alpha and 
Beta.  The same rules of inference apply to both.

 

For Peirce's version of 1911 with my commentary, see  
 http://jfsowa.com/peirce/ms514.htm

 

Jerry,

> CSP’s genius [etc.] make it difficult for anyone to project his 

> thoughts into rarefied logical, mathematical, scientific or 

> philosophical atmospheres.

 

Yes.  He wrote volumes of insights that we still need to explore.

But 

Re: Aw: Re: [PEIRCE-L] Re: Cognonto

[Mike Bergman]

  
  
Hi Helmut, List,
I had missed that reference and update. Thank you! I have
  corrected the notes to the table, but have retained his earlier
  names because they are more commonly referenced and it retains the
  idea of 'representation', more allied with the idea of knowledge
representation, which is my particular focus. You probably
  also saw that at the end of CP 4.3 Peirce also stated that "How
  the conceptions are named makes, however, little difference."
  Thanks again, Helmut.
Mike


On 11/24/2017 1:06 PM, Helmut Raulien
  wrote:


  

  Mike, List,
   
  I especially like your table "C.S. Peirce’s Universal
Categories in Relation to Various Topics". Just one thing:
Peirce later replaced "quality, relation, representation",
as which he had named the categories in "On a new list of
categories" with "quality, reaction, mediation" (I donot
oversee Peirces work at all, so I dont know if he later
replaced it back or again...): CP 4.3., looked up at the
Commens Dictionary under the catchword "categories":
   
  "I then named them Quality,
  Relation, and Representation. But I was not then aware
  that undecomposable relations may necessarily require more
  subjects than two; for this reason Reaction is a
  better term. Moreover, I did not then know enough about
  language to see that to attempt to make the word representation
  serve for an idea so much more general than any it
  habitually carried, was injudicious. The word mediation
  would be better. Quality, reaction, and mediation will
  do." 
   
  Best,
  Helmut
   

   24. November 2017 um
16:52 Uhr
"Mike Bergman" 
 
  Hi List,

The knowledge artifact used by Cognonto is KBpedia [1].
It's upper ontology (KKO) [2] is based on our
interpretation of Peirce's universal categories (not
EGs, which I have not studied, nor strictly on Peirce's
sign classifications, either). The approach to this
interpretation of Peirce is described in this article
[3]. My listing of articles on Peirce related to the
semantic Web and knowledge representation may be found
here [4].

In many ways this is a provisional use of Peirce's
categories. I welcome any commentary for improvement,
and would gladly revise KKO wherever I have mistakenly
misinterpreted Peirce's insights or intent.

Best, Mike

[1] http://kbpedia.com
[2] http://kbpedia.com/docs/kko-upper-structure/
[3]http://www.mkbergman.com/2077/how-i-interpret-c-s-peirce/
[4]http://www.mkbergman.com/category/c-s-peirce/
 
On November 23, 2017 2:11:08 PM
  CST, John F Sowa  wrote:
  
Dan, Terry, and list,

Dan

http://www.dataversity.net/cognonto-takes-knowledge-based-artificial-intelligence/
  Interesting claim for application of Peircean
  ideas in the tech industry.

Thanks for the pointer. I'm happy to see more
interest and applications
of Peirce's logic and ontology.

Terry
Bergman’s
  work is pretty closely related to yours, isn’t it,
  John Sowa?

I googled +"Peirce" +"Michael Bergman" and found
some interesting
web pages. I would say that there are overlaps. I
found references
to his "knowledge graphs", but I couldn't find a
clear specification
of how they may be related to Peirce's EGs.

Bergman and his company have assembled a very large
ontology
by combining the already large OpenCyc with several
other large
resources. That is indeed an impressive
contribution, but I
couldn't see how they used Peirce's semiotic to
develop it.

However, I did not follow up all the search paths.
If anybody 

RE: [PEIRCE-L] Lowell Lecture 2.14

[gnox]

List,

I must apologize to the list for introducing the term "dot" into this
discussion, as Peirce actually uses that term not in Lowell 2, but in some
of his other explanations of existential graphs, notably CP 4.438:

"Let a heavy dot or dash be used in place of a noun which has been erased
from a proposition. A blank form of proposition produced by such erasures as
can be filled, each with a proper name, to make a proposition again, is
called a rhema, or, relatively to the proposition of which it is conceived
to be a part, the predicate of that proposition."

In Lowell 2.13, Peirce refers to this heavy dot as a "decidedly marked
point":

"Since the blackboard, or the sheet of assertion, represents the universe of
discourse, and since this universe is a collection of individuals, it seems
reasonable that any decidedly marked point of the sheet should stand for a
single individual; so that . should mean "'something exists'." (The dot
between "that" and "should" may not even be visible in some mail readers,
which could cause even more confusion!)

With this in mind, I will copy 2.14 here again, but with some interpolations
of my own (in a contrasting font) that will try to clear up the confusion
regarding the analysis of propositions as represented in EGs. 

Gary f.

Continuing from Lowell 2.13,

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13620

 

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.


Gf: The point marked with a dot, . , like a blank in a rheme, represents
some individual which can serve as a subject of a proposition. In that
respect it is equivalent to a demonstrative pronoun, or a proper name the
first time it is heard, in ordinary language. But in this lecture Peirce
introduces this "decidedly marked point" . before introducing the rheme or
spot which represents the predicate. This has the effect of emphasizing the
fact that . denotes an individual subject within the universe of discourse.

 

CSP: 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. 

Gf: This entails that a line made up of . points can denote a single
individual, and this becomes the "line of identity" in EGs.

 

CSP: 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). 

Gf: In the linguistic expression of a proposition, a "proper name" (or a
pronoun) can serve as a subject while the rest of the sentence is the
predicate. In the "blank form" of a proposition, the "blank" occupies the
place of the subject which in EG notation is a "marked point" .. But notice
that a common noun, such as "sinner" or "saint" in Peirce's examples above,
is not a subject but is part of the predicate, or rheme. Thus a complete
proposition which includes only general terms is still a rheme, a medad with
no blanks. The number of blanks is the "valency" or 'adicity' of the rheme,
the number of individual subjects it can take (such as Cain or Abel or ..
Translating this into ordinary language about propositions, common nouns and
verbs together (along with some structure words and modifiers) make up the
predicate, and it can take any number of subjects, but each of these must be
an individual denotable by a proper name or a demonstrative pronoun.

 

CSP: 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.) 

Gf: After this, Peirce very rarely used the term "lexis", but consistently
used both "rheme" (or rhema) and "spot" to denote this aspect of the EG
system. (That's why I made my parenthetical remark about not confusing the
"spot" with the "dot", which appears to have caused the very confusion I was
trying to avoid!) 

 

CSP: Such a spot has a particular point on its periphery appropriated to
each and every one of its blanks. Those points, which, you 

[PEIRCE-L] Re: Lowell Lecture 2.13 and 2.14

[Jon Awbrey]

John, Kirsti, List ...

JFS:
> In 1911, Peirce clarified that issues by using two distinct terms:
> 'the universe' and 'a sheet of paper'.  The sheet is no longer
> identified with the universe, and there is no reason why one
> couldn't or shouldn't shade a blank area of a sheet.

There is a difference between *being* a universe of discourse
and *representing* a universe of discourse.  The basement level
universe of discourse X is part of some object domain O in view
and the systems of signs that represent aspects of the universe
belong to whatever sign domain S and interpretant domain I are
relevant to the context of discourse at hand.

With logic as formal semiotics and semiotics as the study of
triadic sign relations, properly understanding how Peirce's
graphical symbol systems manage to represent universes of
discourse requires us to consider the larger contexts of
triadic sign relations in which they play their role.

Regards,

Jon

On 11/27/2017 6:49 AM, kirst...@saunalahti.fi wrote:

John,

Thank you very much! - I was wondering why I did not find PEG in the list.

Now it's all making sense.

With gratitude,

Kirsti

John F Sowa kirjoitti 27.11.2017 09:05:

Gary F, Mary L, Kirsti, Jerry LRC, and list,

In 1911, Peirce presented his clearest and simplest version of EGs.
He explained the essentials in just 8 pages of NEM (3:162 to 169).
I believe that it is his final preferred version, and I'll use it
for explaining issues about the more complex 1903 version.

Gary

[Mary's] question about the “blot” has me thinking again about
“the two peculiar graphs” which are “the blank place which asserts
only what is already well-understood between us to be true, and
the blot which asserts something well understood to be false”


Kirsti,

instead of warning against confusing SPOT, DOT and BLOT, it would
have been most interesting to hear how they are related.


In his 1911 terminology, Peirce did not use the words 'spot', 'dot',
or 'blot'.  Instead, a spot is just a very short line of identity.
The line represents an existential quantifier, and there is no
reason to distinguish long lines from short lines (spots).

He used the word 'peg' instead of 'dot'.   Each relation has zero
or more pegs, to which lines of identity may be attached.

He also shaded negative areas (nested in an odd number of negations)
and left positive areas unshaded (nested in an even number, zero or
more, negations).  A blot is just a shaded area that contains
nothing but a blank.

Gary

[The blank place and the blot] are peculiar in several ways,
and each is in some sense the opposite of the other.


Each is the negation of the other.  The blank place is unshaded,
and the blot is a shaded blank.

Gary

For instance, the blank cannot be erased, but any graph can be
added to it on the sheet of assertion; while the blot can be
erased, but nothing can be added to it, because it “fills up
its area.”


One reason why the "the blank place" is "peculiar" is that Peirce
had talked about it in two different ways.  He called the sheet
of assertion the universe of discourse when it contains all the
EGs that Graphist and Grapheus agree is true.

But the blank, by itself, is true before anything is asserted.
In modern terminology, the blank is Peirce's only axiom.  Any EG
that can be proved without any other assumptions is a theorem.

In 1911, Peirce clarified that issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.

Gary, quoting Peirce

[A blot] "fills up its area."


In 1911, Peirce no longer used this metaphor.  With the rules
of 1903 or 1911, a blot or a shaded blank implies every graph.
To prove that any graph g can be proved from it:

 1. Start with a sheet of paper that contains a shaded blank.

 2. By the rule of insertion in a shaded area, insert the graph
    for not-g inside the shaded area.  All the shaded areas of not-g
    then become unshaded, and the unshaded areas become shaded.

 3. The resulting graph consists of g in an unshaded area that is
    surrounded by a shaded ring that represents a double negation.

 4. Finally, erase the double negation to derive g.

Another important point:  In 1911, Peirce allowed any word, not
just verbs, to be the name of a relation.  From NEM, page 3.162:

Every word makes an assertion.  Thus ——man means "There is a man"
in whatever universe the whole sheet refers to.  
The dash before "man" is the "line of identity."


This EG is Peirce's first example in 1911.  And note that he begins
with a Beta graph.  In fact, he does not even mention the distinction
between Alpha and Beta.  The same rules of inference apply to both.

For Peirce's version of 1911 with my commentary, see
http://jfsowa.com/peirce/ms514.htm

Jerry,

CSP’s genius [etc.] make it difficult for anyone to project his
thoughts into rarefied logical, mathematical, scientific or

Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[kirstima]

John,

Thank you very much! - I was wondering why I did not find PEG in the 
list.


Now it's all making sense.

With gratitude,

Kirsti

John F Sowa kirjoitti 27.11.2017 09:05:

Gary F, Mary L, Kirsti, Jerry LRC, and list,

In 1911, Peirce presented his clearest and simplest version of EGs.
He explained the essentials in just 8 pages of NEM (3:162 to 169).
I believe that it is his final preferred version, and I'll use it
for explaining issues about the more complex 1903 version.

Gary

[Mary's] question about the “blot” has me thinking again about
“the two peculiar graphs” which are “the blank place which asserts
only what is already well-understood between us to be true, and
the blot which asserts something well understood to be false”


Kirsti,

instead of warning against confusing SPOT, DOT and BLOT, it would
have been most interesting to hear how they are related.


In his 1911 terminology, Peirce did not use the words 'spot', 'dot',
or 'blot'.  Instead, a spot is just a very short line of identity.
The line represents an existential quantifier, and there is no
reason to distinguish long lines from short lines (spots).

He used the word 'peg' instead of 'dot'.   Each relation has zero
or more pegs, to which lines of identity may be attached.

He also shaded negative areas (nested in an odd number of negations)
and left positive areas unshaded (nested in an even number, zero or
more, negations).  A blot is just a shaded area that contains
nothing but a blank.

Gary

[The blank place and the blot] are peculiar in several ways,
and each is in some sense the opposite of the other.


Each is the negation of the other.  The blank place is unshaded,
and the blot is a shaded blank.

Gary

For instance, the blank cannot be erased, but any graph can be
added to it on the sheet of assertion; while the blot can be
erased, but nothing can be added to it, because it “fills up
its area.”


One reason why the "the blank place" is "peculiar" is that Peirce
had talked about it in two different ways.  He called the sheet
of assertion the universe of discourse when it contains all the
EGs that Graphist and Grapheus agree is true.

But the blank, by itself, is true before anything is asserted.
In modern terminology, the blank is Peirce's only axiom.  Any EG
that can be proved without any other assumptions is a theorem.

In 1911, Peirce clarified that issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.

Gary, quoting Peirce

[A blot] "fills up its area."


In 1911, Peirce no longer used this metaphor.  With the rules
of 1903 or 1911, a blot or a shaded blank implies every graph.
To prove that any graph g can be proved from it:

 1. Start with a sheet of paper that contains a shaded blank.

 2. By the rule of insertion in a shaded area, insert the graph
for not-g inside the shaded area.  All the shaded areas of not-g
then become unshaded, and the unshaded areas become shaded.

 3. The resulting graph consists of g in an unshaded area that is
surrounded by a shaded ring that represents a double negation.

 4. Finally, erase the double negation to derive g.

Another important point:  In 1911, Peirce allowed any word, not
just verbs, to be the name of a relation.  From NEM, page 3.162:
Every word makes an assertion.  Thus ——man means "There is a man" in 
whatever universe the whole sheet refers to.  The dash before

"man" is the "line of identity."


This EG is Peirce's first example in 1911.  And note that he begins
with a Beta graph.  In fact, he does not even mention the distinction
between Alpha and Beta.  The same rules of inference apply to both.

For Peirce's version of 1911 with my commentary, see
http://jfsowa.com/peirce/ms514.htm

Jerry,

CSP’s genius [etc.] make it difficult for anyone to project his
thoughts into rarefied logical, mathematical, scientific or
philosophical atmospheres.


Yes.  He wrote volumes of insights that we still need to explore.
But you can't put words in his mouth.  If you can't find where he
stated something explicitly, you can't claim him as the source.

Note my discussion above.  Every one of my claims is based on
something that Peirce explicitly wrote.

John



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RE: [PEIRCE-L] Lowell Lecture 2.14

[kirstima]

Gary f. wrote:

- “Categories”, “elements”, “Firstness”, “Secondness”

and “Thirdness” are all technical terms of Peircean phenomenology...


Many mistakes in this. - Just offer one example where CSP explicitly 
states that these are TECHNICAL TERMS. (If you can.)


Categories concern definitely not only Peircean phenomenology. Which 
present A PART embedded in Peirce's philosphy.


He continues:

..which also have “meanings” (i.e. intensions) in ordinary language.


The question of MEANING cannot be reduced just to intensions, especially 
not into those in ordinary language.


With CSP we are dealing with PHILOSOPHICAL THEORY, not just ordinary 
language.


Then he continues:


"As Peirce said and wrote repeatedly, the last three are concepts which
are extremely difficult to grasp;"


Are you making a claim that Categories and Elements are not concepts? Or 
are claiming that they are easy to understand?


It seems to me you get into difficulties with all of them, not just the 
last three.


To me they have all become quite easy. After harduous work, of cource.

The way you both Gary's are dealing with legitimate questions posed by 
Jerry F. Chandler seems to me just evasive, at best.


Best,

Kirsti

P.S. I am not asking for "detailed explanations". I wish to be saved 
from such.


g...@gnusystems.ca kirjoitti 27.11.2017 00:01:

Jerry, Kirsti, list,

“Spot”, “dot” and “blot” are three of the many technical
terms used by Peirce to explain his system of existential graphs.
Peirce has given both visual examples and definitions of all three in
those parts of Lowell Lecture 2 which I have posted to the list. If
you are confused about their exact role in the EG system, you probably
need to review Lowell 2 by studying the complete text, which is online
at http://gnusystems.ca/Lowell2.htm [1] . Secondary sources such as
Roberts are also helpful, but you need to study them carefully in
order to see how the system elucidates Peirce’s logic of relations,
and perhaps set aside your preconceptions about the meanings of key
terms.

“Categories”, “elements”, “Firstness”, “Secondness”
and “Thirdness” are all technical terms of Peircean phenomenology
which also have “meanings” (i.e. intensions) in ordinary language.
As Peirce said and wrote repeatedly, the last three are concepts which
are extremely difficult to grasp; sometimes the ordinary-language
meanings of terms listed above are helpful, and sometimes they are
misleading. These concepts are pretty much unique to Peirce, so you
have to pay close attention to Peirce’s usage of them _in context_
if you want to understand what they mean. Lowell Lecture 3 is one of
his most extensive and cogent explanations of his phenomenology, which
is (from 1902 on) foundational to both his logic and his
classification of signs. This will all be discussed in connection with
Lowell Lecture 3, and I don’t have time now for dozens of examples
and detailed explanations of these points, so that’s all I’ll say
about them for now.

My previous commentary on 2.14 consisted mostly of direct quotations
from Peirce and some factual observations about the sources of those
quotations, which I identified in the post. Kirsti, it’s not clear
what you are disagreeing with, or what exactly you think I am
“mistaken” about. If you will quote my words that you disagree
with, I’ll try to resolve the disagreement. But if you don’t
believe that Peirce used both “categories” and “elements” as
terms referring to Firstness, Secondness and Thirdness, I think you
need to read the Peirce texts (especially the Lowells and the Syllabus
texts given in EP2) and see for yourself. As I said, I don’t have
time right now to search out and paste in dozens of examples to
demonstrate what should be obvious from a careful reading of Peirce.
The question of _why_ Peirce chose the terms that he did is
interesting, but I’ll leave that for the discussion of Lowell 3. If
you want to get a head start on that, there’s a fairly large chunk
from Lowell 3 starting at CP 1.343.

And finally, my comments on the Lowell bits I’m posting are just
that, comments — they are not meant to be a substitute for reading
the actual Peirce texts, and probably don’t make much sense to those
who haven’t read those Peirce texts.

Gary f.

-Original Message-
From: kirst...@saunalahti.fi [mailto:kirst...@saunalahti.fi]
Sent: 26-Nov-17 08:29
To: g...@gnusystems.ca
Cc: 'Peirce List' 
Subject: RE: [PEIRCE-L] Lowell Lecture 2.14

Gary f.,

Seems to me you are mistaken. Categories and elements have a different
meaning. It not just giving new names. I.e. not just about
terminonology. They are not synonyms.

But if anyone uses  Firstness, Secondness and Thirdness  as just names
for classes of signs, it may appear so. A most grave simplification.

If one is allowed to disagree in this discussion. Perhaps  not.

Kirsti

g...@gnusystems.ca kirjoitti 26.11.2017 02:47:


Kirsti, you asked why my post about 2.14 put “categories” in