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

[Jon Awbrey]

Peircers,

Still trying to catch up with the dailies from November.
Here are links to my latest rewrites of my last couple
of substantive comments.  These serve mostly as pegs
to remind me of issues that deserve more discussion.

Peirce's 1903 Lowell Lectures • Comment 9
https://inquiryintoinquiry.com/2017/11/28/peirces-1903-lowell-lectures-%e2%80%a2-comment-9/

Peirce's 1903 Lowell Lectures • Comment 10
https://inquiryintoinquiry.com/2017/12/16/peirces-1903-lowell-lectures-%e2%80%a2-comment-10/

Regards,

Jon

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

[Jon Awbrey]

Kirsti, List,

I have been occupied with other work and not had the
opportunity to keep up with all the list discussions.

I appreciate the work Gary and Jeff and the other SPINners
are doing to reconstruct the text of Peirce's lectures and
I understand all the reasons why people encountering this
material for the first time would want to keep their noses
close to the text as it's writ.  Still, my first encounter
with this material was fifty years ago and the edges of my
work on the graphical formal systems for logic it inspired
have advanced a ways beyond these first inklings, at least,
in certain directions.

At any rate, I think I left off responding about here.
I'll stick a pin in it and try to get back off and on.

Regards,

Jon

On 11/28/2017 10:47 AM, kirst...@saunalahti.fi wrote:

John, Jon, list,

Thank you for a most interesting discussion.

Not being so keen on set theory, or the utterly simple assertions formal logic has so far dealt with, I would like to 
draw your attention to these assertion of mine:


If there exists a sheet of assertion, for example a blackboard or a piece of paper, there has to have been some 
co-operative human beings to make even the empty ones.


If there exists any assertion stated on it, there has to have been a human 
individual to draw/write (etc) it.

As you can see, I have taken time into the timelessly considered issue of empty 
sets.

Thus, empty sheets may exist, but they can only become real (have any effect) if and only if some community (of whatever 
kind) not only exists, but has become real.


How about these? Comments?

These present some outcomes from taking BOTH formulations of the Pragmatic Maxim simultanously seriously. Which they 
usually are not. People tend to take sides at the outset.


I have made wonders with modulations of Aristotelian syllogisms on this basis. With the help of two new concepts, 
experiential time and experiential meaning. Which have been exploited, but not funded.


Which kind of reminds me of someone else... Who on earth could it be...

With kind regards,

Kirsti



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

[kirstima]

John, Jon,

I agree with John on the issue of "every word.."

Opening the pdf by John did not succeed. So a little note on his wording 
in:



JFS; In summary, the range of contexts for writing or using EGs is as

open ended as the contexts for using any other kinds of signs.
It's best to distinguish the act of drawing an EG from any use or
speech act, such as assertion.


Shouldn*t the last word be "asserting", thus using the verb, not the 
noun?
This may sound trifle, but I do think it is important to make clear 
whether and when one is talking about an act, or an entitity.


Kirsti

John F Sowa kirjoitti 28.11.2017 22:03:

Jon A and Kirsti,

Jon, replying to JFS

[In] a proof by contradiction... 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.


Yes, but there are several reasons why Peirce's original discussion
about the Sheet of Assertion is too restrictive.

Jon

By the way, to assert “Every word makes an assertion”
is either word magic, word animism (?), or nominalism...


No.  Every use of signs, especially natural language, can only
be interpreted in context.  The sentence that precedes the in
question states the context:  "This syntax is so simple that
I will describe it." (NEM 3:162)

I didn't quote that sentence because the context was a  comparison
with the Lowell lectures, in which Peirce distinguished "verbs"
that named rhemes (or predicates) from "nouns" that named the kinds
of entities in the universe of discourse.

In 1911, he did not limit the part of speech of the words or phrases
that named rhemes or predicates.  See Peirce's own examples in
http://jfsowa.com/peirce/ms514.htm :

From the first two graphs:  -man, -eats.  Fig 1:  -phoenix.
Fig 3: -thunder, -lightening.   Unlabeled graph:  -is-.
Fig 5: -will die.  Fig 7: -boy, -industrious.
Fig 9: -known for certain, -communication with-.  Fig 10: -deceased.

Kirsti

If there exists a sheet of assertion, for example a blackboard or
a piece of paper, there has to have been some co-operative human
beings to make even the empty ones.


Yes, and those people must have some reason or intention for doing so.
Assertion is just one reason among many.

Peirce discussed the kinds of "speech acts" long before John Austin.
Any of those acts may be performed with EGs:  metalanguage (talking
about an EG); hypothesis (suggesting an EG without claiming it's true);
proof (drawing implications before the conclusion is known); teaching
the syntax and rules for EGs (what Peirce was doing in his lectures)...

In summary, the range of contexts for writing or using EGs is as
open ended as the contexts for using any other kinds of signs.
It's best to distinguish the act of drawing an EG from any use or
speech act, such as assertion.

For more examples of contexts in language and logic, see the
slides in http://jfsowa.com/contexts.pdf .

John



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

[kirstima]

John & Jon,

The two paragraphs offered by John to clarify the meaning of the verb 
'to indentify'  did not do the job for me. Quite the contrary.  Many 
questions arose.


JFS:  "In mathematics, it is common practice to "identify" two 
structures that are isomorphic.  Some mathematicians call that practice 
"abuse of notation" and insist on adding some annotations to the marks 
in order to distinguish the references.  But most do not bother to 
clutter their notations with such annotations."


Question:  Which (variety of) notations do you mean?   2 = 2  and  a = a 
?

Both can be read aloud as – equals – ,  OR – is identical with – .

The mark remains the same, but there is change of meaning, depending on 
the (mathematical) context.
With cardinals,  2 = 2 can be taken as equal and identical with  1+1 = 
1+1. With a = a the situation is not that simple.


With ordinals this does not apply.  As was shown by CSP in his cyclical 
arithmetics.


Not only does "how many?" count, "how many times? " counts. (This is a 
joke, mind you).


Positions within multiple cycles begin to mean a lot.

Also zero becomes very interesting, indeed.

When zero was introduced (by arabic influence) to our number system, it 
brought with it not only calculus, but also the arabic numbering system.


Thus 000 = 00 (etc.), but 10  and 100 and 1000 (etc.) make a huge 
difference. (As we all may,  sorely or happily, know by looking at one's 
bank accounts.)  This is not as trivial as it may seem to some.  Neither 
mathematically,  nor logically.


The first zero, the second zero, the third zero … acquire a  different 
meaning by their relative position in the chain of numbers.  Which is 
not trivial, either.


Relational logic is needed.  Which is just as complex ( and perplex) as 
CSP has shown it to be.


I have presented my thoughts as simply as I possibly can, but it does 
not follow that the thoughts are inherently simple.


With ordered chains of numbers (or other kindred marks) the problem of 
reversibility and irreversibility acquire a new acuity.


CPS deals with the problem a lot in Lowell Lectures.

I'll leave my second question on the meaning of identifying to a later 
date.


Best,
Kirsti Määttänen



John F Sowa kirjoitti 2.12.2017 23:06:

On 12/2/2017 2:20 PM, Jon Awbrey wrote:

Re: Peirce List Discussion • John Sowa

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.


On your website, please do not imply that I was confusing being
and representing.

In mathematics, it is common practice to "identify" two structures
that are isomorphic.  Some mathematicians call that practice
"abuse of notation" and insist on adding some annotations to the
marks in order to distinguish the references.  But most do not
bother to clutter their notations with such annotations.

If you are not convinced by mathematical practice, note the first
definition of 'identify' in the Merriam-Webster dictionary:
"1 a: to cause to be or become identical b: to conceive as united
(in spirit, outlook, or principle)."

Request:  Please remove the initials "JFS" from that page on your
website, or please insert the above two paragraphs to clarify the
meaning of the word 'identify'.

John



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

[Jon Awbrey]

John,

Okay, recommendation noted.

(I am partly addressing this series of blog posts to the Laws Of Form
discussion group and attempting to focus on the features of Peirce's
logical graphs that were drawn out and developed further in that
line of inquiry, so I sometimes stumble on the requirements
of illocutionary presupposition for multiple audiences.)

At any rate, we can now proceed on the understanding
of a distinction between the object universe and the
Modifications In Assorted Semiotic Media (MIASM).

Regards,

Jon

On 12/3/2017 9:19 AM, John F Sowa wrote:> On 12/2/2017 7:08 PM, Jon Awbrey 
wrote:
>> I thought it was clear I was simply echoing and elaborating
>> on your statement that drew a distinction between the two
>
> OK.  In such cases, I usually say "Yes, but..."
>
> The "Yes" agrees with the general point, and the "but" adds
> some quibble, qualification, or clarification.
>
> John
>

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

[Jon Awbrey]

John,

I thought it was clear I was simply echoing and elaborating on your statement 
that drew a distinction between the two, the universe of discourse itself and 
the sheet paper that represents it. 

An earlier version referred to your post only by link, which would be my normal 
practice, but I added the quote so as not to appear to be taking credit for 
your insight. 

Will try to emphasize the connection or just delete the quote in favor of a 
link to your whole post. 

Apologies for any confusion. 

Regards,

Jon

http://inquiryintoinquiry.com

> On Dec 2, 2017, at 4:06 PM, John F Sowa  wrote:
> 
>> On 12/2/2017 2:20 PM, Jon Awbrey wrote:
>> Re: Peirce List Discussion • John Sowa
>> 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.
> 
> On your website, please do not imply that I was confusing being
> and representing.
> 
> In mathematics, it is common practice to "identify" two structures
> that are isomorphic.  Some mathematicians call that practice
> "abuse of notation" and insist on adding some annotations to the
> marks in order to distinguish the references.  But most do not
> bother to clutter their notations with such annotations.
> 
> If you are not convinced by mathematical practice, note the first
> definition of 'identify' in the Merriam-Webster dictionary:
> "1 a: to cause to be or become identical b: to conceive as united
> (in spirit, outlook, or principle)."
> 
> Request:  Please remove the initials "JFS" from that page on your
> website, or please insert the above two paragraphs to clarify the
> meaning of the word 'identify'.
> 
> John


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

[John F Sowa]

On 12/2/2017 2:20 PM, Jon Awbrey wrote:

Re: Peirce List Discussion • John Sowa

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.


On your website, please do not imply that I was confusing being
and representing.

In mathematics, it is common practice to "identify" two structures
that are isomorphic.  Some mathematicians call that practice
"abuse of notation" and insist on adding some annotations to the
marks in order to distinguish the references.  But most do not
bother to clutter their notations with such annotations.

If you are not convinced by mathematical practice, note the first
definition of 'identify' in the Merriam-Webster dictionary:
"1 a: to cause to be or become identical b: to conceive as united
(in spirit, outlook, or principle)."

Request:  Please remove the initials "JFS" from that page on your
website, or please insert the above two paragraphs to clarify the
meaning of the word 'identify'.

John

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

[Jon Awbrey]

Peircers,

Still cleaning up leftovers from last month ...
I spent some time trying to write a clearer version of that
last post on being vs. representing a universe of discourse.
Here's a link to my blog rewrite:

Peirce's 1903 Lowell Lectures • Comment 9
https://inquiryintoinquiry.com/2017/11/28/peirces-1903-lowell-lectures-%e2%80%a2-comment-9/

And here's a transcript:

Re: Peirce List Discussion • John Sowa

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.

• On the one hand we have an initial universe of discourse X.
  This provides the basis for a prospective object domain O
  to be constructed out of its elements as our description
  of the universe develops.

• On the other hand we have the various systems of signs that
  we use to represent aspects of the universe of discourse X.
  These go to make up whatever sign domain S and interpretant
  domain I are needed for the ongoing discussion and inquiry.

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.

Resources
=

• Semeiotic
  http://intersci.ss.uci.edu/wiki/index.php/Semeiotic

• Sign Relation
  http://intersci.ss.uci.edu/wiki/index.php/Sign_relation

• Triadic Relation
  http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation

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

[Gary Richmond]

Gary F, John,

Thanks for this clarification, Gary, as it was very helpful, perhaps
especially.

Gf: Peirce’s terminology in referring to a graph as a “word” is rather
sloppy, but after all, this is a personal letter from a self-described
“garrulous old man” to a new acquaintance. It is not an explanation of EGs
intended for publication. I’d like to know your reasons for claiming that
this presentation is Peirce’s “preferred” version of EGs.


I too would like to know why John  sees this as the "preferred" version of
EGs (John's made a few comments on this matter, but I'm still not entirely
clear as to the reasons for this preference).

Best,

Gary R


[image: Gary Richmond]

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
*718 482-5690*

On Tue, Nov 28, 2017 at 6:07 PM,  wrote:

> John, Gary R,
>
>
>
> See my insertions below …
>
>
>
> Gary f.
>
> -Original Message-
> From: John F Sowa [mailto:s...@bestweb.net]
> Sent: 28-Nov-17 15:52
>
> On 11/28/2017 3:07 PM, Gary Richmond wrote:
>
> > why he and others think Peirce would have written this as late as 1911
>
> > (unless it is. indeed, simply " sloppy pedagogical rhetoric."
>
>
>
> There was nothing sloppy about Peirce's note or my comment.
>
> Following is the context from my note of 12 noon, Nov. 27:
>
>
>
> > But that is just one of many ways of using logic.  In 1911, [Peirce]
>
> > 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.
>
>
>
> Gf: Peirce’s example, “*—*man”, is also part of the context; and shows
> that “every word” means, in the syntax of EGs, every graph composed of a
> line of identity connected to the “peg” or “hook” of a “spot” or rheme. It
> could be argued that Peirce’s terminology in referring to a graph as a
> “word” is rather sloppy, but after all, this is a personal letter from a
> self-described “garrulous old man” to a new acquaintance. It is not an
> explanation of EGs intended for publication. I’d like to know your reasons
> for claiming that this presentation is Peirce’s “preferred” version of EGs.
>
>
>
> And note my response to Jon at 3:03 pm, Nov. 28:
>
>
>
> >> [Jon A] By the way, to assert “Every word makes an assertion”
>
> >> is either word magic, word animism (?), or nominalism...
>
> >
>
> > No.  Every use of signs, especially natural language, can only be
>
> > interpreted in context.  The sentence that precedes the one in
>
> > question states the context:  "This syntax is so simple that I will
>
> > describe it." (NEM 3:162)
>
> >
>
> > I didn't quote that sentence because the context was a comparison with
>
> > the Lowell lectures, in which Peirce distinguished "verbs"
>
> > that named rhemes (or predicates) from "nouns" that named the kinds of
>
> > entities in the universe of discourse.
>
>
>
> Gf: No, Peirce only made this distinction in the *Cambridge Lectures of
> 1898*, from which I included a couple of excerpts in one of my comments.
> As I also posted, the main distinction in this part of Lowell 2 is between
> general terms and signs that refer to individuals, such as proper nouns,
> demonstrative pronoouns and “marked points” such as the ends of lines of
> identity.
>
>
>
> John
>
>
> -
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>
>
>
>
>
>

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

[gnox]

John, Gary R,

 

See my insertions below …

 

Gary f.

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 28-Nov-17 15:52



On 11/28/2017 3:07 PM, Gary Richmond wrote:

> why he and others think Peirce would have written this as late as 1911 

> (unless it is. indeed, simply " sloppy pedagogical rhetoric."

 

There was nothing sloppy about Peirce's note or my comment.

Following is the context from my note of 12 noon, Nov. 27:

 

> But that is just one of many ways of using logic.  In 1911, [Peirce] 

> 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.

 

Gf: Peirce’s example, “—man”, is also part of the context; and shows that 
“every word” means, in the syntax of EGs, every graph composed of a line of 
identity connected to the “peg” or “hook” of a “spot” or rheme. It could be 
argued that Peirce’s terminology in referring to a graph as a “word” is rather 
sloppy, but after all, this is a personal letter from a self-described 
“garrulous old man” to a new acquaintance. It is not an explanation of EGs 
intended for publication. I’d like to know your reasons for claiming that this 
presentation is Peirce’s “preferred” version of EGs.

 

And note my response to Jon at 3:03 pm, Nov. 28:

 

>> [Jon A] By the way, to assert “Every word makes an assertion”

>> is either word magic, word animism (?), or nominalism...

> 

> No.  Every use of signs, especially natural language, can only be 

> interpreted in context.  The sentence that precedes the one in 

> question states the context:  "This syntax is so simple that I will 

> describe it." (NEM 3:162)

> 

> I didn't quote that sentence because the context was a comparison with 

> the Lowell lectures, in which Peirce distinguished "verbs"

> that named rhemes (or predicates) from "nouns" that named the kinds of 

> entities in the universe of discourse.

 

Gf: No, Peirce only made this distinction in the Cambridge Lectures of 1898, 
from which I included a couple of excerpts in one of my comments. As I also 
posted, the main distinction in this part of Lowell 2 is between general terms 
and signs that refer to individuals, such as proper nouns, demonstrative 
pronoouns and “marked points” such as the ends of lines of identity.

 

John


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

[John F Sowa]

On 11/28/2017 3:07 PM, Gary Richmond wrote:
why he and others think Peirce would have written this as late as 1911 
(unless it is. indeed, simply " sloppy pedagogical rhetoric."


There was nothing sloppy about Peirce's note or my comment.
Following is the context from my note of 12 noon, Nov. 27:


But that is just one of many ways of using logic.  In 1911,
[Peirce] 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.


And note my response to Jon at 3:03 pm, Nov. 28:


[Jon A] By the way, to assert “Every word makes an assertion”
is either word magic, word animism (?), or nominalism...


No.  Every use of signs, especially natural language, can only
be interpreted in context.  The sentence that precedes the one
in question states the context:  "This syntax is so simple that
I will describe it." (NEM 3:162)

I didn't quote that sentence because the context was a comparison
with the Lowell lectures, in which Peirce distinguished "verbs"
that named rhemes (or predicates) from "nouns" that named the kinds
of entities in the universe of discourse. 


John

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

[Gary Richmond]

Jon A, John, Kirsti, list,

Jon A wrote:

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.


I would tend to agree that it is not so "that every word [or rheme] makes
an assertion" *except*, *perhaps*, in the very limited technical sense in
which Peirce gives "  ——man means "There is a man" as an example.

Yet Peirce can rarely, at least in my experience, be accused of "sloppy
pedagogical rhetoric." So I'd be very interested in why John singled out
this comment, and why he and others think Peirce would have written this as
late as 1911 (unless it is. indeed, simply " sloppy pedagogical rhetoric."

Best,

Gary R



[image: Gary Richmond]

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
*718 482-5690*

On Mon, Nov 27, 2017 at 4:00 PM, Jon Awbrey  wrote:

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

[John F Sowa]

Jon A and Kirsti,

Jon, replying to JFS

[In] a proof by contradiction... 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.


Yes, but there are several reasons why Peirce's original discussion
about the Sheet of Assertion is too restrictive.

Jon

By the way, to assert “Every word makes an assertion”
is either word magic, word animism (?), or nominalism...


No.  Every use of signs, especially natural language, can only
be interpreted in context.  The sentence that precedes the in
question states the context:  "This syntax is so simple that
I will describe it." (NEM 3:162)

I didn't quote that sentence because the context was a  comparison
with the Lowell lectures, in which Peirce distinguished "verbs"
that named rhemes (or predicates) from "nouns" that named the kinds
of entities in the universe of discourse.

In 1911, he did not limit the part of speech of the words or phrases
that named rhemes or predicates.  See Peirce's own examples in
http://jfsowa.com/peirce/ms514.htm :

From the first two graphs:  -man, -eats.  Fig 1:  -phoenix.
Fig 3: -thunder, -lightening.   Unlabeled graph:  -is-.
Fig 5: -will die.  Fig 7: -boy, -industrious.
Fig 9: -known for certain, -communication with-.  Fig 10: -deceased.

Kirsti

If there exists a sheet of assertion, for example a blackboard or
a piece of paper, there has to have been some co-operative human
beings to make even the empty ones.


Yes, and those people must have some reason or intention for doing so.
Assertion is just one reason among many.

Peirce discussed the kinds of "speech acts" long before John Austin.
Any of those acts may be performed with EGs:  metalanguage (talking
about an EG); hypothesis (suggesting an EG without claiming it's true);
proof (drawing implications before the conclusion is known); teaching
the syntax and rules for EGs (what Peirce was doing in his lectures)...

In summary, the range of contexts for writing or using EGs is as
open ended as the contexts for using any other kinds of signs.
It's best to distinguish the act of drawing an EG from any use or
speech act, such as assertion.

For more examples of contexts in language and logic, see the
slides in http://jfsowa.com/contexts.pdf .

John

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

[kirstima]

John, Jon, list,

Thank you for a most interesting discussion.

Not being so keen on set theory, or the utterly simple assertions formal 
logic has so far dealt with, I would like to draw your attention to 
these assertion of mine:


If there exists a sheet of assertion, for example a blackboard or a 
piece of paper, there has to have been some co-operative human beings to 
make even the empty ones.


If there exists any assertion stated on it, there has to have been a 
human individual to draw/write (etc) it.


As you can see, I have taken time into the timelessly considered issue 
of empty sets.


Thus, empty sheets may exist, but they can only become real (have any 
effect) if and only if some community (of whatever kind) not only 
exists, but has become real.


How about these? Comments?

These present some outcomes from taking BOTH formulations of the 
Pragmatic Maxim simultanously seriously. Which they usually are not. 
People tend to take sides at the outset.


I have made wonders with modulations of Aristotelian syllogisms on this 
basis. With the help of two new concepts, experiential time and 
experiential meaning. Which have been exploited, but not funded.


Which kind of reminds me of someone else... Who on earth could it be...

With kind regards,

Kirsti






John F Sowa kirjoitti 27.11.2017 19:00:

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

[kirstima]

Jon,
I agree!
Kirsti

Jon Awbrey kirjoitti 27.11.2017 17:30:

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

[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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[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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[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