Robert,
Thanks for finding that quotation:
> Thought is
a thread of melody running through the succession of our sensations (CP
5.395)
Now that you mention it, I recall reading that some
time ago. It must have been lurking somewhere in my mind, but well
beneath the conscious level.
In any
Bill,
Your comment is very close to what I was trying to
say.
> I have been a musician for seventy years, and I was a
serious
mathematician until age twenty. (I graduated with a double degree.) I
can assure you that I dont think only in terms of the patterns . . .
In fact, in my most
Gary R,
My remarks were ad rem, not ad hominem. Mathematics is
like music. A mathematician or a musician thinks only in terms of the
patterns, the operations on those patterns, and their relationship to
whatever notation is used to represent them.
The words used to
describe those patterns
Auke,
I agree with your observation, and the conclusion: "It
is a line of thought I can see leading to what Jon
wrote."
Charles' father Benjamin Peirce gave him a thorough
training in mathematics from early childhood, and Charles devoured
Whateley's logic book in a week when he was 13. He
Auke> I was thinking in terms of goals, i.e. what is the object you
try to understand, not credentials. I can connect Jon's answer to my
question with his line of reasoning and I did like that. There might
be differences in the goals and then it is always better to asses and
value the
Auke> Since perspective is important, it might be a good idea to
explicate the differences in purpose each of you entertain.
That's
a good question.
I have been working on research and teaching in
logic, computer science, artificial intelligence and related areas for
many years. In the
Jon, List,
A few more points:
1. The quotations you cited
are from a time when Peirce still thought that a sign of illation was
important for deduction. Note that in R670, he says that the EGs have
just three syntactic features: a line of identity, a spot for a rheme
and a shaded area for
Jon AS, List,
The *opinion* that the EG version of June 1911 is
Peirce's best is Peirce's own, as he stated in December, after six months
of further consideration. The fact that he stated it in a lengthy letter
to a member of Lady Welby's significs group is further evidence of its
importance.
Jon, List,
Again, you have not cited any statements by Peirce
after June 1911. Therefore, nothing in your note contradicts the evidence
that the 1911 version of EGs is Peirce's best and last available
version.
Furthermore, Peirce's letters of Sept. and Dec. 1911
explicitly reject the version
Jon AS,
All your citations are prior to R670, which demotes the
scroll to nothing but a way of drawing two ovals (negations) without
raising the pen.
In R670, Peirce states the three primitives:
existence, conjunction, and negation. And in L231, he drops the adjective
'illative' in front of
Jon AS, List,
For anyone who is not familiar with Peirce's 1911
EGs, see my
introduction to EGs, which is based on the 1911 version.
The first
10 slides are sufficient for an overview. The remaining
slides show
features of the 1911 EGs that make a major advance over
the logics
of the 20th
Azamat,
People observe the intension/extension distinction
without learning the name for the distinction.
AA>It
implies that operational meanings or definitions could be more
significant than an intension/extension or representation/reference or
connotation/denotation dichotomy.
Helmut,
In every version of language and logic -- ancient or
modern, informal or formal -- the intensional definition is fundamental.
It corresponds to the definition you'll find in a typical dictionary of
any natural language or in any formal specification in science,
engineering, business,
Helmut,
The distinction between intesion and extension is
important for every version of logic since antiquity. The oldest example
is "rational animal" vs. "featherless biped" -- those
are two terms with different intensions, but the same extension. Diogenes
the Cynic plucked a chicken and
Terry, I completely agree with what you wrote (copy below).
But
I emphasized database relations because they are the most commonly used
examples of relations that are defined by extension.
However, the
meaning of the data is specified by the rules or axioms that state the
intensions. Those
Jon A,
It's important to distinguish the intension and the
extension of a function or relation. The *intension* is its definition by
a rule or set of axioms. The *extension* is the set of instances in some
domain or universe of discourse:
JA> We can now define a
relation L as a subset of a
Dear Jacob,
Let me express my condolences on your loss. We'll
miss your father's contributions to this list and to the study of Peirce's
writings and their relationship to linguistics.
When I read your
note, I checked your father's list of publications at
Ben, I agree with your analysis, and I'd like to add a comment about
modal logic.
Consider the sentence "It might rain tomorrow,
and it might not." That sentence cannot be falsified because neither
side makes a firm promise.
But if you replace 'might' with 'will',
the following statement is
Jon, List,
I have a high regard for the work that Ahti and
Francesco have been doing, and I read the article you cited (copy of the
reference below). They have been doing meticulous scholarship on the
development of Peirce's EGs up to 1911. But unfortunately, they overlooked
the implications
Jeff, All versions of logic, by Peirce and by any logicians before or
after Peirce, represent propositions. Induction, abduction, and deduction
are operations that relate propositions to one another in various ways.
Those operations can be performed in equivaent ways with any notation for
Robert and Edwina,
I agree with both of you that the lattice is
more than a taxonomy. It shows the direction of the development of the
categories. It is active, not passive.
And I also believe that
Peirce's 1903 classification of the sciences is much more than a
taxonomy. The most important
Jon A> the question of Peirce's sources on Medieval and
Scholastic
Logic, especially with regard to 1st and 2nd and maybe 3rd
intentions.
Peirce's source for that distinction is Ockham's Summa
totius logicae.
His most important application is in the 1885
Algebra of Logic. He
adopted the term
David and Jon, C. S. Peirce made a very clear and sharp distinction
between formal or mathematical logic and logic as semiotic.
Peirce's algebra of logic (1885) is the foundation for Peano's
version of logic and the predicate calculus of Whitehead and Russell. The
term Peano-Russell notation
Robert,
I thought that the following paragraph in your article
was especially informative:
>From the "Five paths"
article": We now have a semiotic tool of greater scope than the
lattice itself, since it does not only classify signs, but also
"streams of signs", that is, interpretative habits
Today, the TV program "60 Minutes" reran an interview with the
neuroscientist Marcel Just at Carnegie-Mellon University.
Title: "Scientists are using MRI scans to reveal the physical
makeup of our thoughts and feelings"
Abstract "Ten
years ago, 60 Minutes met a team of scientists at Carnegie
Auke,
I apologize for my previous note. I accidentally hit SEND
before I wrote anything.
JFS> Formal EGs are the
foundation. As Peirce himself said, logic as semiotic is much broader.
It includes the methodeutic for analyzing and developing the immense
variety of the empirical sciences.
> John,
>
>
>> Op 30 augustus
2020 om 20:55 schreef "John F. Sowa"
:
>>
>>
>>
Auke, I agree with you about the issues and priorities.
>>
>> AvB> Peirce is multi facetted. Each of us looks from a
particular
>> angle...
Auke, I agree with you about the issues and priorities.
AvB> Peirce is multi facetted. Each of us looks from a particular
angle... I am not interested in what might be the final version Peirce
wrote on the negation vs scroll issue... I can agree with you if we are
discussing EG as a formal
Jon AS, List
This thread began with my note of August 2nd,
which I include below in the file 2aug20.txt. All the points in that note
are based on the citations included in it. But I changed the subject line
of this note to emphasize Peirce's fundamental insight of 2 June 1911
shortly after
Jeff BD, Terry R, Jon AS, List
I endorse Jeff's comments about
the need to relate any author's work to his or her predecessors,
contemporaries, and successors. I copied an excerpt from his note after
my signature below.
A major reason why Peirce's logic and semiotic
were so advanced is that he
Jon A, Helmut R, Terry R, Jon AS, List,
JA> I can't imagine
why anyone would bother with Peirce's logic if it's just Frege and Russell
in another syntax, which has been the opinion I usually get from FOL
fans.
That is true. But the EG structure and rules of inference are
elegant, and the
Gary F,
To answer your questions:
Classical first-order
logic, usually abbreviated FOL, has pride of place among the open-ended
variety of logics that have been specified during the past century.
Primary reason: FOL is sufficient to specify 99.99% of all versions of
mathematics from ancient
Jon AS,
In NEM 3:140, Peirce made a clear distinction between the
vague words of ordinary language, and the precise terminology of
science:
CSP> The language and symbols of ordinary life are
short, defective and figurative. As little as possible is spoken, as much
as possible is left to
Gary R,
The primary claim of this thread is that Peirce's 1911
version of EGs, which he sent in the letter L231 to Mr. Kehler (a member
of LadyWelby's significs group) is the one which he intended as a
definitive statement of EGs. For Peirce's text and some commentary, see
Robert M, Gary F, List,
Before saying anything else, I'll remind
everybody of two points: (1) theorematic reasoning is a special case of
diagrammatic reasoning. (2) In Peirce's classification of the sciences,
there is a two-way flow of information: every science (including every
branch of
Jeff,
To be iconic, a notation must have some resemblance to the
structure or image of which it is an icon. Any claim that some notation
is iconic must be justified by showing the original which it
resembles.
JBD> As far as I can
see, the scroll is a
special kind of iconic sign because it
Jeff,
In the note I just sent, I was talking about the version
of EGs in L231. For that version of logic, there can be no difference in
semantics between a scroll and a nest of two ovals.
JBD> In the
case of inductive and abductive inferences, the conditionals may
take a variety of forms:
Jon AS,
This is yet another case where the mathematical
structures are precise, but the words that describe them leave enough
ambiguity to cause confusion.
The beauty of eg1911, as specified in
L231, is its brevity, simplicity, precision, and bare minimum of
verbiage. Every EG that conforms
Auke, Jon A, List,
AvB> I did like this ms fragment very
much: "It is not so much the history of science as it is the history
of sound scientific thinking which I am considering" [Peirce MS
12801].
JA> Exactly! We interpret texts in relation to the
object in view.
Yes. Words are highly
Jon AS, List,
As I mentioned in my reply to Jeff, Peirce's ideas
were often far ahead of his time, and it's important to see which of them
not only stood the test of time, but even improved on later developments.
I changed the subject line to emphasize a critical issue that famous
logicians
Jeff,
I agree with your points and concerns. The following
issue is critical:
JBD> The future of mathematics is hard to
see--even for the best of mathematicians.
Yes. And Peirce was far
ahead of his time in many aspects of mathematics, logic, psychology, and
philosophy. Therefore, it's
Jon AS,
JAS: I continue to agree that NEM 3:162-169 is
Peirce's simplest and clearest explanation of existential graphs.
That'a good. But the reason why it appears so clear and simple is that
Peirce discovered a simple, universal, notation-independent mathematical
structure that underlies
Jon AS,
Comparing Peirce's texts to the instructions on a 5th grade
exam is like comparing quantum mechanics to 2+2=4.
William James
was Peirce's closest friend. He had spent years talking with CSP and
reading his writings. But he described Peirce's lectures as flashes of
brilliant light
Jon,
Peirce's writings are a "How-to manual" about
thinking and reasoning.
If you have a how-to manual about cooking,
skiing, or growing flowers,
it's impossible to understand the manual
without doing the work. If
it's a manual on cooking, you have to buy
the ingredients and follow the
Jeff D> What is more, one can ask if Peirce is using the right
methods. Where we have doubts about his methods or results that persist,
it is only natural to ask how might we improve on those methods in a
manner that is consonant with the aim of seeking the truth about what is
really the case.
Robert Marty noticed that I forgot to upload two files that I cited in my
previous
note:
http://jfsowa.com/peirce/r670.pdf
http://jfsowa.com/peirce/L378.htm
I
thank Robert, and I apologize for any inconvenience.
John
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply
I have often said that the excerpt of L231 published in NEM 3:162-169 is
Peirce's best and final version of existential graphs. For a copy and
some brief comments, see http://jfsowa.com/peirce/eg1911.pdf
Following are some objections to the claim that eg1911 is definitive:
1. In his 1973
Jeff,
I strongly agree with the points you made in this thread.
My only recommendation is to modify the last line below by replacing
"seems to involve facts" with "requires facts and
actions".
Peirce made the strongest possible justification for
that change: "The elements of every concept
Robert,
I agree with Peirce and with your interpretation. But
the cost of your article is $42. Do you have a web site with a less
costly version?"Let it be
repeated that all the terms of the division must be strictly relevant to
logic,
and that consequently all accidents of experience,
Jon A and Paola,
The amount of research in neuroscience in
the past 50 years is immense compared to the studies of the left &
right hemispheres in the 1970s. Among other things, the neuroscientists
today have much more sympathy with introspective studies than they have
with people (in the
The following article is relevant to our recent discussions about
mathematics, logic, and reasoning in words.
"Cortical circuits
for mathematical knowledge: evidence for a major subdivision within the
brain's semantic networks"
Marie Amalric and Stanislas
Dehaene
Gary F,
I have a great deal of sympathy for your Turning Signs. And I
believe that issues of normative science deserve a great
deal of attention especially now.
For any points that I may criticize or quibble, I emphasize that my comments
are about
details, rather than the main issues you
I apologize for accidentally sending my note to Peirce-L. I intended
it only for Gary and with a cc to Auke and Edwina.
John
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
PEIRCE-L to this message. PEIRCE-L posts should go to
Gary,
I agree with Auke that JAS is frustrating to the point of
nastiness Trying to communicate with JAS is like beating your head
against a concrete wall. See the thread attached below.
JAS has a
right to his own opinions. But instead of recognizing that other people
are making valid
Iris and Jerry R,
The question of what Peirce knew or thought
about deriving ethics from esthetics is problematical. He analyzed issues
of science and logic to such a great depth, that his knowledge of
esthetics would seem trivial by comparison, at least to himself. But
before claiming that
I came across a recent article that sheds some light on what Peirce may
have meant by "fusing minds" that share a common experience.
See below for the abstract of the article, the URL, and some
excerpts.
>From Peirce's brief comments about that issue, we can only
guess what he meant. But the
Terry,
That's a good way to explain the issues -- especially
because you and Peirce illustrate your interpretations with concrete
examples. A definition or discussion of any new term must have one or
more examples to show (1) that the term is not vacuous, and (2) the kinds
of features or
Robert,
That's an excellent summary of the issues. For my comments,
I divided it in three parts:
> The representamen should
therefore be rehabilitated in order to confine it to the universe of
possibilities andthe term sign should be reserved to the incarnate form.
This is the reason why in
Gary F, Edwina, Jon AS, List,
I am delighted to read about GF's
applications of Peirce's writings to the issues that Edwina copied:
"the continuity between the processes of semiosis and those of
life
itself" and "the recursive and nonlinear nature of
those processes".
In 2006, I wrote an
Bernard Morand summarized the meaningful content of this debate in one
sentence plus one image:
BM> In place of the old, often
recurring debates on this subject I propose to muse over a painting from
René Magritte entitled "Le sens des réalités"
That image,
which shows a large boulder
Jon AS, Gary F, and Edwina,
No two people think alike, and
anybody as complex and insightful as Peirce has a wide range of different
ways of thinking. I agree that discussions about methodologies outside of
any particular context are of minor interest to this list. But the most
important
David,JFS> Until 1270, bell ringers depended on sun dials and
hour glasses. But by 1300, every town in Europe of any size had a church
with a clock that automatically rang the bells.
DP> Do you have
a reference for that?
I recommend a rather short book (245 pp.):
Crosby, Alfred W. (1997)
Jon A,
Those three criteria (copied below) are Plato's.
Aristotle's father was a physician, and he trained his son for the first
18 years. Aristotle admitted that Plato's mathematical forms are perfect,
but he recognized the need to value and deal with the facts of life and
the world.
Gary R, Jon AS, and Robert,
There are many ways of thinking, and
no method is ideal for all purposes. But when trying to understand what
Peirce wrote, it's essential to interpret his words according to his way
of thinking.
GR> I must immediately add that I do not see Jon as
distorting Peirce's
Terry,
I agree that Peirce's "mind fusion" is a good
metaphor. It reminds me of Spock's "mind meld" in Star Trek.
But the Trekkies don't explain how the Vulcan neural system (in
conjunction with the human neural system) could establish that
meld.
TR> Im delighted to find this remark in
Robert and Jon,
To determine whether students understand a topic,
teachers often ask them to explain it in their own words. Since much of
Peirce's terminology is radically different from common usage today, it
would be a good exercise to translate or at least explain his comments in
21st c.
Jon A,
I agree that (NEM 4:20) is one of Peirce's best
definitions of 'sign'. I also believe that it is his clearest definition
of 'formal semiotic'. But in talking about Peirce's logic. it's essential
to distinguish three distinct kinds of logic that he developed in detail:
mathematical
Jon,
Peirce devoted his life to developing mathematical-logical
methods for making all the sciences, including philosophy, as clear and
precise as possible.
JAS> This
post ... consists mostly of Peirce's words, with
a few of mine interspersed, but I hope that the arrangement enables it
all to
Robert and Jon,
I was browsing through and deleting some old
email, and I came across the points quoted below. I also remember that
Jon claimed that Peirce's word 'classificatory' for normative science made
it sound trivial.
But there are only three kinds of science: (1)
mathematical, (2)
Biosemiotic has two branches: zoosemiotic and phytosemiotic.
For a
review of the literature about plants up to 2016, see "Intelligence,
cognition, and language of green plants", by Anthony Trewavas:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4845027/
The Wikipedia
article on plant
Jon and Auke,
General principle: Never assume that Peirce was
unaware of or hadn't considered some issue. Peirce had studied Aristotle
in depth, and he would certainly be familiar with the first paragraph of
_On Interpretation_:
Aristotle> First we must determine what are
noun (onoma)
and
Robert, I strongly agree with the issues you raised and your
interpretation of them.RM> it may not be a good methodology
to give such
a preference for interpretation in semiosis without focusing the analysis on
the whole process... how individual semiosis articulates with global
semiosis?Yes.
Jon AS,
I noticed that I hadn't answered the question about
incomplete propositions. In the 1930s, the logician Alonzo Church
introduced lambda expressions as a notation for deriving a predicate
(rheme) from a proposition. In effect, Peirce invented "lambda
expressions" about 40 years before
Edwina,
I certainly agree:
> I don't think that
Peircean semiosis is just about 'interpretation' in the sense of human
language or communication
When I cited Peirce's _Photometric
Researches_ as a good source of examples, I wanted to show how the two
sources of knowledge -- pure
Robert,
Your summary of the issues is very good, and I strongly
agree with the need for examples.
In a search for examples, I went
back to _Photometric Researches_, which I believe is essential for
understanding the development of Peirce's philosophy. It's not an
accident that it was
Original Message
Subject: Re: [Peirce-L] To put an
end to the false debate on the classification of signs
From:
"John F. Sowa"
Date:Tue, May
19, 2020 10:05
To: "Peirce-L"
Robert M,
Robert M, Gary F, Jon AS, List
For quotations by Peirce on
these issues, see the attached file, science.txt.
Also note the last
quotation by Edward Moore:
ECM> Peirce has left us, not any kind
of final word, but a work in progress, one eminently worth carrying on, in
the spirit of the one who
Jerry and Jon,
In mathematics -- including mathematical logic -- the
notation is absolutely precise. Two different notations that are
isomorphic (one-to-one mappings in both directions) have identical
semantics, independent of any words used to describe them.
JLRC> I suggest that CSP was
Auke,
The point I was trying make: Either/Or debates are a waste
of time. There is an open-ended number of different ways of perceiving,
thinking, talking, reasoning, and acting. In the abstract, there is no
reason to debate whether method M175 is better or worse than method
M837926.
AB>
Robert and Auke,
I agree with the points you made. But I believe that a
good way to put an end to the "false debate" is to broaden the
dichotomy to an open-ended diversity. Every branch of the sciences (i.e.,
every branch in Peirce's 1903 classification) has methods that are
specialized for
Michael,
I strongly agree:
MCJM> What we should be
doing IMO is not so much "agreeing to differ" as leaving our
ideas on the table for continued evaluation (at everybody's leisure). If
we don't want to agree do we have to say more than "I shall think
about it" or even just stay momentarily
Gary R,
As Mike said, please stop.
GR>To be perfectly
clear, in my estimation this horrible 'harangue'
began about a year ago, shortly after John Sowa joined the list and
began harassing Jon Alan Schmidt, not on any substance of any of
his post, but on his methodology.
Thank you for providing
Mike,
MB> Please stop.
Excellent advice. I stated all
the issues in my previous note, and I have no desire to
continue.
MB> Despite Gary R telling me offline to resign from
the list, I will
continue to monitor. I am curious to see if the human animal has
the capacity to learn and
Jon, et al.
I just want to emphasize one point: It's extremely
rare for anybody to approve or be satisfied with anybody else's summary or
paraphrase of what they said or wrote. If it's highly favorable, they
probably won't complain. But even then, they realize that the paraphrase
is not what
Jon, Michael, Edwina, Robert M, and Gary R,
Peirce's range of
interests, talents, and research was so broad that there is no single best
method for studying and interpreting his writings. For different aspects
of his work, some methods are better than others. But even for those
areas where
Jon,
The principle of charity in philosophy does *not* require
the listener/reader to assume that the statements by the speaker/author
are true. Its only requirement is to assume that other participants in
the discussion are rational human beings who are making meaningful
statements, which
Jon,
Charity is an important virtue in dealing with people. What
made me angry is Gary R's attitude that he is an authority who is capable
of making blanket judgments about the accuracy of anybody else's
arguments. He has the right to point out what he belives are mistakes,
but he has an
Jon ,
On the following point, we agree. And since Gary R takes
your side in all these issues, I wish you would tell him to accept
it.
JAS> I find it extremely inappropriate to make sweeping
judgments about who
is (or is not) capable of understanding Peirce's writings and discussing
them
Gary,
That is the most anti-Peircean statement
imaginable:
GR> It would once again appear
that Edwina and John expect everyone to have always and only the same
interests as they do. Edwina, for example, characterizes anything else,
notably, theorizing, as "an irrelevant exercise" undertaken
Edwina, I strongly agree with that point:
ET> Helmut - your own
experiences in 'the real world' are what you should be trying to
understand - semiosically.
Abstract theories are useless, unless
they can be applied to something useful. Chess and Go, for example, are
mathematical theories
Jon,
Peirce was using the word 'category' in rhe tradition from
Aristotle to Kant. That tradition is still alive and well in
philosophy.
It's unfortunate that the 20th c mathematicians used the
same term for a different kind of mathematical theory. But as Robert M.
hass been saying, it's
Robert and Jon,
As a mathematician, I appreciate the power of
category theory. But I also spent 30 years working on reseach &
development proejcts at IBM, where I had to present many mathematical
issues in ways that engineers could appreciate. That gives me quite a bit
of sympathy for Jon's
Jon,
When Peirce called a theory 'fallible, he did not mean
"free to make adjustments". There is a huge difference between
"free to apply to new areas" and "free to adjust (i.e.
change) the theory itself"', The first (new applications) is
"normal science" in Kuhn's terms. But the second is
Edwina and Mary L,
I agree with the points that both of you
have made.
ET> It is extremely difficult to come to a final
conclusion about which meaning is 'right'.
For an essay or book
about Peirce, it's important to discuss his original terminology and not
claim that any of the 21st c. terms
Gary R and Jon AS,
Peirce's ethics of terminology is important.
But he made an important distinction: If an author's term is adopted and
used by other authors, then the person who coined that term has an
obligation to continue using it in the same sense in which it is being
used. But if
Edwina and Jon,
Induction always begins with data -- a set of
observations about some subject. By finding analogies and commonalities
among the observations, it derives a probable hypothesis about the
subject matter. Further testing is necessary to increase the probability
and generalize
Edwina, Gary F, Jon AS,
ET> My question about
'pure theorizing' so to speak, also arises from the quote below: "Now
the whole process of development among the community of students of
those formulations by abstractive observation and reasoning of the
truths which must hold good of
all signs
Jon AS, Gary F, and Auke,
Jon's recent note shows a serious failure
in communication:
JAS> To be honest, none of this [a quotation by
Auke] makes much sense to me, which is not to say that it is
incorrect--again, I suspect that it simply reflects my different purpose,
different standpoint,
Edwina,
I strongly agree. And as I wrote in the thread
"Tree structure", I believe that the best way to analyze and
explain the issues is to illustrate them with actual examples. He used
more examples in his lectures and letters to actual people. But his MSS
to himself had very few examples
Auke and Jon,
Peirce developed his semeiotic as a tool for
analyzing the many kinds of signs and their use in science and everyday
life. Unfortunately, Peirce did not provide enough examples to clarify
exactly how his terminology could be applied in all the many
variations.
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