Gary, list,
To prevent confusion, two remarks at the outset:
1. in a sense all sheets (of assertion {EG} of phaneroscopy/phenomenology
and semiotis) are semiotic sheets in the sense that they model the process of
semiosis. But each from a different perspective. ‘semiotic sheet’ is for me
shorthand for the sheet on which the process is modeled in technical semiotic
terms, including the sign – and the interpretant aspects. The same goes for the
phaneroscopic/phenomenologic sheet.
2. I did not in the mail try to promote the semiotic program to which I
contribute. By means of comparison: I provided a suggestive list of ingredients
that might contribute to a good meal of a certain type, I did not try to
present a recipe for a certain meal. Above that it is an incomplete list.
Vinicius Romanini for instance would add from his Solenoid perspective the
different types of objects and interpretants.
What I would ague for is that the most fruitful way to proceed is to try to
conceptually co-ordinate the different perspectives on each other. The key to
that is the process of semiosis expressed as a sign process.
Gary, you remarked about my assumed position: (perhaps, as you're
suggesting, modifying EG notation)
Re: most definitely I am not suggesting that. I only suggest to mimic the EG’s
approach to sheets, but with a broader focus, not just propositions and not
abstracting from the apprehension of the sign. The concept of a sheet is very
helpful for that.
GR did ask:
Yet perhaps I'm missing something here (again, I'm no expert in EGs). To aid
our comprehension, could you possibly draw even a crude draft modeling what
might appear on a "phaneroscopic sheet"? That would certainly be most helpful.
Re: First of all I do not profess to mimic the EG in Phenomenology, my interest
is primary modeling the semiotic process. For me phaneroscopy is helpful for
thinking about the sign aspects and the relations between them, like with the
correspondence between feeling and qualisign. I mentioned De Tiene’s suggestion
for completeness sake. And also since it delivers according to the
architectonic the principles for semiotics, which is precisely the way I look
at it.
Lets start with your remark:
In addition, the application of the phenomenological categories to semeiotics
(according to the 'principle of principle' recently discussed) frequently
occurs with no sense of their origins in phenomenology (also, their
anticipation in the valencies of the simplest math).
Indeed thus they deliver in terms of a valency connections categorically
organized the basic dependency structure for the process of semiosis. The 1.1
qualisign – 3.3 argument structure of the sign aspects.
Hope to have clarified my mail a little.
Best,
Auke van Breemen
Van: Gary Richmond <[email protected]>
Verzonden: vrijdag 15 februari 2019 20:20
Aan: Peirce-L <[email protected]>
Onderwerp: Re: [PEIRCE-L] was EGs and Phaneroscopy
Auke, list,
Auke wrote: "You provided an excellent quote to point to the difference between
sheets of assertion and phaneroscopic or semiotic sheets."
I found it difficult to grasp exactly what you're suggesting in this message
beginning with your distinguishing "between sheets of assertion and
phaneroscopic or semiotic sheets"
This is doubly confusing because sheets of assertion would seem to me to be
"semiotic sheets" rather than whatever your proposed "phaneroscopic sheets"
might be. Indeed, the seemingly contradictory language you use appears to me to
work to conflate phenomenology (the 1st cenoscopic science) with logic as
semeiotic (3rd branch of the 2nd second cenoscopic science, viz., normative
science). In a word "phanerocopic" doe not = "semiotic".
Expanding on this a little, in my view, the categories of phenomenology are all
too often also confused/conflated with the metaphysical categories (which, as I
see it, are the Universal Categories applied--offering principles--to
metaphysics, perhaps recast at Three Universes of Experience). In addition, the
application of the phenomenological categories to semeiotics (according to the
'principle of principle' recently discussed) frequently occurs with no sense of
their origins in phenomenology (also, their anticipation in the valencies of
the simplest math).
Be that as it may, despite your intriguing comments, it is entirely unclear to
me what a phaneroscopic (or "semiotic" as your wrote) sheet might look like,
what its purpose might be, its rules, etc.
I'm not an expert in EGs by a long shot, but my earlier stated reservation
concerning the possible use of EGs within Peirce's science of Phenomenology is
based exactly on the Peirce quotation I'd earlier given and which you
reproduced in your message, namely, that "All that existential graphs can
represent is propositions, on a single sheet, and arguments on a succession of
sheets, presented in temporal succession."
(Btw, following de Tienne, I tend to limit my use of the expression,
"Phaneroscopy," to the initial stage of phenomenological research; de Tienne
adds another stage, I a third.)
So, as I see it now, unless an entirely original kind of graph can be created
to aid in phenomenological research (perhaps, as you're suggesting, modifying
EG notation), at present, EGs seem to me capable only of (a) helping to clarify
those logical moves by Peirce which served to reveal the connection between
types of propositions and the three categories, or (c) explicating the findings
of phenomenological research in graphic form.
Yet perhaps I'm missing something here (again, I'm no expert in EGs). To aid
our comprehension, could you possibly draw even a crude draft modeling what
might appear on a "phaneroscopic sheet"? That would certainly be most helpful.
Best,
Gary
Gary Richmond
Philosophy and Critical Thinking
Communication Studies
LaGuardia College of the City University of New York
718 482-5690
On Fri, Feb 15, 2019 at 10:07 AM Auke van Breemen <
<mailto:[email protected]> [email protected]> wrote:
Gary (List),
You provided an excellent quote to point to the difference between sheets of
assertion and phaneroscopic or semiotic sheets:
CSP:
All that existential graphs can represent is propositions, on a single sheet,
and arguments on a succession of sheets, presented in temporal succession.
-
A semiotic sheet could be modeled with the sign aspects. The interpretant
aspects could bridge the gap with phaneroscopy: emotional interpretant (a
feeling of a quality is an instance of it, but it can encompass much more).
This differs from representing propositions on sheets. I think it should start
with a sheet and a sign that gets inscribed and must find a way to model the
interaction. On the most general level there are 9 sign aspects according to
Peirce, but only six interpretant aspects, so it seems reasonable to suppose
that the three missing interpretant aspects are concerned with the (object of)
the sign. I found the three missing to be the index, the legisign and the
symbol position.
If we suppose a line of identity, it could appear on a semiotic sheet as a dot.
It is the index signifying the interaction between sheet and inscribing sign.
If the legisign position is not ‘satisfied’ the interpreting system (sheet) has
no collateral knowledge of the sign. And it will not be able to ‘satisfy’ the
symbol position, which provides the meaning of the sign.
I use ‘satisfy’ to prevent a mechanical interpretation of the interpretation
process. The goal operative in the sheet and the sign co-determine the
responding sign. The model has, in my opinion, to provide a process of
translation from qualisign to the response sign that is guided by the doleme.
The categories have to deliver the dependency structure in between.
Looked at from this angle the extended Welby classification refines the
analysis on several aspects already made. P. 162 of the Welby correspondence
offers a lot to ponder. Just in order to illustrate the importance of looking
at the responding sign as the outcome of the interpretation process, I give the
last trichotomy.
10. Assurance of interpretants by signs.
a. assurance by instinct
b. assurance by experience
c. experience by habit.
It is a measure for the adequacy of the response.
Best,
Auke van Breemen
Van: Gary Richmond < <mailto:[email protected]> [email protected]>
Verzonden: woensdag 13 februari 2019 21:23
Aan: Peirce-L < <mailto:[email protected]> [email protected]>
Onderwerp: Re: [PEIRCE-L] Analyzing Propositions (was EGs and Phaneroscopy)
Jon, John, list,
Jon, this post is quite helpful in clarifying what you've recently been
arguing, perhaps especially "that "according to Peirce, 'the proper way in
logic" is to treat anything that refers to content as a Subject, not a
predicate.' " It seems likely that what you've written so far will need further
support to be convincing to many. After all, you're arguing for an
interpretation just the opposite of the standard one, an analysis which Peirce
himself also argued for (as you've admitted). I expect that it will be an
uphill battle, but one worth undertaking.
In addition, your post seems to me to help prepare the way for a discussion of
logic and EGs in relation to phenomenology. However, I hope that that
discussion doesn't begin in earnest too soon as both Gary F and I (and perhaps
others) haven't yet completed Atkins book on Phenomenology.
Personally, while I have a great deal of interest in Phenomenology, I haven't
as much interest in EGs as some on the list, notably, John, Gary F, Jeff, and
yourself and some others have, in part, because of what Peirce says in the 1908
letter to Lady Welby which Gary F recently shared a link to:
The system of Existential Graphs (at least, so far as it is at present
developed) does not represent every kind of Sign. For example, a piece of
concerted music is a sign; for it is a medium for the conveyance of Form. But I
know not how to make a graph equivalent to it. So the command of a military
officer to his men: “Halt!” “Ground arms!” which is interpreted in their
action, is a sign beyond the competence of existential graphs. All that
existential graphs can represent is propositions, on a single sheet, and
arguments on a succession of sheets, presented in temporal succession.
So, for example, John's recent EG'd musical notation example, besides being
unwieldy and inelegant, was not at all convincing to me because it left so much
out that is essential in music, say, of the Romantic era (e.g. dynamics,
expressive marks, changes in tempo such as ritardando and accelerando,
phrasing, the 'voicing' of the counterpoint, etc., etc., etc.), and this in
consideration of the Sign which is a simple musical composition's notation
only. It's possible that some of the things just mentioned could be included in
the graph, but most likely that would add to the awkwardness and inelegance of
it.
So, imho, EGs being isomorphic to first-order logic in their beta part, they
ought direct themselves towards what first-order logic can best express in its
graphic form. As you know, the gamma part has not been much developed and may
never be. Finally, while I'm eager to read what Atkins has to say about EGs in
relation to Phenomenology, at the moment I have difficulty imagining that they
might be of very much value to that science except in explicating its
discoveries logically, clearly and unequivocally. But I continue to study EGs
time permitting, and hope to benefit from the upcoming discussion of them in
relation to Phenomenology.
Your post today seems to me modest in its claims, but supported strongly by CSP
quotes; also in consideration of their chronology and the frequency of certain
terminology. Yet it also makes clear that you are only making a 'stab' at
something which Peirce had not completed, and this is the "additional step"
which you are taking. So far, I find your exposition of Peirce's mature logic
to be clear and increasingly convincing. And I am finding your dialogue with
John especially helpful.
Best,
Gary R
Gary Richmond
Philosophy and Critical Thinking
Communication Studies
LaGuardia College of the City University of New York
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On Wed, Feb 13, 2019 at 1:37 PM Jon Alan Schmidt <
<mailto:[email protected]> [email protected]> wrote:
John S., List:
I changed the subject heading, since we are still not actually discussing EGs
and Phaneroscopy.
JFS: But "Bob owns a red car" could be separated in four ways: (1) "Bob / owns
a red car." (2) "A red car / is owned by Bob." (3) "A car owned by Bob / is
red." (4) "A car / is red and is owned by Bob."
You left out a fifth way--"Bob, owning, car, redness / _____ is in the dyadic
relation of _____ to a _____ that possesses the character of _____."
JFS: Therefore, the set of subjects is disjoint from the set of predicates.
My point was that non-continuous predicates, such as "owns/owning" and
"red/redness," can be analyzed either as predicates or as subjects.
JFS: The predicate "is a car owned by Bob" can be true or false *of* something
only when it is linked to a subject, for example, "That Chevy / is a car owned
by Bob."
We can also analyze that "predicate" as four Subjects (something, car, owning,
Bob) "married" by two Continuous Predicates--"_____ is identical to a _____
that is in the dyadic relation of _____ to _____."
JFS: The "proper way" on p. 885 would replace the verb 'breathes' in the
sentence "Every mammal breathes oxygen" with the verb 'is' in "Every mammal is
an oxygen-breathing animal."
No, we have been over this already. The "proper way" is Peircean, not
Aristotelian, and analyzes that sentence as "Every mammal is in the dyadic
relation of breathing to oxygen." There is no need to insert the word "animal."
JFS: Yes, but that is continuity of *pure* predicates, not of predicates that
refer to content in the universe of discourse.
In Peirce's "proper" or "ultimate" analysis of Propositions, "pure" predicates
are the only predicates. Anything that refers to content in the universe of
discourse--i.e., anything that can only be understood by an interpreting
Quasi-mind that has had previous Collateral Experience with it--is a Subject;
it belongs to the Object of the Proposition. The only information that a
Proposition can convey, which therefore belongs to its Interpretant, is the
logical form of the relation that "marries" all of the referenced Subjects. In
order to understand "Bob owns a red car," I need Collateral Experience with not
only Bob and cars, but also owning and redness. In order to understand "Every
mammal breathes oxygen," I need Collateral Experience with not only mammals and
oxygen, but also breathing.
JFS: In CP 4.538, Peirce said that the triad rheme/dicisign/argument would
have to be widened to cover those image-like things. His earlier definition of
quasi-predicate would cover those aspects. Therefore, the widened term 'seme'
includes both 'predicate' and 'quasi-predicate'. But no logical subject could
ever be a seme.
That is not what the text says at all. The trichotomy that had to be "much
widened" was term/proposition/argument; "rheme" and "dicisign" are not
mentioned, and as I have pointed out repeatedly, "quasi-predicate" never
appears in any of Peirce's writings, other than its one occurrence in 1903.
The definition of "Seme" is "anything which serves for any purpose as a
substitute for an object of which it is, in some sense, a representative or
Sign," which clearly encompasses all logical subjects.
JAS: The additional step that I am taking is to recognize...
JFS: If Peirce did not explicitly take that step, don't put words in his mouth.
But I did not put words in his mouth; I said quite plainly that I was taking an
additional step.
JAS: Bellucci cites another passage where Peirce clearly endorsed...
JFS: If he didn't explicitly say something that seems "clear" or "obvious", he
probably had some reason for not doing so.
But he did explicitly say something in this case--three times!
CSP: I regard everything to which the assertion relates and to which reference
can be removed from the predicate, although what is referred to be a quality,
relation, state of things, etc. as a Subject. (R 611)
CSP: But the proper way in logic is to take as the subject whatever there is
of which sufficient knowledge cannot be conveyed in the proposition itself, but
collateral experience on the part of its interpreter is requisite ... The
result is that everything in a proposition that possibly can should be thrown
into the subjects, leaving the pure predicate a mere form of connection ...
(NEM 3:885)
CSP: When we have analyzed a proposition so as to throw into the subject
everything that can be removed from the predicate, all that it remains for the
predicate to represent is the form of connection between the different subjects
as expressed in the propositional form ... when we have carried analysis so far
as to leave only a continuous predicate, we have carried it to its ultimate
elements. (SS 71-72)
I already acknowledged that the EGs reflect his earlier analysis, and that
maintaining such an approach makes perfect sense when using EGs to teach
first-order predicate logic today. I have a different purpose in mind, for
which his "proper" and "ultimate" analysis is more suitable.
JAS: Perhaps what you mean is that CSP's logic was a logic of Subjects, as I
am now employing that (capitalized) term ...
JFS: That conclusion is not just imprecise. It's false. Peirce never did and
never would say that EGs are "a logic of subjects'.
In context, I was directly responding to the assertion that Peirce's logic was
a "logic of proper names"; and all I mean by a "logic of Subjects" is what
Peirce described to Jourdain as "the proper way in logic." He apparently never
discussed how to interpret EGs in accordance with that analysis, which is why I
am taking a stab at doing so myself.
JFS: It's impossible to have a logic without *both* subjects and predicates.
And predicates that refer to content are never "pure".
Of course; but again, according to Peirce, "the proper way in logic" is to
treat anything that refers to content as a Subject, not a predicate.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt>
- twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt>
On Wed, Feb 13, 2019 at 9:29 AM John F Sowa < <mailto:[email protected]>
[email protected]> wrote:
Gary F, Jon AS, and Jerry LRC,
I started to write this note several days ago, but had some other
things on my agenda. The following comments begin with the older
material with just two brief comments about the newer.
GF
> Given your emphasis on precision, you are apparently referring
> to formal (i.e. mathematical) logic, and not to logic as semeiotic...
> you seem to have skipped over the science which comes between
> mathematics and logic/semeiotic in Peirce’s classification of the
> sciences, namely Phenomenology (or Phaneroscopy)
In Peirce's classification of the sciences, *formal* logic is a
branch of mathematics. I hadn't seen Atkins' book, but I read the
Google excerpts and ordered it.
GF
> the new Atkins book on Charles S. Peirce’s Phenomenology, which
> Gary Richmond mentioned a few days ago. Atkins has quite a lot to
> say about the overlaps among logic, semeiotic, EGs and phenomenology,
From the Google excerpts of Atkins' book:
> p. 5: Peirce... concludes that the categories ought to be found
> first in mathematics, a part of which is formal logic, and then
> traced through phenomenology, normative science (including logic
> as semiotics), and metaphysics.
>
> p. 6: The analysis of the phaneron, moreover, involves both
> logical analysis and inspective analysis.
As an example, consider the questions about logical subjects and
logical predicates. To show the difference, consider the EG for
"Bob owns a car." That EG can be drawn on a straight line:
Bob———Owns———Car
There are two lines of identity, one for Bob and one for the car.
The two monads have one peg each (Bob- and Car- ); and the dyad
has two pegs ( -Owns- ).
Peirce said that an EG can be "separated" into a logical subject
and predicate "in more than one way". The simplest example is
"Bob" as the subject and "owns a car" as the predicate:
Bob——— -Owns———Car
In this case, the line of identity for the subject remains with
Bob, the left peg of Owns is unattached, but the right peg of
Owns remains attached to the line of identity for Car.
With this short example, there is only one other option:
"A car is owned by Bob": Car——— Bob———Owns- . In this
case, the right peg of Owns is unattached.
But "Bob owns a red car" could be separated in four ways:
(1) "Bob / owns a red car." (2) "A red car / is owned by Bob."
(3) "A car owned by Bob / is red." (4) "A car / is red and
is owned by Bob."
In every case, the logical subject has a line of identity with
one end free; and the logical predicate has an unattached peg
where that line had been attached.
JAS
> How can subjects be disjoint from predicates if they can denote
> properties?
Consider Bob's red car. There are four possible subjects.
Case (4) "A car" is probably insufficient to determine the referent.
If there is only one Bob in the context, case (1) "Bob" may be
sufficient. Cases (3) or (4) depend on the context and what the
speaker knows about the listener.
In every logical subject, all the predicates in the subject have lines
of identity attached to every peg. But every logical predicate has at
least one peg that is not attached to any line of identity.
Therefore, the set of subjects is disjoint from the set of predicates.
JAS
> How can predicates by themselves be "true of things" when only
> a complete proposition is capable of being true or false?
Note the difference in syntax. A proposition by itself can be true
or false. But the phrase "true of things" indicates that a predicate
is not true by itself. The predicate "is a car owned by Bob" can
be true or false *of* something only when it is linked to a subject,
for example, "That Chevy / is a car owned by Bob."
JAS
> JFS: By "the proper way", he was talking about transforming an EG
> into one of Aristotle's sentence patterns...
>
> Peirce did not say anything about Aristotle in his letter to Jourdain
There was no need to. Every university graduate in the 19th c. was
familiar with Aristotle's syllogisms. For a summary of the patterns
for syllogisms, see slides 15 ff of <http://jfsowa.com/talks/aristo.pdf>
http://jfsowa.com/talks/aristo.pdf
Compare the methods in those slides to the attached NEM3_885.pdf.
The "proper way" on p. 885 would replace the verb 'breathes' in
the sentence "Every mammal breathes oxygen" with the verb 'is'
in "Every mammal is an oxygen-breathing animal."
In that "Aristotelian" transformation, the pure predicate -is- has
two pegs. In the full sentence, each of the two logical subjects
has a line of identity with a free end, which can be attached to
one of the pegs.
Note that EGs for both logical subjects would contain embedded monads
or dyads for the content: Mammal- Animal- Oxygen- -Breathe- .
The logical subject for "oxygen-breathing animal" would contain
a teridentity with one line of identity attached to Animal-, one
line of identity attached to the left peg of -Breathe-, and one
line of identity with a free end. That free end could be attached
to the right peg of the pure predicate -is-.
JAS
> Peirce's further insight in 1906 about this continuity of the Line
> of Identity, as well as that of the blank Sheet of Assertion, was
> what eventually led him to formulate the concept of the Continuous
> Predicate two years later.
Yes, but that is continuity of *pure* predicates, not of predicates
that refer to content in the universe of discourse. Those pure
predicates are structural elements of EGs -- and of Aristotle's
syllogisms. Both Aristotle and Peirce intuitively recognized the
central role of the copula 'is' long before 1906.
Bellucci (p. 20) said that after 1908 Peirce never again mentioned
continuous predicates: "continuous predicates are by no means
abandoned. Instead, they are incorporated within the system
of Existential Graphs."
Note that predicates that refer to content may refer to discrete
content or continuous content. But continuity in the content is
independent of the two pure predicates in the the EG structure.
Furthermore, these issues about pure predicates are unrelated to semes.
As Peirce said, semes are wider than predicates because they refer to
content such as images and percepts of images. That is why the letter
to Jourdain is irrelevant to any questions about semes.
JAS
> Subject, Proposition, and Argument obviously correspond to rheme,
> dicent, and argument in this text and to Seme, Pheme, and Delome
> in the later division
No. A rheme is never a subject. See the examples above. For
a second opinion, note what Bellucci (2013, p. 38) said: "It thus
appears that “rhema” and “predicate” are used interchangeably, but
that a rhema is better called a predicate when considered in the
context of a proposition."
The same criteria distinguish quasi-subjects and quasi-predicates,
which are images or percepts of images. When an image is used as
a quasi-predicate some places on the image could serve as quasi-pegs.
When an image is used as a quasi-subject, an index of some sort
could serve as a quasi-line of identity.
The terms 'quasi-peg" and 'quasi-line' are mine. I'm using them
only to emphasize the parallels between a symbolic notation for
logic and the kind of semiosis that occurs during perception.
In CP 4.538, Peirce said that the triad rheme/dicisign/argument
would have to be widened to cover those image-like things. His
earlier definition of quasi-predicate would cover those aspects.
Therefore, the widened term 'seme' includes both 'predicate' and
'quasi-predicate'. But no logical subject could ever be a seme.
JAS
> The additional step that I am taking is to recognize...
> Bellucci cites another passage where Peirce clearly endorsed...
No. If Peirce did not explicitly take that step, don't put words
in his mouth. If he didn't explicitly say something that seems
"clear" or "obvious", he probably had some reason for not doing so.
Bellucci's article, which I strongly endorse, is a detailed analysis
of the limited amount of evidence -- just five short comments that
Peirce wrote between 2006 and 2008. Bellucci suggests a good reason
why Peirce never mentioned continuous predicates after 1908:
Bellucci, p. 4
> Peirce does not abandon continuous predicates after 1908; quite the
> contrary, they just merge with the continuous graphs within the
> diagrammatic system of Existential Graphs that he is then developing
> and perfecting.
In short, three pure predicates form the structural foundation of EGs:
the line of identity, the blank Sheet of Assertion, and the triad for
teridentity. After recognizing their fundamental nature in EGs,
Peirce found no further need to discuss them separately from EGs.
JAS
> I am not a logician, so please forgive my imprecision. Peirce
> was quite clear about the scope of "everything" in his own
> statements, and also provided helpful examples.
>
> CSP: ... I regard everything to which the assertion relates and
> to which reference can be removed from the predicate,
>
> Perhaps what you mean is that CSP's logic was a logic of Subjects,
> as I am now employing that (capitalized) term;
That conclusion is not just imprecise. It's false. Peirce never
did and never would say that EGs are "a logic of subjects'. It's
impossible to have a logic without *both* subjects and predicates.
And predicates that refer to content are never "pure". See the
examples above.
For a clearly written tutorial about EGs in MS 514 (1909), which Peirce
regarded so highly that he sent a clean copy to Mr. Kehler in 1911, see
<http://jfsowa.com/peirce/ms514.htm> http://jfsowa.com/peirce/ms514.htm
In ms514.htm, Peirce's words are in black, and my commentary is in red.
For more examples, see <http://jfsowa.com/talks/egintro.pdf>
http://jfsowa.com/talks/egintro.pdf
JLRC
> Jean-Yves Beziau, 13 QUESTIONS ABOUT UNIVERSAL LOGIC
> <http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf>
> http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf
> This short and terse essay is a good starting point for comparing
> CSP’s views with modern logics.
I agree. But I don't believe it's possible to have a single unified
logic. However, I believe that Peirce's EGs would be an excellent
common core with other logics as extensions or variations of the core.
Following are the slides for two lectures I presented in 2015:
At a Peirce session of the APA in Vancouver in April 2015, I presented
"Peirce, Polya, and Euclid: Integrating Logic, Heuristics, and Geometry"
For the slides, see <http://jfsowa.com/talks/ppe.pdf>
http://jfsowa.com/talks/ppe.pdf
At a Smart Data conference in San Jose in August 2015, I presented
a 3-hour tutorial on natural logic, which included some of the slides
in ppe.pdf: <http://jfsowa.com/talks/natlog.pdf>
http://jfsowa.com/talks/natlog.pdf
Starting with the natlog.pdf slides is good for an intro and overview.
See the last slide of each lecture for references and URLs.
John
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