Gary, Jon Alan, Jon Awbrey, List
*1 *-First I note that the formulation "3ns involves 2ns, which involves
1ns" is very dangerous car it forgets that 2ns has its autonomy and 1ns
too. If you look at the podium on remains in the inner cylinder. It seems
to me that Peirce's reproach to Hegel is:
"*He has usually overlooked external Secondness, altogether. In other
words, he has committed the trifling oversight of forgetting that there is
a real world with real actions and reactions. **Rather a serious oversight
that".*
It is therefore important to prefer"3ns involves 2ns and 1ns, while 2ns
involves 1ns" which preserves the autonomy of the Peircian categories so
as not to encourage the idea of a possible peircean hegelianism. "
2 – On the specific question *"about **the conceptual relationship between
Peirce's trichotomic category theory and contemporary mathematical category
theory if any"*, I will mainly have a limited response to the field at
hand, that
is, the classification of signs. Then I can give some personal reflections
on the general scope of mathematical category theory in the humanities.
I was just preparing a text on the comparison of the ways in which classes
of signs are generated by different authors and I chose the most
interesting and successful in my eyes, i.e. Gary's trikônics, the triangles
of Priscila Farias and Joao Queiroz and the signtree of Priscila Borges. It
can be said at first glance that they are equivalent since they generate
the same classes of signs that can be characterized by sequences of numbers
of length n = 3, 6 or 10 taken in the set {1,2,3} and verifying that each
number must be less or equal to the previous number. But the question is,
since these are classes based on different graphic metaphors, what is the
common formal structure - if there is one - of which they are the graphic
inscriptions. For this it is necessary to go in the field of posets and
more precisely totally ordered sets the simplest that are the chains:
" A set with a partial order is called a *partially ordered set* (also
called a *poset*). The term *ordered set* is sometimes also used, as long
as it is clear from the context that no other kind of order is meant. In
particular, totally ordered sets
<https://en.m.wikipedia.org/wiki/Total_order> can also be referred to as
"ordered sets", especially in areas where these structures are more common
than posets.
For *a, b*, elements of a partially ordered set *P*, if *a* ≤ *b* or *b* ≤
*a*, then *a* and *b* are *comparable
<https://en.m.wikipedia.org/wiki/Comparability>*. A partial order under
which every pair of elements is comparable is called a *total order
<https://en.m.wikipedia.org/wiki/Totally_ordered_set>* or *linear order*; a
totally ordered set is also called a *chain* (e.g., the natural numbers
with their standard order)".
( https://en.wikipedia.org/wiki/Partially_ordered_set)
Clearly the abstract diagram *3ns**à**2ns**à**1ns* (let's call the P) is a
chain which is common to all three approaches.
We have also the maps between partially ordered sets
" Definition 6: A function f : P → Q between partially ordered sets is
order-preserving if x ≤P y ⇒ f(x) ≤Q f(y).
Definition 7: Two partially ordered sets P and Q are isomorphic if there
exists a bijective, order-preserving map between them whose inverse is also
order-preserving"
(http://www-math.mit.edu/~levine/18.312/alg-comb-lecture-7.pdf )
To use this notion of the preservation of order, it is necessary to
identify in each graphic metaphor a Q chain .
*I claim that these Q chains are materialized at the moment when everyone
chooses the convention that consists of locating the sign, the object of
the sign and its interpretant on the graphic icon he has chosen.*
*As for Gary*: starting from the object at the lower corner of his trikône
he goes up to the sign at the top corner following the "vertical" side and
then from there he should go to interpretant it from the top side but if
his graph indicates a direct relationship between the object and the
interpretant, which is the same because it is the concatenation of the
first two paths. What is thus traced is an OàS àI chain.
*As for **Priscila Farias et Joao Queiroz :* (
https://www.researchgate.net/publication/249933979_On_diagrams_for_Peirces_10_28_and_66_classes_of_signs
)
it is the same ; the way is taken from Peirce for which the categories are
assigned thereby : the object to the upper left corner to go to the sign at
the bottom corner and from there to interpretant it in the upper right
corner. They create what they call "triangular coordinates" but it's the
same OàS àI chain and it's do the same it when they process graphically n
= 6 and n = 10 which has the effect of multiplying the triangles.
*Priscila Borges* uses the graphic metaphor of the developing tree:
https://www.researchgate.net/publication/263463845_THE_SIGNTREE_FROM_SIGN_STRUCTURE_TO_PEIRCE'S_PHILOSOPHY_THROUGH_READING_A_VISUAL_MODEL_OF_THE_66_CLASSES_OF_SIGNS
"So, the diagram construction begins by the idea of tree rings. They are
used in dendrocronology to count the age of trees. As years go by rings
grow in trees, but they are also affected by climate factors. More than
sign of time, tree rings show interaction between systems. All these
concepts are welcome in semiotic process. Each ring corresponds to one
trichotomy: the first trichotomy comes in the centre, the second trichotomy
in the second ring and so on. "
In this text she does it for n =10:
"Consequently, since the object determines the sign, and not the sign
determines
the object, it was necessary to put the dynamical object in the central
ring, followed by the immediate object and the ground of sign. Given the
first three correlates, comes the first relation: between sign and
dynamical object. This relation determines the possible interpretants,
called immediate interpretants that when are existent become dynamical
interpretants. So, the elements that compose the second relation are given:
between sign and dynamical interpretant."
Moving from a growth ring of its tree to the next it builds the de facto
chain for n = 6:
Od àOiàSàIiàIdàIf
And for n =1 0 she obtient very beautiful diagrams intelligently colored.
*My conclusion is that all these iconographic constructions are isomorphic;
they are produced in the same way using the applications of the immutable
suite of the three **3ns**à**2ns* *à**1ns **and the f application in
n-length chains similar to the protosigns I defined in the article on the
trichotomic machine. They all lead - we just saw - to sets (in the sense of
set theory). The results: classes of signs without explicit relations
between them. *
*Now here's the jump in the category theory :*
*"Every poset (and every **preordered set
<https://en.m.wikipedia.org/wiki/Preorder>**) may be considered as a **category
<https://en.m.wikipedia.org/wiki/Category_(mathematics)>** where, for
objects x and y, there is at most one **morphism
<https://en.m.wikipedia.org/wiki/Morphism>** from x to y. More explicitly,
let hom(x, y) = {(x, y)} if x ≤ y(and otherwise the empty set) and (y, z)*
*∘**(x, y) = (x, z). Such categories are sometimes called **posetal
<https://en.m.wikipedia.org/wiki/Posetal_category>**."*
"Posets are equivalent
<https://en.m.wikipedia.org/wiki/Equivalence_of_categories> to one another
if and only if they are isomorphic
<https://en.m.wikipedia.org/wiki/Isomorphism_of_categories>. In a poset,
the smallest element, if it exists, is an initial object
<https://en.m.wikipedia.org/wiki/Initial_object>, and the largest element,
if it exists, is a terminal object
<https://en.m.wikipedia.org/wiki/Terminal_object>. Also, every preordered
set is equivalent to a poset. Finally, every subcategory of a poset is
isomorphism-closed <https://en.m.wikipedia.org/wiki/Isomorphism-closed>." (
https://en.wikipedia.org/wiki/Partially_ordered_set#Mappings_between_partially_ordered_sets
)
so the same mathematical objects that are involved in the ensemblist
mathematical models that I have just listed can be looked at differently;
they are now algebraic categories. On can use all the conceptual apparatus
of the categories and first the functors and especially the bonus of
natural transformations of functors which brings us back to the trichotomic
machine. This machine naturally produces the same classes of signs of
course but with the order of a lattice revealed by the natural
transformations of functors that we will be able to exploit to increase our
knowledge of the signs and especially to create a methodology as an example
I did in the case of nicotine.
The general idea that has guided me for a long time is that Peirce's
thought is "functorial" and that his universe of thought is above all
relational. This is the reason for the fact that I continued work started
in my book "The Algebra of Signs". I try to express all its semiotics by
starting with a formalization of the "percipuum" in the category of
relational structures. But that's another story...
For now I am sorry to find that I submitted my nicotine analysis to the
criticism on May 3rd and that I did not get any reaction. I believe that I
show and demonstrate how a positive image of semiotics is formed and how it
gains in "semioticity" until it becomes able to compete with the negative
image of nicotine installed in a Dicent Symbol, at the top of the lattice.
See
https://www.academia.edu/42930701/Nicotine_a_semiotic_confrontation_between_life_and_death
Best regards,
Robert Marty
Le mer. 6 mai 2020 à 06:47, Gary Richmond <gary.richm...@gmail.com> a
écrit :
> Jon, Robert, List,
>
> JAS: Overall, we seem to be more or less on the same page.
> GR: I think that's so.
>
> JAS: I understand the impetus for using "presupposition" rather than
> "involution," since the former term is more familiar to modern
> mathematicians and logicians than the latter.
> GR: I too understand the impetus for Robert's using "presupposition" as
> being more familiar to modern mathematicians than "involution." But how
> many of them are familiar with Peirce's three category theory at all? I
> continue to believe that in consideration of Peirce's semeiotic (and all
> that follows from it) that "involution" is the more accurate and evocative
> term.
>
> JAS: I have no objection to saying that 3ns involves 2ns and 1ns, while
> 2ns involves 1ns. I just find it more succinct and equally accurate to say
> that 3ns involves 2ns, which involves 1ns; this already entails that 3ns
> also involves 1ns.
> GR: Logically, of course, you are correct and your more succinct version
> is equivalent. But saying that "3ns involves 2ns and 1ns" brings the
> fundamental trichotomy into high relief immediately. But it is a minor
> point, perhaps one merely of emphasis.
>
> JAS: I am not wedded to Peirce's adaptation of Aristotelian terminology
> (1ns/2ns/3ns = form/matter/entelechy), which is most prevalent in his
> writings around 1904--e.g., in "New Elements" (EP 2:303-305) and "Sketch of
> Dichotomic Mathematics" (NEM 4:292-300)--but I find it helpful in certain
> contexts.
> GR: I suppose it is helpful in certain contexts to employ Peirce's
> tricategorial adaptation of Aristotelian terminology. But is it possible
> that the movement from one equivalent terminology to another -- especially,
> but not only, within a single analysis -- has impeded the more general
> acceptance of some core Peircean ideas? I don't think there's an easy
> solution to this or any of the terminological questions we've taken up on
> the list over the last few years, but I think that there may be a
> communicational problematic here worth considering.
>
> JAS: I share Gary R.'s interest in learning more about "the conceptual
> relationship between Peirce's trichotomic category theory and contemporary
> mathematical category theory if any." I am more familiar with Fernando
> Zalamea's opinion (which I share) that Peirce's mathematical conception of
> continuity is more consistent with category theory (synthetic/top-down)
> than set theory (analytic/bottom-up).
> GR: Zalamea is, in my estimation, one of, if not the leading contemporary
> expert writing on mathematical continuity today. Again, I would be most
> interested in your thoughts, Robert, about "the conceptual relationship
> between Peirce's trichotomic category theory and contemporary mathematical
> category theory if any."
>
> Best.
>
> Gary R
>
> "Time is not a renewable resource." gnox
>
> *Gary Richmond*
> *Philosophy and Critical Thinking*
> *Communication Studies*
> *LaGuardia College of the City University of New York*
>
>
>
>
>
>
>
> On Tue, May 5, 2020 at 9:29 PM Jon Alan Schmidt <jonalanschm...@gmail.com>
> wrote:
>
>> Gary R., Robert, List:
>>
>> Overall, we seem to be more or less on the same page.
>>
>> I understand the impetus for using "presupposition" rather than
>> "involution," since the former term is more familiar to modern
>> mathematicians and logicians than the latter.
>>
>> I have no objection to saying that 3ns involves 2ns and 1ns, while 2ns
>> involves 1ns. I just find it more succinct and equally accurate to say
>> that 3ns involves 2ns, which involves 1ns; this already entails that 3ns
>> also involves 1ns.
>>
>> I am not wedded to Peirce's adaptation of Aristotelian terminology
>> (1ns/2ns/3ns = form/matter/entelechy), which is most prevalent in his
>> writings around 1904--e.g., in "New Elements" (EP 2:303-305) and "Sketch of
>> Dichotomic Mathematics" (NEM 4:292-300)--but I find it helpful in certain
>> contexts.
>>
>> I share Gary R.'s interest in learning more about "the conceptual
>> relationship between Peirce's trichotomic category theory and contemporary
>> mathematical category theory if any." I am more familiar with Fernando
>> Zalamea's opinion (which I share) that Peirce's mathematical conception of
>> continuity is more consistent with category theory (synthetic/top-down)
>> than set theory (analytic/bottom-up).
>>
>> Thanks,
>>
>> Jon Alan Schmidt - Olathe, Kansas, USA
>> Professional Engineer, Amateur Philosopher, Lutheran Layman
>> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>>
>> On Tue, May 5, 2020 at 3:29 PM Gary Richmond <gary.richm...@gmail.com>
>> wrote:
>>
>>> Robert, List,
>>>
>>> Robert wrote:
>>>
>>> RM: I spent a year extracting all the definitions of the sign that
>>> Peirce could have imagined and I was not disappointed since I found 76;
>>> they're on peirce.org. I have taken this effort when I realized the
>>> incredible number of scholars who thought in a non-critical way about the
>>> definition of the sign they attributed to Peirce. In particular, I have
>>> seen impossible triangles and confusions, especially with the Saussurian
>>> tradition, with the conceptions of Hjemslev and in the end of Greimas and
>>> his Ecole de Paris. It would have taken a titanic job to denounce all
>>> distortions, fanciful borrowings and undue annexations.
>>>
>>>
>>> That was certainly time *very* well spent by you! I know of no Peirce
>>> scholar who isn't aware of your list of Peirce's 76 definitions of 'sign',
>>> and many who have referenced it in their own work. I myself have read
>>> through it several times over the years. It is surely a major contribution,
>>> especially since, as you commented, there were any "number of scholars who
>>> thought in a non-critical way about the definition of the sign they
>>> attributed to Peirce."
>>>
>>> Your scholarship has certainly contributed to dispelling the many
>>> "distortions, fanciful borrowings and undue annexations" regarding Peirce's
>>> semeiotic. I sometimes think, how much better Peirce's semeiotic might
>>> today be known, understood, further developed and applied, had it not been
>>> for Sassurean thinking having taken hold and rooting itself so deeply in
>>> Continental thinking for most of the 20th century; and, as a consequence,
>>> drawing attention away from Peirce's triadic semeiotic, distorting it with
>>> Sassurean concepts and language, dyadic and nominalistic thinking, etc. To
>>> some extent it seems to me that that remains the case to this very day.
>>>
>>> Shifting to an entirely different topic prompted by your most recent
>>> off-list email to me (I'm afraid the math in it, as the American English
>>> idiom has it, was "above my pay grade"), a question which has come upon the
>>> list before, albeit infrequently, concerns the conceptual relationship
>>> between Peirce's trichotomic category theory and contemporary mathematical
>>> category theory if any. What, may I ask, are your thoughts about that?
>>>
>>> Best,
>>>
>>> Gary R
>>>
>>> "Time is not a renewable resource." gnox
>>>
>>> *Gary Richmond*
>>> *Philosophy and Critical Thinking*
>>> *Communication Studies*
>>> *LaGuardia College of the City University of New York*
>>>
>>> On Tue, May 5, 2020 at 6:19 AM Robert Marty <robertmarty...@gmail.com>
>>> wrote:
>>>
>>>> Gary, Jon Alan, List
>>>>
>>>> I fully respect yours concerns and of course it is clear that everyone
>>>> can invest them in the podium that is quite honored. For the part
>>>> concerning me I see no difficulty in using "involution" rather than
>>>> "presupposition" and I do not think I have strayed too far from Peirce with
>>>> "presupposition" since I think I have shown on the basis of Frege's
>>>> definition that the relationships of determination between the elements of
>>>> the phenomena as stated by Peirce verified this assertion. For I just need
>>>> to inscribe the abstract arrows of the mathematical object that I build
>>>> "*without
>>>> reference to their real existence",** within* Peirce's empirical
>>>> discourse. C.S. Peirce, 1976: NEM, vol. IV, 1122 :
>>>>
>>>> *"It is obvious that a Possible cannot determine anything other than
>>>> a Possible, and likewise a Necessitant cannot be determined by anything
>>>> other than a Necessitant** " *( letter to Lady Welby of December 23,
>>>> 1908)
>>>>
>>>> I understood very early on that I had to trace a personal path in what
>>>> J.M. Chevalier quite rightly called "Le continent peircien" (
>>>> https://www.academia.edu/3383353/La_d%C3%A9couverte_du_continent_peircien)
>>>> but by justifying at every step a very close and verifiable proximity
>>>> to the fundamental conceptions of phaneroscopy and semiotics. And when we
>>>> received in Perpignan the MS microfilms that we had ordered from the
>>>> Harvard Library (32 reels of 100m each - 3.2 km!) I don't regret my
>>>> decision ... I spent a year extracting all the definitions of the sign that
>>>> Peirce could have imagined and I was not disappointed since I found 76;
>>>> they're on peirce.org. I have taken this effort when I realized the
>>>> incredible number of scholars who thought in a non-critical way about the
>>>> definition of the sign they attributed to Peirce. In particular, I have
>>>> seen impossible triangles and confusions, especially with the Saussurian
>>>> tradition, with the conceptions of Hjemslev and in the end of Greimas and
>>>> his Ecole de Paris. It would have taken a titanic job to denounce all
>>>> distortions, fanciful borrowings and undue annexations.
>>>>
>>>> A practical consequence is that I have not acquired the skill to
>>>> discuss the relevance of the intellectual investments that can be made on
>>>> the podium. Let me reveal the picture came to mind when I read Jon Alan's
>>>> first and almost immediate reaction above; it is not derogatory: I saw a
>>>> child jumping from level 3 on the steps of the podium and I imagined all
>>>> the possible choices he could make to get down. Obviously there are 10 and
>>>> even there are 6 in the inner cylinder 3 in the outside cylinder and only 1
>>>> outside the two cylinders. To each his obsessions! Since this (dynamic)
>>>> image no longer leaves my mind because I wonder if it does not open another
>>>> way to go to the lattice of the classes of signs that would not go through
>>>> the constraints of purely algebraic formalization. I think about it often
>>>> ...
>>>>
>>>> Best regards
>>>>
>>>> Robert
>>>> Le mar. 5 mai 2020 à 06:04, Gary Richmond <gary.richm...@gmail.com> a
>>>> écrit :
>>>>
>>>>> Jon, Robert, List,
>>>>>
>>>>> I began a draft response to your post, Jon, shortly after you wrote
>>>>> it, but things began to move so quickly on the list that my initial
>>>>> thoughts soon seemed to be superseded in the rapid fire exchanges
>>>>> following. So I am glad that you reposted it as it gives me another chance
>>>>> to respond (*if* I can complete it soon enough not to lose it again
>>>>> as things move on).
>>>>>
>>>>> I certainly agree with Jon that your paper, Robert, is most
>>>>> interesting and that your podium diagram effectively represents the
>>>>> relations holding among the three categories. But I also agree with you,
>>>>> Jon, that 'involution' is not only Peirce's term, but indeed expresses the
>>>>> concept of the logical relations holding among the categories more
>>>>> accurately than does 'presupposition', really optimally. I would
>>>>> very slightly modify Jon's expression of these involutional relations: 3ns
>>>>> *involves *2ns *and* 1ns; 2ns *involves *1ns.
>>>>>
>>>>> JAS: Applying this to the "podium" diagram, 1=essence, 2=existence,
>>>>> and 3=reality. What about the inner portions? I suggest that
>>>>> 1/2=inherence, 2/3=persistence, and 1/2/3=governance.
>>>>>
>>>>> GR: I think that inherence, persistence and governance make good
>>>>> terminological sense in consideration of "the inner portions" of the
>>>>> podium
>>>>> based on CP 1.175. But as I see it the Aristotelian terminology of
>>>>> NEM 4:292-300, "form for 1ns, matter for 2ns, and entelechy for 3ns" is
>>>>> potentially misleading, especially if we forget that for Peirce 'form' is,
>>>>> as you commented, Jon, "whatever it is in itself, irrespective of
>>>>> anything else/" (1=essence), matter as "all that it is in reference to
>>>>> something else than itself" (2=existence), and entelechy as "that which
>>>>> brings things together" (3=reality)."
>>>>>
>>>>> In short, I see no reason to employ the Aristotelian terminology,
>>>>> loaded as it is with pre-Peircean notions especially of form. 'Matter' and
>>>>> 'entelechy' fare somewhat better, but still bring with them the
>>>>> Aristotelian associations. I think that it is possible and desirable to
>>>>> move beyond these in Peircean scholarship.
>>>>>
>>>>> Indeed, I found it helpful to my own understanding to substitute
>>>>> Peirce's terms for Aristotle's in distinguishing the inner relations. So:
>>>>> "the determination of "[the existent] by [essence]" (1/2=inherence),
>>>>> "the reaction of [existent] with [existent] " (2=existence), and "a
>>>>> determination of [an existent] to [an essential form]"
>>>>> (1/2/3=governance).
>>>>>
>>>>> Jon, your quoting Colapietro helped clarify the following, I think,
>>>>> truly important notion: that "reality, is *persistence*, is
>>>>> regularity (or, persistence *in/as* regularity?).
>>>>>
>>>>> VC: Existence is the mode of being of an individual substance
>>>>> considered as a continuity of *reactions*; insofar as it is
>>>>> *actually *reacting against other things, it exists. Persistence is
>>>>> the mode of being of such a substance seen as a *continuity *of
>>>>> reactions; insofar as it endures throughout a series of reactions, it
>>>>> persists. In other words, existence (because it is an instance of
>>>>> opposition) designates the aspect of secondness exhibited by any
>>>>> individual
>>>>> substance, while persistence (because it is a case of continuity)
>>>>> designates one of the ways in which it manifests thirdness. (Vincent
>>>>> Colapietro, *Peirce's Approach to the Self: A Semiotic Perspective on
>>>>> Human Subjectivity,* 83).
>>>>>
>>>>>
>>>>> In a word, 'persistence' is the existential form of continuity.
>>>>>
>>>>> JAS: Peirce describes two different classes of possible states of
>>>>> things that may be realized at a lapse of time--*prolonged **states*,
>>>>> which are *realized at any instant within a lapse; *and *gradual *
>>>>> *states**, which are realized only at an entire lapse during which a
>>>>> change occurs from one **prolonged state** to another*, these two
>>>>> states being "logically incompossible" (see NEM 3:1074-1077, c.1905).
>>>>> Such
>>>>> diversity requires *real *qualities to be continuous (1/2/3), rather
>>>>> than isolated (1), and *real *things to persist (2/3), not merely
>>>>> exist (2). (*Boldface* and *underlining *as emphasis added by GR.)
>>>>>
>>>>> To repeat: In a nutshell, real *qualities* are *continuous* (not
>>>>> isolated); real *things* persist (not just exist).
>>>>>
>>>>> I expect to spend more time reflecting on the following quotations
>>>>> (which I've read numerous times over the years) and your succinct comment
>>>>> which separates them.
>>>>>
>>>>>
>>>>> CSP: Time with its continuity logically involves some other kind of
>>>>> continuity than its own. Time, as the universal form of change, cannot
>>>>> exist unless there is something to undergo change [2/3] and to undergo a
>>>>> change continuous in time there must be a continuity of changeable
>>>>> qualities [1/2/3]. (CP 6.132, EP 1:323, 1892)
>>>>>
>>>>>
>>>>> JAS: This is one specific sense in which all three categories are
>>>>> always present within our existing universe.
>>>>>
>>>>> CSP: I chiefly insist upon continuity, or Thirdness, and, in order to
>>>>> secure to thirdness its really commanding function, I find it
>>>>> indispensable
>>>>> fully [to] recognize that it is a third, and that Firstness, or chance,
>>>>> and
>>>>> Secondness, or Brute reaction, are other elements, without the
>>>>> independence
>>>>> of which Thirdness would not have anything upon which to operate. (CP
>>>>> 6.202, 1898)
>>>>>
>>>>>
>>>>> Best,
>>>>>
>>>>> Gary
>>>>>
>>>>> "Time is not a renewable resource." gnox
>>>>> *Gary Richmond*
>>>>> *Philosophy and Critical Thinking*
>>>>> *Communication Studies*
>>>>>
>>>>> *LaGuardia College of the City University of New York*
>>>>>
>>>>>>
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
