Sung, Jerry, List,
I understand that we are using somewhat different language and graph systems as
bases for understanding Peirce's arguments in his phenomenology and semiotics.
Jon has suggested that Peirce's different ways of diagramming these relations
are hardly more than hints of ideas, so we should be careful about how much we
derive from one or another manner of representing these things graphically. I
want to resist Jon's suggestion. As such, let me try to restate the question.
Given your way of putting things, let me ask the following question: is there
anything that is obscured if you assume that there is an "internal node" at the
heart of every elementary relation? I am suggesting that any graphical system,
including the one that you have formulated or a bipartite system of graphs that
allows nodes to be connected to several lines (i.e. edges, relations, etc.)
will run the risk of obscuring things that Peirce wanted to analyze further.
I recognize that you and Jerry seem to have different dispositions towards the
way Peirce is using graph theory to analyze these things. You are saying that
your system is equivalent to Peirce's and that it expresses the heart of what
he is really trying to say. Jerry, on the other hand, seems to suggest that
Peirce is hamstrung by limitations that have their source in outmoded 19th
century ways of thinking about and graphing chemical relations.
So, let me try to state the question I've been trying to push as a challenge.
For those who think that the most elemental relations can be understood as a
node with one, two or three relations jutting out from it (such as you have
characterized them in your diagrams, and as the nodes and edges are
characterized in the example of the bipartite graph on the WikiPedia site I
referred to earlier), are you able to articulate the basic points Peirce is
making against Kempe's analysis of mathematical form in your terms? My hunch
is that Peirce's arguments are valid, that they can be used against alternate
analyses of the reasonings--and that these alternate analyses fail because they
tend to obscure points about the elemental character of a triadic relation that
Peirce wanted to make as clear as possible.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
________________________________________
From: Sungchul Ji [s...@rci.rutgers.edu]
Sent: Monday, April 07, 2014 11:23 AM
To: Jeffrey Brian Downard
Cc: Peirce List
Subject: RE: [PEIRCE-L] de Waal Seminar: Chapter 5, Semeiotics, or
the doctrine of signs
Jeff wrote (040714-1) and (040714-2):
". . . I don't believe that I'm using monad, dyad and (040714-1)
triad to refer to the number of nodes in a network."
If my classification of the networks shown in Table 1 is correct, you are
indeed not using the terms “monad”, “dyad”, and “triad” to refer to the
number of nodes in a network but rather the number of edges (which is
synonymous with your “binding sites”) of a network (see the last two
columns in Table 1).
_____________________________________________________________
Table 1. A network representation of the Peircean “medad”,
“monad”, “dyad”, and “triad”.
_____________________________________________________________
Number of
________________________________
Name (N) network nodes* binding edges
sites (x)
_____________________________________________________________
medad o 1 0 0
(1-node N,
or a point)
_____________________________________________________________
monad o – x 2 1 1
(2-node N)
_____________________________________________________________
Dyad x – o – x 3 2 2
(3-node N)
_____________________________________________________________
x
|
triad o 4 3 3
(4-node N) / \
x x
_____________________________________________________________
*There are two kinds of nodes – the focal (denoted by “o”) and the
peripheral (denoted by “x”). The peripheral nodes are also called
“binding sites” and can be occupied by n-node network where n can be 0,
1, 2, 3 or 4.
“As far as I can tell, it appears that your (040714-2)
characterization of the four node network might
be doing the same thing.”
In what sense do you think the 4-node network representation of the
Peircean sign (i.e., the 4-node network in Table 1 with three x’s replaced
by representamen, object, and interpretant) is like a “bipartite system of
graphs” that “obscure relations that Peirce wanted to analyze” ?
With all the best.
Sung
___________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
> Sung, Jerry, list,
>
> I am trying to use the terms and the relations in a manner that fairly
> represents what Peirce says in the texts. For the sake of clarity I don't
> believe that I'm using monad, dyad and triad to refer to the number of
> nodes in a network. Rather, I'm using it to refer to the number of
> unsaturated bonding sites on three kinds of relations that Peirce claims
> are elementary. One of those, the monad, functions like a terminal node
> with with only one unsaturated bonding site. The others are not nodes.
> Rather, they are relations with two or three unsaturated bonding sites.
> The difference between them is not merely a matter of the number of sites
> available, it is also a matter of one being a relation with no branches
> and the other having a branch. Topologically, those are fundamentally
> different kinds of relations. The dyadic and triadic relations can, of
> course, be saturated by being bound to two or three monadic nodes. Once
> that has been done, there are no more bonding sites available and either
> can be treated as a medad. Having said that, medadic complexes can always
> be altered by the insertion of triadic relation--creating new bonding
> sites within the complex.
>
> There are several different ways that graphical systems could be set up
> with different systems permitting or forbidding different kinds of
> combinations. I'm not claiming that the graph theoretical system that I'm
> describing--which seems to fit Peirce's two primary descriptions of the
> elementary kinds of relations in his phenomenology best--is the only kind
> of graph theoretical system that could be used to analyze mathematical
> diagrams and inferences. I'm simply saying that a bipartite system of
> graphs seems to obscure relations that Peirce wanted to analyze further
> and thereby make clearer. As far as I can tell, it appears that your
> characterization of the four node network might be doing the same thing.
> If that is the case, they both obscure the very same things that Peirce
> found problematic in Kempe's graphical system.
>
> I haven't laid out the arguments. Thus far, I've only pointed to them. I
> do think, however, that his arguments against Kempe's analyses of
> different kinds of mathematical diagrams and inferences might be
> instructive for understanding aspects of the kinds of relations are taken
> to elemental in his semiotic theory.
>
> --Jeff
>
> Jeff Downard
> Associate Professor
> Department of Philosophy
> NAU
> (o) 523-8354
> ________________________________________
> From: Sungchul Ji [s...@rci.rutgers.edu]
> Sent: Saturday, April 05, 2014 3:04 PM
> To: Jeffrey Brian Downard
> Cc: Jerry LR Chandler; Peirce List; Vinicius Romanini
> Subject: RE: [PEIRCE-L] de Waal Seminar: Chapter 5, Semeiotics, or
> the doctrine of signs
>
> (For undistorted Fgirue 1, see the attached.)
>
> Jeff wrote:
>
> ". . . the fundamental elements of experience (040514-1)
> studied in the phenomenological theory are
> diagrammed as a node with a single bonding site
> (e.g., a monad), a straight line with two bonding
> sites (e.g., a dyad), and a branching line with
> three bonding sites (e.g., a triad). I think
> there is much to be gained by using these kinds
> of figures in the graphs we construct to analyze
> the objects, relations and inferences in mathematical
> (or any other) kind of reasoning."
>
> It seems that you are using the terms "monad", "dyad", and "triad" in
> (040514-1) to refer to the number of the nodes in a network. Thus, the
> “branching line”, i.e., -<, is a triad because it has three nodes or
> “binding sites” as you called them, a line segment is “dyad” because it
> has two ends (or nodes), and a point is “monad” because it is just one
> node all by itself. This way of interpreting the terms is also employed
> by John and Edwina.
>
> But these same terms can be used to refer to “edges” of a network as well
> as I have been advocating against the opinions of John and Edwina. For
> example, the word “triad” can refer to “a triadic relation” as represented
> by the three edges of the “branching” line, -<. But when it comes to the
> word “dyad”, things get somewhat complicated, because “dyad” can mean
> “two nodes” of a line segment as you explained above or “one edge”
> (i.e., one relation) which a line segment is. In other words, “dyad” can
> mean, confusingly, “two nodes” or “one edge”, i.e., “two relata” or “one
> relation”. Similarly, the word “monad” can mean one “node” (or relatum)
> with no edge (or relation). So, depending on whether these terms refer to
> nodes or edges of a network, their meanings change.
>
> The 4-node network representation of the Peircean sign (see Figure 1 in
> [biosemiotics:5631]) seems able to provide a convenient visual tool to
> analyze Statement (040514-2) as shown in Figure 1. Focusing on the
> components of the Peircean sign only, Figure 1 can be read as
>
> “A representamen is determined by its object and determines
> (040514-2)
> its interpretant in such a way that the interpretant is indirectly
> determined by (or is consistent with) the object.”
>
> One of the main points of Figure 1 is that the sign, ‘n-ad’, has at least
> two choices, denoted as (. . .) and [. . .], as its representamen,
> object, and interpretant. Hence, “n-ad” can be interpreted in two (I
> would say “complementary”) ways, depending on which aspect of the sign is
> prescinded in one’s mind, just as light can be “interpreted” in two ways,
> as particle or as wave, depending on which aspects of light is measured
> by an instrument, leading to the following dictum:
>
> “The word ‘n-ad, as represented by a network, can (040514-3)
> be viewed as the complementary union of nodes and
> edges, just as light is the complementary union of
> waves and particles.”
>
>
> (node-adicity)
> [edge-adicity]
> REPRESENTAMEN
> |
> |
> |
> “n-ad”
> SIGN
> / \
> / \
> / \
> (node) (relata)
> [edge] [relation]
> OBJECT INTERPRETANT
>
> Figure 1. The application of the 4-node network representation of a sign
> to clarifying the ambiguity of the word ‘n-ad’ such as monad, dyad, triad,
> etc.
>
> Statement (040514-3) applies to Piece’s tripod, -<, leading to the
> conclusion that
>
> “Peirce’s tripod network, -<, can be interpreted (040514-4)
> in two complementary ways -- as a node-triad
> or as an edge-triad. That is, as a set of three
> relata/nodes or as a set of three relations/edges.”
>
> The significance of (040514-4) lies in the fact that, if the three nodes
> of the tripod are arranged linearly, and not “triangularly”, the
> node-adicity would be 3 and the edge-adicity two.
>
> With all the best.
>
> Sung
> ___________________________________________________
> Sungchul Ji, Ph.D.
> Associate Professor of Pharmacology and Toxicology
> Department of Pharmacology and Toxicology
> Ernest Mario School of Pharmacy
> Rutgers University
> Piscataway, N.J. 08855
> 732-445-4701
>
> www.conformon.net
>
>> Jerry, List,
>>
>> You make the following claim: "In today's mathematics, a chemical icon
>> is
>> an exact mathematical object, a labelled bipartite graph." I'd like to
>> ask: if we understand the chemical icon to be a formal diagram
>> involving
>> vertices and lines like the ones that Peirce uses in his discussions of
>> possible diagrams of chemical molecules, then what might be missed if we
>> analyze the diagrams using bipartite graphs as a logical tool?
>>
>> For now, I'd like to set to the side a number of points you make that I
>> would consider matters of metaphysics. The question of whether Peirce's
>> phenomenology and semiotics provides the conceptual tools needed to
>> establish a metaphysics that will be adequate to explain the real nature
>> of molecules and molecular relations is a difficult question, and it's
>> one
>> that I wait until the discussion of the chapter on metaphysics to
>> broach.
>>
>> Having set such issues to the side, I'd like to focus on a set of points
>> you make that starts with the mathematics of formal graphs, runs into
>> the
>> phenomenological account of the categories, and then proceeds into
>> Peirce's critical grammar. Starting with the math, you say that
>> Peirce's
>> understanding of graph theory is based on diagrams used to study
>> chemical
>> relations. I'll grant that much. Sylvester explored these kinds of
>> diagrams to examine character of algebraic invariants, and Peirce drew
>> on
>> the same kinds of chemical diagrams for a number of mathematical and
>> logical purposes. One of Peirce's purposes was to to challenge a claim
>> Kempe makes in his essay on mathematical form. Kempe asserts that all
>> mathematical objects, relations and inferences can be analyzed in terms
>> of
>> a simple set of graphs that he developed for the purpose. Peirce denies
>> the claim. He argues that the analysis of the objects, relations and
>> inferences in any part of mathematics requires triadic relations. In
>> effect, he is claiming that the proper analysis of the relations between
>> monads, dyads and triads, is obscured in Kempe's account.
>>
>> Let me see if I can turn one of the points Peirce makes in his argument
>> against Kempe against a 20th or 21st century analysis of mathematical
>> form
>> in terms of bipartite graphs. Like a modern bipartite graph, the main
>> elements of Kempe's system are nodes and edges. In this system we treat
>> every vertex in a diagram as a node, and every line that connects
>> vertices
>> as edges. I'm no expert in graph theory, but my understanding is that a
>> graph is bipartite if all of the nodes can be grouped into two sets in
>> such a fashion that every line connecting vertices in a given formal
>> diagram are represented by edges connecting nodes in one or the other of
>> two sets. See, for instance, the WikiPedia entry on bipartite graphs
>> for
>> a simple explanation and a set of examples. In order to have an example
>> before us, let's consider the graph at the top of that webpage:
>> http://en.wikipedia.org/wiki/File:Simple-bipartite-graph.svg
>>
>> What concerns does Peirce have about the use of these kinds of graphs as
>> a
>> tool for analyzing the objects, relations and inferences used in one or
>> another area of mathematical inquiry? Well, it would help to have a
>> clear
>> example of a mathematical diagram. That way, we have an example of a
>> diagram that is being analyzed and an example of the kind of graph that
>> can be used to analyzed it. The diagram that Peirce draws on in the
>> Harvard Lectures of 1903 in his argument against Kempe is Pappus' proof
>> of
>> the 9-ray theorem in projective geometry.
>>
>> You seem to be saying that Peirce's analysis of mathematical form is
>> inadequate because it fails to take into account the kinds of
>> developments
>> that were made in the 20th century as work in graph theory marched
>> forward. I beg to differ. My hunch is that these bipartite graphs
>> obscure the very same points that Kempe obscured. As such, we should be
>> careful if we intend to use such mathematical systems to explore the
>> adequacies or inadequacies of Peirce's approach to analyzing the
>> possible
>> systems of hypotheses that might lie at the foundations of any area of
>> mathematics and the inferences that can be drawn from such hypotheses.
>>
>> What is being obscured? In short, the bipartite graphs allow several
>> edges to meet on one node. What Peirce analyzes the form of such
>> intersections, he says that allowing this kind of combination fails to
>> bring out the dyadic or triadic character of the relations being
>> analyzed.
>> As such, he fundamental elements of experience studied in the
>> phenomenological theory are diagrammed as a node with a single bonding
>> site (e.g., a monad), a straight line with two bonding sites (e.g., a
>> dyad), and a branching line with three bonding sites (e.g., a triad). I
>> think there is much to be gained by using these kinds of figures in the
>> graphs we construct to analyze the objects, relations and inferences in
>> mathematical (or any other) kind of reasoning. To press one of Peirce's
>> points, what is needed in the way of a formal graph if we're going to
>> analyze the character of the projective space in which the diagram of
>> Pappus' theorem is constructed. It is a two-dimensional surface, and it
>> is different from other surfaces in that there is a peculiar twist in
>> the
>> space. One of the things that Pappus's proof enables us to see--and I
>> mean literally "see"--is the commutivity of the mathematical space that
>> contains the lines, points and rays of the diagrams used it the proof.
>> The key thing that we see is that it wouldn't matter how the lines are
>> moved in this space. Any movement would result in the rays intersecting
>> in fashion that produces three points that are collinear. Peirce
>> insists
>> that seeing this relationship is crucial to the proof, and that the
>> analysis of what it is that we're seeing is obscured if we think of the
>> formal relations as nothing more than nodes and edges where more several
>> edges meet at one node. It's not just a matter of not seeing what is
>> being packed into the meeting of those several edges at this one node.
>> Rather, we don't see the order involved in constructing the rays and the
>> intersection of those rays. In effect, the act of constructing those
>> rays
>> and intersections is what defines the character of the surface as a two
>> dimensional projective space.
>>
>> --Jeff
>>
>>
>>
>> Jeff Downard
>> Associate Professor
>> Department of Philosophy
>> NAU
>> (o) 523-8354
>> ________________________________________
>> From: Jerry LR Chandler [jerry_lr_chand...@mac.com]
>> Sent: Friday, April 04, 2014 10:48 AM
>> To: Peirce List
>> Cc: Vinicius Romanini; Jeffrey Brian Downard
>> Subject: Re: [PEIRCE-L] de Waal Seminar: Chapter 5, Semeiotics, or the
>> doctrine of signs
>>
>> Vinicius, Jeff, Ben:
>>
>> (This post is a bit on the technical side. Do not have time today to
>> make
>> it simpler with longer explanations of the categories of exact relations
>> mentioned in this text.)
>>
>> A simple interpretation of the Peircian distinction between the meaning
>> associated with the grounding terms "icon" and "index" is possible if
>> one
>> recognizes that both terms are consequences of his knowledge of
>> chemistry
>> as it stood in his day.
>>
>> An chemical icon, as a visual form, either internal to a mind or
>> external
>> as a form of an existent object, is only one form of a material object.
>>
>> An index, as a set of marks or as a listing of multiple terms or objects
>> in some form or another, is a necessary concept for chemical
>> representations. Furthermore, this index is essential to GENERATING or
>> CREATING the chemical icon. In today's mathematics, a chemical icon is
>> an
>> exact mathematical object, a labelled bipartite graph.
>>
>> Both the chemical icon and the chemical index are absolutely necessary
>> to
>> create the semantic notion of a symbol (which CSP defines a symbol as
>> either a word OR a concept.) [This is one possible understanding of the
>> conundrum of why CSP used the "or" conjunction here.]
>>
>> Thus, this interpretation is congruent with the philosophical categories
>> of Quality, Representation and Relations.
>> It is also consistent with the more pragmatic view of CSP's thoughts
>> about: Thing, Representation and Form.
>>
>> Thus, this chemical interpretation of the three terms, icon, index and
>> symbol are congruent with the ontology of matter as CSP understood it in
>> the late 19 th Century.
>>
>> Finally, this interpretation is necessary for the completeness of the
>> medad as a sentence representing a complete thought. In the case of
>> chemical logic, as it stood in CSP's day, the medad can be thought of as
>> a
>> sentence describing the binding of chemical elements into a "radical".
>>
>> With these insights as part of the ground, I would like to extend my
>> remarks to CSP's motivations in general.
>> My recent posts are parts of a broad thesis of CSP's motivations for his
>> inquiry into semiotics and its meaningfulness in terms of today's usage
>> of
>> symbols in scientific notations. (Jeff's posts raise comparable
>> issues.)
>>
>> The philosophical hypothesis is simple:
>>
>> Peircian semiotics is grounded in the 19th Century view of chemical
>> semiotics as well as the logic of 19th C. mathematical terms.
>>
>> Unfortunately for this world view, 21 st Century chemical semiotics are
>> both numerically, logically, and symbolically remote from 19th Century
>> chemical semiotics. Chemical terms have been given new meaning in order
>> to
>> be congruent with the electrical structures of atoms as a atomic
>> numbers.
>> Consequently, the meaningfulness of Peircian semiotics is problematic as
>> it severely restricts the conceptualization of information as the
>> breadth
>> and depth of the intentions embedded in a symbol by a speaker or writer.
>>
>> The reasoning for the emergence of modern chemical semiotics from the 19
>> th century Peircian semiotics is also simple. In the 19th Century, the
>> chemical table of elements was based on the relative masses of each
>> element as a means of explaining correlates.
>>
>> In the first half of the 20 th Century, modern chemical semiotics
>> emerged
>> from the Peircian forms by the inclusion of electrical logic into the
>> iconization of chemical objects. Consequently, a chemical icon of today
>> is an exact representation of BOTH mass and electricity (as illustrated
>> by
>> physical quantum mechanics.) This representation of a chemical object
>> as
>> a binary object necessarily infers that it can not be represented as a
>> geometric point.
>>
>> The gradual shift of representation of matter as weight (19 th C., a
>> singular point, a measure of "beingness") to the representation of
>> matter
>> as both mass and electricity (21 st C., a form comparable to an
>> extension
>> of a beta-existential graph) forced the change in meaning of chemical
>> and
>> biological and medical symbols.
>>
>> By simple extension, a biological icon of today represents both mass and
>> electricity and iconic correlates (in addition to many other predicates
>> and copulas.)
>>
>> Cheers
>>
>> Jerry
>>
>>
>>
>>
>>
>>
>>
>>
>> On Apr 3, 2014, at 7:50 PM, Vinicius Romanini wrote:
>>
>> Jeff, list
>>
>> Jeff said: Having taken a look at MS 7, I'd like to ask a quick question
>> about the first assertion. What is Vinicius claiming when he says that
>> icons don't *enter* our concepts as such? Looking at page 15 of the MS,
>> I
>> see Peirce saying the following: "An icon cannot be a complete sign;
>> but
>> it is the only sign which directly brings the interpretant to close
>> quarters with the meaning; and for that reason it is the kind of sign
>> with
>> which the mathematician works." Shortly after making this point, he
>> develops the examples of the weather vane and the photograph.
>>
>>
>> V: A pure icon would be an immediate intuition of the form of the
>> object,
>> which Peirce denies. Every cognition is based on previous ones. But we
>> can use abstract concepts to diagram an idea iconically, as when we use
>> mathematical symbols to express the truth of a theorem. We then
>> contemplate the icon represented in the symbol. The quote bellow might
>> help:
>>
>> "The third case is where the dual relation between the sign and its
>> object
>> is degenerate and consists in a mere resemblance between them. I call a
>> sign which stands for something merely because it resembles it, an icon.
>> Icons are so completely substituted for their objects as hardly to be
>> distinguished from them. Such are the diagrams of geometry. A diagram,
>> indeed, so far as it has a general signification, is not a pure icon;
>> but
>> in the middle part of our reasonings we forget that abstractness in
>> great
>> measure, and the diagram is for us the very thing. So in contemplating a
>> painting, there is a moment when we lose the consciousness that it is
>> not
>> the thing, the distinction of the real and the copy disappears, and it
>> is
>> for the moment a pure dream -- not any particular existence, and yet not
>> general. At that moment we are contemplating an icon." (CP 3.362)
>>
>> Vinicius
>>
>>
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