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 xs 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 ones 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 Pieces tripod, -<, leading to the
> conclusion that
>
> Peirces 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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