List, This post is a continuation of the commentary on the triadic triple. My goal is unchanged, that is, to find meaningful pragmatic examples of the application of this particular set of semantic terms that CSP used to describe the foundations of logic and pragmaticism. In the absence of meaningful scientific examples, the foundational logic of pragmatism lack a significant justification.
In last post, of Nov. 27, 2018, (reproduced below) I presented a simple diagram labeled with abstract symbols rather than CSP’s original terms. > A1, A2, A3 > B1, B2, B3 > C1, C2, C3 > and the differentiation between CSP’s terms and John Sowa’s terms and John’s interpretation of CSP's terms. > Thus, we can re-write the matrix, perhaps without lose of meaning, as: > A1(x1,y1), A2(x1, y2), A3(x1,y2) > B1(x2,y1), B2(x2, y2), B3(x2,y2) > C1(x3,y1), C2(x3,y2), C3(x3,y3). This simple substitution of abstract symbols that preserved the order relations among the triadic triple generated several exciting insights into the style of John Sowa’s reasoning. Here, I simply extend the commentary and then add some preliminary comments about the part - whole relationships among the triadic triple. Let us look at Fig 6.15 once again. The neural network lists four qualisigns (rows 1,2,3,&4) as inputs and four symbols (rows 1,2,3 & 4) as outputs. In the text, page 400, the following bold assertion “In the hidden layers of the network, some signals represent sinsigns that indicate the existence of external features combinations of features and the pattern of weights that are created by the learning algorithm determine the conditioned reflects or legisigns that map qualisigns to symbols.” (The meaning of this sentence may include modes of extension of logical symbols, of semantic terms, of syntactical terms as well as approximations.) Since the neural network takes qualisigns as inputs and generates symbols as outputs, this assertion infers that qualisigns are the origin of sin-signs. Given these graphic connections, the input -output relations appear as deductive arguments. But CSP defines sin-signs as 1903 | Syllabus: Nomenclature and Division of Triadic Relations, as far as they are determined | EP 2:291 A Sinsign (where the syllable sin is taken as meaning “being only once,” as in single, simple, Latin semel, etc.) is an actual existent thing or event which is a sign. It can only be so through its qualities; so that it involves a qualisign, or rather, several qualisigns. But these qualisigns are of a peculiar kind and only form a sign through being actually embodied. One can generate several possible conclusions from these pages on the relation between semiotics and the logic of Artificial Intelligence as presented here. (Section 6.6 p. 396-402. 1. The logic of AI differs in a fundamental way from the semantics of triadic triples since the AI network only uses six of the nine terms of the matrix. 2. The mathematics of AI generates sin-signs from qualisigns as needed to create symbols. 3. The logic of the mathematics of AI (neural networks) uses the notions of sin-signs, legisigns, icons and indices to generate symbols. 4. Propositional Arguments (C3), formed semantically and syntactically from Rhema (C1) and Dici-signs (C2) are not essential to the interpretations of semiotics that relate quali-signs to symbols. It is unclear how the addition of several terms fit into the concept of either AI or neural networks. The above matrix representing the triadic triple shows that all nine of the terms are interrelated. It is the interrelationship among the nine matrix terms that clearly separate CSP’s foundational views of pragmatic logic from the current notions of the foundations of logic. (see for example the texts of jean-yves beziau and Gila Sher) In the natural sciences, the nine terms must be interdependent upon one another, either directly or by concatenation within the matrix. If any one of the terms was not related to the truth (or falsehood) of the logical conclusion, why would it be included in the matrix? How does one show that meaningful interrelations among these nine terms of the triadic triple are essential for a foundation for CSP’s notion of logic and the nature of its indexical extensions of scientific symbols? Happy New year to all. May the New Year bless everyone with peace, joy and good fortune. Cheers Jerry > On Nov 27, 2018, at 2:03 PM, Jerry LR Chandler <[email protected]> > wrote: > > List, > > This post is a continuation of the commentary to John F. Sowa section 6.6 in > Knowledge Representation, 2001, p.394-402 entitled Semiotics. > > The issue is, What are the meanings of CSP's nine terms of the triadic triple > used to represent knowledge? In particular, what are the relationships to > adductive logic? to graph theory? to chemical logic? to propositional > arguments? > > On page 396, the text associates each of nine terms with two further terms. > In order to a more efficient logical representation of the Sowa triadic > triple, I will introduce a matrix notation: > > A1, A2, A3 > B1, B2, B3 > C1, C2, C3 > > to represent the nine terms given in my earlier post (see below). > > The text augments this matrix with additional terms for each row and column > of the matrix. > The terms for the rows are labeled x1, x2, and x3 for augmentation as > material, relational and formal respectively. > The terms for the columns are labelled y1, y2, and y3 for augmentation as > quality, indexicality, and Mediation, respectively. > > Thus, we can re-write the matrix, perhaps without lose of meaning, as: > A1(x1,y1), A2(x1, y2), A3(x1,y2) > B1(x2,y1), B2(x2, y2), B3(x2,y2) > C1(x3,y1), C2(x3,y2), C3(x3,y3). > > the text continues to assert that this matrix is meaningful for the > relationships between Qualisigns and Symbols. Figure 6.15, page 401, shows a > neural network with inputs A1(1), A1(2), A1(3) and A1(4), that designated as > 4 separate and distinctive Quali-signs, each labeled as inputs of the neural > network.These inputs are the initial conditions for the mathematical > functions of the computations of the network. > These four inputs are processed by the network into 4 Outputs, labeled as > B3(1), B3(2), B3(3) and B3 (4). > On page 400, the text asserts of the nine terms of the matrix, the first five > (presumably > A1(x1,y1), A2(x1, y2), A3(x1,y2) > B1(x2,y1), B2(x2, y2),) > could be called sub-symbolic, the last three, presumably > C1(x3,y1), C2(x3,y2), C3(x3,y3), > could be called super-symbolic. > > After describing the role of “hidden layers” in the construction of neural > networks, the text states, > “some signals represent sinsigns that indicate the existence of external > features or combinations of featuresand the patterns of weights that that are > created by the learning algorhithms determine the conditional reflexes or > legisigns that map qualisigns to symbols." > > This phrase suggests that the neural network calculates B3 from A1 via the > path through A2 and A3. > > A role for C1,C2,C3 in this network is not apparent to this reader. > The role of the augmented logical terms C1(x3,y1), C2(x3,y2), C3(x3,y3) is > not only not clear, it appears simply to add unwarranted perplexity to the > already challenging logic. > > After pondering this interpretation of CSP triadic triple for several years, > my basic questions, > "The issue is, What are the meanings of CSP's nine terms of the triadic > triple when used to represent ontologic knowledge? In particular, questions > like: what are the relationships of these nine terms to adductive logic? to > graph theory? to chemical logic? to propositional arguments?” remain open. > Of keen concern is the anaphoric and deictic order of the matrix and the > augmented matrix with the six categorical extensions. > > Can anyone suggest how this interpretation of CSP’s semeiotic and the triadic > triple relates to either logic or to the example of the linkage between the > dog being induced to bark whenever he was shocked by the incoming telephone > call? > > Does the inability to identity a pragmatic example of the connective > relationships of the nine terms of CSP's triadic triple cast long shadows on > the meaning of signs in semiotics? > > If signs are to be a universal basis for semiosis, then I would speculate > that an unbounded number of pragmatic examples of triadic triples should > exist and be as common as the falling leaves in the autumn. > > John, would you like to comment on your reasoning? > Do you have any other examples where data was actually used in the network > described? > > Cheers > > Jerry > > > > > >> On Nov 18, 2018, at 9:08 PM, Jerry LR Chandler <[email protected] >> <mailto:[email protected]>> wrote: >> >> List, >> >> This post continues the inquiry into the triadic triple. (see post of >> Sunday, Oct 28.) >> >> In this post, I will comment on the interpretations of the triadic triples >> of John F Sowa. >> see section 6.6, p. 396-398, 2000. Later versions have also been published. >> >> CSP proposed the triadic triple of” >>>> Qualisign Sinsign Legisign >>>> Icon Index Symbol >>>> Rhema Dicisign Argument >> >> >> JFS interprets these 9 terms with an example of a pseudo failure of a phone >> which occurred when the dog barked. The causal relation was due to the dog >> lease was short circuited with the telephone wires. He posted Figure 6.14 >> on this list recently. >> >> As I interpret this Figure, the rows and columns of the CSP table is >> augmented by three more terms. >> The augmented terms for columns are the three terms, 1. Quality, 2. >> Indexicality 3. Mediation >> The augmental terms for rows are 1. Material 2. Relational and 3. Formal >> >> Thus, as I understand this table, each of the nine triadic triple terms >> given above are augmented by two further terms. Consequently, as I read >> this table, three separate and distinct terms are included in the >> interpretation of each element of the 3x3 table. >> >> Within each box within the 3 x 3 rectangle, a further interpretative phrase >> is adjoined to each of the nine terms of the triadic triple. >> These are: >> Qualisign A quality which is a sign. >> Sinsign An actual existent thing or event which is a sign. >> Legisign A law which is a sign. >> >> Icon -Refers by virtue of some similarity to object. >> Index -Refers by virtue of being affected by the object. >> Symbol -Refers by virtue of some law or association. >> >> Rheme - A sign of a qualitative possibility. >> Decent Sign - A sign of actual existence. >> Argument - A sign of law. >> >> On first reading, I was impressed with this example of a barking dog and the >> explanation of the context via these nine terms. It is a good pragmatic >> narrative that interprets the facts. >> In Figure 6.15, a diagram shows the projected relations between quali-signs >> and neural networks. >> >> With each of many subsequent readings, I slowly lost my enthusiasm. for this >> Figure. >> In particular, my belief waned for several reason, but three come to mind. >> >> 1. How do these augmented terms relate to mapping from icons to rhemes and >> the role of monads, dyads, etc as “blank” terms in propositional sentences? >> see CW 3.418 - 421. >> >> 2. How do these augmented terms relate to abductive logic? >> >> 3. How do these augmented terms relate to scientific symbol systems? >> >> In other words, my search for a path from these augmented terms to pragmatic >> examples that fit all nine of the terms into a meaningful scientific example >> failed for several years. >> >> So, several years ago, I started to search for such a hypothetical path that >> would conserve the conceptual context of the triadic triple and logically >> support the numerical calculations used in the pragmatic sciences. >> >> Perhaps some readers may find Fig. 6.14 and 6.15 meaningful in a general >> sense; that is, not restricted to the singular example of the barking dog. >> >> Alternative interpretations of the nine terms of the triadic triple can be >> informed from considerations of the symbolic deixis. Such alternatives can >> lead to nascent compositions related to abductive reasoning. >> >> Cheers >> >> Jerry >> >> >> >> >> >>> On Nov 9, 2018, at 3:55 PM, Jerry LR Chandler <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> List, JAS, >>> >>> First, thank you Jon for the reference to J K Sheriff’s work. >>> >>> His table of relations among the triadic triples is rather cute. Cute, but >>> hardly compelling. >>> But, his attempt to constrain the triadic triples to both columns and rows >>> seems ill-advised from the perspective of logic. >>> >>> The potential formal logical nature of the triadic triple seems to be >>> excluded from this (Sheriff) perspectives of the categorization of nine >>> terms. In particular, in my interpretation of the table, the bottom right >>> corner of the matrix, which CSP labels as “argument”, infers the purpose of >>> the matrix is to construct a material proposition that may be True or >>> False, and which is true if and only if it is compossible into a symbol >>> that represents the legisign. >>> >>> The generalized question is whether or not a thirdnesses of representation >>> (Rhema) maps to the thirdnesses of legi-signs. Would you like to opine on >>> this particular form (or proform?) of categorization? >>> >>> JFS has subsequently noted (on Nov. 2, 2018) >>> "For EGs, Peirce used the terms monad, dyad, triad, tetrad, pentad... >>> He also showed that relations with more than 3 "logical subjects" >>> could be defined in terms of relations with 3 or less. He also >>> observed that a proposition or dicent sign is a medad.” >>> >>> CSP associates the “matrix of terms of the triadic triple with the >>> relationships to blanks in propositional space. It appears to me that >>> Sheriff misses this vital concept in the composition of his interpretation >>> of the triadic triple. >>> >>> (I cite JFS paragraph merely for convenience of time.) >>> >>> I will offer my own interpretation in a later post, which will differ >>> sharply from JFS categorization of the triadic triple. I plan to connect >>> the triadic triple to the composition of arguments, using a schema of >>> reasoning that is consistent with modern scientific diagrammatic reasoning >>> over the matrix of the nine terms. >>> I will seek to include a reason for developing the generative notion of >>> abductive logic. >>> >>> Cheers >>> >>> Jerry >>> >>> >>> >>>> On Oct 31, 2018, at 2:34 PM, Jon Alan Schmidt <[email protected] >>>> <mailto:[email protected]>> wrote: >>>> >>>> Jerry C., List: >>>> >>>> As I have said before, I do not have John Sowa's book. I suppose that I >>>> could request it via Interlibrary Loan, but it would take at least a few >>>> days to get to me. I will ask again--could you (or John himself) please >>>> post an image of Figure 6.14, so that I can better understand what you >>>> mean by "any complete schema for addressing all nine terms of the triple >>>> triad in a coherent narrative"? Does this table from a 1981 paper by John >>>> K. Sheriff, "Charles S. Peirce and the Semiotics of Literature," perhaps >>>> fit the bill? >>>> >>>> <image.png> >>>> >>>> It also appeared in his 1994 book, Charles Peirce's Guess at the Riddle. >>>> >>>> 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 Sun, Oct 28, 2018 at 9:23 PM Jerry LR Chandler >>>> <[email protected] <mailto:[email protected]>> wrote: >>>> List, JonAS: >>>> >>>> Shortly after you posted this message, I departed on an extended business >>>> trip and sort of dropped out of this discussion. Recent thoughts bring me >>>> back around to these questions from a different and I believe, a better >>>> grounded perspective on the grammar of the triple triad. >>>> >>>> The specific triple triad that I am referring too is as follows: >>>> >>>> Qualisign Sinsign Legisign >>>> Icon Index Symbol >>>> Rhema Dicisign Argument >>>> >>>> Over the past two decades, inquiries into these nine terms have resulted >>>> in multiple “back and forths” among list members. Often, these posts have >>>> included two or three or four of these terms and there interrelated >>>> meanings and associated grammatical renderings. >>>> >>>> In one exceptional case, John Sowa has opened new territory by presenting >>>> a detailed narrative that related all nine terms. This is in Figure 6.14 >>>> of his book, Knowledge Representation (2000). The book is directed toward >>>> Artificial Intelligence students as well as others. One should also note >>>> Gary R.s schema is somehow related to this issue. >>>> >>>> Several years ago, I posted to this list serve, a narrative that was >>>> coherent for four of the nine terms, >>>> >>>> Qualisign Sinsign >>>> Icon Index >>>> >>>> I now have reason to believe that this is only partially correct with >>>> respect to CSP’s views on material propositions. >>>> >>>> The following open question is addressed to all list members. >>>> >>>> Is anyone aware of any complete schema for addressing all nine terms of >>>> the triple triad in a coherent narrative? >>>> >>>> This is a (rather superficial) search is for any published or un-published >>>> schema. If anyone has unpublished versions that they wish to keep >>>> private, please respond to my private email and I will respect your >>>> confidentiality. >>>> >>>> To re-iterate, has anyone else besides John Sowa developed a coherent view >>>> of CSP triple triad? >>>> >>>> Cheers >>>> >>>> Jerry >>>> >>>> ----------------------------- >>>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >>>> PEIRCE-L to this message. PEIRCE-L posts should go to >>>> [email protected] <mailto:[email protected]> . To UNSUBSCRIBE, >>>> send a message not to PEIRCE-L but to [email protected] >>>> <mailto:[email protected]> with the line "UNSubscribe PEIRCE-L" in the >>>> BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm >>>> <http://www.cspeirce.com/peirce-l/peirce-l.htm> . >>>> >>>> >>>> >>>> >>> >> > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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