Charls Pearson
Professor Charls Pearson, PhD, hPSS, is the former Academic Ambassador to China for Logic, Semiotics, Philosophy of Science, and Peirce Studies. He is also the former editor of the Peirce Section of the Chinese Journal of Semiotic Studies.His subject areas include experimental semiotics, general semitics, theoretical semiotics, and mathematical semiotics.His application interests include logic, linguistics, esthetics, mathematics, and semiotics of law.
Phone: 404-313-0202
Address: 4063 Champion Dr.
Austell, 30106, USA
Phone: 404-313-0202
Address: 4063 Champion Dr.
Austell, 30106, USA
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I have written several papers announcing the discovery of various new laws of semiotics, each utilizing, in one way or another, one other discovery also involving a new law: one that I call “Uni-versal Semiotic Factorization”. Each of the afore mentioned papers involves something more general than factorization and yet factorization is more general than any of the other laws.
Surprisingly, I have never written in detail about factorization itself, altho I have often men-tioned some of its laws. Therefore, I now pay this overdue debt with the present paper, concentrating on my Theory of Universal Semiotic Factorization, some of the laws of semiotics that it generates, and a new mathematical concept designed to provide an intuitive notation for many semiotic pro-cesses.
Semiotic factorization is similar to, but different from, factorization of ordinary numbers. Some numbers can be factored and some cannot. For instance, the number 12 can be factored in two ways into 26 and 34, but the number 11 cannot be factored at all. The operation “” used in this factor-ing analysis is ordinary numerical multiplication. Those numbers that cannot be factored are called “prime numbers” and play a very important role in number theory.
Likewise, some relations can similarly be factored and some cannot. Peirce spoke of relations that could be factored as “degenerate” and relations that could not be factored as “genuine”. Howev-er, in 20th century mathematics, we tend to follow the same nomenclature as in number theory. Rela-tions that cannot be factored are called “Prime Relations”, while those that can are called “Composite Relations”. For instance, the composite triadic relation, Tijk, can be factored into the two dyadic rela-tions Rij Sjk, using the operator “” for the operation of relational multiplication.
Just as prime numbers play an important role in number theory, prime relations play an im-portant role in semiotics. Peirce defined any prime triadic relation Sijk as a sign, and semiotics in a narrow sense is the study of prime triadic relations. In a larger sense, however, because of Peirce’s theorem, semiotics is the study of all relations of addicity of three or more and their use in modeling intangible nature.
However, many signs have so much additional structure, structure that we want to take advantage of in any semiotic analysis, that I introduce a new kind of operator; one that I call a “Semiotic Com-binator”. A semiotic combinator may loosely be described as an operator that can take on any kind of argument, especially signs, functions, operators, and even other combinators. A combinator is powerful enough that it can take advantage of all semiotic structure. This means that a combinator can operate directly on a sign and also on other combinators. Details about certain kinds of semiotic combinators will become more clear as the chapter proceeds.
Many of the examples of simple factorization used in this paper could be analyzed with nothing more than the operators of mathematical string theory, altho they cannot be analyzed with anything as weak as the transformations of transformational grammar. Transformations and string theory op-erators themselves are merely simplified forms of semiotic combinators. The real power of semiotic combinators only shows up in advanced analysis, such as the analysis of the pragmatic combinator, analysis of the interpretant, and the dynamic combinators only hinted at later in section 7.
The original idea for a combinator of any kind must be credited to Peirce. In his later research, Peirce discovered that all inferences, all reasoning, and even all thought processes of any kind can be formalized using only three different operators. Just a few years after Peirce’s death in 1914, Haskell Curry began, in the 1920’s, to develop Peirce’s three operators into the foundations of a formal theo-ry which is now called combinatory analysis, using what he called the theory of combinators (Curry & Feys 1968). A semiotic combinator is just a combinator developed with the special kinds of prop-erties useful for analyzing the structure of signs (Pearson I/P).
The USST is a Peircean based advance in semiotic theory that goes far beyond Peirce’s taxonom-ic theory to include nomological theory and even abductive/subductive theory. It is restricted to a static macro theory of the sign. The latest version, USST-2000, was adopted by the Semiotic Society of America’s Committee on Empirical Standards as the standard static macro theory from which dis-cussion may start without including special comment or justification. Other theoreticians develop their approach from a micro or even dynamic standpoint, but are unable to derive an experimental methodology from this.
One can think of a static macro theory of the sign, such as the USST-2000, as an understanding of the large concepts of semiotics, a cosmology for semiotics, if you will. While on the other hand, micro theories, such as those developed by Göran Sonesson or Eliseo Fernández, may be thought of as an understanding of the detail concepts of semiotics, a quantum theory for semiotics, if you allow me this freedom of expression. Only a macro theory allows for a pathway connecting all the con-cepts leading from theory to specific, systematic, experimental methodology with verifiable results.
I have written several papers announcing the discovery of various new laws of semiotics, each utilizing, in one way or another, one other discovery also involving a new law: one that I call “Uni-versal Semiotic Factorization”. Each of the afore mentioned papers involves something more general than factorization and yet factorization is more general than any of the other laws.
Surprisingly, I have never written in detail about factorization itself, altho I have often men-tioned some of its laws. Therefore, I now pay this overdue debt with the present paper, concentrating on my Theory of Universal Semiotic Factorization, some of the laws of semiotics that it generates, and a new mathematical concept designed to provide an intuitive notation for many semiotic pro-cesses.
Semiotic factorization is similar to, but different from, factorization of ordinary numbers. Some numbers can be factored and some cannot. For instance, the number 12 can be factored in two ways into 26 and 34, but the number 11 cannot be factored at all. The operation “” used in this factor-ing analysis is ordinary numerical multiplication. Those numbers that cannot be factored are called “prime numbers” and play a very important role in number theory.
Likewise, some relations can similarly be factored and some cannot. Peirce spoke of relations that could be factored as “degenerate” and relations that could not be factored as “genuine”. Howev-er, in 20th century mathematics, we tend to follow the same nomenclature as in number theory. Rela-tions that cannot be factored are called “Prime Relations”, while those that can are called “Composite Relations”. For instance, the composite triadic relation, Tijk, can be factored into the two dyadic rela-tions Rij Sjk, using the operator “” for the operation of relational multiplication.
Just as prime numbers play an important role in number theory, prime relations play an im-portant role in semiotics. Peirce defined any prime triadic relation Sijk as a sign, and semiotics in a narrow sense is the study of prime triadic relations. In a larger sense, however, because of Peirce’s theorem, semiotics is the study of all relations of addicity of three or more and their use in modeling intangible nature.
However, many signs have so much additional structure, structure that we want to take advantage of in any semiotic analysis, that I introduce a new kind of operator; one that I call a “Semiotic Com-binator”. A semiotic combinator may loosely be described as an operator that can take on any kind of argument, especially signs, functions, operators, and even other combinators. A combinator is powerful enough that it can take advantage of all semiotic structure. This means that a combinator can operate directly on a sign and also on other combinators. Details about certain kinds of semiotic combinators will become more clear as the chapter proceeds.
Many of the examples of simple factorization used in this paper could be analyzed with nothing more than the operators of mathematical string theory, altho they cannot be analyzed with anything as weak as the transformations of transformational grammar. Transformations and string theory op-erators themselves are merely simplified forms of semiotic combinators. The real power of semiotic combinators only shows up in advanced analysis, such as the analysis of the pragmatic combinator, analysis of the interpretant, and the dynamic combinators only hinted at later in section 7.
The original idea for a combinator of any kind must be credited to Peirce. In his later research, Peirce discovered that all inferences, all reasoning, and even all thought processes of any kind can be formalized using only three different operators. Just a few years after Peirce’s death in 1914, Haskell Curry began, in the 1920’s, to develop Peirce’s three operators into the foundations of a formal theo-ry which is now called combinatory analysis, using what he called the theory of combinators (Curry & Feys 1968). A semiotic combinator is just a combinator developed with the special kinds of prop-erties useful for analyzing the structure of signs (Pearson I/P).
The USST is a Peircean based advance in semiotic theory that goes far beyond Peirce’s taxonom-ic theory to include nomological theory and even abductive/subductive theory. It is restricted to a static macro theory of the sign. The latest version, USST-2000, was adopted by the Semiotic Society of America’s Committee on Empirical Standards as the standard static macro theory from which dis-cussion may start without including special comment or justification. Other theoreticians develop their approach from a micro or even dynamic standpoint, but are unable to derive an experimental methodology from this.
One can think of a static macro theory of the sign, such as the USST-2000, as an understanding of the large concepts of semiotics, a cosmology for semiotics, if you will. While on the other hand, micro theories, such as those developed by Göran Sonesson or Eliseo Fernández, may be thought of as an understanding of the detail concepts of semiotics, a quantum theory for semiotics, if you allow me this freedom of expression. Only a macro theory allows for a pathway connecting all the con-cepts leading from theory to specific, systematic, experimental methodology with verifiable results.