Category Archives: semiotics

fourfolds, logic, semiotics

The Semiotic Square

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sq_greimasFrom Wikipedia:

The semiotic square, also known as the Greimas square, is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, and of extending the relevant ontology.

Notes:

In an earlier post I combined an unusual representation of the semiotic square with that of the Tetralemma. Instead of using that one, please use this one instead.

References:

https://en.wikipedia.org/wiki/Semiotic_square

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fourfolds, Philosophy, semiotics

Categories of Experience

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sq_categoriesThe philosophy of Charles S. Peirce is chock-full of triples, but especially present are his three universal categories of experience. Threes aren’t really my specialty, but while reading a chapter of Richard Bernstein’s book on the “pragmatic turn”, I was reminded of Peirce’s relational ontology: Firstness, Secondness, and Thirdness. Wondering how these could be extended to a Fourthness, I immediately found a fair amount of work on the subject.

Of course, Peirce argued that such a Fourthness was redundant, unnecessary to the structure of his systematic philosophy. He used various reasons for his conclusions, including mathematical, logical, and semiological. There is also a wealth of subsequent work by later researchers on defending this claim, but what is interesting is that others have investigated extending his three into a four.

So, what might be Fourthness? Some of the aspects of fourfolds collected here have commonalities with some of the attributes of Firstness, Secondness, and Thirdness. For Firstness: feeling, quality, possibility; For Secondness: will, fact, existence; For Thirdness: knowledge, law, representation. I really don’t have anything to add at the present time and I have merely gathered these notions together for my future consideration.

References:

http://en.wikipedia.org/wiki/Categories_%28Peirce%29

http://en.wikipedia.org/wiki/Hypostatic_abstraction

http://www.paulburgess.org/triadic.html

http://tetrast.blogspot.com/2006/09/compare-to-aristotle-aquinas-peirce.html

Carl G. Vaught / Semiotics and the Problem of Analogy: a critique of Peirce’s theory of categories. Trans. of the Charles S. Peirce Society, Vol. 22, No. 3 (1986) 311-326

http://www.jstor.org/stable/40320143

Carl R. Hausman / Fourthness: Carl Vaught on Peirce’s categories. Trans. of the Charles S. Peirce Society, Vol. 24, No. 2 (1988) 265-278

http://www.jstor.org/stable/40320211

Donald W. Mertz / Peirce: logic, categories, and triads. Trans. of the Charles S. Peirce Society, Vol. 15, No. 2 (1979) 158-175

Richard J. Bernstein / The Pragmatic Turn. Polity (2010)

Also:

Ben Goertzel / The Hidden Pattern: a patternist philosophy of mind

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fourfolds, logic, semiotics

The Tetralemma and Semiotic Square

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The Tetralemma is a list that is supposed to exhaust all logical possibilities. Something is either X, or not X, or both X and not X, or neither X nor not X. Nagarjuna’s Fourfold Negation expresses a paradox by negating the Tetralemma, and asking what is not X, nor not X, nor both X and not X, nor neither X nor not X.

The Semiotic Square is an analytical tool to explore relationships between two semiotic signs, usually considered opposites of each other. The S1 and S2 in the figure are the signs in opposition, so that S2 is the dual of S1. S1+~S2 (S1 and not S2) would be X, ~S1+S2 would be not X, S1+S2 would be both X and not X, and ~S1+~S2 would be neither X nor not X.

References:

http://en.wikipedia.org/wiki/Tetralemma

http://en.wikipedia.org/wiki/Semiotic_square

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fourfolds, Philosophy, semiotics

Hjelmslev’s Net

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“God is a lobster, or a double pincer, a double bind.”

— From A Thousand Plateaus by Deleuze and Guattari

Linguist Louis Hjelmslev developed a semiotic model which elaborated Saussure’s two part signifier and signified into the double dual of the substance of content, the form of content, the substance of expression, and the form of expression. Contents are “formed matters”, and expressions are “functional structures”. Both are further separated into a substance and a form. The original signifier can be considered the form of expression, while the original signified can be considered the form of content. The two types of forms are like a net of warp and woof (why else a net?), dividing an undifferentiated unformed matter (Earth, purport) into two types of substances.

Deleuze and Guattari cast this net from Hjelmslev’s use in language into universal application by way of examples in geology and biology: sedimentation/folding and molecular genetics. The two planes of content and expression are the First Articulation and Second Articulation, respectively, the first of which “chooses or deducts”, and the second of which establishes “functional, compact, stable structures”. In their geology example, the First Articulation is the process of sedimentation, and the Second, folding. Generally, the two substances deal with territorialization, deterrritorialization, and reterritorialization, and the two forms are concerned with coding and decoding (and recoding?).

Additionally, there is talk of the molar versus the molecular (as continuous/discrete or unity/multiplicity?) but the molar is not form, nor is the molecular substance, nor vice versa. The First Articulation moves from molecular substances to molar forms; the Second Articulation moves from molecular forms to molar substances. How confusing! What does it all mean? One could spend a lifetime lost in these fun-house reflections!

I propose that the four basic logical operators of Linear Logic are in correspondence to the double articulation of Hjelmslev’s Net.  Content is Conjunction, Expression is Disjunction, Substance is Additive, and Form is Multiplicative. Content and Expression is Substance or Form; Conjunction and Disjunction is Additive or Multiplicative.

References:

Gilles Deleuze and Felix Guattari / A Thousand Plateaus: capitalism and schizophrenia

Manuel De Landa / The Geology of Morals: a neo-materialist interpretation http://www.t0.or.at/delanda/geology.htm

Luke Feast / The Science of Multiplicities: post-structuralism and ecological complexities in design http://researcharchive.vuw.ac.nz/handle/10063/142

[*3.170, *4.46, *4.88, *4.112, *4.146, *5.70, *5.174, *6.10]

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alchemy, anime, logic, Philosophy, semiotics

Introduction

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“Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy’s first law of Equivalent Exchange. In those days, we really believed that to be the world’s one, and only truth.”

—Alphonse Elric, in the first opening to Fullmetal Alchemist

The concept of Equivalent Exchange introduced in the anime quoted above inspired the title of this blog. “To obtain, something of equal value must be lost.” Though this term was recently coined, the concept is a familiar one and has been around for a long time. It is found as guides, rules, and laws in philosophy, religion, and science. For example:

  • Do unto others as you would have them do unto you.
  • Don’t take more than you give.
  • Give and you shall receive.
  • What goes around comes around.
  • There’s no such thing as a free lunch.
  • You get what you pay for.
  • You get what you deserve.
  • An eye for an eye, a tooth for a tooth.
  • You scratch my back, and I’ll scratch yours.
  • Energy is neither created nor destroyed.
  • Every action has an equal and opposite reaction.
  • Yin and yang.
  • Karma.

I’m sure many more can be listed. I invite my readers to submit them.

These are all conservation laws: total value is maintained, even while it changes hands. And they certainly seem to be “conservative”:  all things being equal, they usually hold.

That being said, this blog isn’t specifically about “equivalent exchange”, except for hopefully obtaining the value of knowledge for the effort expended. Instead, I hope to explore a common thread that runs through philosophy, logic, and semiotics in the form of “double duals” (which themselves seem to have the property of equivalent exchange), with the goal of understanding and classifying different philosophical subjects and systems, exploring the nature of pluralism, and enhancing dialogue between opposing viewpoints. The image of the Tower of Babel in the title banner was chosen because public discourse has become fragmented and even broken.