Tag Archives: Louis Hjelmslev

J.-Y. Girard’s Transcendental Syntax, V2

March 11, 2015 Martin K. Jones 1 Comment

Meaning is use.

– Ludwig Wittgenstein

If people never did silly things nothing intelligent would ever get done.

– Ludwig Wittgenstein

The latest two preprints by logician J.-Y. Girard continue his program for transcendental syntax, divided into deterministic and nondeterministic. He defines transcendental syntax as the study of the conditions of the possibility of language: to begin by discovering the preliminary suppositions in the creating of a logical sentence such as a proposition or deduction.

What are the presuppositions for using propositions? Girard claims the main one is the balance between the creation and the use of words, which is at the heart of meaning. But the notion that a proposition has a meaning that is well defined is prejudice, albeit one that allows us identify the terms of a sentence and thus to perform deductions.

Girard wants instead to find inner explanations of logical rules: explanations based on syntax instead of a semantics that correlates to a mandated “reality”. To emphasize this, he gives the term Derealism as another expression for transcendental syntax. Logical rules should have a normative aspect because of their utility, so his project appears to be one of pragmatism. Others have said that Linear Logic is the logic of the radical anti-realist.

Girard divides all of logical activity into four blocks that weave together: the Constat, the Performance (please forgive my shortening on the diagram above), L’usine (factory), and L’usage (use). These four blocks are partitioned by Kant’s analytic-synthetic and a priori-a posteriori distinctions. The analytic is said to have “no meaning”, that is, “locative”. The synthetic is said to have “meaning”, that is, “spiritual”. The a priori is said to be “implicit”, and the a posteriori is said to be “explicit”.
Can we find all the explanations we need to create logic internally? If so, perhaps it is only because of how the brain works, like how John Bolender posits that social relations described by the Relational Models Theory are created out of symmetry breaking structures of our nervous systems, which are in turn generated by our DNA. A realist would certainly say that our understanding of logical rules is enabled but also limited by our brains, whereas an idealist would say that our minds could “transcend” those limits. But it seems pragmatic to say that the mind is what the brain does.

I believe a closer analogy for the fourfold of Transcendental Syntax is to Hjelmslev’s Net than to Kant’s Analytic-Synthetic Distinction. If so, then Performance and L’usage are Content (Implicit), whereas Constat and L’usine are Expression (Explicit). Performance and Constat are Substance (Locative), and L’usine and L’usage are Form (Spiritual). Hjelmslev was a linguist that developed a theory of language as consisting of only internal rules.

Or even to analogy with Aristotle’s Four Causes, which is how I’ve arranged the first diagram: the Constat is the Material cause, the Performance is the Efficient cause, L’usine is the Formal cause, and L’usage is the Final cause. Material and Efficient causes are often considered mere matter in motion, which could be Locative, or meaningless (physical). Formal and Final could be Spiritual, or meaningful, as patterns of matter and motion, respectively.

Notes:

How can we know that a given named term is the same as another one in a different part of our formula? Rather than using names, or linking them through semantics or a well-defined meaning, we can tie terms together by their locations in our sentences and deductions.

References:

J.-Y. Girard / Transcendental syntax 1: deterministic case (January 2015 Preprint)

J.-Y. Girard / Transcendental syntax 2: non deterministic case (February 2015 Preprint)

https://girard.perso.math.cnrs.fr/Accueil.html

V. Michele Abrusci, Paolo Pistone / On Transcendental Syntax: a Kantian Program for Logic?

https://www.academia.edu/10495057/On_Trascendental_syntax_a_Kantian_program_for_logic

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

[*8.122, *8.123]

fourfolds, Philosophy, semiotics

Hjelmslev’s Net

November 29, 2010 Martin K. Jones 10 Comments

“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]

fourfolds, linear logic, Metaphysics, Philosophy

Monism = Pluralism

November 5, 2010 Martin K. Jones Leave a comment

PLURALISM = MONISM

– From A Thousand Plateaus by Deleuze and Guattari

Jeffrey Bell’s blog entry about William James’ radical empiricism reveals relations between Hjelmslev’s Net and Linear Logic. To begin with, Hume was concerned with disjunctive relations (of expression) to the exclusion of conjunctive relations (of content). In addition, James sought the solution to the problem that consciousness (here content) has between the “one and the many”, one consciousness in relation to many consciousnesses. Unable to resolve this problem, James did not realize that conjunction can come in two modes, an additive one and a multiplicative one, a substance and a form.

The substance of content (here consciousness, agency, …) is constituted incrementally from choices between actions, either thoughts (thoughts-as-action) or actual actions (actions-as-action). This is additive AND. The form of content (essence, existence) is assembled by the ordering of those choices, a multiple choice of choices. This is multiplicative AND. These are the powers of AND.

However, Hume’s disjunction (expression) also comes in two flavors: additive and multiplicative (substance and form). It also has a problem with the “one and the many”. The substance of expression is either identity or generation (accident, substance). This is additive OR. The form of expression doesn’t seem like much in Linear Logic, but it is the very form of the logic, invertible with the connective tissue of the calculus (the comma). This is multiplicative OR. These are the powers of OR.

Content and expression are dual to each other, as conjunction is logically dual to disjunction. Is content the “subjective” and expression the “objective”? Is substance the “one” and form the “many”? Each is dual to the other, not distinguishable except by perspective. Perhaps these double duals are like a Mobius Strip, which only has one side, weaving in and out and forming a unity out of multiplicity.

Note that the elements of the double dual shown here are taken from the Protreptikos page “Monism and Pluralism”. The fourfold is made up of different “compositions in being”, each in two parts. There are many echoes to other double duals in these compositions, such as potency/actuality (existence) and substance/form.

References:

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

http://schizosoph.wordpress.com/2010/08/11/monism-pluralism/