The concept of “semantic closure” was introduced and developed by Howard H. Pattee in the context of Biology [1][2][3][4]. L. M. Rocha called this concept “semiotic closure”. In a special issue of Biosystems journal (Volume 60, No: 1-3) edited by L. M. Rocha you can find many papers discussing the concept of semantic/semiotic closure.
Semantic closure is related to the concepts of self-reference and self-replication.
“Self-reference has many meanings. In symbol systems, like logic and language, self-reference may lead to well-known ambiguities and apparent paradoxes as in “This sentence is false.” In material systems, like molecules and machines, self-reference is not clearly defined but may describe causal loops such as autocatalytic cycles, feed-back controls, and oscillators. At the cognitive level, self-reference occurs in introspection and is often considered one aspect of consciousness. I define a specific form of self-reference that applies to a closure relation between both the material and the symbolic aspects of organisms. I argue that this view of self-reference is necessary to understand open-ended evolution, development, and learning at all levels of organization from the origin of life to the cognitive level.” [3]
“To state my position as briefly as possible, self-reference that has open-ended evolutionary potential is an autonomous closure between the dynamics (physical laws) of the material aspects and the constraints (syntactic rules) of the symbolic aspects of a physical organization. I have called this self-referent relation semantic closure.” [3]
Earlier, von Neumann discussed a similar concept called “universal constructor”. The authors of reference [5] do an excellent job of explaining both the “universal constructor” and the “semantic closure” concepts.
“…universal constructor architecture (UCA) first explored by von Neumann. In a UCA, machines interact with an abstract description of themselves to replicate by copying the abstract description and constructing the machines that the abstract description encodes. DNA-based replication follows this architecture, with DNA being the abstract description, the polymerase being the copier, and the ribosome being the principal machine in expressing what is encoded on the DNA. This architecture is semantically closed as the machine that defines what the abstract description means is itself encoded on that abstract description. ” [5]
“The term semantic closure, introduced by Pattee, refers to the concept that a system can enclose its meaning within itself. Consider a string of DNA, with a given reading frame and start location we can say that the DNA, through its messenger RNA (mRNA), codes for a particular protein. This assumes particular triplets of DNA bases code for given amino acids. In biology, this encoding can and has evolved, altering the meaning of DNA by ‘rewiring the keyboard’ of the genetic code.” [5][6]
In his web page “What is Biosemiotics?” [7] Alexei Sharov comments on self-replication.
“In the process of self-reproduction, an organism defines itself; in other words, self is what is preserved in the process of self-reproduction. Self-reproduction is simultaneously a process of self-measurement, self-interpretation, and communication from parents to offsprings.” [7]
“Bacteria are not able to build mental models of objects but they can build material models of themselves, i.e. their offspring. ” [7]
For additional commentary on “semantic closure” you can read Jay L. Lemke’s paper “Opening Up Closure: Semiotics Across Scales” [8].
Now, let’s focus on a concern H.H. Pattee voiced in his paper from 2006 titled “The Physics of Autonomous Biological Information” [4]
“Without this semiotic closure that includes the grounding of symbols in the material world, all our symbol systems, all languages, all mathematics and formal systems could appear to exist outside the physical world as if they were pure Platonic forms.” [4]
“Unfortunately, two controversial schools of thought about symbols and dynamics have developed. This controversy has entered the fields of artificial intelligence, cognitive theory, artificial life, and even physics. One school emphasizes dynamical models; the other emphasizes symbolic computational models. The former argue that symbols are a derived concept reducible to dynamical systems. The latter argue that all events are informational and that continuous dynamics is itself a derived concept (e.g., Wheeler, 1990). Controversy over this difference obscures the central point: Life and evolvability require the complex interaction of rate-independent symbol constraints and rate-dependent physical dynamics. Like the physicist’s laws and initial conditions, the meaning of biological information cannot make sense if taken out of this inseparable context.” [4]
Searching in the dark
Even though it is not mentioned in the quotes above, the term “self-organized” needs to be mentioned here. Self-organized pattern formation in biological systems is a major research subject in academic circles. We know very little about the mechanisms of self-organization but we know the result of self-organization: cognitive core. Other terms similar to “cognitive core” are: intrinsic properties, symbols, rate-independent memory structures.
Cognitive cores interact. This is a fundamental principle. Interactions among cognitive cores are governed by dynamical (rate-dependent, time-dependent) laws.
History of physics is the history of identifying various units (galaxy, star, planet, molecule, atom, proton, electron, etc.) and their cognitive cores (mass, charge, spin, …) and discovering the dynamical laws of interactions among cognitive cores. In my previous post, I proposed that the conservation laws, being time-independent, should be considered as part of cognitive cores.
Going deeper, when we examine how cognitive cores are formed we run into many unknowns. For example, the confinement mechanisms responsible for the formation of elementary particles are not known. At the level of biology, the confinement mechanisms responsible for the formation of self-organized patterns are not clear.
Can we explain the formation of cognitive cores using the dynamical laws? More specifically, can we explain the formation of elementary particles using the dynamical laws of physics?
My answer is no. If we consider the conservation laws as part of the cognitive cores and acknowledge the fact that the dynamical laws and the conservation laws are categorically distinct then we are led to the conclusion that dynamical laws cannot explain the formation of cognitive cores. For example, dynamical laws expressed by Maxwell and Dirac equations are not enough to explain the formation of electrons and their cognitive cores. If you think of Noether theorem as a counter example, i.e., if you say that a certain symmetry of the Maxwell equations implies the conservation of charge, I remind you that Maxwell equations were the generalization and quantification of the empirical observations of all electromagnetic phenomena including the conservation of charge. Maxwell equations describe the dynamics of a charged particle but they do not explain what “charge” is.
Now, let’s revisit the concepts of individuality and agency.
Agency emerges from matter and becomes a causal factor influencing matter. This ‘agency effect’ is ontologically distinct from the categories of ‘dynamical laws’ and ‘cognitive cores’.
Agency: causal aspects of individuality
Individuality: in Individuality and Collectivity I suggested that the ‘cognitive core’ constitutes the minimum degree of individuality. Individuality is a temporal expression related to structural integrity over time. The degree of individuality should include a measure of complexity and compositeness of the structure as well.
What is matter? My answer is that matter is a collection of cognitive cores and their interactions. Recall that ‘interactions’ refers to the dynamical laws.
matter = {cognitive cores, dynamical laws}
Remember, ‘cognitive core’ is the minimum degree of individuality which does not possess agency yet. Therefore, matter does not possess agency.
What is mind? Mind is the functional aspect of agency. What is agency? Causal aspect of individuality. What is individuality? See above.
Agency emerges after a certain degree of individuality. Agency has causal impact but the realization of this act has to obey the natural laws.
As mind develops in the course of evolution subtler functions of the mind develop (ego, memory, thinking, intuition) and the degree of control increases. These higher functions of the mind are beyond mysterious. We are clueless about the higher functions of the mind!
As the evolution of mind-matter continues different levels of organization form. Each level exhibits a different degree of materiality. Each level is governed by different cognitive cores and their interactions. Also, each level may have different degrees of agency therefore exhibit different degrees of mind functionality. This means that the individuals at each level are subject to different kinds of laws. Physical laws are not violated but additional laws come into play.
In passing we should note that individuality can be nested. One individual can exist inside another. At each level of organization a different model of the self may have to be considered.
What is the closure problem?
Those additional laws at higher (agency dominated) levels of organization are irreducible to the laws at the lower levels. This is the closure problem.
H.H. Pattee is hopeful that closure can be achieved by describing the complex interplay between the ‘cognitive cores’ (Pattee’s “symbols”) and dynamical laws. Pattee thinks that closure can be demonstrated within the framework of matter. I have my doubts.
Primordial fabric, agency
In my post titled “On the emergence of space and time” I said, intuitively speaking, the progression order of physical manifestation is : (space 
In this post, I provide a definition for “matter” which is {cognitive cores, dynamical laws}. Since, dynamical laws use “physical time” as a parameter, I should replace “time
space
The “space” here is more like “primordial fabric”
primordial fabric
As agency develops in the course of evolution “matter” evolves into “mind+matter”
primordial fabric
My point is that primordial fabric is special. Agency has its roots in the capabilities of the primordial fabric.
Solution of the closure problem awaits breakthroughs in the understanding of the primordial fabric.
Roger Penrose expresses the closure problem pictorially
Penrose’s “Platonic mathematical world” shown in the diagram below may correspond to the “primordial fabric”. Both concepts (“Platonic mathematical world” and “primordial fabric”) have similarities to the “Citta” concept.
“Platonic-mathematical, physical, and mental – has its own kind of reality, and where each is (deeply and mysteriously) founded in the one that precedes it (the worlds being taken cyclicly). I like to think that, in a sense, the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very self into existence.” [9]
References
[1] H.H. Pattee (1973), “Physical Basis and Origin of Hierarchical Control”, Hierarchy Theory, ed. Howard Pattee, George Braziller, New York
[2] H.H. Pattee (1982), “Cell Psychology: An Evolutionary View of the Symbol-Matter Problem”, Cognition and Brain Theory, v. 5, pp. 325-341
[3] H.H. Pattee (1995), “Evolving self-reference: matter symbols, and semantic closure”. Communication and Cognition Artificial Intelligence 12(1-2), 9-27.
[4] H.H. Pattee (2006), “The Physics of Autonomous Biological Information“, Biological Theory, Vol. 1, No. 3: 224–226
[5] Edward B. Clark, Simon J. Hickinbotham and Susan Stepney, “Semantic closure demonstrated by the evolution of a universal constructor architecture in an artificial chemistry”, https://royalsocietypublishing.org/doi/10.1098/rsif.2016.1033
[6] Knight RD, Freeland SJ, Landweber LF, “Rewiring the keyboard: evolvability of the genetic code”, Nat. Rev. Genet.2, 49–58. (doi:10.1038/35047500)
[7] Alexei Sharov’s web page “What is Biosemiotics?“
[8] Jay L. Lemke, “Opening Up Closure: Semiotics Across Scales“
[9] Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005), p:1029
Suresh Emre
Renaissance Universal 