Saturday, March 20, 2010


Toward a





ALGEBRA OF PROBABLE INFERENCE/INQUIRY: The Algebra of Probable Inference/Inquiry is a common sense foundational reformation of the concepts of Probability, by the simple generalization of implication among logical statements in the Boolean algebra to degrees of implication, and of Entropy, by generalizing a particular function of the question lattice to a valuation called relevance which is a measure of the degree to which a statement answers a given question. This effectively establishes probability theory as an inductive (inquiry & inference) logic.
AUTOGNOME: The AutoGnome is a self-knowing general purpose software system of automated (autonomous) inquiry, inference and intuition exploiting a mechanized carrier system for relational semiosis as a synthetic (virtual) mind.
BOUNDARY MATHEMATICS: Boundary Mathematics is a semiotic formalism generated by creating a distinction (a boundary) in non-existence (of system) thus resulting in a first system. Extended to multiboundaries with a common sense reiterative reduction rule leading either to one distinction or non-existence, this mathematical form and process is the germ of an approach to the formulation of a universal language of mathematics.
COGNOME: The CoGnome is a selected WebGnome which, inter-connecting two or more Intellisites in a Network of Intellisites, provides a computerized collective intelligence, an automated co-intelligence, i.e. the Collective-AutoGnome (Auto(Co)Gnome) or simply the CoGnome.
COGWEB: The CogWeb is the Network of Intellisites implemening the CoGnome for Network Decision-Making by autonomously formed Intellisite-defined groups, organizations, communities and societies, i.e. a WikiGnome.
INTELLISITE: The Intellisite (an Intelligent WebSite) is a constructed software environment (a Website) with an embedded form of the AutoGnome known as a WebGnome, an intelligent agent residing in this cyberspace environment which, with its continuous adaptive learning from mimicking the user’s behavior, will grow into a likeminded replica (MyWebGnome) of a user-self acting in the Virtual Reality of the Internet with the synthetic mind capabilities of the AutoGnome.
MAXIMUM ENTROPY (MAXENT) PRINCIPLE: MaxEnt is a technique for automatically acquiring probabilistic knowledge from incomplete information without making any unsubstantiated assumptions. Entropy is a mathematical measure of uncertainty or ignorance: greater entropy corresponds to greater ignorance. Hence, the MaxEnt solution is the least biased possible solution given whatever is experimentally known, but assuming nothing else.
MULTICORELATIONAL SYSTEMS (MCRS): A MCRS is a System of Relations exhaustively admitting all forms of interrelatedness among systems and/or relations.
MULTICORELATIONAL SEMIOTIC SYSTEMS (MCRSS): A Semiotic MCRS is a system of relations exhaustively admitting all forms of interrelatedness among systems and/or relations and with certain systems or relations (called signs) taking the place of (i.e. imaging (signifying)) other systems or relations to a specific mind.
ORDER/DISORDER/REORDER (ODORO) FORM: It is a tenet of MCRS that any semiotic act must, of necessity, express the Form of experience as the inseparable conjunction of:
  • Ordered (i.e. determined or certain) experience: a formal algebra/logic of semiosis
  • DisOrdered (indeterminate or uncertain) experience: a theory of probable inference/inquiry
  • ReOrdering DisOrdered experience: via a generalized probabilistic optimization principal
That is to say, experience is all at once partially ordered, partially chaotic and partially organizable.
PHANERON: The Phaneron is Peirce’s cognitive model containing anything that the mind requires to think, including experiential data and relational information, as well as processes or strategies to manipulate and/or retrieve information. All of these elements of the Phaneron exist within the triadic form that Peirce describes for creating a triadic recording of basic data and relational information.
PRAGMATIC ACTION METHODOLOGY: A Pragmatic Action Methodology is an inquiry process which, by analogy, applies the principles of the scientific method to all levels of abstraction in the inquiry including, in inseparable conjunction, the philosophical and formal through the theoretical to the technological and applied levels, by iteratively adapting the levels until the signified expectations are satisfactorily consistent with experience.
VIRTUALITY: Virtuality is an Autonomous Semiotic Universe (the Cyberverse) in which a sign (e.g. a piece of information) is transferable (communicatable) only among virtual minds resident in this Cyberverse and relatable to (Human) Reality only through the Virtual Reality of the Internet.


PREMISE: Given a ChaotiCosmos which we come to “know“ through Mind, it is evident that understanding mind, as oft-thought, should be the most satisfying as the first subject of inquiry among three of the great chaoticosmic mysteries—namely, the “origin”, nature and evolution of the ChaotiCosmos (the Universe and its Worldviews), the “origin”, nature and evolution of Life and the “origin”, nature and evolution of Mind(Consciousness). Since “understanding”, being a function of mind, can be enhanced by first understanding mind, it is inevitable that Evolution through Human Co-Creation should forge a Synthetic Mind (SynMind) from an experientially consistent well-formed Theory of Mind.
BACKGROUND: Recognizing that there is an accelerating growth in awareness of the limits of the Systemic (thing-based or mechanistic) Worldview, it is becoming ever more urgent for the sustainability of humanity to turn to a concomitant focus emphasizing the necessity of a Relational Worldview as the future. With this realization, however, there comes the need to foundationally re-examine the notion of “relation”.

A Person’s Experiences, ranging from common sense to the highly abstract, can all be fundamentally (without addressing uniqueness) recorded either as experience of Systems (objects, things, stuff, matter, etc.) or experience of Relations (connections, interactions, functions, transformations, etc.). Perhaps no contemporary author has explored and reassessed the treatment of the philosophical notion of Relation from the perspective of the Western Worldview more exhaustively and profoundly than has Gasché,1999. In moving from the ontological conception of relation as a thing of diminished being and yet holding to the conviction that relation is a being-towards-another, he has shown that the history of evolving thought of philosophers on the notion of relation has at least demonstrated that it is not constrained to exclusive subordination by the traditional ontological and formalist interpretations of relation as being-towards-another-thing, but allows the possibility of relation as being-towards-another-relation. “One of the most profound scientific recognitions of modern times is that the Universe no longer can be categorized only through objects, but rather must be seen as fundamentally relational. If the manifest Universe is relational, then it behooves us to understand how relations relate!” From Hamann and Rindge (1978).
Personal Experience is the Existence of Relational Systems.
By Presumption, this is the Essence of Existence (Nonexistence) Beyond the Personal.

FOUNDATIONS OF MULTICORELATIONAL SYSTEMS: [Multi=multiple; Co=interrelated] In formulating the notion of relations relating relations by adding specificity to the foregoing Experiential/Existential/Essential Foundations statement, the General Foundations Presumption of the existence of four relational forms has been introduced where logically, these four forms exhaust the number of possible categories of relational forms that can be obtained by combining Systems and Relations through Relations; hence, the origin of MultiCoRelationism (Hamann, n.d.) as a potentially (R)Evolutionary symbol-form for a Relational Worldview.
  • Based on the foregoing general presumptions and of the Specific Presumtions of the existence of an Inter (Actional) Relation (decision relation) among certain Systems or Relations, and with certain Systems or Relations being-as-other Systems or Relations (this being the notion of image or sign), and with certain Systems or Relations being-of-other Systems or Relations (this being the notion of subsumption or distinction), the foundation of a (R)Evolutionary Relational paradigm, MultiCoRelational Systems (MCRS), was promulgated.
  • The expression (communication) of the Experience Beyond the Personal rests in-and- on Signs (for Systems or Relations), signs being acknowledgeably both the Essence of Mind (recognizing the carrier role of the brain/body) and of Virtuality.
  • Not only are the processes of mind (i.e. what we can think and communicate) constrained by the languages (signs) we use (Northrop, 2002), language itself requires a different logic for inquiry vs. inference vs. intuition. This consideration is inherent in the applied multicorelational premise regarding synthesis of both language and mind.
  • As a MCRS derivative, the form of a theory of theory formation with an inherent FORM requiring co-existent Order, DisOrder and ReOrdering (ODORO) MutiCoRelations is being promulgated as a candidate upon which to formalize a Theory of Mind (AG/GnosTeks) and to engineer its technological instantiation as Synthetic Mind (the AutoGnome).

HISTORICAL RECORD OF THE “NOTION OF RELATION: The course of the cultural evolution of Western Experience (expressed in-and-about signs) as cumulative Human Knowledge has, by the very nature of existing recorded Western sign (image) systems (including “natural” languages and the constructed languages of mathemetics), actually “filtered” the Essence of Relation from signified Experience and, hence, prevented the Human Mind from discovering a form of sign appropriate for signifying Mind Itself. Historically, this record has been largely confined to a form in which relations were assumed to exist only between/among systems, Systems Related to other Systems. Between 1963-1968 (see Hamann 1978, n.d.), work was introduced in which relations were also taken to formally exist both as Relations between/among Systems and other Relations and as Relations between/among Relations and other Relations, i.e. MultiCoRelationalism was initiated

THE NOTIONS OF “RELATION” AND “WHOLE: An important requirement of a potentially transforming symbol-form such as MultiCoRelationalism for World Culture/Society is that it is adaptively a satisfactorily consistent experience as an inseparable conjunction (i.e. as a “whole”) of its philosophical, formal, technological and applied foci of attention. This makes clear that the next evolutionary stage is necessarily to consciously manifest Wholeness. (see Bortoft, 1996). The critical property of the whole is that of its presencing in every part. It is, everywhere, "whole" – not "built up" from its parts. It is this existence of the "the Whole as No-Thing", the essence of which is the Interrelation of Relations, which is a novel, unique derivative principle of MCRS, and is hypothesized to be conditionally necessary and sufficient for Creating Mind as a Whole (Field).

Since relations are not "things", this process of relating relations cannot be conceived of in "object" terms. However, we can begin to think about no-thingness (which is not nothingness!) when we discuss the nature of Fields. Fields also are no-things having the property of relating both things and events. Fields manifest the "wholeness" of things (objects, organizations, systems) and phenomena (processes, events, connections) [Field being is relation as being-towards-another-thing-or-relation; System and Relation are a Whole, each manifesting and manifest in the Other]. Hence, a Field is primarily a wholing interrelation of relations, quantifiable as "information/energy" or “value”, and which is a distinguishing essence of MultiCoRelational Systems theory.

A Relational Conjecture (Hamann and Bianchi, 1970) is here restated to form and substantiate the notion of image: it is conjectured that the origin of an image (or sign) system as a chaotic ordering (emergent) event in the evolution of manifest material systems is a necessary and (possibly) sufficient condition for the origin of Life (and thus Intelligence/Mind). From this beginning conjoined with the simplest fundamental relative of the Presumption of subsumption, i.e. the notion of distinction (Spencer-Brown, 1969; Shoup, 2008; Whitaker, n.d.) whereby there is formed a boundary which generates twoness, a mathematics of distinction has been created and grown into a general candidate for an approach to a universal language for formal systems, i.e. multiboundary mathematics. Inherent to this Boundary Mathematics is a Boundary Logic (from which Boolean Logic is derivable as a special case) which is leading to a more powerful computer design. (Bricken, 2004, 2007) Generally, taking a universal formal system as an axiom system with the property that any other consistent axiom system can be interpreted within it, the mathematics of distinction implies a mathematics of subsumption which, in turn, implies a membership theory as a first step towards a universal language for mathematics. (Etter, 2006) To turn this interrelation of systems form of “boundary mathematical relation” into an interrelation of systems or relations form of “formal field relation”, the notion of distinction must be re-cast in an interrelation of relations form of relation; this effort has been initiated in very simplistic manner as System of MutiCoRelational-graphs (MCR-graphs) (Hamann, 1978, n.d. - (Northrop, - as a pointer toward general MutiCoRelational-formalisms.

An approach to the synthesis of both language and mind is in development based loosely at this point in the process on the System of Boundary Mathematics. Although this is initially confined explicitly to the interrelation of systems form of “boundary mathematical relation”, it allows for interpretation as deriving from the Foundations notions of MCRS, specifically via MCR-graphs (or MCR-formalisms). A theoretical architecture has been posited regarding the formalization of an order (an instantiation of the mathematics of subsumption in terms of a degree of partial subsumption) and its derivative calculus, the latter taken as a formulation of the disorder experientially related to the given order, which also implies a reorder(ing) disorder format. Within a Nonseparable System of order/disorder/reorder Relations, this architecture suggests the Form of a meta-theory of theory formation. The Form, in turn, is being invoked in formulating Theories of Intelligence/Mind and Virtuality.

Assume, in a simple, but common instance of the foregoing, that ordered experience is formally signifiable as a Boolean Network (lattice, algebra, graph or diagram) composed of points (nodes, objects, states or Systems) and lines (edges, connections, transitions or Relations). Assume further that experience is not totally ordered and that the disorder is formally signifiable by extending the Boolean Network to the form of a Bayesian Network via a Coxian theory of the algebra of probable inference/inquiry. (Cox, 1946, 1961, 1979) And finally, assume that reordering disorder is formally signifiable via the Cox/Jaynes (Jaynes, 2003; Knuth, n.d.) form of maximum entropy (maxent) or its generalized probabilistic optimization principal. This approach to modeling both the Web (as a Virtual Reality) and Mind is warranted by the ‘natural’ Network-of-Images view of the Web and by the historical predominance of connectionist theories of Mind, and neural-network analyses of mental processes and states.

The resulting synthesis of the foregoing is an approach to MultiCoRelational Science of signs, including signification and communication, i.e. a Theory of MCR Semiotic Systems. This is the necessary basis upon which is built a Theory of Mind and of Virtuality with technologically engineered applications as Synthetic Intelligence(s)/Synthetic Mind and Virtual Reality. (Hamann, 2007)

Within the Foundations Purpose of the ChaotiCosmos Institute/University/Campus [] of introducing the historically missing Formalization of MultiCoRelational Forms into the Sign/Communication (Semiotic) Systems of Humanity and the related Mission of “MINDing the World through Synthetic Intelligence/Mind Technology” is the overarching long term Strategy of Re-Creating A Virtual Universe as a MultiCoRelational WHOLE. This begins with the creation of Synthetic Intelligences enroute to a Synthetic Mind based on a Formal Theory of MultiCoRelational Semiotic Systems. This encompasses MCR-formalisms of semiosis and theory of probabilistic decision making including a generalized probabilistic optimization principal, all functioning on a TriCoRelational “record” (memory structure).
The intent is to develop the Synthetic Mind Technologies and efforts needed to move from the current (2010) State of Humanity to the Singularity; that is, to the point of realization of the technological creation of an on-the-average smarter-than-human synthetic intelligence. The methodology invoked envisions an Open Participation Institute/University/Campus (from Latin, campus means “field”) for Fundamental SynMind Research and Development with periodic Proprietary Commercial Rollouts of Limited SynIntelligence Applications as they appear responsive to an applied need or offer an advance in the extant technology.

AG/GnosTeks {AutoGnomic (AG)=Self-Knowing / GnosTeks (G)=KnowledgeTechnology} is formed by constraining the AutoGnomic Experiential Specification (of Pendergraft, 1997) to the GnosTek Formal Foundations (of Hamann, n.d.) [specifically focusing on the Optimum Systemic/subSystemic Probabilistic Decision System] functioning on a TriCoRelational Memory (developed as the Triadic Continuum Computer Data Recording Structure (Relational Space or R-Space) and all subsuming the Phaneron (cognitive model) of Peirce.

Peirce, although attuned to the notion of relation as being-towards-another-relation,
seemingly did not capture the possibility of the four forms of the notion of relation.
Peirce, Virtuality, and Semiotic
The concept of virtuality is deeply embedded in Peirce's doctrine of signs and hence in his semiotic doctrine of mind. In this Peircean doctrine, which has been more recently echoed in the writings of Wittgenstein and Popper, we find the most promising philosophical framework available for the understanding and advancement of the project of augmenting human intellect through the development and use of virtual technologies.” (Skagestad, n.d.). Inspired by the work of Charles Sanders Peirce and his successor, Charles Morris, Gene Pendergraft (Pendergraft, 1993, 1997) -550 pg. dbl. spaced spec, proposed the architecture of a special kind of system, called the AutoGnome, which would be able to perform mechanized (automated) inference using principles derived from semiotics. A venture for the implementation of such an architecture in software code was begun and has resulted in the building of a first release of an AutoGnome.

The AutoGnome is a self-knowing general purpose software system for automated (autonomous) inquiry, inference and intuition exploiting a mechanized (computerized) carrier system for relational semiosis, that is, a virtual (synthetic) mind. A Semiotic Relational System is a system of relations in which certain relational forms (called signs, e.g. natural language, mathematics or art) take the place of (i.e. they “image or signify”) other relational systems (objects) to yet a third relational form called the interpretant. Simplistically, a theory of Mind must account for both structure and process while recognizing that each is partially determined by the other. Roughly, the AutoGnomic structure (memory system) is a dynamic sign storage system (the R-Space) which partially determines the form of the AutoGnomic processes (relational order/calculi/logics) as a three-level semiotic hierarchy on which interactions of induction, deduction and abduction manifest functionally as intuition, inquiry and inference. Communicatively this is experienced in common parlance as Intelligence [perceptual processes focused on syntactic (linguistic structuring) functions], Knowledge [conceptual processes focused on semantic (meaning) functions] and Wisdom [valuational processes focused on pragmatic (action selection) functions].

As the memory system of the AutoGnome, the R-Space represents a radically new semiotic paradigm for data storage and analysis which, unlike a traditional relational database, does not store “data” as data in pre-defined tables, arrays or files, but stores only the relationships between the data elements (relations of relations). This removes the need to precondition data, eliminating custom building of database schemas and cubes and thus significantly reducing the computer memory requirement and the timeline for transforming “data” to “information” and then to Intelligence, Knowledge and Wisdom. As a stand-alone system outside of the memory structure of a synthetic mind, R-Space is a novel, unique, highly efficient, embedded enabling data storage technology.

Consistent with the early identifiable functions of the infant human mind, that being “distinction” (recognizing differences (or similarities) among relational systems and grouping them by way of their degree of difference (similarity), the first version of the AutoGnome (AutoGnome1 or AG1) is a thin client computer (program) providing a user access to a server-based (i.e. in cyberspace) software system performing as an autonomous categorizer [i.e. an autonomous recognizer of distinctions (or similarities) and aggregator (grouping) of them in terms of a measure of their degree of difference (or similarity)], i.e. a semi-independent, virtual (in cyberspace – on server) partial, rudimentary clone of the intelligence of the user.

As a first instantiation of this AutoGnome1, the IntelliSite (an Intelligized Website) generically branded as TrueThinker (, is a constructed software environment (a Website) with an embedded form of the AutoGnome known as a WebGnome, an intelligent agent residing in this cyberspace environment which, with its continuous adaptive learning from mimicking the user’s behavior, will grow into a likeminded replica (MyGnome) of a user-self acting in the Virtual Reality of the Internet with capabilities initially including knowledge organization (learning), knowledge creation (thinking) and knowledge applications (acting). (Hamann, 2008)

The Intellisite obviously has a broad spectrum of applicability apart from its key functionality as an individual's mirrored Intelligence/Knowledge, including a Collective-AutoGnome (CoGnome) and the CogWeb (cognitive network of Intellisites). As a specific example, a first generative instantiation of the AutoGnome implied by its MCRS foundations is a form as a general [meta order(ing)] theory of theory formation, i.e. an Autonomous Scientific Intelligence (AScI) which promises to automate the scientific method. (Knuth, 2003)
In the context of the AutoGnomic approach to Synthetic Mind, the following stages might be projected to emerge in characterizing the Web:
Web 1.0 – Syntactic Web (Perceptual; Intelligence) Web 2.0 – Syntactic-based Social Web
Web 3.0 – Semantic Web (Cognitive; Knowledge) Web 4.0 – Semantic-based Social Web
Web 5.0 – Pragmatic Web (Valuational; Wisdom) Web 6.0 – Pragmatic-based Social Web
Web 7.0– AutoGnomic (Semiotic) Web; a Semiotic Web holistically incorporates the Syntactic, Semantic and Pragmatic functionalities as well as including each Social Web.

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