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ThinkArt Lab Animation: A.T. Kelemen© November 12, 1998 Dr. Rudolf Kaehr
"No, I'm not watching cartoons! It's cultural anthropology."
"This isn't smut, it's art."
"It's not a bald spot, it's a solar panel for a sex-machine."
Reasonable people can disagree forever on how to describe something. Arguably, your Self is the collection of associations and descriptors you ascribe to ideas. Requiring everyone to use the same vocabulary to describe their material denudes the cognitive landscape, enforces homogeneity in ideas.
And that's just not right.
Metacrap: Putting the torch to seven straw-men of the meta-utopia
Cory Doctorow
http://ontology.buffalo.edu/
1 Life as Polycontexturality
By showing how Becoming has a component of Being as well as Nihility, he (Hegel) unwittingly laid ground to a theory of "poly-contexturality". Because, if we want to establish such a theory, we should not assume that all contexturalities can be linked together in the way a geographical map shows one country bordering on the next in a two-dimensional order. If the contexturality of Becoming overlaps, so to speak, the contexture of Being as well as of Nothingness, and the contexture of Becoming in its turn may be overlapped by a fourth contexture which extends beyond the confines of the first three, we will obtain a multi-levelled structure of extreme logical complexity.
Table I
Hegel´s logic further shows that if a plurality of contextures is introduced one cannot stop with three. In fact, one has to postulate a potential infinity of them. If one believes Hegel and there are most convincing arguments that one should - then each world datum in the contexturality of Being should be considered an intersection of an unlimited number of contextures. Table II with its seeming chaos of straight lines crossing each other at all possible angles may illustrate what is meant. Each contexture is logically finite insofar as its structure is confined to two values. But their respective ranges are infinite because one can generate, within the respective domain, a potential infinity of natural numbers. We have indicated the logical finiteness of the different contextures by having them represented by lines no longer than 2 inches.
The concept of contexturality illustrates the age-old logical distinction between identity and sameness. If I count 1, 2, 3, 4, º and so does my neighbor, then the numbers we both count are the same. However, insofar as these numbers have their existence only in the counting process, they are not identical because the two counting procedures can be clearly distinguished as having different origins in two separate organic systems. In other words: in the situation described above the sequence 1, 2, 3, 4, º turns up in two separate contextures. And no matter how far I count there is no number high enough to permit me to cross over to the psychic space of my neighbor.
Gunther, Life as Polycontexturality
This essay presents some thoughts on an ontology of cybernetics. There is a very simple translation of the term "ontology". It is the theory of What There Is (Quine). But if this is the case, one rightly expects the discipline to represent a set of statements about "everything". This is just another way of saying that ontology provides us with such general and basic concepts that all aspects of Being or Reality are covered. Consequently all scientific disciplines find their guiding principles and operational maxims grounded in ontology and legitimized by it. Ontology decides whether our logical systems are empty plays with symbols or formal descriptions of what "really" is.
The following investigation arrives at the result that our present (classic) ontology does not cover "everything". It excludes certain phenomena of Being from scientific investigation declaring them to be of irrational or metaphysical nature. The ontologic situation of cybernetics, however, is characterized by the fact that the very aspect of Being that the ontologic tradition excludes from scientific treatment is the thematic core and center of this new discipline. Since it is impossible to deny the existence of novel methods and positive results produced by cybernetic research, we have no choice but to develop a new system of ontology together with a corresponding theory of logic The logical methods that are used faute de mieux in cybernetics belong to the old ontological tradition and are not powerful enough to analyze the fresh aspects of Reality that are beginning to emerge from a theory of automata.
1.1 System Architecture in XML
"Also obvious is that by the default the communication between observers can only be of informal nature. Consistent logical systems are only defined within a given context and, in general, cannot be used for knowledge transfer between different ontologies. The consequence is that some means of informal communication, such as natural language or heuristic mediation systems, is inevitable." Daum, 185
Inevitable only from the point of view of the local logical systems, but not under consideration of the more global logical operations of transjunction, which are exactly introduced for the purpose of trans-contextural interactions. Polycontexturality in the sense of Gunther, which is quite different from followers like Niklas Luhmann, is not only a "combined system of multiple ontologies (polycontexturality) with a multileveled logic calculus" as Daum recognized well, but also a complex system of interactivity between different contextures ruled by trans-contextural operations. These transjunctional and trans-contextural operators are operators in a exact formal sense, not only defined logically inside a contexture but also between contextures. The concept and formal definition of transjunctions had been introduced by Gunther in his famous paper Cybernetic Ontology and Transjunctional Operations (1962) even before he radicalized his position to a transition from multiple-valued ontologies to poly-contexturality. A more general approach of interactivity between contextures was introduced by Gunther in "Natürliche Zahl und Dialektik" (1972) but this concept goes back at least to the concept of an inter-ontology as considered in "Natural numbers in Trans-Classic Systems" (1970), "The philosophical theory on which cybernetics may rest in the future may well be called an inter-ontology." Following Gunther´s work I developed a complex philosophical and mathematical theory of interactivity in the framework of polycontexturality, developing and using notions like proemiality, chiasms, diamond strategies and co-algebras (SKIZZE-0.9.5).
We shouldn't forget to distinguish between different switches of contextures and bifurcational transitions of trans-contextural operations. Bifurcations, Replications, Merging
1.2 Heuristic mediation of contextural switches
Also the introduction of trans-contextural operations is formal and operative, this interactions are not mechanical and predictable, but possible. Each decision a system takes to change contextures or to split into different contextures is spontaneous and creative. But this creativity is not based on chaotic "Willkür" it is not ruled but rule-guided by the trans-contextural operators. If we speak about the speechless of the counting process of natural numbers, the change from one contexture to another contexture of distributed natural numbers has to be commented, it is open to negotiation and interpretation, therefore we can speak not only about but of numbers. This way of speaking about trans-contextural changes, in other words of creativity, is not the free flouting way of speaking reclaiming deep insights about negativity and irrationality as opposed to mechanical rule-systems, but a new interweaving and interlocking process of speaking, conceptual writing and formal notations.
Rational decision-making of creative systems is in itself a polycontextural procedure, it is an interlocking mechanism of cognition and volition, a double gesture and not reducible to ultimate meta- or proto-systems.
2 Heideggers radical deconstruction of ontology
2.1 self-modifying media
Gunther´s chain of notions deliberating thinking from ontology:
2.2 Freezing and melting ontologies
Ontology based web semantics, Semantic Web, is in danger to freeze the processuality of the development of the internet.
Classical ontology, with pluralities in score and upper dimensions are not prepared for self-referential processes: the arrival of Web semantics in the internet is changing the internet in introducing itself. It is a self-modifying media.
Heidegger, Whitehead, Gunther on self-modifying media processuality.
Web semantics as based on ontologies is accepting classical logic as an ultimate system of rational reasoning. But logic itself is based on ontology, maybe analytic philosophy has forgotten this. Ask Quine.
Conflicts between flexibility, navigation and normation.
2.3 Ontology and logics of multi-media
2.4 Morphogrammatics of XML
3 Ontologies in different fashions
3.1 many-sorted logics
3.2 fibred category systems
3.3 polycontexturality
4 Revival of classic ontology in Web Semantics?
The four systems concerned by this project provide this structure in very different ways and with different conceptual 'textures'. For example, the AGROVOC and ASFA thesauri put "aquaculture" in the context of different thesaurus hierarchies: according to AGROVOC the terms more specific than "aquaculture" are "fish culture" and "frog culture", whereas in ASFA they are "brackishwater aquaculture", "freshwater aquaculture", "marine aquaculture". Two different contexts relating respectively to species and environment point of view.
With such different interpretations of a term, we can reasonably expect different search and indexing results. Nevertheless, our approach to information integration and ontology building is not that of creating a homogeneous system in the sense of a reduced freedom of interpretation, but in the sense of navigating alternative interpretations, querying alternative systems, and conceiving alternative contexts of use.
To do this, we require a comprehensive set of ontologies that are designed in a way that admits the existence of many possible pathways among concepts under a common conceptual framework. This framework should reuse domain-independent components, be flexible enough, and be focused on the main reasoning schemas for the domain at hand. Domain-independent, upper ontologies characterise all the general notions needed to talk about economics, biological species, fish production techniques; for example: parts, agents, attribute, aggregates, activities, plans, devices, species, regions of space or time, etc. On the other hand, the so-called core ontologies characterise the main conceptual habits (schemas) that fishery people actually use, namely that certain plans govern certain activities involving certain devices applied to the capturing or production of a certain fish species in certain areas of water regions, etc.
Upper and core ontologies provide the framework to integrate in a meaningful and intersubjective way different views on the same domain, such as those represented by the queries that can be done to an information system.
http://www.loa-cnr.it/Publications.html
http://www.ifomis.uni-leipzig.de/People/People.html
http://ontoweb.aifb.uni-karlsruhe.de/
http://www.websemanticsjournal.org/
Ontology Groups
http://www.cs.utexas.edu/users/mfkb/related.html
"To do this, we require a comprehensive set of ontologies that are designed in a way that admits the existence of many possible pathways among concepts under a common conceptual framework."
Why should the common "conceptual framework" be thought in a hierarchical way? There are two possible ways of dealing with the task of finding an "upper ontology" which is "domain-independent" and so on. One is the classical way of hierarchy, as well established and studied and transformed to new applications like the search for a semantics of the Web. The other possibility which is able to cover all mentioned attributes of the "upper ontology" is offered by the strategy of heterarchy and proemiality. Heterarchy is neither hierarchy nor anarchy.
The classical approach seems to guarantee a good flexibility on the core base, the regional ontologies, by stabilizing its concepts on the upper level of the "common conceptual framework" which includes basic ontological and logical terms like "parts, agents, attribute, aggregates, activities, plans, devices, species, regions of space or time, etc." but the game doesn't stop here. What are "parts" from one vantage point are "wholes" from another, "agents" can be understood as "attributes", "activities" as "plans", etc.
"Nevertheless, our approach to information integration and ontology building is not that of creating a homogeneous system in the sense of a reduced freedom of interpretation, but in the sense of navigating alternative interpretations, querying alternative systems, and conceiving alternative contexts of use."
What is the range of navigation? To navigate between alternative interpretations sound quite polycontextural. But where are the limits, if not in the supposed basic logic and how does the navigation work? What are the rules of navigation? Are they ontological or logical or spontaneous?
Different ontologies, if not anyway based on a common upper ontology and common first-order logic, have, even if they are incomparably different, irreducible to a common ground, one thing in common, they have, each for itself, a position. They take a position, occupy a position, a locus, where?, in some very general sense, in the world. This does not mean that they have in common a general concept of the world. This would be released by a general ontology and logic. But even general ontology and logic are taking place, are placing themselves in the world. It also does not mean that they share in abstracto a common empty locus. Each ontology is based on its own locus. And also the loci are empty they are not the same.
These loci have no attributes, no predicates, no relations, no processualities etc. nevertheless they exist, in a non onto-logical sense, but give place for ontology and logic, and ontologies and logics. There is also not a single primordial place, like nothingness or ultimate emptiness, there is multitude of empty places, differentiated between the same and not the same, in a non-logical sense.
These monsters of negative conceptuality are inscribed as kenograms (kenos, gr. empty). The grid of kenograms is the non-basic base of the distribution and mediation, the interactivity and navigationality of different ontologies.
The conflicting restless of interactivity between different ontology can come to a rest in a common upper ontology based on negotiation and agreement. But this upper ontology turns out to be a lifeless abstraction. Another result of negotiation could be a mediation between different ontologies which accepts the differences between the ontologies but is able to find intermediating rules of interactivity. Only in well established and simple situation we can discover a translation from one ontology to an other ontology conserving their ontological categories, like sorts to sorts, operations to operations, and so on.
This happened recently in the funny conflict of taxonomic notions and cultures between Scotland and the EU. Kilts are skirts, skirts are connected to female, male is connected to trousers, therefore Kilts are female clothes. What to do? Introduce exceptions. In a few turns the ontology consists of thousands of exceptions and some simple general classificatory rules will be left. The other necessary strategy is to ban the object. Therefore nearly all sorts of Camembert cheese have to disappear. This madness happens automatically if we take distinctions like male/female and skirts/trouser as substantial and not as functional and depending on contexts. And how could the european taxonomy run together with one of the many asian taxonomies? Taxonomy and ontology without ethnology is behind globalization movements.
Is this not exactly the situation of XML? XML tries to be a general language not subsuming the thousands real world languages of the Internet but enabling and supporting this diversity.
This interdisciplinary journal focuses on research at the intersection of three major research areas: semantic web, agent technology and grid computing. We call this interdisciplinary field Web semantics. Web semantics investigates and develops the standards, ontology's, protocols and technology that contribute to the development of a knowledge-intensive and intelligent service Web. This is often referred to as the second generation of the Web.
Background
The data in computers exists in a bewildering variety of mutually incompatible forms and ever more intense efforts are needed to smooth the process of data integration. The most important such efforts lie in database standardization achieved through the construction of benchmark taxonomies into which all the classification systems pertinent to a given domain would need to be translated only once. Benchmark taxonomies can ensure that all databases calibrated in their terms would be automatically compatible with each other.
`Ontology' is the name given by information scientists to the construction of such benchmark taxonomies. This name was chosen in reflection of the fact that in building such taxonomies one is confronted by issues with which philosophical ontologists have grappled since Aristotle's day, issues which have once again moved into the center of contemporary philosophy under the heading `analytic metaphysics.'
Information systems ontology has implications beyond the domain of data integration. Its methods are used for purposes of information retrieval and extraction from large corporations and libraries (for example of medical or scientific literature). These methods are currently being applied to the problems of navigation on the Internet in work on the so-called Semantic Web. They are used as a basis for work on natural language processing and automatic translation, in enterprise integration, and, most significantly, as a means of integrating the results of inquiries in neighboring scientific fields - for example when inquiries in computational chemistry or structural biology need to be cross-calibrated with the results of inquiries at higher (for example medical or epidemiological) levels of granularity, as for example in the work of the Gene Ontology Consortium .
http://ontology.buffalo.edu/proto-ifo/
1 Urelements and Sets
One of the basic distinctions of GOL is the distinction between urelements and sets. We assume the existence of both urelements and sets in the world and presuppose that both the impure sets and the pure sets constructed over the urelements belong to the world. This implies, in particular, that the world is closed under all set-theoretical constructions. Urelements are entities which are not sets. They form an ultimative layer of entities without any set-theoretical structure in their build-up. Neither the membership relation nor the subset relation can unfold the internal structure of urelements.
In GOL, urelements are classified into two main categories: individuals and universals. There is no urelement being both an individual and a universal.
"We assume the existence of both urelements and sets in the world" in doing this, do "we" belong to this world or not?
"This implies, in particular, that the world is closed under all set-theoretical constructions." Maybe we can live with that. But didn´t we not just learned that, to develop a non-onto-theo-logical ontology, we should questioning the very presuposition of classical ontology, namely its presuposed "world". Today, it is not nonsensical to ask "Which world do you mean?" There is surely one world which is build up of urelements, but what´s about the other worlds? And what´s between these worlds? And what happens if we cannot resist to clone this very concept of Ur-Elements, too?
"Ur-Elements", are they not Kant´s Ding an sich-type monsters?
What is your Urelement is my "chronoid", why not?
In the world of Ur-Elements there is no lifeliness and metamorphosis. All changes in this world concept are based on Ur-Elements, which are stable and eternal.
2 Formal Ontology and First Order Logic, revisted
The new, post-analytic movements towards a reformulation of ontology goes back to Brentano, Meinong and some Husserl and is restoring a lost discussion about the relationship between ontology and logics which went lost during the success of formal logic and later by the dominance of computer science paradigms. This discussion is extensively documented in the German literature of the 50th.
Gotthard Gunther, again, was a lonely voice, in America and Germany, to empathize the importance of the connection between ontology and formal logic after the early discussion disappeared from the academia. But in contrast to the new neo-Aristotelian movement, Gunther was able to connect his work to another, still not recognized movement of ontology, the transcendental ontology of Husserl, called phenomenology and the deconstructive efforts to surpass the limits of classical ontology by Martin Heidegger, as a radical non-Aristotelian ontology, called polycontextural theory going hand in hand with an equal non-Aristotelian logic. Not surprisingly Gunthers work was intrinsically connected with attempts to formalize Hegels dialectics and to develop a "Cybernetic Theory of Living Systems" at the BCL.
His ontology is therefore not "conservative" and "descriptive" but "constructive" and "revolutionary" concerning not so much about what just is, as given or even natural, but what has to be done, the artificial, and what is primordially interwoven with time, the ontology of living tissues, natural and artificial, and beyond.
The present paper outlines a formalisation of elementary formal ontology. In contradistinction to a material ontology, formal ontology is concerned, not with the specification of the constituents (individuals, properties and relations) in a particular domain or region of the world, but with the axiomatisation of the most general, pervading categories that partition and shape reality as a whole.
As Barry Smith has pointed out, the use of the qualifier "formal" is liable to give rise to a fundamental misunderstanding: formal ontology is not merely the application of formal-logical methods to the study of metaphysics.
Rather, the very success of mathematical logic has led to a "running together of the formal and formal logical", and ultimately to a confusion of ontology with logic and with the study of the structure and semantics of artificial languages, at least as far as much philosophy in the analytic tradition is concerned.
Only fairly recently, in an influential collection of studies in the philosophy of Brentano, Husserl and their followers was there triggered a revival of a scientific metaphysics in the Aristotelian tradition that is not a mere appendix to predicate logic and set theory.
Indeed, the formal/material distinction has a wider range than just the specialist area of mathematical logic; it reflects the general opposition between form and matter in the realm of things as well as in the realm of truths. Just as formal logic studies the abstract relations between propositions, so formal ontology is concerned with the formal relations between entities.
Formal-ontological constants are like formal-logical ones insofar as their meaning can be characterised purely in terms of operations and transformation 2 rules. Formal relations (such as parthood, dependence, but also identity and instantiation) are not mediated by ties (accidents, moments) of any sort, in contrast to material relations (such as "being a parent of", "being the moon of", and so on), but hold directly of their relata. Formal properties and relations can therefore be instantiated by objects in all material domains or spheres of being.
That is why formal ontology as the study of formal categories can justifiably be claimed to be the most general possible theory about the world.
Thus it should not come as a surprise that formal ontology is realist rather than conceptualist, inasmuch as it is an inquiry into the general features, the real aspects of the denizens of the world out there, and not into the basic characteristics of the conceptual framework which we happen to be equipped with as members of the human species or a particular ethnic group.
Formal ontology is conservative or "descriptive" instead of revolutionary or "revisionary", insofar it takes - salva consistentia - our everyday ways of speaking about the world at face value as the most detailed and corroborated description of reality available, but proceeds to theoretical revisions of so-called commonsense if required for the sake of coherence and, above all, scientific adequacy. p. 2-3
Formalised Elementary Formal Ontology, p. 2-3
ISIB-CNR Internal Report 3/2002
3 Contributions to the Axiomatic Foundation of Upper-Level Ontologies
An ontological signature ? is determined by a set S of symbols used to denote sets (in particular extensional relations), by a set U of symbols used to denote universals, and by a set K of symbols used to denote individuals. An ontological signature is summarized by a tuple ? = (S ,U;K).
KIF adopts a version of the Neumann-Bernays-Gödel set theory, GOL assumes ZF set theory.
The development of an axiomatized and well-established upper-level ontology is an important step towards a foundation for the science of Formal Ontology in Information Systems. Every domain-specic ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. For this purpose it is important to understand what an upper-level category means, and we proposed some conditions that every upper- level ontology should satisfy. The development of a well-founded upper-level ontology is a difficult task that requires a cooperative effort to make signicant progress.
4 System-Level Design Languages:
4.1 Distribution of hierarchical ontologies on heterarchies
4.1.1 UML diagrams of UML diagrams
Heterarchization of the hierarchy ontology UML diagram in respect to the heterarchy UML diagram.
4.1.2 Disseminated formalisms
The same procedure can be applied to the heterarchization of the formal hierarchical ontologies. There whole formalism has to be distributed, including the specific ontological and the general logical definitions.
Dissemination of the kernel of GOL
Interactivity, metamorphosis and simultaneity of different GOLs
4.1.3 Towards poly-GOL
Metamorphic GOL; Proemiality of algebraic and co-algebraic GOL
4.1.4 Gunther´s Hierarchy of First Order Ontologies
Gunther is developing his First Order Ontologies (FOO) an the basis of the distinction between logic and ontology using two further distinctions "affirmation/negation" and "designation/non-designation" in many-valued logical systems.
"We shall define an ontology as a structural system in which the distinction between designating and non-designating values is inapplicable, and witch is determined by nothing else but the number of values available. In an ontology all values designate. However, if values permit a division between designation and non-designation, the system in question may be considered a logic.", Gunther 1968, p. 37/p.149
By a first order ontology he understands a "theory of Being (ontos on) in contrast to the plurality of second order ontologies referring to the plurality of classes of existing objects." These second order ontologies are referred in philosophy as regional ontology (Regionalontologie), in contrast to fundamental ontology or simply ontology.
This many-valued ontology allows the additional distinctions of mono-, dia- and polythematic ontologies and reflectional mappings, with and without repetitive redundancy, of the ontologies in the logical systems.
"No self-reference is possible unless a system acquires a certain degree of freedom. But any system is only free insofar as it is capable of interpreting its environment and choose for the regulation of its own behavior between different interpretations." p. 44/p.156
As we can see, the term "self-reference" is not understood as in the tradition of the famous Circulus Creativus of Heinz von Foerster, both at the BCL, or the re-entry figure of George Spencer Brown, but in the tradition of complex transcendental logics as introduced by Kant, Hegel, Schelling and further developed also by the Soviet cyberticians (Levebvre). On the other hand, the second order circular interpretation of self-reference is not excluded, it is a quite special case of the complex reflectional mapping process of a living system reduced to a cognitive system.
Gunthers approach to self-referentiality in the framework of polycontexturality involves simultaneously cognitive and volitive procedures. It is not enough to make the statement "Living systems are cognitive systems, and living as a process is a process of cognition." Maturana, p.13, 1970. Excactly, because we learn nowhere anything in the texts of Second Order Cybernetics about the ontology and the logics of the "as"-operator of this statement concerning with system and process, living and cognition. As far it is an interesting, and at its time, a provocative statement, but it is still "magic". Why not?
"However, there is a fundamental distinction between the idea of a self-referential universe as it was conceived in a former mythical philosophy of nature, as, for example, in Fechner´s "Weltseele", or, if we want to go back to the most ancient Scriptures of mankind, as in the saying of the Chhandogya Upanishad "Self is all this", and the idea of self-referentiality as we conceive it here. In the mystical philosophy of nature it was assumed that the universe was self-referential as a whole-because no distinction was made between auto-referentiality and self-referentiality. This led, if a living system was considered to be a (complete or incomplete) structural replica of the Universe, automatically to the holistic interpretation of an organism. In contra-distinction to this tradition we maintain, however, that, althoug the universe as a whole may be considered to be auto-referential, it can have the property of self-reference only in preferred ontological locations of suitably high complexity structure." Gunther, Natural Numbers, p. 32/33; p. 250/251
The Internet is not given, its elements are not entities; the Internet has to be read and its elements have to be interpreted. Interpretation involves freedom to chose a thematization, a perspective of cognition, it involves not only an observer but hermeneutical procedures. Otherwise we understand by the Internet a system of being to be studied and classified by means of ontology in the very sense, also modernized and formalized, by the Aristotle-Leibniz tradition.
The project Semantic Web is a challenge for a formalized and operative hermeneutics. Set-theoretical and mereological ontology is mapping only an extremely static and one-sided hierarchical aspect of the "living" tissue of the Web.
A multitude of interacting hierarchies is a question of cognition and volition interpreting the textures of the Web.
Translations from one language to another are not based on a common natural ur-language, but on the co-creative interplay between different languages, natural or artificial.
Ontology in the sense of GOL is "subjectless". It is a theory of being excluding self-referentiality by definition. Therefore it is a monolitical theory of what is, of objectivity without any freedom of interpretability. Again, this is very useful for subjectless domains, but useless, if not dangerous, in all sense of the word, for worlds including subjects. Today it seems to be quite tricky to find such a subjectless world. Especially if we are forced to ask who is producing this ontology of a subjectless world and even our robot are asking for more "subjectivity". Ontology as "the most general possible theory about the world" is fundamentally incomplete. To insist on a realist point of view to build a general ontology in contrast to a conceptualist understanding of ontology allowing some interpretability of the world is a decision which can not be justified easily using scientific and philosophical arguments. At least this decision is not part of the "new" formal ontology.
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