Categorical ontology of complex systems--论文代写范文精选

思想的理论水平接近多元化观点,把新的认知科学的语义模型进行阐述。预期系统和复杂的因果关系在现实的高层上，讨论了心理学、社会学和生态学。下面essay代写范文进行讲述。

Abstract
Relational structures of organisms and the human mind are naturally represented in terms of novel variable topology concepts, non-Abelian categories and Higher Dimensional Algebra– relatively new concepts that would be defined in this tutorial paper. A unifying theme of local-to-global approaches to organismic development, evolution and human consciousness leads to novel patterns of relations that emerge in super- and ultra- complex systems in terms of compositions of local procedures [1]. The claim is defended in this paper that human consciousness is unique and should be viewed as an ultra-complex, global process of processes, at a meta-level not sub–summed by, but compatible with, human brain dynamics [2]-[5]. 

The emergence of consciousness and its existence are considered to be dependent upon an extremely complex structural and functional unit with an asymmetric network topology and connectivities–the human brain. However, the appearance of human consciousness is shown to be critically dependent upon societal co-evolution, elaborate language-symbolic communication and ‘virtual’, higher dimensional, non–commutative processes involving separate space and time perceptions. Theories of the mind are approached from the theory of levels and ultra-complexity viewpoints that throw new light on previous semantic models in cognitive science. Anticipatory systems and complex causality at the top levels of reality are discussed in the context of psychology, sociology and ecology. A paradigm shift towards noncommutative, or more generally, non-Abelian theories of highly complex dynamics [6] is suggested to unfold now in physics, mathematics, life and cognitive sciences, thus leading to the realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and  interactomics. The presence of strange attractors in modern society dynamics gives rise to very serious concerns for the future of mankind and the continued persistence of a multi-stable Biosphere.

Introduction 
Ontology has acquired over time several meanings, and it has also been approached in many different ways, however these are all connected to the concepts of an ‘objective existence’ and categories of items. We shall consider here the noun existence as a basic concept which cannot be defined in either simple or atomic terms, with the latter in the sense of Wittgenstein. Furthermore, generating meaningful classifications of items that belong to the objective reality is a major task of ontology. Without any doubt, however, the most interesting question by far is how human consciousness emerged subsequent only to the emergence of H. sapiens, his speech-syntactic language and an appropriately organized primitive society of humans. 

No doubt, the details of this highly complex process have been the subject of intense controversies over the last several centuries, which will continue as long as essential data remains either scarce or unattainable. The authors aim at a concise presentation of novel methodologies for studying the difficult, as well as the controversial, ontological problem of Space and Time at different levels of objective reality defined here as Complex, Super–Complex and Ultra–Complex Dynamic Systems. These are biological organisms, societies, and more generally, systems that are not recursively– computable. Rigorous definitions of the logical and mathematical concepts employed here, as well as a step-by-step construction of our conceptual framework, were provided in a recent series of publications on categorical ontology of levels and complex systems dynamics (Baianu et al, 2007 a–c; Brown et al, 2007). 

The continuation of the very existence of human society may now depend on an improved understanding of highly complex systems and the mind, and how the global human society interacts with the rest of the biosphere and its natural environment. It is most likely that such tools that we shall suggest here might have value not only to the sciences of complexity and ontology but, more generally also, to all philosophers seriously interested in keeping on the rigorous side of the fence in their arguments. Following Kant’s critique of ‘pure’ reason and Wittgenstein’ s critique of language misuse in philosophy, one needs also to critically examine the possibility of using general and universal, mathematical language and tools in formal approaches to ontology. Throughout this essay we shall use the attribute ‘categorial’ only for philosophical and linguistic arguments. On the other hand, we shall utilize the rigorous term ‘categorical’ only in conjunction with applications of concepts and results from the more restrictive, but still general, mathematical Theory of Categories, Functors and Natural Transformations (TC-FNT). According to SPE (2006): “Category theory ... is a general mathematical theory of structures and of systems of structures.

The Theory of Levels in Categorial and Categorical Ontology 
This section outlines our novel methodology and approach to the ontological theory of levels, which is then applied in subsequent sections in a manner consistent with our recently published developments (Baianu et al 2007a,b,c; Brown et al 2007), and also with the papers by Poli (2008) and Baianu and Poli (2008), in this volume. Here, we are in harmony with the theme and approach of the ontological theory of levels of reality (Poli, 1998, 2001, 2008) by considering both philosophical–categorial aspects such as Kant’s relational and modal categories, as well as categorical–mathematical tools and models of complex systems in terms of a dynamic, evolutionary viewpoint. We are then presenting a categorical ontology of highly complex systems, discussing the modalities and possible operational logics of living organisms, in general. Then, we consider briefly those integrated functions of the human brain that support the ultra-complex human mind and its important roles in societies. 

Mores specifically, we propose to combine a critical analysis of language with precisely defined, abstract categorical concepts from Algebraic Topology (Brown et al 2007a) and the general-mathematical Theory of Categories, Functors and Natural Transformations (Eilenberg and Mac Lane 1943, 1945; Mitchell, 1968; Popescu, 1973; Mac Lane and Moerdijk, 1992; Mac Lane 2000) into a categorical framework which is suitable for further ontological development, especially in the relational rather than modal ontology of complex spacetime structures. Basic concepts of Categorical Ontology are presented in this section, whereas formal definitions are relegated to one of our recent, detailed reports (Brown, Glazebrook and Baianu, 2007). On the one hand, philosophical categories according to Kant are: quantity, quality, relation and modality, and the most complex and far-reaching questions concern the relational and modality-related categories. 

On the other hand, mathematical categories are considered at present as the most general and universal structures in mathematics, consisting of related abstract objects connected by arrows. The abstract objects in a category may, or may not, have a specified structure, but must all be of the same type or kind in any given category. The arrows (also called ’morphisms’) can represent relations, mappings/functions, operators, transformations, homeomorphisms, and so on, thus allowing great flexibility in applications, including those outside mathematics as in: Logics (Georgescu 2006), Computer Science, Life Sciences (Baianu and Marinescu, 1969; Baianu, 1987; Brown and Porter, 1999; Baianu et al, 2006a; Brown et al 2007a), Psychology and Sociology (Baianu et al, 2007a). The mathematical category also has a form of ‘internal’ symmetry, specified precisely as the commutativity of chains of morphism compositions that are uni-directional only, or as naturality of diagrams of morphisms; finally, any object A of an abstract category has an associated, unique, identity, 1A, and therefore, one can replace all objects in abstract categories by the identity morphisms. (When all arrows are invertible, the special category thus obtained is called a ‘groupoid’, and plays a fundamental role in the field of mathematics called Algebraic Topology).

The categorical viewpoint– as emphasized by William Lawvere, Charles Ehresmann and most mathematicians– is that the key concept and mathematical structure is that of morphisms that can be seen, for example, as abstract relations, mappings, functions, connections, interactions, transformations, and so on. Thus, one notes here how the philosophical category of ‘relation’ is closely allied to the basic concept of morphism, or arrow, in an abstract category; the implicit tenet is that arrows are what counts. One can therefore express all essential properties, attributes, and structures by means of arrows that, in the most general case, can represent either philosophical ‘relations’ or modalities, the question then remaining if philosophical–categorial properties need be subjected to the categorical restriction of commutativity. As there is no a priori reason in either nature or ‘pure’ reasoning, including any form of Kantian ‘transcedental logic’, that either relational or modal categories should in general have any symmetry properties, one cannot impose onto philosophy, and especially in ontology, all the strictures of category theory, and especially commutativity. Interestingly, the same critique and comment applies to Logics: only the simplest forms of Logics, the Boolean and intuitionistic, HeytingBrouwer logic algebras are commutative, whereas the algebras of many-valued (MV) logics, such as ÃLukasiewicz logic are non-commutative, (or non-Abelian). These ideas about the non-Abelian character of general philosophical and logical theories, including general ontology approaches, will be considered next in further detail.（essay代写)

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