Basic Structure of Categorical Ontology and the Theory--论文代写范文精选

一般来说,分类本体从根本上依赖于空间和时间上的考虑。从不同层次的现实,从物理水平和持续递增的顺序复杂性，对生物、心理、社会和环境进行分析。下面的essay代写范文进行详述。

With the provisos specified above, our proposed methodology and approach employs concepts and mathematical techniques from Category Theory which afford describing the characteristics and binding of ontological levels besides their links with other theories. Whereas Hartmann (1952) stratified levels in terms of the four frameworks: physical, ‘organic’/biological, mental and spiritual, we restrict here mainly to the first three. The categorical techniques which we introduce provide a powerful means for describing levels in both a linear and interwoven fashion, thus leading to the necessary bill of fare: emergence, complexity and open non-equilibrium, or irreversible systems. Furthermore, an effective approach to Philosophical Ontology is concerned with universal items assembled in categories of objects and relations, involving, in general, transformations and/or processes. Thus, Categorical Ontology is fundamentally dependent upon both space and time considerations. 

Therefore, one needs to consider first a dynamic classification of systems into different levels of reality, beginning with the physical levels (including the fundamental quantum level) and continuing in an increasing order of complexity to the chemical–molecular levels, and then higher, towards the biological, psychological, societal and environmental levels. Indeed, it is the principal tenet in the theory of levels that : ”there is a two-way interaction between social and mental systems that impinges upon the material realm for which the latter is the bearer of both” (Poli, 2001). Thus, any effective Categorical Ontology approach requires, or generates–in the constructive sense–a ‘structure’ or pattern rather than a discrete set of items. 

The evolution in our universe is thus seen to proceed from the level of ‘elementary’ quantum ‘wave–particles’, their interactions via quantized fields (photons, bosons, gluons, etc.), also including the quantum gravitation level, towards aggregates or categories of increasing complexity. In this sense, the classical macroscopic systems are defined as ‘simple’ dynamical systems that are computable recursively as numerical solutions of mathematical systems of either ordinary or partial differential equations. Underlying such mathematical systems is always the Boolean, or chrysippian, logic, namely, the logic of sets, Venn diagrams, digital computers and perhaps automatic reflex movements/motor actions of animals. 

The simple dynamical systems are always recursively computable (see for example, Suppes, 1995–2007), and in a certain specific sense, both degenerate and non-generic,consequently also structurally unstable to small perturbations. The next higher order of systems is then exemplified by ‘systems with chaotic dynamics’ that are conventionally called ‘complex’ by physicists, computer scientists and modelers even though such physical, dynamical systems are still completely deterministic. It has been formally proven that such systems are recursively non-computable (see for example, Baianu, 1987 for a 2-page, rigorous mathematical proof and relevant references), and therefore they cannot be completely and correctly simulated by digital computers, even though some are often expressed mathematically in terms of iterated maps or algorithmic-style formulas. 

Higher level systems above the chaotic ones, that we shall call ‘Super–Complex, Biological systems’, are the living organisms, followed at still higher levels by the ultra-complex ‘systems’ of the human mind and human societies that will be discussed in the last section. The evolution to the highest order of complexity- the ultra-complex, meta–‘system’ of processes–the human mind–may have become possible, and indeed accelerated, only through human societal interactions and effective, elaborate/rational and symbolic communication through speech (rather than screech (as in the case of chimpanzees, gorillas, baboons, etc).

Towards Biological Principles and the Emergence of Highly Complex Dynamics through Symmetry Breaking 
Quantum symmetries occur not only on microphysical scales, but also macroscopically in certain, ‘special’ cases, such as liquid 3He close to absolute zero and superconductors whereextended coherence is possible for the superfluid, Cooper electron-pairs. Explaining such phenomena requires the consideration of symmetry breaking (Weinberg, 2003). Occasionally, symmetry breaking is also invoked as a ‘possible mechanism for human consciousness’ which also seems to involve some form of ‘global coherence’–over most of the brain; however, the existence of such a ‘quantum coherence in the brain’–at room temperature–as it would be precisely required/defined by QTs, is a most unlikely event. On the other hand, a quantum symmetry breaking in a neural network considered metaphorically as a Hopfield (‘spin-glass’) network might be conceivable close to physiological temperatures but for the lack of existence of any requisite (electron ?) spin lattice structure which is indeed an absolute requirement in such a spin-glass metaphor–if it is to be taken at all seriously! Now comes the real, and very interesting part of the story: neuronal networks do form functional patterns and structures that possess partially ‘broken’, or more general symmetries than those described by quantum groups.

Such extended symmetries can be mathematically determined, or specified, by certain groupoids–that were previously called ‘neuro-groupoids’. Even more generally, genetic networks also exhibit extended symmetries represented for an organismal species by a biogroupoid structure, as previously defined and discussed by Baianu, Brown, Georgescu and Glazebrook (2006). Such biogroupoid structures can be experimentally validated, for example, at least partially through Functional Genomics observations and computer, bioinformatics processing (Baianu, 2007). We shall discuss further several such interesting groupoid structures in the following sections, and also how they have already been utilized in local-to-global procedures to construct ‘global’ solutions; such global solutions in quite complex (holonomy) cases can still be unique up to an isomorphism (the Globalization Theorem, as to be discussed in Brown, Glazebrook and Baianu, 2007). Last-but-not-least, holonomy may provide a global solution, or ‘explanation’ for ‘memory storage by ‘neuro-groupoids’. Uniqueness holonomy theorems might possibly ‘explain’ unique, persistent and resilient memories.

Towards Biological Postulates and Principles 
Whereas the hierarchical theory of levels provides a powerful, systems approach through categorical ontology, the foundation of science involves universal models and theories pertaining to different levels of reality. It would seem natural to expect that theories aimed at different ontological levels of reality should have different principles. We are advocating the need for developing precise, but nevertheless ‘flexible’, concepts and novel mathematical representations suitable for understanding the emergence of the higher complexity levels of reality. Such theories are based on axioms, principles, postulates and laws operating on distinct levels of reality with a specific degree of complexity. 

Because of such distinctions, inter-level principles or laws are rare and over-simplified principles abound. Alternative approaches may be, however, possible based upon an improved ontological theory of levels. Interestingly, the founder of Relational Biology, Nicolas Rashevsky (1968) proposed that physical laws and principles can be expressed in terms of mathematical functions, or mappings, and are thus being predominantly expressed in a numerical form, whereas the laws and principles of biological organisms and societies need take a more general form in terms of quite general, or abstract–mathematical and logical relations which cannot always be expressed numerically; the latter are often qualitative, whereas the former are predominantly quantitative.

Rashevsky focused his Relational Biology/Society Organization papers on a search for more general relations in Biology and Sociology that are also compatible with the former. Furthermore, Rashevsky proposed two biological principles that add to Darwin’s natural selection and the ‘survival of the fittest principle’, the emergent relational structure that are defining the adaptive organism: 
1.The Principle of Optimal Design, and 2. The Principle of Relational Invariance (phrased by Rashevsky as “Biological Epimorphism”).

In essence, the ‘Principle of Optimal Design’ defines the organization and structure of the ‘fittest’ organism which survives in the natural selection process of competition between species, in terms of an extremal criterion, similar to that of Maupertuis; the optimally ‘designed’ organism is that which acquires maximum functionality essential to survival of the successful species at the lowest ‘cost’ possible. The ‘costs’ are defined in the context of the environmental niche in terms of material, energy, genetic and organismic processes required to produce/entail the pre-requisite biological function(s) and their supporting anatomical structure(s) needed for competitive survival in the selected niche. Further details were presented by Robert Rosen in his short but significant book on optimality (1970).（essay代写)

51Due网站原创范文除特殊说明外一切图文著作权归51Due所有；未经51Due官方授权谢绝任何用途转载或刊发于媒体。如发生侵犯著作权现象，51Due保留一切法律追诉权。
更多essay代写范文欢迎访问我们主页 www.51due.com 当然有essay代写需求可以和我们24小时在线客服 QQ:800020041 联系交流。-X（essay代写)