Topological Ontology and Logic of Qualitative quantity

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Dependent Objects" and "Thoughts Towards a Theory of the Pure Forms of Wholes and Parts". Husserl's theory is concerned also with the horizontal relations between the different parts within a single whole, relations which serve to give unity or integrity to the wholes in question. According to Barry Smith, “To put the matter simply: some parts of a whole exist merely side by side, they can be destroyed or removed from the whole without detriment to the residue. A whole all of whose parts manifest exclusively such side-by-sideness relations with each other is called a heap or aggregate or, more technically, a purely summative whole. In many wholes, however, and one might say in all wholes manifesting any kind of unity, certain parts stand to each other in relations of what Husserl called necessary dependence (which is sometimes, but not always, necessary interdependence). Such parts, for example the individual instances of hue, saturation and brightness involved in a given instance of colour, cannot, as a matter of necessity, exist, except in association with their complementary parts in a whole of the given type. There is a huge variety of such lateral dependence relations giving rise to correspondingly huge variety of different types of whole which more standard approaches of 'extensional mereology' are unable to distinguish.” Husserl's topological ideas on parts, wholes and categories from the Logical Investigations were applied by Stanislaw Lesniewski, the founder of mereology, and the linguist Roman Jakobson in different branches of linguistics, in the early development of categorial grammar. The topological background of Edmund Husserl’s work is presented in his formal ontology. The term ‘formal ontology’ was first used by in his Logical Investigations (1900/01) to signify the study of those formal structures and relations – above all relations of part and whole – which are exemplified in the subject-matters of the different material sciences. We follow Husserl in presenting the basic concepts of formal ontology as falling into three groups: - the theory of part and whole, - the theory of dependence, - and the theory of boundary, continuity and contact. In his Logical Investigations (1900/01), Edmund Husserl, draws a distinction between formal logic, on the one hand, and formal ontology, on the other. Formal logic deals with the interconnections of truths (or of propositional meanings in general) – with inference relations, with consistency and validity. Formal ontology deals with the interconnections of things, with objects and properties, parts and wholes, relations and collectives. As formal logic deals with inference relations which are formal in the sense that they apply to inferences in virtue of their form alone, so formal ontology deals with structures and relations which are formal in the sense that they are exemplified, in principle, by all matters, or in other words by objects in all material spheres or domains of reality. Qualitative quantity seen in Poincare’s topology and his development of the qualitative theory of differential equations is enhanced by the new science of Mereotopology. If Topology is perhaps the most elemental aspect of space, and must be form a fundamental aspect of qualitative spatial reasoning since it certainly can only make qualitative distinctions, Mereotopology is a branch of metaphysics, and ontologigal computer science. 8
Mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. Mereotopology begins with theories A.N. Whitehead articulated in several books and articles he published between 1916 and 1929. The Qualitative quantity is the base cathegory and phenomenom of Qualitative research /QR/. Qualitative Research utilizes methods that seek to discern the quality — as opposed to the quantity — of its subject. QR is more often concerned with explaining the why and how of a phenomenon rather than the what, when and where. Qualitative research methods are most often utilized in fields such as anthropology, the humanities and sociology, although each of these fields can be studied through quantitative methods as well. Since qualitative research is exploratory and focuses on discerning the why of things, such as human behavior, rather than the what of the natural world, it is often criticized for being too subjective. Many make the counter-argument, however, that since qualitative methods are hypothesis generating, they are not only just as valuable as quantitative methods but necessary for the production of theoretical models which come to inform the direction of quantitative research methods. Data collection and analysis is another way that quantitative and qualitative research differ. In qualitative research, data samples are usually not collected through random selection but rather purposive reasoning, which is to say they are chosen for how well they typify the characteristics of a certain class. For example, a qualitative research study on racial inequality will not likely concern itself with affluent minorities or the entire population of a minority, but rather, it might focus on depressed areas where minorities are most prevalent. This approach is chosen because qualitative researchers are not concerned with discerning the quantity of people in a minority class, but rather the quality of life for minorities who are affected by inequality. Qualitative research is thought especially valuable in circumstances where quantitative data does not account for a particular phenomenon. For example, while economics frequently concerns itself with collecting concrete information, like statistics and financial data, it can be said to be flawed because it ignores the humanistic and psychological aspects of the people that are a key component. This human component requires a qualitative understanding. An important variable to consider when analyzing the dependability of qualitative research is validity. It is important to consider how a conclusion was reached, and whether it really represents a dependable and realistic interpretation of its subject. It may or may not be pertinent to ask whether or not a conclusion is reproducible, or whether it was affected by bias. One should also consider whether data from qualitative research is well reasoned and the extent to which it accounts for a substantial majority of the available data. Spatial-temporal reasoning is applicable in ontology. The implication of the concept of qualitative quantity could be found in the work “Spatial Reasoning and Ontology: Parts, Wholes, and Locations”, authored by Achille C. Varzi, Columbia University /Published in M. Aiello, I. Pratt-Hartmann, and J. van Benthem (eds.), Handbook of Spatial, Logics, Berlin: Springer-Verlag, 2007, pp. 945-1038/. The notion of the Quality of the quantity is related with Qualitative Spatial Change. In his study “Qualitative Spatial Change : Space-Time Histories and Continuity”, Submitted in accordance with the requirements for the degree of Doctor of Philosophy, The University of Leeds, School of Computing, January 2005, Shyamanta M. Hazarika provides proofs and examples how quality of the quantity is implemented in Topology, Mereotopology and Qualitative Continuity. Continuity of change is the perception of being seamless and is dependent on the granularity. What seems as continuous at some level of granularity may be discontinuous at a finer level. Nevertheless, continuity may be thought of as the intuitive idea of a gradual variation with no abrupt jumps or gaps. A formal characterization of such an intuitive notion of continuity for a qualitative theory of motion is what Shyamanta M. Hazarika refers to as qualitative continuity. 9
Page 1 and 2: Topological Ontology and Logic of Q
Page 3 and 4: agreements about the representation
Page 5 and 6: Science” (Wissenschaftslehre), Bo
Page 7: Leśniewski's student Alfred Tarski
Page 11 and 12: only that between process and event
Page 13 and 14: hierarchies to represent their mutu
Page 15 and 16: meta attribute value counting_valu
Page 17 and 18: Fig. 2 Detail version of top-level
Page 19 and 20: differentiation enables us to captu
Page 21 and 22: 3.Quality: It is a property associa
Page 23 and 24: 3. The Topological Notion of Qualit
Page 25 and 26: series of Measure Relations” /b/,
Page 27 and 28: The true resurgence of Hegel’s Qu
Page 29 and 30: Kairos, Chora and Topos as follow:
Page 31 and 32: In Philosophical or Dialectical Her
Page 33 and 34: The roots of Hegel’s Qualitative
Page 35 and 36: Richter mentions these developments
Page 37 and 38: Name: Firstness. Secondness. Thirdn
Page 39 and 40: of something in its other. In his e
Page 41 and 42: This is not to say, however, that t
Page 43 and 44: One of the main concerns of hermene
Page 45 and 46: concept of spatiality. But they did
Page 47 and 48: David Gray Carlson’s “A Comment
Page 49 and 50: Hegel's great work on Logic, the
Page 51 and 52: For Paterson, the “true mathemati
Page 53 and 54: The term “social topology” is u
Page 55 and 56: of Leonard Euler and later with the
Page 57: To Meet the Other is to have the id

Topological Ontology and Logic of Qualitative quantity

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