Topological Ontology and Logic of Qualitative quantity

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However, Rene Thom, in his remarkable, if unreadable, 1954 paper “Quelques proprietes globales des varietes differentiables”, gave the full solution to this problem for unoriented manifolds, as well as many powerful insights into the methods for solving it in the cases of manifolds with additional structure. It was largely for this work that Thom was awarded the Fields medal in 1958. The key step was the reduction of the cobordism problem to a homotopy problem, although the homotopy problem is still far from trivial. This was later generalized by Lev Pontrjagin, and this result is now known as the Thom-Pontrjagin theorem. In mathematics, a pair of pants is a simple two-dimensional surface resembling a pair of pants: topologically, it is a sphere with three holes in it. Pairs of pants admit hyperbolic metrics, and their isometry class is determined by the lengths of the boundary curves (the cuff lengths), or dually the distances between the boundaries (the seam lengths). In hyperbolic geometry all three holes are considered equivalent – no distinction is made between "legs" and "waist". In cobordism theory the holes are not equivalent – a pair of pants is a cobordism between one circle (the "waist") and two circles (the "legs"). Jules Henri Poincare may rightly be considered the father of modern topology (Leonhard Euler and the Konigsberg bridges notwithstanding). It is fitting, therefore, that many of the questions explored in this thesis originated with Poincare. Poincare’s famous conjecture – which has driven so much of twentiethcentury topology – arose, in fact, as the successor of an earlier conjecture. Poincare originally conjectured that any 3-manifold with the homology of S3 is homeomorphic to S3. But he soon found a counterexample, known today as the Poincare homology sphere (obtained from S3 by surgery along the right trefoil with framing As a result, Poincar´e re-formulated his conjecture into the now-famous statement that any compact, connected, oriented 3- manifold with trivial fundamental group is homeomorphic to S3. 30
In Philosophical or Dialectical Hermeneutics the “pair of pants” is important because it shows how one can “morph” not only the categories of the “quality” and “quantity” into the fourfold of categories in Hegel, or how one can “morph” Hegel’s fourfold of infinities, but also how one can “morph” the Understanding of human finitude in infinitude and reverse the human infinitude into the finitude, how Hermeneutical Circle can be morph into the Topological Cobordism Ring – how the true Hermeneutical “fusion of horizon” could found in Topology and Topological Hermeneutics. The Cobordism of Hermeneutical Circle shows how Dialectical Hermeneutics must retrieve itself in Topology. Each of the categories, presenting Hegel’s fourfold of infinities: 1. Quantitative quantity; 2. Quantitative quality; 3. Qualitative quantity; 4. Qualitative quantity, could be thought as circle or four circles placed in a 3-manifold. 31
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 and 8: Leśniewski's student Alfred Tarski
Page 9 and 10: Mereotopology is a first-order theo
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: Kairos, Chora and Topos as follow:
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

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