Topological Ontology and Logic of Qualitative quantity

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people (or between a person and a text) rather than of a strictly logical dialectic based on the grammar of the speculative proposition. But this is precisely the sharp divergence that will allow Gadamer to maintain a certain connection to Hegel. (And we should by no means assume that Hegel's formal use of the "middle term" will go unexploited by Gadamer.) The first occurrence of "die Mitte" comes at the very end of the second division of Truth and Method as Gadamer makes the transition from "historicity" Geschichtlichkeit) to "linguisticality'' (Sprachlichkeit). "Every conversation," he writes, "presupposes a common language, or better: it develops a common language from within. This is because something is laid down in the middle [in die Mitte niedergelegt]... in which both conversation partners participate and about which they exchange with one another." At this point in the text we do not yet have a direct identity between language and this "middle" between interlocutors. In the next subsection, however, in fact on the very next page, we find that "Language is the middle [die Mitte] in which the coming-toanunderstanding of the partners [die Verständigung der Partner] and agreement about the subject matter [die Sache] carry them.” 101 For Coltman, “Gadamer is not pretending to identify Hegel's critique of finitude and the socalled spurious or bad infinite as a point where the "Logic of Being" breaks down. .. Gadamer's preference for the bad infinite indicates rather his own Heideggerian orientation toward the inescapable historicity and the radical finitude of human..” The topological notion of Hegel’s “die Mitte” is subject of Rod Coltman’s discussion on Gadamer’s claim - "language is the middle [die Mitte]. For Gadamer as for Heidegger, understanding, rather than being some mechanical activity of the mind, is Dasein's mode of being-in-the-world. Gadamer focuses not on being itself or human being per se, but on human being-conscious as an event, a process, a temporal and historical phenomenon that occurs in and through the "middle of language." For Gadamer, language is a "middle'' – after Heidegger - the Middle of Language is The Middle of Being. This claim is roughly analogous to the middle term in a logical syllogism or in a Hegelian dialectical transition. On one hand, Dasein is essentially linguistic and temporal and, therefore, finite. On the other hand, being and understanding always occur within a linguistic milieu, from within or out of the middle of language ("die Mitte der Sprache" ). Hence precisely at this moment of the most extreme distanciation from his famous mentor Gadamer, too, thinks the Wesen of both being and language in essentially topological terms.” The topological notion in Heidegger's works on language and poetry is pointed out by Coltman, who makes remarks how Heidegger provides us with repeated invocations and metaphors around particular words and phrases such as "path," "clearing," "dwelling," "the house of being,'' and even "the regions" of the fourfold) which evoke images of places, locations, sites. For Coltman “these "topological" words and phrases, however, are not to be construed as metaphorical constructs, but as various ways in which being reveals (and conceals) itself in language. They indicate, in other words, not the dialectical movement of concepts but various places in which we might discern the movement or the turning (die Kehre)onemight even say the counter-turning (die Gegenwendung) in being itself.” 102 7. Topological Hermeneutics of Human Finitude and Infinitude based on Hegel’s fourfold of infinities of Time and Space and Qualitative quantity 101 Rod Coltman, The Language of Hermeneutics, Gadamer and Heidegger in Dialogue, p.120 102 Rod Coltman, The Language of Hermeneutics, Gadamer and Heidegger in Dialogue, p.115-116 42
One of the main concerns of hermeneutic is Hans-Georg Gadamer’s concept of human finitude. For Gadamer, the boudaries of our human finitude are established by the limits of our knowledge and our human practice which are influenced by human tradition, history and prejudice. After Gadamer, the commitment to the finitude of human understanding became the core of the phenomenological hermeneutic tradition, but as L. Sebastian Purcell has remarked in his paper “After Hermeneutics” 103 Purcell discusses the thesis of Alain Badiou 104 and Quentin Meillassoux 105 that human understanding (Verstehen) is finite. Is Phenomenological hermeneutics in a state of crisis Badiou captures the animating sentiment of the critique when he states that the central aim of philosophy today is “to finish up with the motif of finitude and its hermeneutical escort.” Quentin Meillassoux’s claim against the human finitude is established in his book, foreworded by Badiuo – “After Finitude: An Essay on the Necessity of Contingency”. In this debate within the hearth of hermeneutics, the concept of human finitude could be traced back on the ground of Hegel’s “Science of Logic” and Hegel’s interpretation of the two notions of infinity – “good infinity” and “bad infinity”. Hegel’s concept of infinity is related with Hegel’s concept of quality and quantity, in particular with Hegel’s “qualitative quantity”. The position of Badiou and Meillassoux, however, is not the symmetrically opposite claim that human understanding is, instead, infinite. Rather, they argue that advances in mathematics long overlooked by philosophers have irrevocably changed the relation of the finite to the infinite, so that the current account of hermeneutics as a finite endeavour necessarily perpetuates the metaphysics of presence. Badiou rejects hermeneutics, a rejection which is part of his criticism of contemporary philosophy. What makes contemporary philosophy ‘contemporary’ is, in Badiou’s view, twofold: • first, a preoccupation with language as the ultimate horizon of human existence and, • second, a general abandonment of ‘truth’ as a central philosophical category. In particular, Badiou charges contemporary philosophy (including hermeneutics, analytic philosophy and postmodernism) with being ‘too compatible with our world to be able to sustain the rupture or distance that philosophy requires’. For Badiou, ontology is mathematical and phenomenology is a matter of logic. Badiou positions mathematics as the more fundamental term in the relation suggesting that “logic is from within mathematics the movement of thought explaining the being of appearing, that is, of what affects Being as it is Being-there.” 106 103 L. Sebastian Purcell, Symposium: Canadian Journal of Continental Philosophy), “Phenomenological hermeneutics is in a state of crisis” 104 Alain Badiou, Briefings on Existence: A Short Treatise on Transitory Ontology, (tr.) Norman Madarasz (Albany: State University of New York, 2006), 30. 105 Quentin Meillassoux, After Finitude: An Essay on the Necessity of Contingency. 106 Alain Badiou, Briefings on Existence: A Short Treatise on Transitory Ontology, (tr.) Norman 43
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 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: This is not to say, however, that t
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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