Topological Ontology and Logic of Qualitative quantity

of something in its other. In his explanation, Hegel employs term "die Mitte" (The German
87 88
for ‘the middle').
In Hegel’s use of "die Mitte" we could see the topological notion of betweeness, the mediator
between the outside and inside. In this epistemological term and it use by Hegel we could
see and seek an interpretation of Hegel’s Logic toward cobordism. Here lies Hegel’s
dialectical and logical cobordism - something has its determinate being outside (or, as it and
Gadamer’s the middle of language ("die Mitte der Sprache")
In Hegel’s use of "die Mitte" we could see the topological notion of betweeness, the mediator
between the outside and inside. In this epistemological term and it use by Hegel we could
see and seek an interpretation of Hegel’s Logic toward cobordism. Here lies Hegel’s
dialectical and logical cobordism - something has its determinate being outside (or, as it is
also put, on the inside) of its limit; similarly, the other, too, because it is a something, is
outside [its limit]. Limit is the middle term [die Mitte] between the two of them in which
they cease. They have their determinate being beyond each other and beyond their limit; the
limit as the non-being of each is the other of both. 89
Rodney Coltman asserts that “the limit is itself only a preliminary moment here. For we
quickly find ourselves involved in yet a further determination of "something": "Something
with its immanent limit, posited as the contradiction of itself, through which it is directed
and forced out of and beyond itself, is the finite." 90 Something, therefore, becomes
determined as "finite" in that both its being and its ceasing-to-be are equally determinate
and thereby come into contradiction. In the "unrest" brought about by its inability to contain
the contradiction within itself as a contradiction, something is impelled out beyond itself.
Hence the common notion of finitude, the conception of finitude that the understanding
holds on to: A thing is finite insofar as it is limited and its very limitedness necessitates the
thought of something beyond its limit.”
For Coltman, “this way of thinking finitude, of course, appears to make perfect sense, and
Gadamer's thinking of human finitude trades off this to a certain extent.” Here in underline
note, Coltman poits out that “In fact, at one point Hegel seems to come rather close to
Heidegger's thinking of Dasein's finitude in Being and Time as "being toward-death." "Finite
things are not merely limited," he writes, on the contrary, non-being constitutes their nature
and being. Finite things are, but their relation to themselves is that they are negatively selfrelated,
and in this very self-relation send themselves away beyond themselves, beyond their
being. They are, but the truth of this being is their end. The finite not only alters, like
something in general, but it ceases to be, and its ceasing to be is not merely a possibility, so
87
Hegel's Science of Logic, trans. A. V. Miller, trans., Atlantic Highlands: Humanities, 1990.
Original German Text: Wissenschaft der Logik I, Frankfurt: Suhrkamp Verlag, 1970., 127.
88
The German for ‘(the)’ middle’ is ( die ) Mitte. This generates an adjective mittel (‘middle’)
and another noun ( das ) Mittel (originally ‘(the) middle, the thing in the middle’, but now
‘means, what serves the attainment of a purpose ’). It also generates several verbs, especially
mitteln (‘to help someone to, to settle, mediate’, e.g. a quarrel), which is now obsolete but
has left mittelbar (‘mediate, indirect’) and unmittelbar (‘immediate, direct’), and vermitteln
(‘to achieve union, mediate; to bring about’, etc.). The past participle of vermitteln, vermittelt
(‘mediated, indirect’) is used in contrast to unmittelbar. Both give rise to abstract nouns,
Vermittlung (‘mediation’) and Unmittelbarkeit (‘immediacy’). In non-Hegelian philosophy,
unmittelbar is primarily an epistemological term. Immediate certainty is a certainty that is
not mediated by inference or proof, or perhaps even by symbols or concepts.
89
Hegel's Science of Logic, trans. A. V. Miller, trans., Atlantic Highlands: Humanities, 1990.
Original German Text: Wissenschaft der Logik I, Frankfurt: Suhrkamp Verlag, 1970., 127.
90
Hegel's Science of Logic, trans. A. V. Miller, trans., Atlantic Highlands: Humanities, 1990.
Original German Text: Wissenschaft der Logik I, Frankfurt: Suhrkamp Verlag, 1970., 129.
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