Topological Ontology and Logic of Qualitative quantity

This is not to say, however, that this new unified, "affirmative" infinite will suffice on its
own either. It is only in the very process that we have been trying to elaborate here that the
so-called "true" infinite emerges. After rehearsing the ''double meaning" that the finite had
acquired in the foregoing explication (i.e., that it is both finite and infinite at the same time),
Hegel explains that The infinite, too, has the double meaning of being [first] one of these
two momentsas such it is the spurious infiniteand [second] also the infinite in which both,
the finite and its other, are only moments. The infinite, therefore, as now before us is, in
fact, the process in which it is deposed to being only one of its determinations, the opposite
of the finite, and so to being itself only one of the finites, and then raising this its difference
from itself into the affirmation of itself and through this mediation becoming the true
infinite.” 99
Coltman concludes that „the true infinite, then, is neither the spurious infinite nor the
affirmative infinite alone, but the process itself in which the former mediates its own
transition into the latter. And, as such, the true infinite shows itself to be a further
determination of becoming.”
Coltman closes the circle of his discussion going back from Hegel to Gadamer:
“Even in such a brief sketch we can see that in the one-sided logic that constitutes the
alternation of the finite and the infinite, back and forth "on to infinity," the understanding
tries (and fails) to arrest the movement of the concept which, if allowed to unfold in terms
of its own dialectical Auslegung, logically sublates itself in the infinite. Thus from the
perspective of the "Logic of Being," Gadamer's insistence on a "simple limit" to human
experience appears to be merely an artifact of the perspective of external reflection. But we
must remember that, although (as with Hegel) reflexive thinking per se is problematic for
Gadamer, it makes no sense to speak of it as "external." External to what Reason But
insofar as language is at least the medium of both reflection and speculative reason, this
seems to imply that language itself is "external" to reason. But reason, Gadamer would say,
depends on language just as much as the understanding does. This is not to denigrate reason
as such, but against the transcendental philosophy of the Enlightenmentwhich both Hegel
and Gadamer criticize, and which claims a certain degree of independence from the words
through which it is expressed Gadamer wants to reassert the universality of language..”
(Gadamer’s “Language is the language of reason itself”) 100
We should return to the issue of the use and the topological meaning of "die Mitte" in Hegel
and Gadamer, following Coltman’s discussion and focusing this issue on the Gadamerien
finitude and Hegelian infinity.
For Gadamer the issue of human finitude is related with and embedded in the language. In
the opening paragraphs of "The Middle of Language and its Speculative Structure,"
Gadamer reiterates two primary moments in the development of philosophical
hermeneutics: namely, that "the alldetermining ground [of the hermeneutic phenomenon] is
the finitude of our historical experience" and that "language is the mark of human finitude."
Hegel’s notion of "die Mitte", Gadamer develops in the language and dialoque.
Coltman points out that:
“We see (here) a striking difference from Hegel's usual employment, in the Logic, of "die
Mitte" as the logical "middle term" between two polar "extremes" that allows for the
sublation of these opposites. Of course, as we have already pointed out, Gadamer is
speaking here of what he will call "dialectic" as it occurs in living dialogue between two
99
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., 148.
100
Rod Coltman, The Language of Hermeneutics, Gadamer and Heidegger in Dialogue, p.99-
101
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