Saturday, November 8, 2014

bad infinity

Wayne Martin was kind enough to post a very interesting (and fantastically clear) paper on Hegel's notion of "bad" infinity versus a "true" infinity.  Or in German schlect Unendlichkeit versus echt Unendlichkeit.  His analysis centers mainly on the larger Logic and its section on infinity, but anyone wanting a refresher or just a clear articulation of Hegel's at times just incredibly cumbersome discussion of the metaphysics of infinity ought to read the paper, which interestingly has some larger goals in mind (such as providing a Fichtean response to Hegel's pre Phenomenology of Spirit essay "The Difference Between Fichte's and Schelling's Systems of Philosophy" of 1801).

In a nutshell a bad infinity, for Hegel, is just one that is open-ended.  For Hegel true infinity - accessible by reason, beyond the understanding - is a totality.  Intensive and extensive mathematical infinities, such as those infinitesimally available between any two numbers or those which are sets of numbers to be aggregated indefinitely to any other set, fail before the sort of actual infinity that is an absolute total.

The interesting part isn't Hegel's critique of the bad infinite as one that is a possible infinite.  It is that Hegel states an infinity that "sets itself over and against" any other (such as the finite) is bad precisely because it lacks an infinite nature that is its own, and is therefore delimited by negating something else so as to take on its own identity.  So the logic of contrasts that establishes an infinite precisely because it is not finite, or "in-finite" is one that necessarily fails having no essential nature that is, itself, properly infinite or total.

Hegel compares the "true" infinite for this reason to a circle.  A circle does not "go on and on forever" yet is unending as a closed actual total.  God, for Hegel, in traditional definitions fails to capture the logical meaning of true infinity because God's nature and infinitude is always set over and against finite creation.  God in that sense is truly limited and finite.

A final thought.  It seems to me that speculation beyond or after finitude should be able to define the Absolute not necessarily as something unending such as in an unending series of numbers (a potential infinite), but as something absolutely unconditioned.  In and of itself the Absolute is infinite in being unconditioned in identity, or absolutely indifferent to identity but being capable of infinitely determining identity.  In short it seems that Schelling's infinite or Absolute is an open-ended infinite in just this way.  In other words Schelling, unlike Hegel, actually defends a "bad infinity" in that his notion of infinity and its corresponding system is open ended because for Schelling the Absolute is not a closed totality.  It is absolute indifference, unconditioned ground in perpetuity.

Paper "In Defense of Bad Infinity" HERE.