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 (sometimes rendered as "spurious" versus "genuine" infinity). Or in German schlect Unendlichkeit versus wahrhaft Unendlichkeit. His analysis centers mainly on the larger Logic and its section on infinity which is part of chapter 2 "Determinate Being," section c. (a) through (c). 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, but still 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 requiring nothing outside of itself.
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. This total encompasses the finite, or contains it, but is in no way limited by it. 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 limited and finite, but not truly infinite.
A final thought. As the paper's title is "In Defense of Bad Infinity" it seemed appropriate to me to recommend in contradistinction to Hegel's infinite Schelling's take on infinity, for it was Schelling who was the first German idealist I had encountered even before Hegel. For a time in fact it was Schelling's "bad infinity" that served as a model for me to attempt to understand Hegel's own division between true infinite and spurious infinite.
To whit, then: might we be able to define the absolute not necessarily as something unending such as in an unending series of numbers (a potential infinite) or on the other hand as something total as in a closed circle (an actual infinite). Perhaps, rather, might not the absolute be something absolutely unconditioned as Schelling ventured to maintain? That is, an unconditioned infinite?
It was Schelling's view that absolute being - "the Absolute" - must mean unconditioned being, and as unconditioned being, the absolute, must therefore be "endless" for any "beginning" or "end" of it would qualify some condition as being other to that absolute's identity and the result would be a non-absolute identity. Whereas for Hegel the absolute contains its own identity as well as all else, Schelling's absolute is said to be "spurious" for his absolute is absolutely indifferent to identity in the sense that nothing can be other to it save only for itself. Paradoxically to be "itself" it must both be "itself" and "not itself" in different respects (so that there is no "other" conditioning it). Therefore, Schelling's absolute is "endless" but without closure as a totality because there is nothing other than its identity.
Hegel's absolute is a thing, it is an identity: the Absolute, the All, which contains all things. But Schelling's main point was that the absolute, unlike in Hegel's philosophy, could not be a totality or a thing. Schelling claimed that the absolute was no-thing. Hegel railed against Schelling for thinking that the absolute had no identity sensu stricto, and as being "nothing" was a blanket that simply absorbed all things in a cloak of night, in a "blank" identity. Schelling's absolute was said to annul particular things within an indifferent identity instead of raise them up: that is, encircle things within the identity of an absolute. Thus Hegel claimed that Schelling's absolute was an identity that was a "night in which all cows are black."
In short, then, it seems that Schelling's infinite or absolute is conditioned by no other. But it is "absolutely unconditioned" as indifferent to identity in its being unconditioned. Therefore, Schelling's unconditioned infinite is absolute indifference; that is, it is unconditioned ground in perpetuity.
Does this lack of identity within Schelling's notion of the absolute mean that his concept is deficient as compared to Hegel's understanding of the absolute? Or, might it be that in this very deficiency, in this "spurious" nature lies hidden a more adequate conception of the absolute and hence its virtue?
Paper "In Defense of Bad Infinity" HERE.