How does one think infinity? The question seems at first to place an unreasonable demand for provisioning an answer; the structure of the human mind immediately appears finite, conditioned. Yet one soon discovers that it is reason itself which places this demand. Man is irrepressibly driven by his rational faculty to apprehend the infinitely unconditioned ground(s) upon which the finite phenomena of experience are grounded. Limitation is anathema to the most primordial desire of humanity. For nothing is more human than to reject the human — to reject finitude and become God.
The spiritual epic of man is thus guided by his cognitive romance with the Absolute, qua true infinity. In the course of its unfolding, philosophers have variously located the metaphysical domain of infinity as either belonging to the structure of the world or the mind. Classical (pre-Kantian) metaphysics naïvely sought infinity in the predicate structure of the world, a world it had imparted with universality by virtue of its deductions. In other words, infinity was for this metaphysics a mere predicate in its determinations, and bore no necessary relation to its subject apart from its copular attachment (God is infinitely powerful, infinitely knowledgeable, etc.). Rationalist ontology, pneumatology, cosmology, and theology were borne of its efforts. But cracks began to emerge in its objective edifice, and soon Hume arose to shatter the great deductive systems of philosophy. Only with Kant was universality rehabilitated, and even then only at a price. The phenomenal world was recognized for its objective finitude, but infinity was subjectively retained in the pure (a priori) faculties of the understanding. Within this categorical matrix, objectivity was granted to judgments which arranged the manifold of intuition under the twin categories of universality and necessity.[2] Objective laws could be hoped to have infinite application to finite phenomena. But even then this infinity was strictly formal, hence empty, having been methodologically stripped of empirical (a posteriori) content.[3] The philosophers of subjectivity (Kant, Jacobi, Fichte) had correctly diagnosed the dogmatism of the objective infinite, but the infinite they had replaced it with remained definite in its separation from the finite.
Both such conceptions of infinity (objective and subjective alike) ultimately fell short for Hegel. The objective infinity of being and the subjective infinity of thought each failed in its non-relation to finitude, i.e. its abstract isolation from infinity’s negative. The former thought the world all too gracious in its accommodation of the human mind; the latter, by contrast, “sen[t] man to feed upon husks and chaff.”[4] Always seeking some mediating ground between two dialectical opposites, Hegel hoped to recast abstract infinity and abstract finitude into the concrete unity of the speculative infinite, or the infinitum actu of Spinoza. The notion of the “true” or “good” infinity of speculation recurs throughout Hegel’s mature works, from his early collaboration with Schelling in Faith and Knowledge (1802) to the final edition of his Encyclopedia Logic (1831), his last published work. This is hardly a coincidence. For in Hegel’s estimation, “the true infinite is [my italics] the absolute Idea” — the grounding principle of all genuinely philosophical knowledge.[5] As such, a grasp of this immanent feature of Hegel’s thought is central to an appreciation of his philosophy. With reference to the pertinent texts that deal with this topic, its fine points might be thoroughly excogitated. As the concept takes shape, the speculative implications of its particulars will be briefly discussed, wherever appropriate.†