Doctrine of Being: Quality - Existence (3)

Infinity

Self-referring infinity can be regarded as a “fresh definition of the absolute.” However, infinity as it negates the finite and thus is a determinateness is still not the absolute, since it is still affected by a one-sidedness due to its negative relation to another. This is thus still a “finitized” or bad infinity.

1. Infinity as simple determination

2. Infinity as the alternating determination – bad infinity

3. Affirmative, true infinity

A. Infinity in general

The infinite is the negation of negation at the level of restricted being. It is the perishing of perishing, or the being external to restriction as such.

“At the mention of the infinite, soul and spirit light up, for in the infinite the spirit is at home, and not only abstractly; rather, it rises to itself, to the light of its thinking, its universality, its freedom” (109).

Infinity is the truth of finitude (as the transcendence of restriction.) Thus, the infinite is not somehow outside the finite, The finite, qua restriction, is destined towards becoming infinite.

B. Alternating determination between finite and infinite

• As the negation of restriction, the infinite has first fallen into being a something
• Infinity is here a non-determinate existence as posited; as such it is also with a limit
• It is mere being which is the result of the negation or the reduction to nothing of everything which went on in the sphere of the finite
• The resulting being is a pure beyond which is 1) empty, yet 2) only existent as an external, qualitative reference to a really existent finite thing
• This being constitutes the bad infinite or the infinite of the understanding
• The bad infinite is the highest truth of the understanding
• The understanding comes to this awareness when, in applying its categories to reality, it finds another world constantly beyond itself
• Here we have two worlds, one finite and the other infinite, with the latter being a limiting and thus finite, kind of infinity
• It is due to the emptiness of immediate infinity that the finite immediately re-instates itself in the momentary void opened up by its own movement
• In this repetition, the finite appears as an independent given being which does not arise out of infinity
• The emergence of this new limit is thus a non-sublated return to where it has begun: the finite as limit
• “And so there arises again the emptiness, the nothing, in which we find again the said determination – and so forth to infinity” (112)
• This repetitive process constitutes the alternating determination of the finite and the infinite, restriction and ought
• “This bad infinite is in itself the same as the perpetual ought” (112)
• However, in its perpetual return to the finite, the infinite is thereby posited as the unity of the two sides
• This is the implicit “impulse” which drives the bad infinite
• This unity is initially seen as existing outside the alterations
• As long as the beyond of the finite is posited as lacking in all determination, bad infinity cannot be sublated

C. Affirmative infinity

• A closer look at the bad infinite will yield the moment prior to the externalization of the two sides of the alternation
• This will be the true infinity as said unity
• The finite contains infinity in its very self-limitation, just as the infinite also has its moment of finitude within its negation of an external other
• Thus, finitude and infinity are merely two different entrances to one and the same infinity
• Hegel calls this result a “scandalous unity”
• This new infinite is comprehensible without a reference to some finite things external to itself – this is its qualitative determinateness, to have finitude within itself
• All that is needed here is to introduce a restriction into infinity as such without externalizing this restriction as that which denies the infinite's infinity
• The sublating of the finite in the infinite is here not an alternation
• Both the finite and the infinite are posited in being sublated through each other, and by being so, they reveal themselves to be in unity (or rather, two unities with different entrances)
• The infinite goes down into one of its finite determinations, sublates it, and posits it as a self-affirming being with a limit – this is the true infinite
• The true infinite negates the negativity of the finite, and in this way becomes a thereness (i.e. the “da” of Dasein)
• This thereness was absent in the bad infinite which was caught up in the first, immediate negation of the finite
• True infinity is also concrete reality – this opens the door to reality being further determined as essence, concept, and idea
• The need to say that a concept or an idea is “real” arises due to the lack of education on the part of the speaker, which results in the speaker's only being able to use and comprehend the most abstract categories of being, existence, determination, etc.
• “Negation [in the true infinite] is thus determined as ideality; the idealized is the finite as it is in the true infinite” (119)
• To persist with the naïve distinction between “reality = being” and “ideality = concept” is to be stuck in bad infinity

Transition

The finite is thus negated by the true infinite, and in this infinity is a return into being. But since this return is the negation of the negativity of the finite being (= Dasein), it is not mere being, nor existence (which only contains the first, immediate negation of the other), but a self-referring being – being-for-itself.

• One of the implications of this result is that this kind of infinity or being-for-itself will make possible an account of how the infinite goes forth out of itself into its own finitude (e.g. how Platonic ideas may be instantiated in reality)
• “It is above all on the answer to this question that whether there is a philosophy is taken to depend” (122)
• The everyday expression “infinite” strongly suggests that this is the external other of the finite – this is one of the sources of incomprehension which gives the chance to everyday talk to shut the door towards philosophy
• But this mutually exclusive definition of infinity and finitude cannot survive theoretical scrutiny – they are conceptually incomprehensible in this rigid separation
• The division itself is only comprehensible by assuming the unity of the two sides
• “The claim that the finite is an idealization defines idealism” (124)
• “Every philosophy is essentially idealism or at least has idealism for its principle, and the question then is only how far this principle is carried out” (124)
• Idealization is commonly equated with subjective representation, but in fact idealization is a process of being which just is both subject and object
• True idealism takes subjectivity and objectivity as two moments of the process of idealization just in the same way as finitude and infinity are taken as two moments of true infinity