The Finite and the Infinite (1)

In my previous blog I mentioned in passing that a theologian can not accept the principle that the finite is contained within the infinite. I hinted at the possibility of understanding the relation between the finite and infinite in a different way by invoking the formula to allow the finite to be finite.

I am aware of the fact that such brief statements more often than not increase confusion and demand a full philosophical demonstration. Bob’s question about my arguments for this statement however opens up a large warehouse full of worms.

But I accept the responsibility of at least elucidating why I said what I said, leaving the true exposition on the list of future assignments.

Let me identify the problem and explain the position that Hegel reaches first. In the next blog I will explain the other option.

If the finite is not contained within the infinite, the finite is external to the infinite and therefore the finite limits the infinite. If the infinite however is limited by the finite, it is finite by default.

The Abstract Infinite

Hegel discusses the nature of spurious or bad infinity in paragraph 94 of his Encyclopedia. There is such a thing as a negative infinity which is only the negation of the finite. When we conceive of reality as simply existing, as a simple something (Etwas), we use a category that implies both affirmation and negation or limitation. Something is always different from something else (Anderes). Something always becomes something else, which then in turn becomes something that becomes something else again and so forth. This movement that arises from the inner nature of the category of something, seems to go on ad infinitum. The world seems to present itself as the endless transition from something to another something.

Hegel argues that this endless transition is an abstract or negative infinity. It has no positive meaning but it simply expresses the necessity to move beyond anything finite. The transitoriness implies that something becomes an other, and the finitude implies that every something is different from something else. The abstract infinite appears as the endless transition between both these determinations. Now this is what we normally would think of as infinity, as that which simply goes on and on. Our understanding can easily create such an infinity because it’s the product of a simple negation. Infinity is then just the abstract negation of the finite, the unending.

The Abstract Infinite is Finite

If the infinite is just the opposite of the finite however, then this opposition implies a limitation of the infinite. If the finite is not the infinite, then the infinite is not the finite. It is limited by what it is not, i.e. by the finite. But that was the nature of the finite to begin with! If the infinite is limited by the finite, then it is finite itself. True infinity therefore cannot stand in opposition to the finite. The only way that is left for the infinite to be genuinely infinite will then be for it to contain the finite within itself. The opposition between the finite and the infinite would have to be removed. If the infinite however absorbs the finite as its internal moment it can remain what it is. The infinite and the finite should not be seen as externally related, but as internally related. Only because the true infinite contains the finite with the itself it is not limited, or defined by anything other than itself.

True Infinity

In paragraph 95 of the encyclopedia Hegel explains the nature of true infinity. In the transition of something to something else, i.e. its other, logically speaking something remains the same. Although we move from one to the other, this other is logically the same, because it again is a something. We did not change the something so that it becomes something else, in a way we changed the something else, the other, to become something. So what happened? We had something from which we distinguished something else, and then this something else, the other, became something. The otherness of this other therefore was negated and by this negation of the negation the positive meaning of something was reestablished. This is what Hegel called the true infinity; the transition from one to the other implies the negation of its own otherness, which is called being for it (Für-sich-sein).

The False Dualism of Finite and Infinite

As such these remarks about finitude and infinity belong to the first cycle of the logic of being which deals with the categories of quality, that is to say the categories that  express reality as a positive immediate like being, or something, or becoming. But already these categories of immediacy have been used to express the nature of God and reality as such. In the addition to paragraph 95 Hegel points to a way of thinking in which the opposition between the finite and infinite is taken to be something absolute. The finite and infinite limit each other and therefore the infinite is in itself finite. The result is that the finite has the same kind of existence and independence as the infinite, and the infinite has the same kind of determination and limitation as the finite. It is obvious that in such a dualism between the finite and the infinite the meaning of both has been changed completely.

The Infinite as Spirit and Idea

In a positive sense Hegel identifies the spirit with the Infinite, which is expressing itself according to paragraph 95 in the shape of the dialectic process, with the Absolute Spirit operating through the dialectic process in the annihilation of all finite determinations. It is the nature of the finite to be only in transition, as a continuous transcending of itself, in other words the finite is not, i.e. it is not the True. The spirit however is the eternal infinite in itself, as the negation of the finite from within. (Compare paragraph 386 of the encyclopedia.)

Infinity of the Spirit

The infinite therefore according to Hegel must ultimately be conceived as subjectivity, as idea or spirit. It is identical with itself. But this identity is not abstract or witout movement. It has to have an identity that goes through its other and returns to itself. That other must be identical however. In some way this ‘other’ must be itself. How can we express that? We can say that the spirit in order to be identical to itself, has to oppose itself to itself, and by transcending that very opposition become identical to itself. In as much as it opposes itself to itself, it also determines and negates itself as the finite, that can now be understood as a moment within the movement of the absolute as Spirit. The absolute in other words alienates itself from itself, and posits itself externally as nature. By understanding the nature that is its other, it returns to itself as Spirit.

Hegel’s Critique of Traditional Theology

It is on this basis that Hegel holds that traditional theology is fundamentally mistaken. By claiming that the infinite God and finite creation must be absolutely distinct, theology actually cancels God’s infinity. It is therefore necessary to argue that God contains the world as a moment of his own being. Any other way of looking at it must imply that  infinity is limited by the finite, and therefore becomes finite itself.

To be continued…

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