Commentary on Infinity

Some additional problems with the concept of infinity:

It is impossible that an absolutely infinite series of different facts, each of them consisting of the existence of something at a different moment of time, should have elapsed in given moments. An infinite series of this sort is impossible. These impossible unending phenomena are just that, phenomena in a factual world. They are supported by a series of facts. In other words, facts can not be infinite.

We must apply the notion of the infinite to real things and to facts; that is to the things that exist in time, and when we do this, the notion of infinity has no factual meaning for us. We can, of course, approach infinity factually, as is done in mathematics (calculus etc), but this is a tool for measurements etc., and we never actually reach infinity in mathematics.

We may speak about the movement of ideas, the relation of ideas, and the rational development of these ideas as they logically relate to each other as human constructs. We may speak of these thoughts in infinite terms, but if they are related to facts in the universe, then there is no infinite knowledge that can be determined, based upon the above statements.

We can not apply factual properties to the concept of an infinite God, since the concept of God contains the attribute of infinity, which attribute is inseparable from the concept of God. Since this infinity concept can not be excluded from any conclusion about the deity’s existence, then we may only include the existence of God as an idea and not a fact. This places the existence of God in a separate domain of being, that is, that God is not a fact, but an idea.

Hegel would agree that factual properties can not be used to establish the existence of an infinite God and he uses this to attempt to refute Kant. But Kant did not use factual properties to challenge the arguments for the existence of the deity. Kant merely showed that we do have some sense of realty with these factual properties, but we have no cognitive sense of the reality without factual properties and thus no cognitive sense of reality of God. Kant also showed that these factual properties could not lead to the proof for the existence of God.


Some of these thoughts come from G.E.Moore’s “Some Main Problems in Philosophy.”