Quoted By:
An irrational number is a number. But what is a number? A number is a quantity. But what is a quantity? A quantity is a relation that relates itself to itself, or is the relation's relating itself to itself in the relation; a quantity is not the relation but is the relation's relating itself to itself. An irrational number is a synthesis of the infinite and the finite, of the temporal and the eternal, of freedom and necessity, in short, a definition. A definition is a relation between two. Considered in this way, an irrational number is still not a quantity.
In the relation between two, the relation is the third as a negative unity, and the two relate to the relation and in the relation to the relation; thus under the qualification of the mathematical the relation between the mathematical and the physical is a relation. If, however, the relation relates itself to itself, this relation is the positive third, and this is a quantity.
Such a relation that relates itself to itself, a quantity, must either have established itself or have been established by another.
If the relation that relates itself to itself has been established by another, then the relation is indeed the third, but this relation, the third, is yet again a relation and relates itself to that which established the entire relation.
An irrational number is such a derived, established relation, a relation that relates itself to itself and in relating itself to itself relates itself to another. This is why there can be two forms of quantification in the strict sense. If an irrational number had itself established itself, then there could be only one form: quantifying another, to do away with oneself, but there could not be the form: to quantify oneself.
