On the relation between conceptualization and reality

Round things, like circles, appear like magic for science. The fact that the relation between the diameter and the circumference of a circle is the irrational number called “pi” means that if we start from one position on the circumference of a circle and mark a point on that circumference at every point that is one diameter away, we will never mark a point on another point. The number of such points is thus infinite.

This fact suggests that the number of numbers is infinite, which is a contradiction. For example, it suggests that the number of odd numbers equals the number of even numbers, which contradicts the consistent assumption that the number of numbers is the sum of the number of odd numbers and the number of equal numbers.

So, how can the fact of circles be true? Well, the answer is that there are two orthogonal (ie, diametrically opposed) approaches to reality, whereof both are inconsistent. The factual approach is inconsistent in suggesting that the number of odd numbers equals the number of even numbers, whereas the approach that the number of numbers is the sum of the odd numbers and the even numbers is false.

The fact of circles does thus tell us that the door to the truth is closed by two orthogonal (ie, diamerically opposed) locks. There is thus no way to find out what is hidden behind this door, but  instead we have to be content with being able describe reality consistently.

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