More of my Untenable Thoughts on Euclidean Geometry

The parallel postulate is an axiom, and the real world is more easily described by non-Euclidean geometry. This is not to say that Euclidean geometry doesn’t apply to the real world.

 

To say that only Euclidean or non-Euclidean geometry applies to the real world are both metaphysical statements. There is no evidence that denies Euclidean geometry from applying to the real world, because nothing says its IMPOSSIBLE for you to describe space and light as Euclidean.

 

In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not. It would be silly to attempt this. Its an arbitrary designation made for modeling.

 

However, to say that the mind perceives things as Euclidean is correct. You cannot visualize any non-Euclidean geometry, without visualizing it as Euclidean geometry. That is mental capacity of our mind, and is an inductive observation.

 

I can prove this by asking you to draw an instance where the parallel postulate is invalid. Since its not possible for you to draw this, then its sufficiently proven.

 

Schopenhauer had similar arguments shown here: http://en.wikipedia.org/wiki/Schopenhauer%27s_criticism_of_the_proofs_of_the_Parallel_Postulate

 

So when people say the universe is Euclidean, it is the same as saying the mental capacity of the human mind only perceives Euclidean space. Objectively, the universe is not necessarily Euclidean, non-Euclidean, or any geometry at all. Any geometry is a mental analytical conception.

 

This is where the confusion arises. Mises never used the term “axiom” because the basis of praxeology is formed of statements about the nature of how humans perform actions, which is inductive.

 

Everything derived from this is apriori, and is based on the analysis of the causal factors of human actions.

 

This isn’t like geometry because these are not constructions for the purposes of modeling reality. They are observations about reality itself. They are inductions from introspection that are validated by literally asking any person.

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