Two Systems
Table of Contents
We will compare the Aristotelian and Ptolemaic system versus the Copernican system.
Copernicus places the earth among the movable heavenly bodies, making it a globe like a planet.
We will examine the Peripatetic steps in arguing the impossibility of that hypothesis.
what they are, and how great is their force and effect. For this it is necessary to
We introduce 2 substances which differ essentially:
- Celestial
This is invariant and eternal
- Elemental
This is temporary and destructible.
Aristotle explains this in his book De Caelo.
Simplicio is the defender of Aristotelian doctrines.
The first step in the Peripatetic arguments is Aristotle’s proof of the completeness and perfection of the world.
He tells us that the world is not a mere line, nor a bare surface, but a body having length, width, and depth.
This makes the Whole perfect.
What about his definition of “continuous”?
He first proved that there are no more than 3 dimensions, since Three is everything, and everywhere?
This is confirmed by the doctrine of the Pythagoreans who say that all things are determined by 3 – beginning, middle, and end – which is the number of the Whole.
He says 3 is used, as if by a law of nature, in sacrifices to the gods.
“All” means those things that are three, and not less.
- For two are called “both,” and one does not say “all” unless there are three.
Therefore among figures only the solid is complete.
Solid is alone determined by three, which is All.
Solid is divisible in 3 ways, so it is divisible in every possible way.
Of the other shapes, one is divisible in one way, and the other in two. This is because their divisibility and continuity depend on the number of dimensions allotted to them.
Thus one figure is continuous in one way, the other in two.
But the third, namely the solid, is so in every way.
Aristotle has sufficiently proved that:
- there is no passing beyond the 3 dimensions, length, breadth, and thickness
- the body, or solid, which has them all, is perfect
Whatever has a beginning, middle, and end may and should be called perfect.
I do not feel that 3 is a perfect number.
I do not believe that 3 legs is more perfect than 4 or 2.
4 is not an imperfection in the elements.
3 is not more perfect than 4.
But these are the doctrines to the Pythagoreans.
The Pythagoreans held the science of the human understanding and believed it to partake of divinity simply because it understood the nature of numbers.
I agree a little with them.
But Pythagoras and his sect was totally wrong to venerate the science of numbers.
The Pythagoreans:
- condemned as sacrilegious the publication of the most hidden properties of numbers or of the incommensurable and irrational quantities which they investigated.
- taught that anyone who had revealed them was tormented in the other world.
I am not among those curious about the Pythagorean mysteries.
Aristotle’s reasons for having only 3 dimensions is conclusive.