Part 8

Errors of the Platonists and Pythagoreans

by Aristotle Icon

Some philosophers say that:

  • The universe is One.
  • It is made up of one kind of thing* as physical matter which occupies space

*Superphysics Note: In Superphysics, this is the aether. In modern physics, this seems to be the Higgs Field.

They mean the 4 elements of physical bodies only. These elements are:

  • air [spacetime]
  • fire [electromagnetism]
  • water [weak force (radioactive in Superphysics)]
  • earth [strong force (matter in Superphysics)]


They do away with the cause of movement* when:

  • trying to state the causes of creation and destruction
  • giving a physical account of all things

*Superphysics Note: This is because the Pythagoreans assign the cause of movement to a change in internal state.


  • do not believe in The Substance*, which I equate to The Essence which is the cause of anything, and how it produces the 4 elements.
  • call all the simple non-earth [non-material] bodies as The First Principle.

*Superphysics Note: In the Treatise of Human Nature, David Hume already tried to chase down what Aristotle’s Substance is. He concluded it to be Aristotle’s imagination. This is similar to Eintein’s spacetime being arbitrary, depending on the imagination of the theoretical physicist (i.e. Anyone can imagine his own spacetime structure just as Penrose uses General Relativity to imagine a universe that expands and collapses in cycles).

Some things are produced out of a combination of the 4 elements.

  • Others are produced by separation.
  • This creates the biggest errors to their cause and effect.

‘Error’ 1 of the Platonists and Pythagoreans

The property of being most elementary of all would belong to the First Thing from which they are produced by combination.

  • This property would belong to the most fine-grained and subtle of bodies.

This is why those who make fire [electromagnetism] the principle would mostly agree with my argument.

  • But the other thinkers agree that The One, the element of physical things is of fire.

At least none of those who named The One as the ultimate element claimed that earth [strong force] was that element, evidently because of the coarseness of its grain.

  • Of the other 3 elements, each has found some judge on its side. Some maintain that fire, others that water, others that air as the ultimate element.
  • Yet why do they not name earth* also, as most men do?

*Superphysics note: This is because Earth or solid matter is the end effect of The One.

People say all things are earth*. Hesiod says earth [strong force] was produced first of the physical things. So primitive and popular has the opinion been.

*Superphysics note: Yes, all material things are made up of matter (strong force). The strong force really is essential for physical matter.

One camp says that The First Principle is any of the elements other than fire.

  • Another camp says that The First Principle is denser than air but rarer than water.

According to this argument, none of them are correct.

‘Error’ 2 of the Platonists and Pythagoreans

The believers of The One say that:

  • that which is later in generation is prior in nature*
  • that which is concocted and compounded is later in generation

It follows that the contrary of what I have been saying must be true:

  • water must be prior to air
  • earth must be prior to water.

*Superphysics Note: This merely means that ’the latter in generation’ has its own properties. For example, electromagnetism (fire) is needed to create the strong force (earth). But the strong force has its own properties different from electromagnetism. Both electromagnetism and strong forces is generated by the idea (form) of The One.

So much, then, for those who posit One cause.

Empedocles’ Theory

Empedocles says that the matter of things is made up of 4 bodies.

  • But he too is confronted by consequences that have been mentioned.

Since those bodies are produced from one another, if follows that the same body does not always remain fire or earth.

In general, a change of quality is necessarily done away with for those who believe in The One, because it follows from their principles that cold will not come from hot nor hot from cold.

If it did, then:

  • there would be something that accepted the contraries themselves*
  • there would be some One entity that became fire and water, which Empedocles denies.

*Superphysics Note: The One does not change. It is the ideas from the One that changes. This has already been explained in full by Parmenides. Somehow, Aristotle mixes up the One and the ideas (forms) from the One, and treats them as one entity.

Anaxagoras’ Theory

Anaxagoras believes that there were 2 elements*. My supposition agrees with his.

*Superphysics Note: In 19th century physics, this was matter and ether. Einstein destroyed the ether and so matter became the First Principle to physics. This is why the Big Bang comes from a material singularity which the other elements of gravitation, electromagnetism, weak, and strong forces were mixed in. This is why physcists smash particles in expensive colliders to see what other elements are mixed in.

Is is true that in the beginning, all things were mixed. But it is absurd on other grounds because it follows that:

  • they existed before in an unmixed form
  • nature does not allow any chance thing to be mixed with any chance thing
  • modifications and accidents could be separated from substances (for the same things which are mixed can be separated)

Anaxagoras was somewhat modern in his views.

If nothingness was separated out of existence, then nothing could be truly asserted of the substance that then existed.

I mean that it was neither white nor black, but of necessity colourless. If it had been coloured, it would have had one of these colours. Thus, it had no attribute.

It could not be either of any quality or of any size, nor could it be any definite kind of thing.

  • For if it were, one of the particular forms would have belonged to it.
    • This is impossible, since all were mixed together
    • For the particular form would necessarily have been already separated out, but he all were mixed except reason, and this alone was unmixed and pure.

This is why Anaxagoras must say the principles are the One (for this is simple and unmixed) and the Other.

  • The One is the indefinite before it is defined and gets some form.

But these thinkers are at home only in arguments about generation and destruction and movement.

  • In reality, they were seeking my Substance as the source of the principles and causes.

Those who look at all things that exist suppose some to be perceptible and others not perceptible. They evidently study both classes.

  • This is why we should devote some time to seeing what is good and bad in their views from the viewpoint of Substance.

The Pythagoreans’ Theory

The ‘Pythagoreans’ treat of principles and elements stranger than those of the physical philosophers.

This is because:

  • they got the principles from non-sensible things
  • the objects of mathematics, except those of astronomy, are things without movement.

Yet their discussions and investigations are all about nature.

  • They generate the heavens
  • They observe phenomena with regard to their parts, attributes, functions
  • They use up the principles and the causes in explaining these

This implies that they agree with the physical philosophers that the real is just all that which is perceptible and contained by the so-called ‘heavens’.

But the causes and the principles which they mention are:

  • steps that go up to the higher realms of reality
  • more suited to higher realms than to nature.

They do not tell us at all:

  • how there can be movement if limit and unlimited, and odd and even, are the only things assumed.
  • how there can be generation and destruction without movement and change
  • how the bodies that move through the heavens can do what they do*.

*Superphysics Note: This was later explained by Descartes who gave 3 Rules of Movement

If space consists of these elements how would some bodies be light and others have weight*?

*Superphysics Note: This is answered by gravitation which is a property of spacetime or the Air element which is an idea from The One

The Pythagoreans deal only with theoretical mathematical bodies and not of perceptible ones.

  • This is why they have said nothing about fire, earth, or the other bodies made up of their elements.
  • I suppose this is because they have nothing to say which applies to perceptible things.

They believe that:

  • the attributes of number, and number itself, are causes of what exists and happens in the heavens from the beginning up to now
  • the One is the only number out of which the world is composed.

How is it possible to combine* both beliefs?

*Superphysics Note: We solve this by creating two domains of reality – the physical domain of Aristotle and the metaphysical domain of Plato. This is done in programming where there is a codebase which then is the foundation of the app or virtual reality.

They say that in a region:

  • opinion and opportunity, and a little above or below, injustice and decision or mixture, are each of them a number
  • a plurality of the extended bodies composed of numbers exist because these attributes of number attach to the various places

These numbers represent each of these abstractions.

Are they the same numbers exhibited in the material universe, or are they different*?

*Superphysics Note: They are different just as the code for a website that you write becomes different when rendered by the web server or web browser. But they are the same if you see the code and website as one idea or one goal. This unificiation is what Qualimath will do, by assigning numbers to qualities, instead of just quantity.

Plato says it is different.

  • Yet even he thinks that both these bodies and their causes are numbers, but that the intelligible numbers are causes, while the others are sensible.


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