The 4th to 11th Tetractys

Fourth Tetractys: The Four Elements

The fourth tetractys is of the simple bodies fire, air, water, and earth, which have an analogy according to numbers.

What the monad was in the first tetractys, that fire is in this.

• The duad is air
• The triad is water
• The tetrad is earth.

For such is the nature of the elements according to tenuity and density of parts.

Hence fire has:

• the ratio of 1 to 2 to air
• the ratio of 1 to 3 to water
• the ratio of 1 to 4 to earth

In other respects, also they are analogous to each other.

Fifth Tetractys: Simple Bodies

The fifth tetractys is of the figures of the simple bodies.

• The pyramid is the shape of fire
• The octaedron is the shape of air
• The icosaedron is the shape of water
• The cube is the shape of earth

Sixth Tetractys: Life

The sixth tetractys is of things rising into existence through the vegetative life.

The seed is analogous to the monad and a point.

But if it increases in length it is analogous to the duad and a line. If in breadth, to the triad and a superficies; but if in thickness, to the tetrad and a solid.

Seventh Tetractys: Society

The seventh tetractys is of communities. The principle as the monad, is man. The duad is a house. The triad a street; and the tetrad a city. A nation consists of these.

These are the material and sensible tetractys.

Eighth Tetractys: Sense and Intellect

These are in the powers which form a judgment of things material and sensible, and which are of a certain intelligible nature – intellect, science, opinion, and sense.

Intellect, indeed, corresponds in its essence to the monad.

Science corresponds to the duad because science is the science of a certain thing.

Opinion subsists between science and ignorance.

Sense is as the tetrad because the touch which is common to all the senses being fourfold, all the senses energize according to contact.

Ninth Tetractys: Soul and Body

The ninth tetractys is that from which the animal is composed, the soul and the body.

The parts of the soul are:

• the rational
• the irascible
• the epithymetic, or that which desires external good
• the body in which the soul subsists.

Tenth Tetractys: Seasons

The tenth tetractys is of the seasons of the year, 334 through which all things rise into existence, viz. the spring, the summer, the autumn, and the winter.

Eleventh Tetractys

The eleventh is of the ages of man:

• the infant
• the child
• the adult
• the old adult

Hence there are eleven tetractys.

1. The first is that which subsists according to the composition of numbers.
2. The second is the multiplication of numbers.
3. The third subsists according to magnitude.
4. The fourth is of the simple bodies.
5. The fifth is of shapes.
6. The sixth is of things rising into existence through the vegetative life.
7. The seventh is of communities.
8. The eighth is the judicial power.
9. The ninth is of the parts of the animal.
10. The tenth is of the seasons of the year.
11. The eleventh is of the ages of man.

All of them however are proportional to each other.

A monad manifests as the following:

1. A monad
2. A monad
3. A point
4. A fire
5. A pyramid
6. A seed
7. A man
8. Intellect

Thus, if the first tetractys is 1, 2, 3, 4:

• The second is the monad, a side, a square, and a cube.
• The third is a point, a line, a superficies, and a solid.
• The fourth is fire, air, water, earth.
• The fifth the pyramid, the octaedron, the icosaedron, and the cube.
• The sixth, seed, length, breadth and depth.
• The seventh, man, a house, a street, a city.
• The eighth, intellect, science, opinion, sense.
• The ninth, the rational, the irascible, and the epithymetic parts, and the body.
• The tenth, the spring, summer, autumn, winter.
• The eleventh, the infant, the lad, the man, and the old man.

The universe is composed from these tetractys. It is perfect and being elegantly arranged in geometrical, harmonical, and arithmetical proportion. It comprehends every power, all the nature of number, every magnitude, and every simple and composite body.

But it is perfect, because all things are the parts of it, but it is not itself the part of any thing.

Hence, the Pythagoreans first used the before-mentioned oath, and asserted that “all things are assimilated to number.”

P. 111. This number is the first that partakes of every number, and when divided in every possible way, receives the power of the numbers subtracted, and of those that remain.

Because 6 consists of 1, 2 and 3, the two first of which are the principles of all number, and also because 2 and 3 are the first even and odd, which are the sources of all the species of numbers; the number 6 may be said to partake of every number.

In what Iamblichus afterwards adds, I suppose he alludes to 6 being a perfect number and therefore equal to all its parts.