HISTORY OF ANCIENT PHILOSOPHY: A SUMMARY (based on the book of Ignatius Yarza: History of
Ancient Philosophy)
ANCIENT PHILOSOPHY
AB PHILOSOPHY
SACRED HEART SEMINARY
II. The Pythagoreans
Pythagoras and his school
Pythagoreanism is more of a religious sect than a Philosophical school.
Derived its name from their founder named Pythagoras.
Pythagoras himself wrote nothing , and his disciples shrouded his teachings in an atmosphere of
secrecy, revealing them only to the initiated members of the sect.
Number, the principle of all things
Pythagorean philosophy shows interest in cosmology. They studied nature like the Ionians.
They sought to discover the unifying principle of all reality.
They identified this with number, and hence, for the first time, departed from the tradition of
designating a material substance (air, water, fire, etc) as the first principle.
For them, numbers are not beings of reason, concepts which results from the use of abstraction.
So what are then numbers?
The answer to this question will be clearer if we understand how the Pythagoreans arrived at
their solution. It was their study of Mathematics that led them to reduce all of reality to a series
of numerical relations.
Like previous philosophers, they had observed the different characteristics of phenomena. From
their observations, they saw that these characteristics followed clear mathematical patterns. Natural
Phenomena followed an order which could also be measured numerically- the duration of the year,
the seasons, the length of day, etc. Hence, they concluded that number and its elements constituted
the principle of all things: Number constituted the essence and substance of all that was real.
Elements of Number: Odd- Even; Limited- Unlimited
Everything then is reducible to number. But in its turn, number itself is further divisible into a
number of categories.
This means that every number can always be divided into even and odd elements. It follows
from this that even and odd elements constitute the universal elements of number, and hence,
all things as well.
But since the even is identified with the unlimited and the odd with the limited, everything must
be composed of this pair of contrasts.
The pythagoreans arrived at this reduction of the even and odd to the unlimited and the limited
through their study if number and through the geometrical interpretation they gave to it.
Since they did not have any way of representing the different numbers, they used points instead,
and with these points they made different geometrical figures.
The figure that represented an even number they found to be infinitely divisible, whereas that
which represented an odd number was not.
Hence, they identified the even number with the unlimited or infinite, and the odd number with
the limited or finite. Therefore, every reality was composed of and unlimited element and a
limited element.
The Pythagoreans associated the unlimited to the imperfection and the lack of reason and
intelligibility in things.
They therefore, did not identify the unlimited with God, for if the infinite is conceived in material
things, it cannot be identified with a being which, like God, is supposed to be supremely perfect.
Man and the Soul
Pythagoreanism taught the immortality and transmigaration of the soul.
Ancient Philosophy)
ANCIENT PHILOSOPHY
AB PHILOSOPHY
SACRED HEART SEMINARY
II. The Pythagoreans
Pythagoras and his school
Pythagoreanism is more of a religious sect than a Philosophical school.
Derived its name from their founder named Pythagoras.
Pythagoras himself wrote nothing , and his disciples shrouded his teachings in an atmosphere of
secrecy, revealing them only to the initiated members of the sect.
Number, the principle of all things
Pythagorean philosophy shows interest in cosmology. They studied nature like the Ionians.
They sought to discover the unifying principle of all reality.
They identified this with number, and hence, for the first time, departed from the tradition of
designating a material substance (air, water, fire, etc) as the first principle.
For them, numbers are not beings of reason, concepts which results from the use of abstraction.
So what are then numbers?
The answer to this question will be clearer if we understand how the Pythagoreans arrived at
their solution. It was their study of Mathematics that led them to reduce all of reality to a series
of numerical relations.
Like previous philosophers, they had observed the different characteristics of phenomena. From
their observations, they saw that these characteristics followed clear mathematical patterns. Natural
Phenomena followed an order which could also be measured numerically- the duration of the year,
the seasons, the length of day, etc. Hence, they concluded that number and its elements constituted
the principle of all things: Number constituted the essence and substance of all that was real.
Elements of Number: Odd- Even; Limited- Unlimited
Everything then is reducible to number. But in its turn, number itself is further divisible into a
number of categories.
This means that every number can always be divided into even and odd elements. It follows
from this that even and odd elements constitute the universal elements of number, and hence,
all things as well.
But since the even is identified with the unlimited and the odd with the limited, everything must
be composed of this pair of contrasts.
The pythagoreans arrived at this reduction of the even and odd to the unlimited and the limited
through their study if number and through the geometrical interpretation they gave to it.
Since they did not have any way of representing the different numbers, they used points instead,
and with these points they made different geometrical figures.
The figure that represented an even number they found to be infinitely divisible, whereas that
which represented an odd number was not.
Hence, they identified the even number with the unlimited or infinite, and the odd number with
the limited or finite. Therefore, every reality was composed of and unlimited element and a
limited element.
The Pythagoreans associated the unlimited to the imperfection and the lack of reason and
intelligibility in things.
They therefore, did not identify the unlimited with God, for if the infinite is conceived in material
things, it cannot be identified with a being which, like God, is supposed to be supremely perfect.
Man and the Soul
Pythagoreanism taught the immortality and transmigaration of the soul.
