Cosmology: The early pythagoreans believed that the limited
and the unlimited
are the ultimate principles of the Kosmos. The basic cosmological idea is that definition (the definite or the limited) is imposed upon what lacks definition (the indefinite or the unlimited) to form being. Everything other than the limited and the unlimited is ultimately composed of numbers. (Here the One
is taken to be the first number, but the One has a special status and may not have been considered a number. Zero was unknown to the Greeks at this time.) The mathematical unit was believed to possess actual magnitude; the abstract was, thus, considered to be concrete; hence, the magnitude of the mathematical unit serves as a kind of "stuff", along the lines of the stuff of the Milesians.
There are three stages in the development of the Kosmos: First, numbers are generated from the limited (the odd) and the unlimited (the even); second, the geometrical solids are generated from numbers; third, physical objects are generated out of the geometrical solids. Early Pythagoreanism seems to be a dualistic system, since it would appear that the limited and the unlimited are distinct and independent kinds of being. However, if the One is the only and ultimate substance, it may have been a monistic system.
-The Kosmos exists eternally, and every individual event in the universe recurs eternally.
-The human soul is immortal. It owes its immortality to its kinship with the divine and universal soul, and it can migrate from body to body. After death, it can be reunited with the universal soul if it is purified. Note the connection here with the Orphic view of the soul.
-The early Pythagoreans understood philosophy to be the means of purifying the soul. Since the human soul -like everything else- is ultimately a harmonious proportion of numbers, philosophy was seen as the method for correlating the ratio of the soul with the ratio of the Kosmos, thereby achieving a harmonious state.