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“One cannot step twice in the same river.”
(ca. 540 – ca. 480 BCE)
•Defend/rebuke and explain your rationale.
•75+ words.
•Select Team member to orally present.
(ca. 540 – ca. 480 BCE)
(ca. 540 – ca. 480 BCE)
Heraclitus lived in Ephesus, an important city on the
Ionian coast of Asia Minor, not far from Miletus, the
birthplace of philosophy.
Little is known, except
from his writings.
(ca. 540 – ca. 480 BCE)
Heraclitus criticizes his predecessors and
contemporaries for their failure to see the unity in
Opposites are necessary for life, but they are unified
in a system of balanced exchanges.
The world itself consists of a law-like interchange of
elements, symbolized by fire.
(ca. 540 – ca. 480 BCE)
Thus, the world is not to be identified with any
particular substance, but rather with an ongoing
process governed by a law of change.
The underlying law of nature
also manifests itself as a
moral law for human beings.
Heraclitus first Western
philosopher to go beyond
physical theory in search of
metaphysical foundations
and moral applications.
(ca. 540 – ca. 480 BCE)
His message:
>reality is constantly changing
>reality an ongoing process rather than a fixed
and stable product.
Buddhism shares a similar metaphysical view:
>annica -- the claim that all reality is fleeting
and impermanent.
(ca. 540 – ca. 480 BCE)
>In modern times Henri Bergson (1859 – 1941)
described time as a process that is experienced.
>An hour waiting in line is different from an hour at
>Today contemporary physics lends credence to
process with the realization that even apparently
stable objects, like marble statues, are actually
moving, buzzing bunches of electrons and other
subatomic particles.
“It is only necessary to make war with
five things; with the maladies of the body,
the ignorances of the mind, with the
passions of the body, with the seditions of
the city and the discords of families.”
•Defend/rebuke and explain your rationale.
•75+ words.
•Select Team member to orally present.
• Pythagoras, (b. 580B.C.-507B.C.)
• ”all things are numerable & can be
– e.g. in geometry, angles are
measured by the number of
– Number is a very vital aspect of
the universe & is fundamental in it.
– Symmetry
580 B.C.E. - 507 B.C.E.
580 B.C.E. -507 B.C.E.
Thales & Anaximander
(1) that at its deepest level, reality is mathematical in
(2) that philosophy can be used for spiritual purification,
(3) that the soul can rise to union with the divine,
(4) that certain symbols have a mystical significance, and
(5) that all brothers of the order should observe strict loyalty
and secrecy.
…the dependence of the dynamics of world structure on the
interaction of contraries, or pairs of opposites;
…the viewing of the soul as a self-moving number
experiencing a form of metempsychosis, or successive
reincarnation in different species until its eventual
purification (particularly through the intellectual life of the
ethically rigorous Pythagoreans);
…understanding ...that all existing objects were
fundamentally composed of form and not of material
Further Pythagorean doctrine ... identified the brain as the
locus of the soul; and prescribed certain secret cultic
Pythagorean Theories
•(i) The sum of the angles of a triangle is equal to two right angles.
Also the Pythagoreans knew the generalization which states that a
polygon with n sides has sum of interior angles 2n - 4 right angles and
sum of exterior angles equal to four right angles.
•(ii) The theorem of Pythagoras - for a right angled triangle the square
on the hypotenuse is equal to the sum of the squares on the other two
sides. We should note here that to Pythagoras the square on the
hypotenuse would certainly not be thought of as a number multiplied
by itself, but rather as a geometrical square constructed on the side. To
say that the sum of two squares is equal to a third square meant that
the two squares could be cut up and reassembled to form a square
identical to the third square.
•(iii) Constructing figures of a given area and geometrical algebra. For
example they solved equations such as a (a - x) = x2 by geometrical
Pythagorean Theories
•(iv) The discovery of irrationals. This is certainly attributed to the
Pythagoreans but it does seem unlikely to have been due to
Pythagoras himself. This went against Pythagoras's philosophy the all
things are numbers, since by a number he meant the ratio of two
whole numbers. However, because of his belief that all things are
numbers it would be a natural task to try to prove that the hypotenuse
of an isosceles right angled triangle had a length corresponding to a
•(v) The five regular solids. It is thought that Pythagoras himself knew
how to construct the first three but it is unlikely that he would have
known how to construct the other two.
•(vi) In astronomy Pythagoras taught that the Earth was a sphere at
the centre of the Universe. He also recognized that the orbit of the
Moon was inclined to the equator of the Earth and he was one of the
first to realize that Venus as an evening star was the same planet as
Venus as a morning star.