Parmenides - On Nature Metaphysical Poem. Parmenides -Plato. A Classic of the Academy : Socrates while Young. Philo :Works. Spinoza -Theological -Political Treatise. St Thomas Aquinas , the 'Angelic doctor' whose. Era of the Scholastic Churchmen. Offered for Critical Appraisal. Metaphysics- Al Kindi.
The Incoherence of the Philosophers - Al Ghazali. The Incoherence of 'The Incoherence' -Averoes. Euclid's Elements. Written in Alexandria B. The Authoritative Text on Geometry. From The College of the Magi. Prologue To Future Metaphysics - Kant. Meditations- Rene Descarte. World As Will and Idea - A. Appearance and Reality- F. Monadology -Leibniz. Who Revived Science from the Age of Darkness. Relativity ;. The Special and General Theory - Einstein. Turner, Global Vision Publishing Ho, , p.
Drozdek, Ashgate Publishing, Ltd. The Good is identified with Being. Being, the One, Intelligence, providence, the Good, divinity, are merely different names for the same thing. Becoming, the many, evil, are the names of its opposite, not-being. Multiplicity is thus identified with evil, and both are declared illusory. Evil has no real existence and only the Good truly is. The various virtues, as benevolence, temperance, prudence, are merely different names for the one virtue, knowledge of Being.
Both Eubulides of Miletus fl.
Clinomachus was the first who composed treatises on the fundamental principles of dialectics and founded the Dialectical school. Diodorus Cronus died ca. Aristotle thought statements about the future lack any truth value. They are neither true nor false until the future time when they become true or false not determined. The Master Argument is a logical contradiction between three propositions: every past truth must be necessary past, actual an impossibility does not follow from a possibility no temporal relation something is possible which neither is nor will be true future, potential Given the first two, it is apparent that the third is false, and we can conclude that nothing is possible which is not true and never will be.
The Master Argument is a question about the ontological status of the possible, the potential, as compared to the actual. Diodorus put forward that the existence of true statements about the future imply that the future is already determined. The aspect of time and growth of information is ignored by Diodorus, because information about future potential events does not come into existence until the potential events become actual e. Pythagoreanism is the philosophy of a group of philosophers active in the fifth and the first half of the fourth century BCE.
Pythagoras ca. For the members what was done and taught among the members was kept a profound secret towards all. Candidates had to pass through a period of probation, in which their powers of maintaining silence or verbal restraint echemythia were especially tested, as well as their general temper, disposition, and mental capacity. For the Pythagoreans 'echemythia' was a discipline to be observed by the initiated in order not to disclose the truths they were learning about the divine.
The verbal restraint also referred to Harpocrates , the Greek god of Silence and Secrecy. The Pythagoreans were divided into an inner circle called the 'mathematikoi' "learners" and an outer circle called the 'akousmatikoi' "listeners". These two groups developed into two separate schools of thought. The 'akousmatikoi' focused on the more religious and ritualistic aspects of Pythagoras' teachings, while the 'mathematikoi' extended and developed the more mathematical and scientific work he began see also The Cambridge Companion to Early Greek Philosophy , A.
Long, Cambridge University Press, , p. The 'akousmatikoi' claimed that the 'mathematikoi' were not genuinely Pythagorean, but followers of the "renegade" Pythagorean Hippasus of Metapontum fl.
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The 'mathematikoi', on the other hand, allowed that the 'akousmatikoi' were indeed Pythagorean, but felt that they were more representative of Pythagoras' real views. The 'mathematikoi' eventually became closely associated with Plato and Platonism , and much of Pythagoreanism seems to overlap Platonism. Horky, Oxford University Press, , p. The Pythagoreans developed both a "theoria" and a "cosmology" about the universe. Theoria is a Greek word meaning contemplation and observation and theoria was the contemplative and mystical part of the tradition held by the 'akousmatikoi'.
The basis of this Pythagorean tradition was the Orphic mythology , especially the Orphic cosmogenesis. Theoria contained the mystical understanding of the universe, and cosmos was the rational or scientific study and perception of the world. Theoria and kosmos were closely linked to each other, like two sides of a single coin. Theoria was the mystery tradition itself, and cosmos the scientific study sprung from it.
The cosmology of the 'mathematikoi' was the beginning of scientific thinking about the world. The division between 'akousmatikoi' and 'mathematikoi' resembles the modern division between faith theology and reason science. The two sides remain, but the joining coin in between faith and reason seems to have disappeared see also Orphism, Pythagoreanism and the Mysteries , C. Buxton, Oxford University Press, , p.
Most notable Pythagoreans were Pythagoras himself, Philolaus ca.
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The last manifestation of Pythagoreanism was Neopythagoreanism. It began already in the second half of the fourth century BCE among Plato's first successors in the Academy, but particularly flourished from the first century BCE until the end of antiquity. Apollonius of Tyana ca. Neopythagoreanism also became influential among the Greeks of Alexandria from the 3 rd century onwards as the Alexandrian School of philosophy.
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Neopythagoreanism also has close connections to Middle and Neoplatonism and from the time of Iamblichus ca. It was the Neopythagorean version of Pythagoreanism that dominated in the Middle Ages and Renaissance. Pythagoras is credited to have initially explored the mathematical relationship within figurate numbers. Figurate numbers are numbers that can be represented by a regular geometrical arrangement or sequence of evenly spaced points. Figurate numbers are most commonly expressed in the form of regular triangles, squares, pentagons, hexagons, etc.
While Pythagoras of Samos ca. Pythagoras founded a brotherhood of disciples in Croton in southern Italy dedicated to philosophia, a term derived from the Greek word philo, meaning "love", and sophia, meaning "wisdom". The term philosophia, "love of wisdom", is first used in Pythagorean circles and Pythagoras said philosophers were "lovers of wisdom".
Stanley, Nicolas-Hays, Inc. Ferguson, Icon Books, Pythagoras became famous for his ideas about number, the fate of the soul Metempsychosis , as a wonder-worker and for the Pythagorean way of life. For Pythagoras and the Pythagoreans Number is a universal archetype of Nature physis , "the principle, source, and root of all things.
Pythagoras developed, from the apeiron boundless concept of Anaximander ca. Pythagoras believed that the apeiron had inhaled the void from outside, filling the cosmos with vacuous bubbles that split the universe into many inter-connected parts separated by "void", and that this play of apeiron and peiron takes place according to a natural harmony.
The cosmos and everything in it is made up of these two basic types of things: limiters peras and unlimiteds apeiron. Unlimiteds are continua undefined by any structure or quantity; they include the traditional Presocratic prote hule or materia prima. Limiters set limits in such unlimiteds and include shapes and other structural principles. Limiters and unlimiteds are not combined in a haphazard way but are subject to a "fitting together" or "harmonia", which can be described mathematically.
As the whole world is structured according to number, we only gain knowledge of the world insofar as we grasp these numbers cfr. The Pythagoreans engaged in the study of number theory or arithmetic number in itself , geometry number in space , harmonics or tuning theory number in time , and astronomy number in space and time. The study of arithmetic was given before anything else, so fundamental was the doctrine of Number for their philosophical school.
Since number and its qualities such as polarity, harmony, and proportion are archetypal principles that underlie physical manifestation, mathematics is discovered rather than invented, and possesses the power to reflect the essential nature of reality, rather than just modeling it or describing it. Moreover, in the Pythagorean view, because number is universal, it is also divine. In a theory known as the Harmony of the Spheres Musica universalis , Pythagoras proposed that the Sun, Moon and planets all emit their own unique hum orbital resonance based on their orbital revolution, and that the quality of life on Earth reflects the tenor of celestial sounds which are physically imperceptible to the human ear.
The central focus of Pythagorean thought is in many respects placed on the principle of Harmonia or Divine Harmony.
The Universe is One, but the phenomenal realm is a differentiated image of this unity, the world is a unity in multiplicity. What maintains the unity of the whole, even though it consists of many parts, is the hierarchical principle of harmony, the Logos of relation, which enables every part to have its place in the fabric of the all.
Pythagoras was the first person to call the universe a kosmos.