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1 The philosopher Zeno of Elea centred one of his paradoxes on an imaginary footrace between "swift-footed" Achilles and a tortoise, by which he attempted to show that Achilles could not catch up to a tortoise with a head start, and therefore that motion and change were impossible.
2 The ancient Greek philosopher Zeno of Elea gave several famous examples of such paradoxes.
3 And: Furthermore, they find Xenophanes, Zeno of Elea, and Democritus to be sceptics: … Democritus because he rejects qualities, saying,"Opinion says hot or cold, but the reality is atoms and empty space," and again, "Of a truth we know nothing, for truth is in a well."
4 He attributes dialectics to Heraclitus rather than, as Aristotle did, to Zeno of Elea.
5 The paradoxes of Zeno of Elea depend in part on the uncertain interpretation of 0. (The ancient Greeks even questioned whether 1 was a number.) The late Olmec people of south-central Mexico began to use a symbol for zero, a shell glyph, in the New World, possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar.
6 He was the founder of the Eleatic school of philosophy, which also included Zeno of Elea and Melissus of Samos.
7 according to doxographer Diogenes Laërtius, he flourished just before 500 BC, which would put his year of birth near 540 BC, but in the dialogue Parmenides Plato has him visiting Athens at the age of 65, when Socrates was a young man, c. 450 BC, which, if true, suggests a year of birth of c. 515 BC. Parmenides was the founder of the School of Elea, which also included Zeno of Elea and Melissus of Samos.
8 This line begins with Xenophenes and goes through Parmenides, Melissus of Samos, Zeno of Elea, Leucippus, Democritus, Protagoras, Nessas of Chios, Metrodorus of Chios, Diogenes of Smyrna, Anaxarchus, and finally Pyrrho.
9 In the case of that apparent paradox of a time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one which leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to. W. V. O. Quine (1962) distinguished between three classes of paradoxes: According to Quine's classification of paradoxes: A fourth kind, which may be alternatively interpreted as a special case of the third kind, has sometimes been described since Quine's work: A taste for paradox is central to the philosophies of Laozi, Zeno of Elea, Zhuangzi, Heraclitus, Bhartrhari, Meister Eckhart, Hegel, Kierkegaard, Nietzsche, and G.K. Chesterton, among many others.
10 Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West and early Indian mathematicians in the East, mathematicians had struggled with the concept of infinity.
11 Significant figures include: the Milesians, Heraclitus, Parmenides, Empedocles, Zeno of Elea, and Democritus.
12 This doctrine was defended by his younger countryman Zeno of Elea (490-430 BC) in a polemic against the common opinion which sees in things multitude, becoming, and change.
13 Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
14 He enjoyed the company of the philosophers Protagoras, Zeno of Elea, and Anaxagoras.
15 The main chapters alternate with dialogues between imaginary characters, usually Achilles and the tortoise, first used by Zeno of Elea and later by Lewis Carroll in "What the Tortoise Said to Achilles".
16 Aristotle said that it was the pre-Socratic philosopher Zeno of Elea who invented dialectic, of which the dialogues of Plato are the examples of the Socratic dialectical method.
17 He has been called the discoverer of logic, Zeno of Elea, a pupil of Parmenides, had the idea of a standard argument pattern found in the method of proof known as reductio ad absurdum.
18 Zeno of Elea (/ˈziːnoʊ ... ˈɛliə/; Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 495 – c. 430 BC) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides.
19 The conceptual origins of the concept of the infinitesimal 1/∞ can be traced as far back as the Greek philosopher Zeno of Elea, whose Zeno's dichotomy paradox was the first mathematical concept to consider the relationship between a finite interval and an interval approaching that of an infinitesimal-sized interval.
20 Zeno of Elea (490 – c. 430 BC) produced four paradoxes that seem to show the impossibility of change.
21 In support of this, Parmenides' pupil Zeno of Elea attempted to prove that the concept of motion was absurd and as such motion did not exist.
22 In note H to his "Zeno of Elea" article, Bayle discussed Malebranche's views on material substance with particular approval.
23 This line begins with Xenophenes and goes through Parmenides, Melissus of Samos, Zeno of Elea, Leucippus, Democritus, Protagoras, Nessas of Chios, Metrodorus of Chios, Diogenes of Smyrna, Anaxarchus, and finally Pyrrho.
24 It had also been common since antiquity to see Xenophanes as the teacher of Zeno of Elea, the colleague of Parmenides, and generally associated with the Eleatic school, but common opinion today is likewise that this is false.
25 The origin of the interest in supertasks is normally attributed to Zeno of Elea.
26 The story was annexed to a philosophical problem by Zeno of Elea, who created a set of paradoxes to support Parmenides' attack on the idea of continuous motion, as each time the hare (or the hero Achilles) moves to where the tortoise was, the tortoise moves just a little further away.