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Zeno of Elea (490BC-430BC)

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in southern Italy

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member of Eleatic School founded by Parmenides

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Eleatic School

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rejected the epistemological validity of sense experience

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Zeno primarily employed the reductio ad absurdum, attempting to destroy the arguments of others by showing their premises led to contradictions

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Parmenides (515BC-430BC)

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founder of Eleatic school of philosophy

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Parmenides describes two views of reality, (1) in the text "way of truth" describes how reality is one, change is impossible, and existence is timeless, uniform, necessary, and unchanging, and then (2) in "the way of opinion," he explains the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful. These ideas strongly influenced the whole of Western philosophy, perhaps most notably through their effect on Plato.

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Zeno's aim

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argue against common sensical statements such as

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there is more than one object

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there is change

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appeals to a reality/appearance distinction, which many philosophers and scientists have done after him

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it appears there is change, but on a more fundamental level it may be an illusion

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e.g. like putting a straight stick into water: the stick appears to be bent, but really it isn't

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Zeno introduced the paradox: an argument in which the premises are plausible but the conclusion is patently absurd (i.e. there is no change, there is only one object)

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since the conclusion is absurd, it is overwhelmingly likely to be false, hence at least one of the premises are false in spite of its initial appearance to be true

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Zeno's most famous paradox

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a thought experiment

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the conclusion is that Achilles will not overtake the tortoise in the race, which is absurd, since Achilles is the superior runner

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Eleatics

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the pre-Socratic school of philosophy founded by Parmenides in the early fifth century BC in the ancient town of Elea

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other members

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Zeno of Elea

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Melissus of Samos

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rejected the epistemological validity of sense experience, and instead took logical standards of clarity and necessity to be the criteria of truth

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main arguments evolved in opposition to the theories of the early physicalist philosophers, who explained all existence in terms of primary matter, and to the theory of Heraclitus, which declared that all existence may be summed up as perpetual change

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what is an argument

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a sequence of statements

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the last one is called the conclusion

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the statements before the conclusion are the premises

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premises are usually meant to support the conclusion

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conclusion is sometimes introduced by a term such as therefore

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logically valid arguments are particularly valid in philosophy

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logically valid: if premises are true then the conclusion must be true as well

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logically valid arguments don't tell you if the premises are true or false

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modus ponens

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Latin: "the way that affirms by affirming"

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"P implies Q; P is asserted to be true, so therefore Q must be true"