Dr Menahem Luz,
Presocratic Philosophers
Summary 8
Eleatic Philosophy
Parmenides, Zeno, Melissus

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Eleatic Philosophy

Contents

1. Parmenides of Elea
   • Background
   • fragments
   • Conclusions

2. Zeno of Elea
   • Background
   • fragments
   • Conclusions

3. Melissus of Samos
   • Background
   • fragments
   • Conclusions

4. Assessment of the Eleatics

1. Parmenides of Elea (515-450 BC)
   Background
   • The philosophy of Parmenides and Zeno is called Eleatic after the name of their home town, Elea, in central Italy (see map).
   • Aristotle therefore classifies them alongside the Italian thinkers, meaning those Greek thinkers of Italy and Sicily like Pythagoras and Empedocles.
   • Although Aristotle makes Xenophanes a teacher of Parmenides (tadpis p. 11 no.9), Parmenides is the actual founder of Eleatic monism.
   • as opposed to Ionian monism that posited a single (monos) substance to explain all change, Parmenides argues that there is no change, but a unified uncreated, unending single reality.
   • Thinkers like Heraclitus and Pythagoras were according to Parmenides deceived by their senses into believing that there is a plurality of substance.Parmenides' monistic philosophy thus stands in complete contrast to their philosophy of pluralism
   • If we trust not sensation, but conceptual logos we will see that their is one being and one reality -- and that non-being and non-reality do not exist
   • not only is being the only thing that can be conceived, it is the only one that can be meaningfully described. We are forbidden to ascribe to being what is not being
   • in this Parmenides' logos is totally different from Heraclitus logos which was a conceptual proportion unifying what is and what is not.

   • Fragments
     There are fragments of two works
     • Truth (Aletheia) in which Parmenides sets out the principles of reality
     • Opinions (Doxai) in which he discusses the confused opinions of mythologists and other philosophers who accepted the conversion of reality into non-reality and vice=versa
     
     Truth
     Fragment 1 (tadpis p. 14)
     • Like Hesiod, Parmenides has a divine revelation, but not revealing self-contradictory myth, but the logic of the mind
     • logos is the law and justice of the universe
     • truth is complete and does not change
     • truth is the reality not what is supposed by humans

     Fragment 2-5 tadpis p 14-15
     • frag. 2: only the real ( to eon = being) truly is -- and the non-real (non-being) is not
     • only the real can be meaningfully conceived (noein = thought of) while the non-real has no real nature and thus cannot be conceived (thought of)
     • only the real can be meaningfully described and expressed -- the non-real cannot be expressed in a meaningful way
       Therefore, only the real is, is conceivable -- and is describable
       it is absurd to speak of the non-real as if in a meaningful way

     • if the real is, it is impossible for it not to be -- equally it is impossible for the non-real to be.
     • The above is the principle of the non-conversion of reality:
       • no object is created out of nothing -- i.e. no conversion of reality from non-reality (a principle called in Latin, creatio ex nihilo)
       • nor is reality destroyed -- i.e. no conversion of reality into non-reality (Latin: destructio ad nihilo)
       • Both these principles were adopted by the pluralists who followed Parmenides (Empedocles and the atomists).
     • frag. 4: the truly real is confined within the bounds of reality and cannot change into non-reality for it would not be
     • frag. 3: a (meaningful) conception (of reality) and reality (being) are the same
     • frag. 4: the mind can and should accept only reality and keep deceptive non-reality away

     Fragments 8-9 (conclusions; tadpis p. 15):
     Therefore, one cannot describe or conceive of the real as non-real or as non-being
     Equally, one cannot describe or conceive of the non-real as real or as being
     Therefore, one cannot say that the real is not -- neither existentially nor attributively
     It follows, that the real cannot be conceived as as other than it is -- i.e. it must be conceived as being, as a unity of reality, as unchanging and continuous and as ever in the present
     • for if it were conceived as non-being it would entail ascribing non-being to being
     • if it were conceived as a non-unity (plurality), it would entail denying that any part of reality is another part of reality -- which means to say that what is real is not what is real
     • if it were conceived as changing, it would entail conceiving being as other than what it is
     • if it were conceived as divided (not-continuous), it would entail conceiving a part of being as other than what it is
     • if it were described as in the past or future (not-present), it would ascribe reality to not-being since both past and future are not real and are not-being
     It follows that that what is (reality) is -- that is, exists -- for ever, with no divisions, is all alike with no beginning and no end
     • Parmenides concept is thus of a circular reality whose end and beginning are one. His universe is thus finite within its own bounds. If it were infinite it would like conclusion, whereas a bounded reality contains everything that is.

     Fragments 6-7 tadpis p 15

     • People who conceive of reality other than this contradict themselves
     • they rely on the senses and not on the mind
     • implying Heraclitus,Parmenides will not conceive of double-thought (stating that being is not being or vice versa)

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   • Coclusions
     • Parmenides' conceived a philosophical system (revelation) that is entirely unified. It is a rational theory based on one single proposition: only that which is (reality) is. All the rest of follows from this premise.He therefore rejects the values of sensation entirely relying on mind and reason.
     • His argument has one flaw: there is no distinction between existential and attributive uses of the verb 'to be'.By forbidding us to meaningfully describe being other than what it is, Parmenides interprets 'what is not..' as entailing not only 'what is not x-' but also 'what is not in existence'
     • He is truly the father of all conceptual accounts of reality from Eleatic monism to Plato and Neo-Platonism -- and hence all ideal philosophies from medieval realism to Berkeley and on.
     • However, Parmenides' account of reality is not that of an ideal conceptual world as in Plato -- nor of a mental world -- but is an account of the real physical universe.
     • This universe is not what it seems to be, but has only the attributes that should be ascribed to reality. The senses thus truly deceive.

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   Zeno of Elea (born 490/485 BC)

   • Background
     • Zeno was a pupil of Parmenides and did not add to his philosophy. He claimed that he merely defended his master against the self contradictions of pluralism
     • Since Parmenides had forbidden us to speak of a plurality that is not, Zeno could not attack plurality directly. Instead, he attacks the pluralists by showing that if we assume their premises (e.g., if we assume that there is a plurality), we would arrive at absurdities that they themselves reject.
     • Zeno's contradiction of the pluralists rests on
       • showing the internal inconsistencies of their argument
       • or showing that their argument reaches conclusions that they would not desire for other reasons
     • The method of assuming the opponents' premisses for aruments sake in order to refute them is called dialectical by Aristotle. He considers that Zeno is the father of the dialectic art. This is of course a different form of dialectic from that later used by Socrates and Aristotle himself.
       • In Socrates, dialectic is the art of live philosophical conversation where you assume your conversant's definition in order to examine it or build on it
       • In Aristotle, dialectic is the method of assuming a poroposition for argument's sake, then listing all the arguments on behalf of it and all the arguments against it. No clear conclusions are drawn from Aristotelian dialectic
     • Zeno's great composition was a list of paradoxes designed to show that if we assume what our senses tell us about the plurality, change and motion of the world, we will reach contradictory conclusions.
       • The word paradox is used in the sense of an argument reducing the hypothesis to absurd or contradictory conclusions. Several of the paradoxes are reductions to the impossible.
       • Many of the paradoxes are in the form of antinomies: if there is x (e.g. a plurality), then x = y and x does not =y. Therefore, x is impossible.
   • Zeno Fragments
     Arguments against plurality (tadpis p. 16 no. 1-2)
     • if there were a plurality of substances, they would have to both finite and infinite in number
       • as substances they would have to comprise their own finite number
       • but between the boundaries of each substance there would be an infinte number of divisables
     • if there were a plurality of substances, it would have to be both both an infinitely great quantity and an infinitely small quantity
       • if there were a plural reality, it would have to be both an infinitely small quantity and an infinitely great quantity:
         • if there were plurality, each unity would have no quantifiable dimensions and would be measured as nothing - or an infinitely small amount
         • but the sum of all plurality would have to be an infinitely great number of parts
     • Both these arguments suppose that real physical objedcts can be divided infinitely like a geometrical line.

       Arguments against motion (tadpis p. 16-17 no. 3-9) show the absurdity and contradictions in any supposition of motion or change

     • The Stadium cannot be crossed in finite time if its length is measured as infinitely divisible units
     • Achilles cannot overtake a moving tortoise for he is moving over a finite length in infinitely divisible time
     • The Arrow will not reach its mark since it occupies its own space in finite time while crossing an infinitely divisible line
     • Oppositely moving bodies cannot overtake each other if this is done in finite time and over infinite divisible space
   • Zeno: Conclusions
     • Zeno's antimonies and other paradoxes show the contradictions of plurality and motion when conceived as taking place either in finite time and over infinite space or in infinite time and over finite space.

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   Melissus of Samos (born about 500 BC)

   Melissos background

   • Melissos accepts all of Parmenides premisses but draws certain new conclusions from them:

   Melissos fragments

   • if reality has no beginning and no end, it is infinite and boundless (rather than Parmenides' bounded reality)
   • if reality is one, it is indivisible and without body -- as opposed to Parmenides' physical universe that is grasped not by the senses but by the mind
   • If there were a plurality, each member would be a Parmenidean one
     (tadpis p. 23)

   Melissos: Conclusions

   • Under the attack of the new pluralists (Empedocles, the atomists and Anaxagoras), Melissos replied to their criticism of Parmenides by yielding to them on the infinite number of unities, the infinity of the universe and the non-physical nature of reality.

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   Assessment of the Eleatics

   • The Eleatics changed the face of philosophy by making it a rigorous system for deductions and dialectical refutation.
   • Their strong denial of the world of sense -- motion, plurality etc -- meant that they ignored the sensible and observed world of science
   • Empedocles tried to answer some of their points by positing a multitude of elements controlled by forces
   • the atomists, especially Democritus, addressed the problem of the infinity of the macrocosm universe as well as the microcosm infinity of the small.
   • to some extent, the points yielded by Melissus let the atomists develop a stronger attack -- if there were a plurality, each member would be a Parmenidean reality.
   • the latter is a good description of Democritus' atom.

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