Parmenides of Elea

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Parmenides of Elea

• 530-450
• Way of Truth
• Logic
• Reason
• Being
• Student Zeno, inventor of dialectic or negative
  logic

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Three Principles

• Logic Principle of Non-Contradiction
• Epistemology Reason is basis, not senses which
  are deceptive
• Metaphysics being is ungenerated,
  imperishable, whole, self-same/unchanging,
  perfect/complete

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I. Logic

• They are carried along by experience, deaf as
  they are blind, amazed, uncritical herds, for
  whom to be and not to be are judged the same and
  not the same, and for whom there are in all
  things opposites.
• That it is and cannot not be is the path of
  persuasion.

• Principle of Non
• Contradiction (PNC)
• Logical truth
• The statements X is A and X is not-A cannot
  both be true.
• Ontological truth
• the same thing cannot be both A and not-A.

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Proof of the PNC?

• PNC cannot be proven true, except by using it.
• Let X say, The PNC is not T, then Z should ask,
  Do you say it is T or not-T? If X says, Not-T
  then Z should accuse him of accepting it if X
  says, Both then Z should reply, Then you admit
  it is T.
• "Anyone who denies the law of non-contradiction
  should be beaten and burned until he admits that
  to be beaten is not the same as not to be beaten,
  and to be burned is not the same as not to be
  burned." (Avicenna, Medieval Eleatic Philosopher)

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PNC and Doctrine of Flux

• We step and do not step into the same rivers. We
  are and we are not.
• That which is cannot also not be in the same
  sense.
• Parmenides
• If PNC is true, then absolute relativism must be
  false, for there must be some things that are
  what they are.

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Questions

• Is the PNC an ontological, as well as a logical
  truth?
• What is the relationship between logic and
  reality? Must reality obey logic?
• What is the meaning of absolute principles like
  the PNC or in mathematics, e.g. the parallel
  principle in geometry?

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II. Knowledge

• For to be is to be the object of thought.
• Do not be led by custom, based on
  sense-experience, by unobservant eye and echoing
  ear and tongue but judge by use of reason.

• Reason (nous) ? Reality (to on)
• Senses (aesthesis) ? Appearances
• (ta phainomena)

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Two Worlds?

• World as known by the intellect (kosmos noetikos)
  world of unchanging, universal laws, objective
  truth(s) known to reason
• __________________________________________________
  ______
• World as perceived by the senses (kosmos
  aesthetos) world of ever-changing, particular
  events, perceptions relative to the individual

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Rationalism vs. Empiricism

• necessary truths things that cannot be
  otherwise, e.g. 224.
• contingent truths things could have been
  otherwise, e.g. the sun is shining.

• Empiricism all knowledge derives from
  sense-perception
• Rationalism most important knowledge is based
  on reason alone

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Questions

• Do necessary truths exist, or are all truths
  contingent, based on experience?
• The geometers circles and lines do not exist.
  Protagoras
• In natural science, there are laws that predict
  what must happen, e.g. that a bridge will fall
  if X lbs are dropped on it. But might these laws
  prove some day to be false?

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III. Metaphysics

• Being
• ungenerated
• imperishable
• whole
• unchanging
• perfect
• Of course, it is also known by reason, not the
  senses.

• On this way there are many signsthat being
  ungenerated it is also imperishable, whole and of
  a single kind, unshaken and complete.

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• Eternal Being Reality
• (arche, origin, principle)
• \ /
• Becoming mere Appearance
• (ta phainomena, appearing things)

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Questions

• Is there an ultimate being God or atoms or
  souls?
• Is there an ultimate Reality as opposed to the
  world of the Appearances, i.e. the physical
  world?
• Is the ultimate being how things are or are
  meant to be, i.e. things in their completed, most
  perfected state?
• Is there an essential structure of reality,
  e.g. universal laws that govern all the
  particular individual things or events?

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Logical Argument

• Nor was it ever, nor will it be, since it is now,
  all together, one, continuous. For what birth
  will you seek for it? How and from where did it
  come forth? I will not permit you to say or think
  that it came forth from what is not for it is
  not to be said or thought that being comes to be
  from not-being.

• That which comes to be must come forth
• from (a) something or
• from (b) nothing.
• But (b) is impossible, since nothing can come
  forth from nothing.
• Therefore what is must come forth from something,
  i.e. there must already have been that which is.

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Eleatic Logic and the Sea-Battle

• It seems to be a contingent thing, whether there
  is or is not a sea-battle tomorrow.
• But it is either true or it is not true that
  There will be a sea-battle tomorrow.
• If it is T that there will be a sea-battle, it
  cannot fail to occur.
• If it is not T that there will be a sea-battle,
  it cannot occur.
• Therefore, the sea-battle either must occur, or
  it cannot occur.
• Therefore whether the sea-battle occurs or does
  not occur is not a contingent thing.

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Being and Perfection

• Remaining self-same in itself, being is what it
  is, and does not change for it is contained by
  Necessity within the bonds of Limit nor is it
  fitting for what is to be incomplete, for being
  cannot be lackingor it would not be.
• Being and essence fulfillment of being or
  perfection , what X is meant to be.

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Zenos dialectic or negative logic

1. The heap.
2. The arrow, Achilles and paradoxes of motion.
3. Paradoxes involving the concept of infinity aimed
   against Atomism, and involving time.

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The heap

1. If a given number of grains of sand n make a
   heap, it will not cease to be a heap, if one is
   taken away, n-1.
2. But this implies that if any given number of
   grains make a heap, so do all lower numbers, down
   to zero.
3. Conversely, if n grains are not a heap, neither
   are n1, up to infinitely.
4. Thus every collection of grains is and is not a
   heap.
5. If one says that heap is just a vague concept,
   so too are many predicates that pertain to
   sensible things, e.g. is tall or is red.
6. Conclusion The sensible world is just
   incoherent.

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The arrow (paradoxes of motion)

• If the arrow flies toward the target, it must
  pass through ½ the distance, then ½ of the
  remaining distance, and so on.
• It will always be traversing another ½, and never
  reach the target.
• Likewise, Achilles will never catch up with the
  tortoise. He makes up ½, again ½, and so on, but
  never catches up.
• Conclusion The realm of motion is just
  incoherent.

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Reductio of Atomism

• If the world were composed of infinitely many
  atoms, it would be unlimited in size.
• However small the atoms were, they would still be
  infinitely large when added together.
• This is impossible.
• For if it were infinitely large it could not be
  made bigger.
• Yet anything can be made bigger, by addition.
• Therefore the world cannot be composed of
  infinitely many atoms.

• If the world or part of it were composed of
  infinitely small atoms, it would have no size.
• For if the atoms were infinitely small, they
  would still be infinitely small when added
  together.
• This is false the world has a size, magnitude.
• Therefore the world cannot be composed of
  infinitely small atoms.

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A Paradox Concerning the Beginning of Time

1. It would seem there could be a T-1, 2, 3, etc.
   in the past before a given moment T-0 (now).
2. But then the present T represents the end of an
   infinite series, which is absurd.
3. Let T-a a point in the infinite past, T-a.
4. It is impossible to traverse from T-a to T-0
   (now).
5. Go as far back T-1, 2, 3, etc. as you wish, and
   add to T-a 1, 2, etc. you will never get from
   T-0 to T-a.
6. Conclusion Time, no less than motion, is just
   incoherent.

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Eleatics

• LOGIC Made logical argument required form of
  philosophical discourse, governed by principle of
  non-contradiction
• EPISTEMOLOGY Introduced idea of epistemological
  rationalism (vs. empiricism)
• METAPHYSICS Defended concept of Being/reality
  vs. Becoming/appearances and defined metaphysical
  attributes of being (adopted by atomists,
  Platonists, Aristotle, medieval theologians)

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Appendix Xenophanes (580-530)

• Said to be a teacher of Parmenides
• Perhaps worlds first theologian
• Credited with 3 powerful ideas
• Anthropomorphism humans imagine gods in human
  form this a projection of ourselves
• Philosophical concept of God one,
  non-corporeal, radically other kind of Being
• Theological skepticism theological ideas are,
  even if true, a matter of belief, not knowledge.

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Anthropomorphism

• If oxen and horses and lions had hands, they
  would draw their gods to have the shape of oxen,
  horses, and lions.
• The Celts give the gods red hair, the Nubians
  make them black.

• Later 3 aspects distinguished gods conceived
  with
• Human physical form
• Human passions, e.g. anger, grief
• Human moral traits, e.g. vengefulness

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Philosophical Concept of God

• God is one, greatest among gods and men, not at
  all like mortals in thought or body.
• Without effort he shakes all things by the
  thought of his mind.

• Like Biblical God
• One not many
• Seemingly all-powerful
• Good/just
• Unlike
• Impersonal

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Is God radically other?

• God is onenot at all like mortals in thought or
  body.
• Is God
• All-good?
• All-powerful?
• All-knowing?
• In-corporeal?
• Beyond space and time?

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Is religious belief knowledge?

• No man has seen nor will anyone know the truth
  about the gods and the things I speak of, for
  even if a man said what is the case, he does not
  know, but only shapes a belief about it.

• Theology nature points beyond itself to God
  who governs the world by the thought of his
  mind
• Theological Skepticism God object of belief,
  not of knowledge