1. The Eleatics:
Parmenides
&
Zeno

2. Parmenides fl 495 BCE?
Confronts the paradoxes that follow from Heraclitus and Pythagoreans.
Resolves these in a poem by appealing to reason.

3. What Paradoxes? Heraclitus Reality is both one (the logos) and many
“The way up and the way down are one and the same.”
Pythagoreans
Reality is made of geometrical points/units
Separated by the void
Reality is dual: Table of Opposites

4. “The steeds that carry me took me as far as my heart could desire,
when once they had brought me
and set me on the renowned way
of the goddess . . .
Come, O youth, . . .
It is no ill chance, but right and justice,
that has sent you forth to travel this way. . . Meet it that you should learn all things.”

5. Come now, and I will tell you
. . . The only way of inquiry that can be thought of,
the one way,
that it is and cannot not-be,
is the path of Persuasion
for it attends upon Truth;
the other,
that it is-not and need must not-be,
that I tell you
is a path altogether unthinkable.

6. There are only two ways of inquiry
“The one way”
This is the path of reason (logos).
“Either it is or it is not. It cannot not be. Therefore, it is.”
Parmenides applies purely deductive reasoning which he argues exposes contradictions in the physics of previous philosophers.
“the other”
The way of “seeming, Becoming or appearances
This is the path of empirical evidence, or knowledge based on sense experiences. It is grounded in a system of oppositions and has led to contradictions, which Parmenides seems to find incoherent.

7. What is, is what can be thought of
It is uncreated
imperishable
entire
immovable
without end
all alike
indivisible
round,
like a ball

8. What is he talking about? language--how we can speak of things?
The ultimate “stuff” of existence?
Reality itself?

9. What is “it”?
Is it material stuff?
Is it the stuff of ideas?
Is it thought?

10. What has Parmenides done?
He has firmly distinguished truth from mere opinion.
He has denigrated sense.
And established reason as authoritative.
Reason (logos) is divine.

11. Parmenides’ student and famous for his 4 “paradoxes of motion”
They seem to offer rational proof that all things are one
and that our perceptions of motion/change are illusory.
Zeno of Elea

12. Achilles and the Tortoise

13. “If there is motion, there will be something which has traversed an infinite series of distances in a finite time.”

14. The arrow paradox
At each moment the arrow occupies a place equal to itself.
And, if it occupies a place equal to itself, it must be at rest.
If it is at rest, then it is not in motion.

15. What is the point of Zeno’s arguments?
If space is a unit, it can be divided.
Each newly divided part is a new unit, which can itself be divided.
In order to move anywhere, one must cross infinite units in a finite amount of time.
This is impossible.
Therefore, movement is an illusion.

16. What’s Zeno’s point?
Is he attacking the Heraclitean notion that all is in flux and constant motion (becoming vs being)?
Is he attacking the logical possibility of plurality? (If there is being, it is one.)
Is he attacking the Pythagorean assumption of the point as a discreet entity separated by the void (by referring to the infinite divisibility of points as units)?

17. We don’t know for certain.
But we do know that for the Greeks “an infinite series” was thought to be incoherent, irrational.
And it took until the 17th century & the discovery of the calculus (Newton and Leibnitz) which provided proof that infinite geometric series CAN converge.

18. What are there standards for right thinking?
New Problems:
What are there standards for right thinking?
How do we distinguish truth and opinion?
Is the reality of our senses really real or an illusion?

19. that all things that are not, are.
For never shall this
be proved,
that all things that are not, are.
But do hold your thoughts back from this way of inquiry,
nor let custom born of much experience,
force you to wander along this road your aimless eye, your echoing ear
or your tongue;
but do judge by reason
the strife-encompassed proof that I have spoken.