Scribes:
Natasha Wall and Daniela Parlagreco
These
minutes were not spoken; for another version,
The
lecture began with a brief introduction to Zeno. Zeno of Elea is believed to have been author to a ‘big
book’ within which there were a series of arguments, however in
actuality, there remains very little evidence of Zeno’s work. Most of what we know comes from reports
by intelligent people, namely Plato.
Aristotle thought that Zeno’s arguments were challenging and worth
discussing. Simplicius, a scholar,
took up Zeno’s arguments and also added to them. We know roughly what Zeno’s
arguments were primed to do, yet we’re not clear as to how many other arguments
exist and how he thought these arguments were meant to be understood.
The
lecture then shifted to Parmenides and his proem, which tells us what he tried
to achieve when he discussed knowing.
It is important to look to Parmenides’ proem, as it is believed
that much of Zeno’s work is based on defending Parmenides’
arguments. Lines 35 – 41 of
fragment 8 (below) shows Parmenides’ suggestion that what-is is one thing that
encompasses all and is unchanging.
He also asserts that non-existence and existence are illusory names for
that one reality.
For you will not find thinking apart
from what-is, on which it depends
For its expression. For apart from what-is nothing else
Either is or will be, since what-is
is what Fate bound
To be entire and changeless. Therefore all those things which mortal
men,
Trusting in their true reality, have
proposed, are no more than names –
A
question was raised regarding Parmenides’ assertion of
limitlessness. However, in
fragment 8, it is stated that what-is does in fact have limits. The following lines reflect this. “Holds it in the bonds of a
limit which restrains it all about” (F8 line 31). “For from every direction it is
equal to itself, and meets with limits” (F8 line 49). The question raised by the student is
important because the concept of limit becomes a crucial concept to philosophy. The Epicureans were the ones to invent
the sphere argument. Their aim was
to prove that the universe is infinite.
The concept of a javelin being thrown was used to illustrate the idea of
the universe being finite or infinite.
If one travels to the edge and throws a javelin, the javelin will bounce
back if the universe is finite, but will continue on if it is infinite.
The lecture then shifted back to Zeno, where it was stated that the issue with which he dealt was that concerning infinity. Zeno defended Parmenides with the use of several techniques derived from exploitation of this concept of infinity. Zeno’s achievement was that he was the first philosopher to assemble a series of arguments. He was the first to lay out similar arguments in similar ways to show that there were parallel uses of reason, even if content is different. 100 years later, Aristotle went on to develop a full-scale logical system.
There exist disputes as to the true
intentions of Zeno. Some thought
his work was an attack on Parmenides, others thought he was second in charge to
Parmenides, while some thought that his work was meant to be a joke. Unfortunately, this remains
unclear. However, there are some
arguments that are clear. (In fact, there are four well-known arguments.)
The second of Zeno’s arguments
was that of Achilles. “This
claims that the slowest runner will never be caught by the fastest runner, because
the one behind has first reach tot he point from which the one in the front
started, and so the slower one is bound always to be in front” (T3, p.
76). This argument is best known
through the story of the tortoise and the hare, whereby the paradox is that the
hare never quite catches up to the tortoise in the race.
Another of Zeno’s arguments
was that of the arrow in flight being never motionless. This argument suggests the lack of
place. Zeno’s argument
seemed to do away with the existence of place. It raised the following puzzle: If there is a place, it will
be in something, because everything that exists is in something. But what is in something is in a place. Therefore the place will be in a place,
and so on ad infinitum. Therefore, there
is no such thing as place. (T4, p.
79) Although these arguments seem
clear, they provide conclusions that no one wishes to accept. They stimulate sceptical responses so
that people can attempt to refute them.
Zeno was the first person to see that infinity has unimaginable complexities. For us, the modern conception of infinity is different because we can use mathematical knowledge to solve the problems. Those who followed Parmenides and Zeno, however, did not have math and thus they had to rely on reason.
A question was asked concerning
how Zeno could suggest that there are an infinite number of things and yet they
are all the same. Looking to
page 78 of the text, it is reasonable to suggest that if there are many things,
there are as many things as there are.
“If there are many things, they are bound to be as many as they
are, neither more nor less; but if they are as many as they are, they are a
finite number” (F1).
However, it is unreasonable to suggest that “if there are many
things, there are infinitely many things, since there are always other things
between any two given things, and others again between any two of those, and so
things are infinite in number” (F1). This second statement is awkward, for does it imply that
between two people there are two other people and so on, even when there
clearly appear to be only two people present? This would be absurd and obviously a finite number (that is,
2). This assumption formed by
these two statements can be looked at in a logical set-up. If A, then P and if A, then not P. This cannot be so, for it is not
possible for A to be both P and not P at the same time. Thus, this assumption must be
discarded.
The lecture ended on the note that
Zeno was the first to set forth deliberate and structured systems of
argumentation, where some are obvious, leaving others not so obvious. This was a call to logical clarity and
rigor.