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Topic #A7



24 September 2001

Scribes: Natasha Wall and Daniela Parlagreco


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         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.