Question 514: I Say Illusion, You Say “Four” Sure

Many Wishes,


My name is Pranav, and I'm happy to help you spend your idle time on the computer NOT macking on manga and memes.
Actually, I kid - let's go right ahead. First post right up.

___X___ was the amongst the most famous of the Pre-Socratic scholars, having forwarded an entire school of thought that was touched upon in Plato’s most complex dialogue. __X__ was only trying to forward the traditional interpretation that the general perception of reality in the physical world (being discussed in doxa) is incorrect, and that the reality of the practical world is 'One Being' (being discussed in aletheia): an unchanging and indestructible whole.

But in the process, he came up with two of the most famous Greek logical constructs known today. 

The first is that of a method of proof called reductio ad absurdum - which means reducing or extending the logical atomic parts of an argument to the point of absurdity.  

The other construct (or a body of logical work - ___X’s  Y___) - it comprised of a body of 40 propositions put forward by __X__ to prove his belief in the illusion of the “Many” by questioning several conventional axioms. Only a few of these have survived, being discussed in great length by Aristotle as well. Lewis Carroll alludes to one of these when he mentions how the tortoise has a deductive argument with the loser (___Z___) at the end of the race, leading the loser into an infinite regression. By some chance, __X__ didn’t really like infinity, and Carroll was simply playing with words when he described __Z’s__ palpable displeasure with the tortoise’s version as well.

Z vs Tortoise - Time heels wounded pride

Name X 

Tell me what X’s Y is (a collective term of reference) 

Who/what is Z?

How does the title figure in this?

Guess 2 for 5 points, 3 for 8, 4 for 10 - it’d be a crime not to get all four if you get two!

Answers:


Zeno
Zeno's Paradoxes
Achilles
There are only 4 surviving

Zeno's Paradoxes

Achilles
There are only Four of his paradoxes surviving in current literature


Paradoxes:

Achilles and the tortoise

“	In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.	”
—Aristotle, Physics VI:9, 239b15

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.^[8][9]

[edit]The dichotomy paradox

“	That which is in locomotion must arrive at the half-way stage before it arrives at the goal.	”
—Aristotle, Physics VI:9, 239b10

Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.