Question

The Greeks (as well as many other ancients) were interested in paradoxes because they seemed to present unresolvable logical or mathematical difficulties but which nonetheless (so they believed) must admit of solution. The paradox that you'll explore in this Forum, while not a sorites paradox, nonetheless exhibits the features that so delighted the ancients.

http://www.youtube.com/watch?v=jd6MWUl9Rmc

Zeno was among the most famous of the Greek thinkers who pondered paradoxes. Take a look at the video (above) which is about the paradox of Achilles and the Tortoise. Then answer the following questions:

Why is this considered to be a paradox? Explain your reasoning by reference to the definition provided in our text.

What is the reason that Achilles can't just run faster and pass the tortoise?

Reconstruct the argument that the paradox contains by using standard reconstruction format (P₁, P₂, P₃, etc., C).

Do you think paradoxes are useful or useless? Give your reasons.

Answer 1

Paradox is the statement which may sound apaprently reasoning but leads to unacceptable or logically unacceotabe conclusions,hence though tortoise was faster as per the this theory Achilles completed first half, second half etc and won.

Since during the start of the race, the tortoise is ahead by some meters, every time Achillies tries to get to the tortoise with his speed, toroise is aheads even by few meters or centimteres.

Paradox are useful, it is a tool for common man or may be uneducated man, it may serve as logical ground for him. Because every time disproving somethings with mathematical equation is not possible. We can see paradox laid examples everywhere, for eg: a particular government promising some returns but what we have is something different.