Homework 1: Popper and paradoxes

1. Read the Wikipedia page on Zeno’s paradoxes. The paradox about Achilles and the Tortoise is 2500 years old and still excellent food for thought.

A paradox consists of three parts.

PREMISE consisting of facts and established truths.

ARGUMENT which is a logical derivation from the premise.

CONCLUSION which seems to be false.

In every paradox, either the premise is wrong, the argument is flawed or the conclusion is in fact true. In Zeno’s paradox, state these three parts as clearly as possible and point out the error in one of them.

2. In a variant of the paradox, Achilles runs the first part of the race at 1 m/s while the tortoise runs at 1/2 m/s, then they slow down to 1/2 m/s and 1/3 m/s, then to 1/3 m/s and 1/4 m/s etc. Now, in which part of the paradox will the error be? (Remember the harmonic series?)

3. Read Popper’s essay on Science as Falsification On the second page is a list of seven conclusions. Choose one of these and find an example in Popper’s essay that supports it. Cite this example and explain how it supports your chosen conclusion.

4. Falsification seems paradoxical.

PREMISE Scientific statements should be falsifiable.

ARGUMENT If a statement is falsified it is not true.

CONCLUSION Scientific statements are not true.

Where is the error in the paradox? Explain!

Handing in your solution

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Peer grading

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Zeno's paradoxes Links to an external site. (Wikipedia)

Science as Falsification

by Karl R. Popper