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HW2

Homework 2: A paradox, Induction and Research basics

Reading:

 

 

1. A Paradox

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,

a) state these three parts as clearly as possible

b) ...and point out the error in one of them.

 

 

2. When does induction work?

 

The Raven Paradox was proposed in the 1940s by the logician Hempel.

It questions the notion that a hypothesis H is supported by an observation that concurs with H, that is, the basis for scientific induction.

 

Hempel's hypothesis was the following: All ravens are black. 

An observation of a non-black raven would falsify the hypothesis, but should not then each observation of a black raven strengthen it? And should observations that do not concern ravens do neither of these?

 

The hypothesis may be expressed in predicate logic as follows:

H1: ∀ Links to an external site.x R(x) ⇒ Links to an external site. B(x)

But there is another, logically equivalent, way of writing this:

H2: ∀ Links to an external site.x ¬B(x) ⇒ Links to an external site. ¬R(x)

 

Thus All non-black objects are non-ravens. 

An observation of a non-black raven would still falsify the hypothesis, but now any observation of a

non-black non-raven, such as a yellow banana, ought to strengthen it!

And sightings of black objects do not seem to matter at all.

 

a) Many attempts at explaining the raven paradox may be found on Wikipedia: Raven paradox Links to an external site.. Which explanation do you think is the best, and why?

 

b) Read Ladyman 2.4 Theory and observation, and lecture notes from lecture 2.

Goodman's "new riddle of induction" is a paradox illustrating the problems with inductive inference.

Give another example of when induction does not work, that is when induction would lead you to draw the wrong conclusion.

 

 

3. Research basics

 

a) Walliman Ch 1 (pages 8-9) lists eight different ways to use research in order to obtain new knowledge: categorize, describe, explain, evaluate, compare, correlate, predict, control.

Select at least two of the above and find examples of these in Computer Science research.

 

b) What is Epistemology? (see Walliman Ch 2)

What assumptions and philosophical approaches are used in Computer Science research?

 

 

Handing in your solution

Please save your solution as a pdf file and hand it in here, on the peergrade page. Do not write your name in the pdf file.

 

Peer grading

You will be asked to review the homework of three other students. Your own solution will also be reviewed in this way.

 

Feedback from your TA

Your teacher will grade your submission and report the result in Canvas

Complete means you have passed this assignment.

Incomplete means you have to hand in a new version.