Homework 2: Induction, Research and Truth

Reading: See reading list (textbooks Ladyman and Walliman), for lectures 1 and 2. You will also want to review the lecture notes from the first two lectures.

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.

1. 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?

2. 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.

Research basics

3. 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.

4 What is Epistemology? (see Walliman Ch 2)

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

What is truth?

Read about truth in Ladyman 5.3.3 and lecture 1.

The purpose of science is to arrive at true statements, but what does that mean? The question is a difficult one. One would like to have a definition of truth that may be used to test all types of statements. But there seems to be no universally accepted definition, despite millennia of philosophy and science. Here are four statements, P1-P4.Let us discuss in what sense these statements are true, using these

four different notions of truth:

P1 The car keys are on the kitchen table.

Correspondence truth If P corresponds to reality, then P is true. P1 is true

because the keys are actually on the kitchen table.

P2 Every differentiable function is continuous.

Coherence truth if P is logically linked to other true statements then P is true. P2

is true since it follows from previous definitions and theorems.

P3 Eddie Murphy is a great comedian.

Intuitive truth If I have a strong internal conviction about P then P is true for me.

P3 is true because I think Eddie Murphy is a great comedian.

P4 One should stick to the truth.

Pragmatic truth If believing in P results in good consequences then P is true. P4

is true because everyone benefits from people telling the truth.

5. What kind of truth concept matches each of the following statements best?

1. The program statement while (true) {} gives an infinite loop.
2. Mergesort has complexity O(n log n).
3. Apple suffers losses in the consumer market.
4. Comments make it easier to modify programs.
5. Agile development provides greater job satisfaction.
6. P is a strict subset of NP.
7. Spotify, Skype and Mentimeter are Swedish programs.
8. This statement is true!
9. This statement is false!

For each statement: say which of the four notions of truth you choose and why.

Handing in your solution

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Peer grading

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