HW1

Homework 1: Popper and Truth 

NB Extended deadline: Wednesday Sep 21 2022, 12:00.

Due to the shorter time available for this first assignment and possible collisions with other
courses mentioned by students, the deadline has been extended. The next homework
assignments will be published earlier so that it is possible to work on them in a more flexible way.

Please remember that you must submit the assignment twice - separately
in Canvas (for grading) and Peergrade (for peer review)! The Peergrade submission is done
by first choosing Peergrade in the let hand menu in Canvas.

Please submit your work as a pdf-file. We recommend using LaTeX for the submission since this is
a standard tool for scientific writing which should be practiced ahead of your master's thesis.

In the peer review submission, you may if you wish submit it anonymously, but the Canvas submission
must contain your name.

It is important to give full answers with careful motivation. When you make use of a result, proof or idea
that is due to someone else, you must make use of references as in a scientific text. References should
primarily be to peer-reviewed publications, not to textbooks or similar, so that one gives credit to the 
original inventor of a concept or idea. Please collect your references in a reference
list at the end of the text. Referencing will be reviewed more later in the course - in the meantime you 
could take a look, e.g., at a guide for the IEEE format such as this Links to an external site..

There is no specified length for the homework submissions, but as rule of thumb more than 2 pages is
in most cases unnecessary, while if your answers fit into half a page you probably have not given sufficient
motivation.

Standard rules against plagiarism apply - you cannot copy text from other sources
(published material, the work of other students, etc) except in the form of explicit quotes with sources
given.

Reading:

• See the reading list (textbooks Ladyman and Walliman), for lecture 1.
• The lecture notes from the first lecture.
• Science as Falsification by Karl R. Popper

1. Science as Falsification

a. Read Karl Popper’s essay on Science as Falsification as preparation for the 
discussion in Seminar 1.

b. Find and describe an example relating to falsification and verification
that does not appear in Popper's article or textbooks, for example:

- where a hypothesis or theory was actually falsified
- an example of someone making a risky hypothesis/prediction that was later verified
(but could have been falsified)
- a current theory (in any field) that appears to be non-falsifiable

Scientific examples are encouraged, but other non-trivial examples are allowed (such as
currently popular pseudo-scientific ideas, or other cases from real life).

2. What is truth?

Read about truth in Ladyman 5.3.3 and lecture 1.

A possible goal of science could be 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 could be used to test
all types of statements, but there is no universally accepted definition, 

Example:

Here are four statements, P1-P4. In what sense are these statements true?

* 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.

Consider each of the statements below, and try to determine

a. whether each is true or false (or neither), and
b. what kind of truth concept matches the statement best (if any) ?

1. The program statement while (true) {} gives an infinite loop.
2. A quantum computer can find the prime factors of an integer in polynomial time.
3. Apple's revenue increased in the third quarter compared to the same period last year.
4. Comments make it easier to modify programs.
5. Agile development provides greater job satisfaction.
6. Vaccination prevented around 15 million deaths from COVID-19 globally from Dec 2020 to Dec 2021.
7. P is a proper subset of NP.
8. This statement is true.
9. This statement is false. (Note - interpret this as "Statement 9 in the second part of HW1 is false")

For each statement 1-9, state which (or several, or none) of the four notions of truth above (correspondence, coherence, intuitive, pragmatic) you believe applies. You must motivate each choice, and give references where appropriate. In several cases, one can argue for multiple answers, or that none of the categories apply. 

Note that it was stated above that you should determine whether the statements are actually true or false, or neither - not only reason hypothetically about what sort of truth they would be if they were true!

Handing in your solution

Please save your solution as a pdf file and hand it both in Canvas (for grading) and Peergrade (for peer review). 
The Peergrade submission is done by first choosing Peergrade in the menu to the left in Canvas.

Peer grading

You will be asked to review the homework of two other students in Peergrade. Your solution will also be
reviewed in this way. The peer review is a mandatory part of the course. 

Feedback from your TA

Your seminar leader will grade your submission and report the result in Canvas. 

Complete means you have passed the assignment.

Incomplete means you have to hand in a revised version. Incomplete should not be viewed as a grade - it is 
a way for your TA to draw attention to issues that you need to address more carefully and provide more
comments and guidance. In practice, essentially all homework is passed after revisions.

Fail means that you will have submit a new version and attend the make-up seminar.
The Fail grade will only be applied in exceptional circumstances such as plagiarized work.