HW1

Homework 1: Popper and Truth 

Deadline: Monday Sep 20, 17:00. Please remember that you must submit the assignment separately
in Canvas (for grading) and Peergrade (for peer review)! The Peergrade submission can be found as a 
separate Canvas assignment called Homework 1 HT2021- peer review submission.

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 or idea
that is due to someone else, you should make use of references as in a scientific text. References should
primarily be to original publications, not to textbooks or similar. 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..

Also note that 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

Read Karl Popper’s essay on Science as Falsification.

a. 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. 

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 whether each is true or false (or neither), and where applicable
what kind of truth concept that matches the statement best?

1. The program statement while (true) {} gives an infinite loop.
2. Mergesort has complexity O(n log n).
3. Apple suffered losses in the consumer market last year.
4. Comments make it easier to modify programs.
5. Agile development provides greater job satisfaction.
6. Two doses of the mRNA Covid-19 vaccine BNT162b2 give a 95% protection for adults.
7. P is a strict 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")

In addition, you may as a voluntary exercise also consider the following statements:

10. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality,  necessarily exists (from Proposition 11 in Baruch Spinoza, Ethics, 1677)

11. There is no set whose cardinality is strictly between that of the integers and the real numbers (the continuum hypothesis in set theory).

12. The  magnitude of the gravitational force as a function of distance R is given by
F = G m₁ m₂ / R²

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. In some cases, one can argue for multiple answers, or that none of the categories apply. All carefully reasoned and motivated answers will be accepted.

(NB: Note that it was stated above that you should try to determine whether the statements are actually true or false, or neither - not only reason about what sort of truth they would be if they were true).

Answers to the more complex statements 10-12 are optional but encouraged. These provide additional insights into the nature of truth and the working processes of science, and will be discussed in the seminars if there is time.

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). 

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. This may happen before
the associated seminar, but if your seminar leader is busy it will 

Complete means you have passed the assignment.

Incomplete means you have to hand in a revised version.

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.