HW1

Homework 1: Popper and Truth

Deadline: Sep 15, 2020 at 22:00.

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 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.

2. What is truth?

Read about truth in Ladyman 5.3.3 and lecture 1.

A goal of science may 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.

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. This statement is true.
8. This statement is false. (Note - interpret this as "Statement 8 in the second part of HW1 is false")
9. 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).
10. There is no set whose cardinality is strictly between that of the integers and the real numbers (the continuum hypothesis in set theory).
11. The gravitational force as a function of distance R is given by
    F = -G m₁ m₂ / R²

For each statement 1-8: 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 different answers.

Answers to the more complex statements 9-11 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 in BOTH here in Canvas as Homework 1a and on the Peergrade page. Do not write your name in the pdf file.

Note - this is a backup procedure to ensure that all your homework is graded by the TAs, since it is likely that Peergrade does not yet work for all students.

Peer grading

You will be asked to review the homework of three other students. Your solution will also be reviewed in this way. This assumes that Peergrade is fully functional - further instructions will be added

Feedback from your TA

Your TA 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.