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Logic (WISP)

I'm teaching logic at Warsaw International Studies in Psychology (University of Warsaw). See the course website here. The course syllabus is to be found below.

The course is intended to get students acquainted with logic as applied to critical thinking and basic scientific methodology. The focus is on acquiring skills in applying logic rather than on logical theory. Accordingly, after attending the course, students should be able to:

  • Analyze arguments in natural language using logical tools

  • Detect formal and informal fallacies in arguments

  • Correct incomplete arguments

  • Define terms correctly
  • Build taxonomies, especially classifications
  • Use basic notions of logic, set theory and relation theory


The course is intensive and requires regular work (usually not more than 30 min./week, though). It is very hard to learn logic just a week before the exam, as you cannot understand the topics introduced later without knowing the basics. Note also that you cannot pass the exam just by reading the textbooks. You should rather do more exercises (see the software and websites recommended below.) You also need to have Internet access and a web browser to do the assignments.

Organization of the course
  1. Informal fallacies in arguments

  2. Introducing basic semiotic concepts: signs and symbols, terms and sentences. Grammatical categories

  3. Defining terms

  4. Various forms of definitions

  5. Classification and basic set theory

  6. Propositional calculus, pt. 1. Truth-tables. Proving validity using truth tables

  7. Propositional calculus, pt. 2. Indirect proofs using truth tables

  8. Discovering logical structure in arguments

  9. Proving validity using natural deduction

  10. Predicate calculus pt. 1. Introducing quantifiers. Venn diagrams

  11. Predicate calculus pt. 2. Regimentation of natural language into predicate calculus.

  12. Formalizing natural language arguments

  13. Finding fallacies in arguments by proving them invalid

  14. Basics of relation theory

  15. Exam

Suggested textbooks
  1. Patrick Hurley, A Concise Introduction to Logic (at you can download LogicCoach 10 for Mac and Windows, runs also on Linux when using WINE). The CD-ROM accompanying the book is highly recommended. Relevant chapters:  1, 2, 3, 6, 7, 8.

  2. Irving M. Copi, Carl Cohen, Introduction to Logic, 11th edition or later. Note: chapter numbers and titles vary across editions. You can skip the sections on induction, categorical statements and syllogisms.

  3. Paul Teller, A Modern Formal Logic Primer. Freely available in PDF format at Relevant parts: Volume I, chapters 1-7; Volume II, chapters 1-6.

Note: the above textbooks do not cover set theory, classification, relation theory and mappings but everything you need to know about these topics will be on the handouts you receive during the lecture.

Other suggested web resources:
  1. Layman’s Power of Logic:

  2. Kelley’s Art of Reasoning:

  3. Truth-table Maker:


 After every class, you will be given individual assignments at my course website Doing all assigned exercises correctly is a prerequisite for passing the course and taking the exam (so if you made a mistake, you will have to correct it and do the same or similar assignment again; the online course makes it easy for you). Please don’t hesitate to ask if you don’t understand why your answer is wrong or how to do your exercises.

Attendance at the lecture is not required. In case of non-attendance, you still have to do the assignments. You will not be be able to write the exam if you don't do the assignments. The final mark in your index books will be based on (1) my evaluation of your activity and your assignments; (2) and the final exam. The rule is simple: if your performance in class and results in assignments were excellent, you can get half of the grade more than what you would normally get from the exam. So, if you scored as many points as to get “4” on the exam but were really good in your homework, you will get “4+” (4.5). If you were really excellent on the exam, your homework won't help you, though.

For the information on possible exemption from the exam, see below.

The textbooks and the course assume that you are fluent in English; however, the purpose of the course is not to grade your linguistic competence but your logical skills. If you are having problems with understanding English examples in textbooks, mail me for resources on the web in Spanish, German or French, or for tips on Polish textbooks.

 The exam will cover the following topics:
  1. Informal fallacies. Identify popular informal fallacies in natural language. Distinguish between formal and informal fallacy.

  2. Semiotic concepts. Distinguish between intension and extension; identify non-linguistic and natural signs. Be able to say whether a sign is mentioned or used.

  3. Definitions. Identify types of definitions relative to its purpose. Be able to give lexical, stipulative and precising definitions. Know the correctness criteria for definitions. Identify extensional and intensional definitions.

  4. Classification and set theory. Be able to say whether an enumeration is a classification or a typology. Construct dichotomies. Know basic operations on sets (union, intersection, complement). Know the notion of an empty set.

  5. General formal logic notions. Understand and use the notions of validity, soundness, tautology, contradiction, material implication, contingency of a statement, vicious circle, petitio principii and reductio.

  6. Propositional calculus. Translate natural language into propositional calculus. Know truth-tables for basic logical operators (negation, disjunction, implication, conjunction). Be able to use truth-table method to check validity and invalidity of statements (in a direct or indirect way). Be able to check validity via natural deduction.

  7. Predicate calculus. Translate natural language into predicate calculus. Use Venn Diagrams. Be able to use natural deduction for predicate calculus to check validity of arguments.

  8. Formalizing arguments. Use propositional or predicate calculus. Identify the structure of arguments, including enthymemes. Check validity. Identify popular invalid forms or check their invalidity via truth-table method. Distinguish soundness and validity of arguments.

  9. Relations. Be able to describe simple relations as symmetric, transitive, or reflexive (or combination). Give examples of relations of a given type.

Note. If you:
  • Scored “5” during the mid-term test and

  • Did all assignments correctly, as well as

  • Excelled in two additional special exercises

… then you can be exempted from the exam and receive the final grade “5”. The two special exercises will be (1) analyzing the logical structure of an argument in a real scientific paper (preferably a short one); (2) checking the validity of an argument in natural language using formal tools.

Learning tips

It makes little sense to learn what a textbook says by heart. You should rather try doing exercises systematically. Logic is like driving a bike – remembering the textbook will not help you if you simply don’t practice. Please take time to schedule how you learn logic – set aside half an hour each week some time after the lecture to do your assignments and make sure you understand. As topics introduced earlier are necessary to understand everything that follows, you won’t be able to continue if you don’t know the basics. You don’t want to end up having to learn everything a week before the exam as that is hard, if not impossible, to do.

You have to remember the truth tables. The most difficult topics are natural deduction and predicate calculus. They will be also given higher priority in evaluating your work, so take time to make sure you are good at it.

Doubts and explanations

Don’t hesitate to ask if you don't understand any of the topics introduced during the lecture, especially if you think you’re confused about basics. Your feedback is important for me. You can come to my office during my office hours and mail me (marcin.milkowski at

My office hours are generally on Mondays, 11 am. till 1 pm., Pałac Staszica (ul. Nowy Świat 72, the palace behind the monument of Copernicus), room 225, second floor. To find the room, go upstairs, then turn right and go into a corridor where you can see displays of books by “Polskie Towarzystwo Filozoficzne”, walk until you find another stairs. Then go upstairs again and turn right. You will see cards saying “242” – that’s in the same direction, but you should go to room 225. Before you come, please e-mail me to make sure I will be there – I’m frequently attending international conferences and might be late or absent.