Unit 4 Valid arguments

Learning outcomes

By the end of this unit you should:

  • have practised discriminating fact from opinion
  • be able to name five valid propositional arguments
  • be able to identify the five valid propositional forms in simple texts

Fact vs. opinion

Activity 1 Reading

Read each statement and decide whether the statement expresses a fact or opinion.

  1. Abenomics was successful.
  2. The standard of English in your country is falling.
  3. The library is a popular place for students to sleep. 
  4. UoA may produce a winner of the Field`s medal.
  5. You should receive an ‘A’ for this course.
  6. Ghosts exist.
  7. Covid-19 was created by the US or Chinese government.
  8. This activity is easy.

Compare your answers with others.

Activity 2 Reading (optional)

Read each statement and decide whether the statement expresses a fact or fiction.

According to wikipedia a fact is defined as "a thing that is known to be consistent with objective reality and can be proven to be true with evidence". In short, facts are known or believed to be true. Opinions are views, judgements or beliefs. Opinions are may or may not be true. To think logically, it is essential to differentiate opinion from fact.

Activity 3 Thinking

Work in alone, in pairs or threes. Consider the differences between the following pairs of sentences.

  1. Everyone in Hong Kong speaks Cantonese.
  2. Many Chinese in Hong Kong can speak Cantonese.

  3. The terrorists destroyed the twin towers.
  4. The freedom fighters destroyed the twin towers.

  5. The terrorists attacked our nation, our buildings and our freedom.
  6. The terrorists attacked our buildings.

  7. A man invaded her home and stole her purse.
  8. A man entered her home and stole her purse.

  9. I conducted a survey on 100 students of mine.
  10. A survey of 100 undergraduates was conducted.

Check which of these words that can be used to explain the differences above.

  • universal, particular
  • denotation (core meaning), connotation (added meaning)
  • snarl word (negative connotation), purr word (positive connotation)
  • rhetorical device (language used in a particular way to persuade)
  • tricolon (the use of a series of three elements)

Five valid propositional forms

There are five valid propositional forms. For these forms, when the premises are true, the conclusion must also be true. These forms can be verified using truth tables. The truth value of each element is considered in turn.

Activity 4 Thinking

Read and remember the following descriptions of the five valid propositional forms.

  1. Modus ponens (MP)
  2. If one part is true, then the other will also be true. The first part is true. Therefore, the second part is also true.

    If A, then B. A. Therefore, B

  3. Modus tollens (MT)
  4. If one part is true, then the other will also be true. The second part is denied. Therefore, the first part should also be denied.

    If A, then B. Not B. Therefore, not A

  5. Hypothetical syllogism (HS)
  6. If one thing happens, another thing will also happen. If the second thing happens, a third thing will also happen. Therefore, if the first thing happens, the third thing will also happen.

    If A, then B. If B, then C. Therefore, if A, then C

  7. Disjunctive syllogism (DS)
  8. There are two options. One option is denied. Therefore, as there is only one option remaining, it must be true.

    A or B. Not A. Therefore, B

  9. Constructive dilemma (CD)
  10. There are two options. If the first option happens, there is a particular outcome. If the second option happens, there is a separate outcome. Therefore, either the first or second outcome will happen.

    A or B. If A, then C. If B, then D. Therefore, C or D

Activity 5 Listening

Listen to an explanation of each of the arguments above. [ selected student work to be placed here ]

“Try to spot valid arguments in movies and dramas.

Activity 6 Watching

Watch this explanation of sound, valid and invalid arguments (6 min 49 secs).

Knowledge and application

Knowledge and application activities are designed to help you activate the key terminology and apply the concepts covered in the course so far. Try to use the terminology and concepts accurately and appropriately.

Activity 7 Audio recording

Submit an audio recording (approximately 60 seconds) via ELMS for one of the arguments in Activity 3. Name the argument, provide your own original example and explain the argument. Your argument is decided by the final digit of your student id number. See the list below for your assigned argument.

  • 1 or 2: Modus ponens
  • 3 or 4: Modus tollens
  • 5 or 6: Hypothetical syllogism
  • 7 or 8: Disjunctive syllogism
  • 9 or 0: Constructive dilemma

The recording can be in English or Japanese. Your audio file may be uploaded for other students to listen to. Do not state your name or personal information! Name the file with the name of the argument. Speak clearly.

Activity 8 Writing

Critically evaluate each numbered point below. Each sentence is numbered for ease of reference. If it is a valid argument, name the argument. If not, state the reason. Submit your work through ELMS.

Disappearance of an airplane

  1. If the flight recorder is found, then the cockpit data is examinable. The cockpit data is not examinable. Therefore, the flight recorder has not been found.
  2. If the plane disintegrated during the flight, then all the passengers are dead. The plane disintegrated. Therefore, all the passengers are dead.
  3. The pilot is either dead or alive. The pilot is not alive. Therefore, the pilot is dead.
  4. If the wreckage is discovered, then the authorities stop searching. If the authorities stop searching, this mystery is solved. Therefore, if the wreckage is discovered, then this mystery is solved.
  5. The flight recorder of the plane either sank in the ocean or is floating on the sea. If the flight recorder sank, it is near the crash site. If the flight recorder floated, it drifted with the current. Therefore, the flight recorder is either near the crash site or drifted with the current.


Make sure you can explain the following 10 logical terms in simple English:

  • valid propositional arguments
  • modus ponens, modus tollens
  • hypothetical syllogism, disjunctive syllogism, constructive dilemma
  • denotation, connotation, snarl word, purr word

Running count: 46 of 108 logical concepts covered so far.