Lesson 2 · about 50 minutes
Thinking Clearly
The three acts of the mind, how a syllogism works, the difference between valid and sound arguments, and five common fallacies.
By the end of this lesson you will be able to
- Name the three acts of the mind and what each produces (terms, propositions, arguments)
- Lay out an argument as a syllogism and tell a valid argument from a sound one
- Recognise five common fallacies - ad hominem, straw man, false dilemma, appeal to popularity, and begging the question
Read first
- Logic — Terms, propositions, syllogisms and valid argument.
Start here: which one gives a reason?
Look at these three statements:
- “Everyone’s switching to this phone. Don’t get left behind.”
- “Anyone who disagrees with me on this is just ignorant.”
- “This bridge is unsafe, because the inspection found cracks in two of the supports.”
Only the third actually gives a reason. The first tells you what other people are doing; the second insults whoever disagrees. Logic is the skill of telling the difference, and of building good reasons yourself.
The three acts of the mind
Aquinas, following Aristotle, says the mind does three things when it thinks:
| Act of the mind | What it does | What it produces | Example |
|---|---|---|---|
| Understanding | Grasps what something is | A term (an idea) | “dog”, “justice” |
| Judging | Joins or separates two ideas | A proposition (true or false) | “A dog is an animal.” |
| Reasoning | Moves from known judgments to a new one | An argument | ”…so this dog is mortal.” |
Each step depends on the one before. If your terms are vague, your judgments will be confused, and your arguments will go wrong. That is why so many arguments are really disagreements about the meaning of a word. Define your terms before you debate.
The syllogism
The classic shape of an argument is the syllogism: two premises leading to a conclusion.
All men are mortal. (major premise) Socrates is a man. (minor premise) Therefore, Socrates is mortal. (conclusion)
Aristotle defined a syllogism as reasoning in which, once certain things are stated, something else follows necessarily. If you accept the premises, you cannot reasonably deny the conclusion.
Notice the middle term, “man”. It appears in both premises and links “Socrates” to “mortal”. Every syllogism works by finding a middle term that connects the two ends.
Valid versus sound
Two different questions can be asked of any argument:
- Is it valid? Does the conclusion actually follow from the premises? This is about the argument’s form.
- Is it sound? Is it valid and are all its premises true?
All fish can fly. A salmon is a fish. So a salmon can fly.
This argument is valid: the form is perfect. But it is not sound, because fish cannot fly. So when you meet an argument, check both: Does it follow? and Is it true?
Five common fallacies
A fallacy is a mistake in reasoning that can look convincing. These five turn up constantly:
- Ad hominem: attacking the person instead of the argument. “Don’t listen to her, she’s only fifteen.”
- Straw man: twisting someone’s view into a weaker version and knocking that down. “You want fewer exams? So you think students shouldn’t learn anything.”
- False dilemma: offering only two choices when there are more. “You’re either with us or against us.”
- Appeal to popularity: treating something as true because many people believe it. “Millions of people can’t be wrong.”
- Begging the question: assuming the conclusion in the premises. “He’s trustworthy because he says he’s honest.”
The most important lesson here: an argument stands or falls on its reasons, not on who makes it. A bad person can make a good argument, and a good person can make a bad one.
Read the text
Read Aristotle, Prior Analytics I.1, where he defines the syllogism. As you read, ask:
- What does Aristotle mean when he says the conclusion follows “of necessity”?
- Why does he insist that nothing outside the premises is needed to reach the conclusion?
Primary texts
- Aristotle, Prior Analytics I.1 Aristotle's definition of the syllogism - a discourse in which, certain things being stated, something else follows of necessity from their being so.
Check your understanding
Choose an answer for each question, then check your score.
Think and discuss
Talk these over with your class or family, or write a short answer to each.
- Can an argument be valid and still reach a false conclusion? Give an example.
- Why is attacking the speaker not the same as answering the argument?
- Find a false dilemma in a debate you have heard. What third option was left out?
- Why do so many disagreements turn out to be about the meaning of a word?
- Is it ever reasonable to believe something because many people believe it?
Key takeaway
Test the argument, not the person.
Homework: Find one fallacy in the media this week - an ad, a news story, a comment thread - and write two sentences naming it and explaining what is wrong with it.