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Critical Thinking & Logical Fallacies Cheat Sheet
A printable reference covering arguments, premises, conclusions, validity, soundness, truth tables, and common logical fallacies for grades 8-12.
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Critical thinking helps students judge whether claims are supported by good reasons. This cheat sheet covers the structure of arguments, the difference between truth and validity, and the most common logical fallacies. Students need these tools to read philosophy, evaluate debates, write stronger essays, and avoid weak reasoning. It is useful for class discussions, written arguments, and analyzing real-world claims. The core idea is that an argument contains premises that are meant to support a conclusion. A valid argument has a structure where true premises would make the conclusion impossible to deny, while a sound argument is both valid and based on true premises. Truth tables test how logical statements behave under different truth values. Fallacies are common reasoning errors, such as attacking a person, using a false dilemma, or assuming that correlation proves causation.
Key Facts
- An argument is a set of premises offered as support for a conclusion.
- A valid argument has this form: if all premises are true, then the conclusion cannot be false.
- A sound argument has this formula: sound = valid structure + true premises.
- Modus ponens has this valid form: P -> Q; P; therefore Q.
- Modus tollens has this valid form: P -> Q; not Q; therefore not P.
- A conditional statement P -> Q is false only when P is true and Q is false.
- De Morgan's laws state: not (P and Q) = not P or not Q, and not (P or Q) = not P and not Q.
- Correlation does not prove causation because two events can be related without one directly causing the other.
Vocabulary
- Argument
- A group of statements in which some statements give reasons for accepting another statement.
- Premise
- A statement that gives evidence or support for a conclusion.
- Conclusion
- The claim that an argument is trying to prove or support.
- Validity
- A property of an argument whose conclusion must be true if all its premises are true.
- Soundness
- A property of an argument that is valid and has all true premises.
- Logical fallacy
- A mistake in reasoning that makes an argument weaker or misleading.
Common Mistakes to Avoid
- Confusing truth with validity: A valid argument can still have false premises, so validity is about structure, not whether every statement is factually true.
- Attacking the person instead of the claim: This is ad hominem reasoning because a person's character does not automatically show that their argument is false.
- Treating two options as the only options: This is a false dilemma when other reasonable choices or explanations exist.
- Assuming that an event caused another event just because it came first: This is post hoc reasoning because timing alone does not prove causation.
- Using popularity as proof: This is an appeal to popularity because a belief can be widely accepted and still be false or poorly supported.
Practice Questions
- 1 In the argument 'All mammals are warm-blooded; all whales are mammals; therefore all whales are warm-blooded,' how many premises are there, and what is the conclusion?
- 2 For the conditional P -> Q, list the truth value of the statement in each case: P true and Q true, P true and Q false, P false and Q true, P false and Q false.
- 3 Identify the fallacy: 'This policy must be good because millions of people support it.' Explain why the reasoning is weak.
- 4 A speaker gives accurate facts but uses them to support a conclusion that does not follow. Is the main problem truth, validity, or soundness? Explain your reasoning.