1. Concise Guide to Critical Thinking
Chapter 4

2. To be good at evaluating arguments, it’s important to be familiar with argument patterns, or forms, the structures on which the content is laid.
Knowing some common argument forms makes it easier to determine whether an argument is deductive or inductive.

3. Common Forms
Since argument forms are structures distinct from argument content, we can easily signify different forms by using letters to represent statements in the arguments. For example, this argument: If the job is worth doing, then it’s worth doing well. The job is worth doing. Therefore, it’s worth doing well. Can be represented like this: If p, then q. p. Therefore, q.

4. Some of the more common argument patterns that you encounter are deductive, and they contain one or more conditional, or if-then, premises.
The first statement in a conditional premise (the if part) is known as the antecedent.
The second statement (the then part) is known as the consequent.

5. Common Argument Forms:
modus ponens (valid)
If p, then q. p.
Therefore, q.
If the job is worth doing, then it’s worth doing well.
The job is worth doing.
Therefore, it’s worth doing well.

6. Common Argument Forms:
modus tollens (valid)
If p, then q.
Not q.
Therefore, not p.
If it’s raining, the park is closed.
The park is not closed.
Therefore, it’s not raining.

7. Common Argument Forms:
Hypothetical Syllogism (valid)
“Hypothetical” means conditional.
A syllogism is a deductive argument made up of three statements— two premises and a conclusion.
Modus ponens and modus tollens are also syllogisms.

8. Common Argument Forms:
Hypothetical Syllogism (valid)
If p, then q.
If q, then r.
Therefore, if p, then r.
If the ball drops, the lever turns to the right.
If the lever turns to the right, the engine will stop.
Therefore, if the ball drops, the engine will stop.

9. Common Argument Forms:
Disjunctive Syllogism (valid)
Either p or q.
Not p.
Therefore, q.
Either Ralph walked the dog, or he stayed home.
He didn’t walk the dog.
Therefore, he stayed home.

10. Common Argument Forms:
Denying the antecedent (not valid)
If p, then q.
Not p.
Therefore, not q.
If Einstein invented the steam engine, then he’s a great scientist.
Einstein did not invent the steam engine.
Therefore, he is not a great scientist.

11. Common Argument Forms:
Affirming the consequent (not valid)
If p, then q. q.
Therefore, p.
If Buffalo is the capital of New York, then Buffalo is in New York.
Buffalo is in New York.
Therefore, Buffalo is the capital of New York

12. Common Argument Forms:
Reductio Ad Absurdum
If the contradictory (negation) of a statement leads to an absurdity or falsehood, then the negation of the statement is false and the statement itself must be true.

13. Common Argument Forms:
Reductio Ad Absurdum p.
If p then q.
Not q.
Therefore, not p.
Suppose that water cannot freeze.
If water cannot freeze, then ice cannot exist.
But obviously ice does exist.
Therefore, water can freeze.

14. Necessary and Sufficient Conditions:
Necessary Conditions: the conditions (or features) that a thing must have in order to be that thing. Sufficient Conditions: conditions that guarantee that something exists or is a certain kind of thing.