Critical Thinking Lecture Four October 5, 2012
Chapter 3
Deductive Argument Patterns
Diagramming Arguments
Deductive Argument Patterns
- There are some common patterns shared by many deductive arguments
- They form a frame that is common to many arguments
- Understanding some basic argument patterns help to determine (a) whether an argument is
deductive (b) whether is it valid or invalid
- Many of these patterns involve two kids of statements
Conditionals (if) & Disjunctions (either or)
Conditional Statements
A conditional statement is a statement of the form
If p, then q
Examples:
- If it rains, then the picnic will be cancelled
- If Jones didn’t commit the murder, the butler did
Conditionals are compound statements composed of two parts:
The antecendent – what follows the word “if”
The consequent – what follows the word “then”
The antecendent always a expresses a sufficient condition for the consequent
The consequent expresses a necessary condition (not on quiz two)
Disjunctive Statement
A disjunctive statement is a statement of the form
Either p or q. Examples Either the picnic was cancelled or it rained
Either Jones commited the murder or the butler didi
Disjunctions are compound statements composed of two parts called the disjuncts.
Some valid conditional argument patterns
1. Affirming the antecedent (Modus Ponens):
If p, then q
p.
Therefore q.
Example:
(1) If the conservatives won the election, then Stepehen Harper is the new Prime Minister
(antecedent)
(2) The Conservatives won the election
Therefore,
(3) Stepehen Harper is the new Prime Minister (from premise (1) and premise (2) by Modus
Ponens)
2. Denying the consequent (Modus Tallens)
If p, then q.
Not q.
Therefore, not p.
Example:
(1) If the liberals won the election, then Paul Martin is the new Prime Minister
(2) Paul Martin is not the new Prime Minister
(3) The liberals did not win the election (From Premise (1) and premise (2) by Modus Tallens)
3. Hypothetical Syllogism
If p, then q.
If q, then r.
Therefore, if p, then r
Example:
(1) If the conservatives won the election, then Stephen Harper is the new Prime Minister
(2) If Stephen Harper is the new Prime Minister, then someone from Alberta is the new Prime
Minister. Therefore,
(3) If the conservatives won the election, then someone from Alberta is the new Prime Minister
(from Premise 1 and Premise 2 by Hypothetical Syllogism)
Some Invalid Conditional Argument Patterns
4. Denying the Antecedent
If p, then q
Not P.
Therefore not q.
Example
(1) If Einstein invented the computer, then he’s a genius
(2) Einstein did not invent the computer
Therefore,
(3) He’s not a genius (From premise (1) and premise (2) by ???)
5. Affirming the Consequent
If p, then q.
q.
Therefore p.
Example
(1) If Einstein invented the computer then he’s a genius
(2) Einstein is a genius
Therefore,
(3) He invented the computer. (From Premise (1) and Premise (2) by ??
A valid disjunctive ar

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