Introduction to Philosophy
Lecture 3
An introduction to Deductive arguments
By David Kelsey
Valid Patterns
of Reasoning
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Patterns of reasoning:
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An argument’s pattern of reasoning is the path it takes from the first premise to its
conclusion.
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When reading a philosophical argument, your task is to:
1-Determine what the philosophical argument’s pattern of reasoning is.
2-Then Evaluate the pattern of reasoning to see if it is valid.
The slides that compose the rest of this lecture consist of some examples of
valid patterns of reasoning.
Deductive Forms
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So in this lesson we present several examples of valid patterns of
reasoning.
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A valid pattern of reasoning is a valid deductive argument form.
Deductive arguments…
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The forms of the valid patterns of reasoning come as such:
– Modus Ponens:
• If P then Q
• P
• Thus, Q
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Note that the letters, I.e. ‘P’ and ‘Q’, are sentence letters. They are used to represent
sentences.
Modus Ponens
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Modus Ponens Again:
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If P then Q
P
Thus, Q
Modus Ponens in action:
– Example #1: the Lakers
– Example #2: optimists
Modus Tollens
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Modus Tollens:
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If P then Q
Not Q
Thus, Not P
Modus Tollens in action:
– Example 1: the dog barking
– Example 2:
• If the universe were infinitely old, no hydrogen would be left in it, because
hydrogen is steadily converted into helium throughout the universe, and this
conversion is a one-way process. But in fact the universe consists almost entirely
of hydrogen. Thus the universe must have had a definite beginning.
Hypothetical Syllogism
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Hypothetic Syllogism:
– If P then Q
– If Q then R
– If P then R
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Hypothetical syllogism in action:
– Example 1: going to Vegas
– Example 2: studying other cultures
• (From A Rulebook for Arguments, chapter 6, page 40.)
Disjunctive Syllogism
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Disjunctive Syllogism:
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P or Q
Not P
Thus, Q
P or Q
or
Not Q
Thus, P
– Disjunctive syllogism in action:
• Example 1: (From A Rulebook for Arguments, chapter 6 page 41.)
– How do we gain social progress?
• Example 2: raising taxes or cutting the budget
Constructive Dilemma
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Constructive Dilemma:
– P or Q
– If P then R
– If Q then S
– Thus, R os S
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Constructive Dilemma in action:
– Example 1: the circus or skiing
– Example 2: John’s baptism
– Example 3 (chapter 6, page 42-3): the hedgehogs
Reductio
ad absurdum
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Reductio ad absurdum:
– means reduce to absurdity
– The form of a reductio is this:
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P
Q
Not Q
Q and not Q
Thus, Not P
3 steps:
– One begins with a claim she wants to show false.
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From this claim a contradiction is inferred.
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What is a contradiction?
One then concludes by asserting that what she initially assumed is false!!!
Reductio ad Absurdum
in action
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An example of a Reductio Ad Absurdum:
Example 1:
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Taken from A Rulebook for Arguments, chapter 6, page 44.
Suppose the world has a creator like a house…
A second example:
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Assume God isn’t omnipotent…