1. Introduction to Philosophy Lecture 3 An introduction to Deductive arguments
By David Kelsey

2. Valid Patterns of Reasoning
An argument’s pattern of reasoning is the path it takes from the first premise to its conclusion.
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.

3. Deductive Forms
So in this lesson we present several examples of valid patterns of reasoning.
A valid pattern of reasoning is a valid deductive argument form.
Deductive arguments…
The forms of the valid patterns of reasoning come as such:
Modus Ponens:
If P then Q P
Thus, Q
Note that the letters, I.e. ‘P’ and ‘Q’, are sentence letters. They are used to represent sentences.

4. Modus Ponens Modus Ponens Again: Modus Ponens in action:
If P then Q P
Thus, Q
Modus Ponens in action:
Example #1: the Lakers
Example #2: optimists

5. Modus Tollens Modus Tollens: Modus Tollens in action:
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.

6. Hypothetical Syllogism
Hypothetic Syllogism:
If P then Q
If Q then R
If P then R
Hypothetical syllogism in action:
Example 1: going to Vegas
Example 2: studying other cultures
(From A Rulebook for Arguments, chapter 6, page 40.)

7. Disjunctive Syllogism
P or Q P or Q
Not P or Not Q
Thus, 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

8. Constructive Dilemma Constructive Dilemma: P or Q If P then R
If Q then S
Thus, R os S
Constructive Dilemma in action:
Example 1: the circus or skiing
Example 2: John’s baptism
Example 3 (chapter 6, page 42-3): the hedgehogs

9. Reductio ad absurdum Reductio ad absurdum: means reduce to absurdity
The form of a reductio is this: P Q
Not Q
Q and not Q
Thus, Not P
3 steps:
One begins with a claim she wants to show false.
From this claim a contradiction is inferred.
What is a contradiction?
One then concludes by asserting that what she initially assumed is false!!!

10. Reductio ad Absurdum in action
An example of a Reductio Ad Absurdum:
Example 1:
Taken from A Rulebook for Arguments, chapter 6, page 44.
Suppose the world has a creator like a house…
A second example:
Assume God isn’t omnipotent…