1. Propositional Logic
1) Introduction
Copyright 2008, Scott Gray

2. What is Logic? The study of the principles of reasoning
There are several different branches of logic, we will examine one: propositional logic
Our text book will be: Introduction to Propositional Logic, second edition, by Howard Pospesel
Copyright 2008, Scott Gray

3. Content & Form We will study the form of arguments, not their contents
At this point we can understand this intuitively, but we will add some definition soon
Copyright 2008, Scott Gray

4. Definitions: Argument
A set of statements intended to support the truth of a proposition (the conclusion)
Statements are declarative; example: “Bear is a dog”
Non-statement example: “Is Bear sleeping?”
Copyright 2008, Scott Gray

5. Definitions: Premise & Conclusion
The two elements of an argument
The conclusion (supposedly) follows from the premises
Example: Bear is a dog All dogs have four legs Therefore, Bear has four legs
Copyright 2008, Scott Gray

6. Definitions: Inductive Logic
Premises support the conclusion with a degree of probability
Leaves room for error
Example: Most presidential candidates are white Jesse Jackson is a presidential candidate Therefore, Jesse Jackson is white
Copyright 2008, Scott Gray

7. Definitions: Deductive Logic
The premises support the conclusion with absolute certainty
Arguments for which this is true are valid, all others are called invalid arguments
It is impossible for a valid argument’s premises to all be true and the conclusion be false
Copyright 2008, Scott Gray

8. Definitions: Validity
The conclusion follows with necessity from its premises
Validity is a matter of form, not content; a valid argument may contain false statements
Example: Bear can write and sew Therefore, he can write
Copyright 2008, Scott Gray

9. Definitions: True and False
For our work, valid & invalid apply only to arguments and true & false apply only to statements
Copyright 2008, Scott Gray

10. Definitions: Sound Arguments
A sound argument has all true premises and a true conclusion
A valid argument may be unsound
Copyright 2008, Scott Gray

11. Deductive Argument Example
All ■ are ● ♦ is a ■ Therefore, ♦ is ●
All 1985 Toyotas were made in Japan My car is an ’85 Toyota Therefore (∴), my car was made in Japan
Copyright 2008, Scott Gray

12. More on Validity
An argument is valid when and only when it has a form such that it is impossible for all the premises to be true and the conclusion false
If the premises are true, the conclusion must be true for the argument to be valid
Validity is a check of form
Copyright 2008, Scott Gray

13. More on Validity cont.
Valid arguments: T T ∴ T F F ∴ F F F ∴ T F T ∴ T F T ∴ T
Invalid argument: T T ∴ F
Copyright 2008, Scott Gray

14. More on Validity cont. Invalid form: All ■ are ● ♦ is ● ♦ ∴ is ■
Structure is what counts, to check validity check form
If not a valid form, then not a valid argument even if argument premises and conclusion are true
Copyright 2008, Scott Gray

15. Test for Validity using Rules for Inference
Our Process
Test for Validity using Rules for Inference
Natural Language
Symbolic Language
Copyright 2008, Scott Gray

16. Assignments Read the Student’s Preface Read Chapter 1, Logic
Do all of the exercises
Copyright 2008, Scott Gray