1. Arguments in Sentential Logic
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Review
Validity
Modus Ponens
Modus Tollens
Chain Arguments
For Next Time: Read Chapter 9 pages
Ch. 9 Homework #1: (9-1): 1,2,3; (9-2): 1,3,8,12,15,20; (9-3): construct only 3 truth tables

2. Fake Quiz! When is the following sentence false?
“If you watch Night of the Living Dead then you will be scared.”

3. Fake Quiz!
How would you translate the following sentence into standard sentential logical notation? Make sure to replace claims with claim variables and logical connectives for indicator terms
“If you are having a difficult time with logic then either you should come to office hours or you should ask me questions via ”

4. Fake Quiz!
How should translate the following sentence into sentential logical notation?
“If we eat turkey then, unless the turkey is small, we will be full”

5. Fake Quiz! Construct a truth table for the following sentences:
~A v B

6. Fake Quiz!
Construct a truth table for the following compound sentence:
(A & ~B) > C

7. Validity Some things to remember about validity:
We assume the premises are true to see if the conclusion must also be true
When we checked the validity of categorical arguments, recall, we diagrammed each claim as if it was true
When we check for the validity of arguments in sentential logic we will also assume that the premises are true

8. A Quick Example Assume that we know that the sentence: A & B Is true
Given what we know about the truth table for a conjunction what else must be true? A B
A & B T F

9. Modus Ponens
Modus ponens is a very common argument form, one that we have already seen quite a bit in this course:
P > Q P
:. Q
If we have a conditional AND the antecedent of that conditional as a premise then we can always derive the consequent of the conditional
Why does this work?

10. Modus Ponens P Q P > Q T F
Knowing that P > Q is true does not allow us to derive the truth value of the antecedent or consequent because a conditional can be true when the two are true or false
If we know that the antecedent is true however we only have one option for the consequent because we must assume the premises are true P Q
P > Q T F

11. Modus Ponens All modus ponens arguments are valid Example:
If it is Monday then we are not having a quiz
It is Monday
:. We are not having a quiz M Q
M > ~Q T F

12. Modus Tollens Modus Tollens is another valid argument form
All Modus Tollens arguments are valid
P > Q ~Q
:. ~P
If you see an argument with a conditional as a premise and where the negation of the antecedent is also a premise then you can safely conclude that the antecedent is false

13. Modus Tollens
Test out Modus Tollens using the truth table on the right:
1. Assume that the conditional is true
2. Assume that the consequent is false
What must follow using those assumptions? P Q
P > Q T F

14. Chain Argument
The Chain argument is an argument made entirely of conditional sentences
The consequent of one of the conditionals must be the antecedent of the second conditional
P > Q
Q > R
:. P > R
The logic of the truth tables again makes it clearer why this is a valid argument form

15. Chain Argument P Q R
P > Q
Q > R
P > R T F

16. Invalid Argument Forms
Modus Ponens, Modus Tollens, and the Chain Argument are all valid argument forms
There are other argument forms that look like these but are NOT valid
Do not use these invalid argument forms
Affirming the Consequent
1. P > Q
2. Q
3. :. P
Denying the Antecedent
1. P > Q
2. ~P
3. :. ~Q

17. Testing the Invalid Argument Forms
Affirming the Consequent
1. P > Q
2. Q
3. :. P
Denying the Antecedent
2. ~P
3. :. ~Q P Q
P > Q T F

18. For Next Time Homework Due! Read Chapter 9 pages 317-328
Ch. 9 Homework #1: (9-1): 1,2,3; (9-2): 1,3,8,12,15,20; (9-3): construct only 3 truth tables