Arguments in Sentential Logic Sign In! Review Validity Modus Ponens Modus Tollens Chain Arguments For Next Time: 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

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

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 e-mail”

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”

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

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

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

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

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?

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

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

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

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

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

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

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

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

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