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Lecture 11

This

**preview**shows page 1. to view the full**5 pages of the document.**Looking at Different Argument Examples

Lecture 11-Chapter 4

PHI1101

We will not cover the material in the section entitled “equivalent forms” (Pg. 64-75)

Common Deductive Argument Types

1. Argument based on Mathematics

- Ex. Mark has twice as many cats as Susan.

- Susan has 3 cats; therefore, Mark has 6 cats.

2. Argument from Deﬁnition

(Truth of conclusion is guaranteed by deﬁnition)

- Ex. Harold is Matilda’s son. Therefore, Matilda is Harold’s son.

3. Categorical Syllogism

(Syllogism— Two premised argument— With each statement with “all,” “some,” “none,” or

“every.” (Ch. 5)

- Ex. All humans are mortal.

- Socrates is a human

- Therefore, Socrates is mortal.

4. Sentential (Propositional) Deductive Arguments

-Modes Pones (MP)

-Modes Tollens (MT)

-Hypothetical Syllogism (HS)

-Disjunctive Syllogism (DS)

-Constructive Dilemma (CD)

-Conjunction (Conj)

-Simpliﬁcation (Simp)

-Addition (Add)

Informal Evolution

Two Questions:

-When evaluating deductive arguments, we ask two independent questions:

1. Are the premises true?

2. How much support does the premises provide to the conclusions?

-There two questions are independent

Sentential Forms (Symbolizing)

-We introduce the following symbols to represent statements and argument forms:

Statement letters (sentential variables): P, Q, R, S…

Connectives:

~ Not (negation)

v Either… Or

• And, but, yet

—> If… Then

( ) For grouping

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Conjunction and Disjunction

Conjunction (“and”) = •

Example:

- Alice rode her bike, and John walked.

- We symbolize as

p • q

Disjunction (“or) = v

Example:

- Either Alice rode her bike, or John walked.

- We symbolize as

p v q

Negation

Negation (“not”) = ~

1. Modus Ponens (MP)

If Spot barks, a burglar is in the house.

Spot if barking.

Therefore, a burglar is in the house.

If p, then q.

p.

Therefore, q.

P —> Q P

P P —> Q

——— ———

QQ

2. Modus Tollens (MT)

Of you work in a bar, you’re over 19.

You’re not over 19.

So, you must not work in a bar.

If p, then 1.

Not q.

Therefore, not p.

P—> Q

~Q

———

~P

If you have not p and not q, you have P.

~P —> Q

~Q

———

P

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