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Lecture 11

PHI 1101 Lecture Notes - Lecture 11: Modus Tollens, Modus Ponens, Fallacy

Course Code
PHI 1101
Sardar Hosseini

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Looking at Different Argument Examples
Lecture 11-Chapter 4
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…
~ Not (negation)
v Either… Or
And, but, yet
—> If… Then
( ) For grouping
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Conjunction and Disjunction
Conjunction (“and”) = •
- Alice rode her bike, and John walked.
- We symbolize as
p • q
Disjunction (“or) = v
- Either Alice rode her bike, or John walked.
- We symbolize as
p v q
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.
Therefore, q.
P —> Q P
P P —> Q
——— ———
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
If you have not p and not q, you have P.
~P —> Q
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