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Lecture 8

# PHI 1101 Lecture Notes - Lecture 8: Syllogism, Venn Diagram, Socialized Medicine

Department
Philosophy
Course Code
PHI 1101
Professor
Sardar Hosseini
Lecture
8

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Chapter 5-Categorical Argument and Venn Diagrams
Common types of deductive arguments
(1) Argument based on Mathematics:
Example: 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.
Example: Harold is Matilda’s son. Therefore, Matilda is Harold’s son.
Or, Jackson is a liar; therefore, he doesn’t tell the truth
(3) Sentential (Propositional) Deductive Arguments:
Modes Pones (MP) Constructive Dilemma (CD)
Modes Tollens (MT) Conjunction (Conj)
Hypothetical Syllogism (HS) Simplification (Simp)
(4) Categorical Syllogism: syllogism (two premised argument) with each statement starting
with “all,” “some,” “none,” or “every.” (chapter 5)
Example: All humans are mortal.
All Greeks are human.
Therefore, all Greeks are mortal.
Categorical Statements
In categorical reasoning the statements, or claims, of interest are categorical
statements.
Categorical statements make simple assertions about categories, or classes, of things.
For example:
All cows are herbivores.
No gardeners are plumbers.

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Some business people are not moral.
Categorical Syllogism (CS)
A categorical syllogism consists of three parts:
Major premise
Minor premise
Conclusion
Example:
All humans are mortal (major premise).
All Greeks are humans (minor premise).
All Greeks are mortal (conclusion).
Validity of Categorical Syllogism
Use Venn Diagram (circles) to evaluate the validity/invalidity of categorical syllogism.
In order to evaluate a categorical syllogism we must evaluate each premise
(Major and Minor) separately, and then see if they support the conclusion.
Analysing Categories (classes)
A categorical claim (premise) contains two distinct categories. For example:
All humans are mortal.
In logic we call these categories:
The subject (humans). The symbol (S)
The predicate (mortal). The symbol (P)
All Greeks are humans?
All Greeks are mortal?

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Four Standard Forms (pure forms)
Four standard forms of categorical statements:
1) All business people are cheaters .
2) No business people are cheaters .
3) Some business people are cheaters.
4) Some business people are not cheaters.
we symbolize them as:
1) All S are P. (Universal Affirmation ) =UA
2) No S are P. (Universal Negation) =UN
3) Some S are P. (Particular Affirmation) =PA
4) Some S are not P. (Particular Negation) =PN
The Full Table
Code quantifier subject copula predicate type
A All S are P UA
E No S are P UN
I Some S are P PA
O Some S are not P PN
Variations of Four Standard Forms
UA:
All astronauts are intelligent people.
Every (each) astronaut is an intelligent person.
Anyone who is an astronaut must be intelligent.
None but (except) intelligent people are astronauts.
(All astronauts are intelligent people)
Only (the only) intelligent people are astronauts.