Ch. 8: deductive arg. Flashcards
deductive argument
claims that its conclusion necessarily follows from the premises.
-presented in the form of syllogisms, with two supporting premises and a conclusion.
form of an argument
determined by its layout or pattern of reasoning.
valid
-the form of the argument is such that the conclusion must be true if the premises are true.
valid ex:
All A are B.
C is A.
C is B.
Sound
- (1) it is valid, and (2) the premises are true.
- Not all valid arguments for sound. Can still be unsound if one of the premises is false.
Sound ex:
All men are mortal (true)
Socrates is a man (true)
Socrates is mortal (has to be true)
Quantity
whether a categorical proposition is universal or particular.
-Particular (qualifiers: “Some”)
Quality
- Affirmative (qualifiers: “All,” “Every,” “Some are”)
- Negative (qualifiers: “No,” “None,” “Some are not”)
Universal Affirmative
All A are B.
Universal Negative:
No A are B.
Particular Affirmative:
Some A are B.
Particular Negative:
Some A are not B.
Arguments by Elimination
Rule out different possibilities until only one possibility remains.
Arguments by Elimination Ex:
It is A, B, or C
It is not A
It is not B
Therefore, it is C
Disjunctive syllogism
-argument by elimination
-Either A or B
Not A
Then, B
Arguments Based on Mathematics
Depend on mathematical or geometric equations to generate conclusions.
Arguments Based on Mathematics Ex:
Chris is 6’2”
I am 5’6”
Therefore, Chris is 8” taller than me
Arguments of Definition
-The conclusion is true because it is based on a key term or essential attribute in a definition.
Arguments of Definition Ex:
Paulo is a father
All fathers are men
Therefore, Paulo is a man
Hypothetical Syllogisms
- A form of deductive argument
- contains two premises, at least one of which is a hypothetical or conditional if…then statement.
patterns of hypothetical syllogisms
- Modus ponens (affirming the antecedent)
- Modus tollens (denying the consequent)
- Chain arguments
Modus Ponens
-Affirming the antecedent
If A, then B.
A
Therefore, B
Modus Ponens Valid ex:
If Barack Obama is president, then he was born in the US.
Barack Obama is president.
Therefore, he was born in the US.
Modus Ponens InValid ex:
If Oprah Winfrey is president, then she was born in the US.
Oprah Winfrey was born in the US.
Therefore, Oprah Winfrey is president.
Fallacy of affirming the consequent
Modus Tollens
-(Denies the consequent)
If A, then B
Not B
Therefore, not A.
Modus Tollens valid Ex:
If Michelle is a physician, then she has graduated from college.
Michelle did not graduate from college.
Therefore, Michelle is not a physician.
Modus Tollens invalid Ex:
If Michelle is a physician, then she has graduated from college
Michelle is not a physician.
Therefore, she did not graduate from college.
Fallacy of denying the antecedent
Chain Arguments
Made up of three conditional propositions: (two premises and one conclusion) linked together
If A, then B. (1)
If B, then C. (2)
Therefore, A, then C. (3)
If A, then B. (1)
If B, then C. (2)
If C, then D. (3 )
Therefore, A, then D. (4)
standard form:
the conditional promise first and the conclusion last.
Categorical Syllogisms
- categorizes or sort things into specific classes.
- conclusion, 2 premises, and 3 terms (each of which occurs exactly twice in 2 of the 3 propositions.)
Example: “All tigers are cats. Some mammals are not cats.
Therefore, some mammals are not tigers.”
S term
subject
Term that appears first in the conclusion.
Minor premise
premise in which the S term appears.
P term
Predicate
Appears second in the conclusion.
Major premise:
: the premise in which the P term appears
M term:
middle term, major and minor term.
Occurs only in the two premises
Hypothetical Syllogisms validity
If the form is valid and the premises are true—> the conclusion is necessarily true.
Universal quant.
- “All,” “Every,” “No,” “None”
- All S are P and no S are P —> universal propositions.
particular quant.
- refers only to some members of the class
- some S are P and some S are not P
