Deductive Entailment
e
4 properties of Deductive Inference
- Non-ampletive
- All or nothing: All true premises and true conclusion (valid/cogent) or false
- Truth Preserving: premises all true. conclusion 100% true
- Erosion Proof:
Categorical Syllogism
Deductive Argument: conclusion is inferred from two premises.
- contains 3 terms
- each term occurs in exactly 2 inferences
Universal Affirmative
(A) All S are P
Universal Negative
(E) No S are P
Particular Affirmative
(I) Some S are P
Particular Negative
(O) Some S are not P
Square of Opposition
An arrangement of the 4 Categorical forms.
Contradictory, contrary, sub-contrary
(of a given statement)
All S is P(A) contradictory to Some S is not P(O)
No S is P(E) contradictory to Some S is P(I)
Contrary
(A) contrary to (E) : can’t both be true, but can both be false
ex:
All flowers are blue = false
No flowers are blue = false
sub-Contrary
(I) sub-contrary to (O) : can both be true but can’t both be false
Some flowers are blue = true
Some flowers are not blue = true
Distributed
(A) subject term = distributed. Predicate term = not.
(E) BOTH subject term and Predicate term is distributed
(I) NEITHER S or P is distributed
(O) subject term = not. Predicate term = distributed.
stereotyping
Problem with Universal Affirmative (A)
- putting them into categories and making universal judgments about all or most members of the category.
ex: All Canadians like snow.
Major term
(predicate term) Term that appears in the predicate position in the conclusion of the syllogism. 1. major term 2. minor term 3. conclusion
Minor term
(subject term)
Term that appears in the subject position in the conclusion of a syllogism
- 2nd premise
Middle term
Term that occurs in both premises of the syllogism and not the conclusion.
- enables us to logically deduce the premise to the conclusion.
- MUST be distributed in at least ONE premise
Fallacy of the undistributed middle
Fallacy committed when the middle term of the syllogism is not distributed in at least 1 premise.
Mood of syllogism
The letters A E I O make the mood
ex: 1. No heroes are cowards
2. Some soldiers are cowards
3. Therefore, some soldiers are heroes
Mood: E I I
4 figures
(1)M-P
S-M
therefore S-P
(2) P-M
S-M
Therefore S-P
(3) M-P
M-S
therefore S-P
(4) P-M
M-S
therefore S-P
Rules for testing Deductive Validity in a Categorical Syllogism
Rule #1: For a syllogism to be valid, the middle term must be distributed in at least one premise
Rule #2: For a syllogism to be valid, no term can be distributed in the conclusion unless that term is also distributed in at least one premise
Rule #3: For a syllogism to be valid, at least one premise must be affirmative
Rule #4: For a syllogism to be valid, if it has a negative conclusion, it must have a negative premise. And if it has one negative premise, it must also have a negative conclusion.
Rule #5: If a syllogism has two universal premises, it cannot have a particular conclusion and be valid.
Steps for the Categorical Syllogism
- Put into form
- identify major term, minor term and middle term
- Identify if each line is A E I or O
- Identify what’s distributed
- Identify the mood
- Apply the rules. Is it valid or nah?
Laughter is the best medicine
form:
All things that are laughter are things that are the best medicine
What is a deductively valid argument?
If the premises are true. The conclusion also must be true.
types:
- affirming the antecedent
- Denying the consequence
- Hypothetical syllogism
- Disjunctive syllogism
What is a deductively invalid argument?
if the premises are true but the conclusion is false.
types:
- Denying the antecedent
- Affirming the consequence
