What is Deductive Inference?
The Principles of Syllogism
Validity:
The Essential Law of Argumentation
Syllogism & Deductive Inference
The Principle of Reciprocal Identity
The Principle of Reciprocal Non-Identity
A valid syllogism is one which contains a conclusion that logically follows from the premises
PRI: Two term that are identical to each other.
PRNI: Two terms, one of which is identical with the third term and the other of which is nonidentical with that third term, are nonidentical to each other.
All men are mortal.
Socrates is a man
Therefore, Socrates is mortal.
- Syllogism is " The verbal expression of deductive inference."
- DI: A type a reasoning
- Reasoning is " The act by which the mind acquires new knowledge by means of what it already knows."
No men are angels.
Socrates is a man.
Therefore, Socrates is not an angel.
- Man = Mortal
- Socrates = Man
- Socrates = Mortal
- Socrates = Man
- Angel =/= Man
- Socrates =/= Angel
If the antecedent is true, the consequent must also be true.
Questions?
1) Deduction (DI)
2)Induction
} antecedents
All men are mortal.
Socrates is a man.
Therefore, Socrates in mortal.
} consequent
The Dictum de Nullo
The Dictum de Omni
All men are mortal.
Socrates is a man.
Therefore, Socrates is a mortal.
} antecedents
All reptiles can fly.
A horse is a reptile.
Therefore, a horse can fly.
} consequent
DO: What is affirmed universally of a certain term, is affirmed of every term that comes under that term.
DN: What is denied universally of a certain term is denied of every term that comes under that term
- Socrates shares the extension of man
No Man is God.
Socrates is a man.
Therefore, Socrates is not God.
- Socrates = Man
- Man =/= God
- Socrates =/= God
Corollaries
}
1) If the syllogism is valid and the consequent is false, then the antecedent must be false.
These two steps are called the antecedent
False (Not all birds can fly.)
All men are mortal.
Socrates is a man.
Therefore, Socrates is a mortal.
True (Ostrich = bird)
All birds are able to fly.
The ostrich is a bird.
Therefore, the ostrich is able to fly.
False (The ostrich can't fly.)
2) In a valid syllogism with a true consequent, the antecedent is not necessarily true. If the conclusion is true it doesn't mean the premises are true.
False (Vegetables are not people too.)
All vegetables are philosophers.
Socrates is a vegetable.
Therefore, Socrates is a philosopher.
False (Believe it or not he was human.)
}
True ( Though, he still is not a vegetable .)
The final step is called the conclusion ( conclusion = consequent)
Examples
Terms in a Syllogism
- Major term: The major term is the predicate (P) of the conclusion.
Deductive Inference is " The act by which the mind establishes a connection between the antecedent and the consequent."
- Minor term: The minor term is the subject (S) of the conclusion.
No man are gods.
Socrates is a man.
Therefore, Socrates is not a god
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal
Examples
- Middle term: The middle (M) term is the term that appears in both the premises, but not in the conclusion.
M
P
M
S
All mammals breath oxygen.
A horse is a mammal.
Therefore, a horse breathes oxygen.
P
S
Labeling the premises
The major premise is " The premise which contains the major term."
The minor premise is " The premise which holds the minor term."
Examples
M
P
~ major premise
S
M
~ minor premise
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
S
P
M
P
~ major premise
S
M
No men are gods.
Socrates is a man.
Therefore, Socrates is not a god.
~ minor premise
P
S
P
M
a) PRI
c) DO
a) PRI
c) DO
M
S
All Americans are brave.
George Washington is an American.
Therefore, George Washington is brave.
S
P
d) DN
b) PRNI
d) DN
P
M
Syllogism is " A group of propositions in orderly sequence, one of which (the consequent) is said to be necessarily inferred from the others (the antecedent)."
S
M
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
All M is P
All S is M
Therefore, All S is P
S
P