logical deduction (with activity)
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LOGICAL DEDUCTION
Deduction and Syllogism
Deduction is a process of reasoning where we begin with a general truth to a particular conclusion.
Syllogism is the set of arguments that derives a conclusion from two previous statements called “premises”.
Quantity of Arguments
Quantity
Universal- signaled by the qualifiers all and no.All humans are mortal beings.No male is female.
Particular- signaled by the qualifiers some, few, most of, not all, ect.Some birds can fly.Not all mammals live on land.
Quality of Arguments
Quality Affirmative- consenting to
something.All humans are mortal beings.Some birds can fly.
Negative- negating or denying somethingNo male is female.Not all mammals live on land.
Premises and Terms of Syllogisms
Major Premise
The first argument that contains the Middle Term and Major Term. Major Term is the predicate of the Major
Premise and the Conclusion. Example:
All mortal beings will die.All human beings are mortal
beings.Therefore, all human beings will
die.
Major TermMajor
Premise
Minor Premise
The second argument that contains the Minor Term and the Middle Term. Minor Term is the subject of the Minor
Premise and the Conclusion. Example:
All mortal beings will die.All human beings are mortal
beings.Therefore, all human beings
will die.
Minor Premise
Minor Term
Middle Term
The subject of the Major Premise and the predicate of the Minor premise. Example:
All mortal beings will die.All human beings are mortal
beings.Therefore, all human beings will
die.
Middle Term
Middle Term
RULES FOR DERIVING CONCLUSIONS FROM TWO GIVEN PREMISES
Rule 1
The conclusion must not contain the Middle Term.
Example:No male is female.John is male.Therefore, female is
male???
Rule 2
No term can be distributed in the conclusion unless it is distributed in the premises.
Example:
All cats have fur.Some furs are orange.Therefore, some fur
are cats???some cats are
orange???
Rule 3
The middle term should he distributed at least once in the premises. Otherwise, the conclusion cannot follow. Example:
All cats have fur.Some furs are orange.Therefore, some fur
are cats???some cats are
orange???
Rule 4
No conclusion follows if both the premises are particular. Example:
Some that can fly are birds.Some ducks can fly.Therefore, some ducks are birds.
Rule 5
No conclusion follows if both the premises are negative. Example:
No mango is bitter.No balsam apple is mango.Therefore, no apple is
bitter???
Rule 6
No conclusion follows if the major premise is particular and the minor premise is negative. Example:
Some dogs are bulls.No tigers are dogs.No dogs are tigers.???
Rule 7
If one premise is negative, the conclusion must be negative. Example:
All grasses are trees.
No tree is shrub.
No grasses are shrubs.
Rule 8
If one premise is particular, the conclusion must be particular. Example:
Some boys are thieves.
All thieves are bandits.
Some boys are bandits.
Rule 9
If both the premises are affirmative, the conclusion must be affirmative. Example:All women are mothers.All sisters are womenAll sisters are mothers.
Rule 10
If both the premises are universal, the conclusion must be universal. Examples:
All mortal beings will die.All human beings are mortal
beings.Therefore, all human beings will
die.
All humans will die. ___________________________ Lito will die.
___________________________ All whales are mammals All whales have lungs.
All animals are living beings. Some flying objects are animals. ___________________________
Angles <90° are Acute Angles. Angle ABC is 40°. ___________________________
___________________________ Beef is a red meat Beef contains iron.
All birds have feathers. ___________________________ Roosters have feathers.