Logical deduction (With Activity)

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.