LOGICAL REASONING

Kinds of Reasoning

Inductive – reaching a likely or probable conclusion from specific facts or observation

The swans in my grandfather’s farm are white.
The swans in your place are also white.
Therefore, all swans are white.

Deductive – drawing a logically certain and specific conclusion about particulars from one or more general premises

All mothers have a child.
She is a mother.
Therefore, she has a child.

Types of Deductive Reasoning

Conditional Reasoning – reasoning by which one attempts to draw a conclusion based on a conditional or if-then proposition and assertion of an existing proposition. The if-then proposition states that if an antecedent condition (p) is met, then a consequent event (q) follows.

Modus Ponens
If p, then q. If you are a mother, then you have a child.
p You are a mother.
Therefore, q. Therefore, you have a child.

Modus Tollens
If p, then q. If you are mother, then you have a child.
Not q. You don’t have a child.
Therefore, not p. Therefore, you are not a mother.

Fallacy – affirming the consequent.
If p, then q.
Therefore, p.

Syllogistic Reasoning – deductive arguments that involve drawing conclusions from two premises

Categorical Syllogisms – comprise a major premise, a minor premise, and a conclusion
All living things are mortal. (major premise)
All human beings are living things. (minor premise)
Therefore, all human beings are mortal. (conclusion)

Types of Premises

 Universal Affirmative – states that all members of the class are members of the second class

   All human beings are living things.
 
 Universal Negative – states that none of the members of the first class are members of the second class

   No human beings are living things.

 Particular Affirmative – states that some of the members of the first class are members of the second class

   Some human beings are living things.

 Particular Negative – states that some members of the first class are not members of the second class

   Some human beings are not living things.

Disjunction – either-or inference

Either all penguins are living things or non-living things.
All penguins are living things.
Therefore, no penguins are non-living things.

Conjuction – uses and to combine statements

Mickey is a mouse.
Pooh is a bear.
Therefore, Mickey is a mouse and Pooh is a bear.

Hypothetical Syllogisms
If p, then q. If his puppy survives, then the boy is happy.
If q, then r. If the boy is happy, then he will have high grades.
If p, therefore r. If his puppy survives, then the boy will have high grades.