Inference

Rules of Inference

1. Modus Ponens
   • aka “the mode that affirms logic”
   • If the precedent is true, then it follows that the consequent is also true.

2. Modus Tollens
   • aka “the mode that denies logic”
   • If the antecedent is false, then the precedent is also false

3. Hypothetical Syllogism

4. Disjunctive Syllogism

5. Constructive Dilemma

6. Simplification

Formal Fallacies

1. Affirming the Consequent
   • Suppose a condition is true.
   • If the consequent is true, then the antecedent is not necessarily true.
   • This is because the antecedent may still be true or false regardless and the condition of the statement is still true.

2. Denying the Antecedent
   • Suppose a condition is true.
   • If the antecedent is not true, then it is not necessarily the case that the consequent is not true.
   • This is because if the antecedent is not true, the consequent may or may not be true but the conditional stays correct.

3. Affirming the Disjunct
   • Suppose that either statements are true.
   • If one of the statements are true, it does not follow that the other is false.
   • This is because the disjunction may still be true yet also both or either of the statements may also be true.

4. Denying the Conjunct
   • Suppose that both statements are false.
   • If a statement is false, then it does not follow that the other is true..
   • This violates the definition of a conjunction.

5. Converting the Conditional
   • If a conditional is true, that doesn’t necessarily indicate that the converse is true.

6. Improper Transportation
   • If a conditional is true, that doesn’t necessarily indicate that the inverse is also true

Categorical Propositions

• It is a proposition that expresses a relationship between two sets or categories
• It can be classified into four types:

Quantity	Quality	Categorical
Universal	Affirmative	A
Universal	Negative	E
Particular	Affirmative	I
Particular	Negative	O