Conditional Statements & Arguments - Salmon

(Originally Written September 5, 2005 in Book 1)

Logic

Wesley C. Salmon

1963

Conditional Statements

-The conditional/hypothetical statement is a complex statement composed of two component statements joined by the conjunction 'if...then...'

-The 'if' part of a hypothetical is called the antecedent

-The 'then' part of a hypothetical is called a consequent

-The form of a conditional statement is expressed as 'If x, then y'

-The form 'If not-x, then not-y' is called a contraposition

Conditional Arguments

-Arguments known as 'affirming the antecedent' are called modus ponens 

-In the 'if X, then Y' the x is the premise and the y is the conclusion

-Arguments known as 'denying the consequent' are called modus tollens

-In the 'if not-x, then not-y' the not-x is the premise and the not-y is the conclusion

-Denying the consequent (modus tollens) can also be expressed as:

1. If x, then not-y

2. x

3. Therefore, not-y

2 logical fallacies: 

-The fallacy of affirming the consequent:

1. If x, then y

2. y

3. Therefore, x

-The fallacy of denying the antecedent

1. If x, then y

2. not-x

3. Therefore, not-y