Working with Double Negations

        We will here introduce and learn how to use certain rules that apply to double negations. Double negation elimination (~~E) enables you to move from a sentence ~~p to p. Here is a case where you need this rule:

1. 2. 3. 4.

~~R R -› S R S

Premise Premise 1 ~~E 2, 3 -›E

You should now:

Go to Lesson 1

        Since any sentence p is logically equivalent to ~~p, we will add a rule allowing the introduction of double negations (~~I). Here is an example:

1. 2. 3. 4.

Q -› ~S S ~~S ~Q

Premise Premise 3. 2 ~~I 4. 1, 3 MT

Note that MT cannot be used on lines 1 and 2. 2 is not as it stands the negation of the consequent of 1. However 3 is the negation of the consequent of 1.

You should now:

Go to Lesson 2
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