Methods of Deduction

Presented by: Vaericke Kingad

Section 6

Expanding the Rules of Inference:Replacement RulesThe nine elementary valid argument forms with which we have been working are powerful tools of inference, but they are not powerful enough. There are very many valid truth-functional arguments whose validity cannot be proved using only the nine rules thus far developed. We need to expand the set of rules, to increase the power of our logical toolbox.

• We need rules that identify legitimate replacements precisely.• Such rules are available to us. Recall that the only compound

statements that concern us here are truth-functional compound statements, and in a truth-functional compound statement, if we replace any component by another statement having the same truth value, the truth value of the compound statement remains unchanged.

• Therefore we may accept as an additional principle of inference what may be called the general rule of replacement—a rule that permits us to infer from any statement the result of replacing any component of that statement by any other statement that is logically equivalent to the component replaced.

Definition of Terms

• Rule of replacement• A rule that permits us to infer from any

statement the result of replacing any component of that statement by any other statement that is logically equivalent to the component replaced.

Transposition

Material Implication

Compromise

Application

2, Trans

3, D.N.

1,4, H.S.