Methods of Deduction

Question 1

Define: rules of inference.

Answer 1

The rules that permit valid inferences from statements assumed as premises. Twenty-three rules of inference are set forth in this book; nine elementary valid argument forms, ten logical equivalences whose members may replace one another, and four rules governing instantiation and generalization in quantified logic.

Question 2

Define: natural deduction.

Answer 2

A method of proving the validity of a deductive argument by using the rules of inference.

Question 3

Define: formal proof of validity.

Answer 3

A sequence of statements each of which is either a premise of a given argument, or follows from the preceding statements of the sequence by one of the rules of inference, or by logical equivalence, where the last statement in the sequence is the conclusion of the argument whose validity is proved.

Question 4

Define: elementary valid argument.

Answer 4

Any one of a set of specified deductive arguments that serve as rule of inference and that may therefore be used in constructing a formal proof of validity.

Question 5

What are the two sets of rules within the rules of inference?

Answer 5

elementary valid argument forms; elementary logical equivalences

Question 6

Define: rule of replacement.

Answer 6

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.

Question 7

What constitutes proof of invalidity?

Answer 7

one (!) row of a truth table showing true premises and a false conclusion; indirect proof through showing contradiction (showing assumed premise = negation of the conclusion)