Posts tagged ‘rules of logic’

January 25th, 2012

Word of the Week Wednesday: Existential Instantiation

by Max Andrews

The Word of the Week is: Existential Instantiation

Definition: A rule of inference that introduces existential quantifiers.  The symbol for an existential quantifier is (∃x).

More about the term: The existential quantifier indicates that there is at least one thing in a categorical reference.  Instantiation is an operation that removes a quantifier and replaces every variable bound by the quantifier with that same instantial letter.  There are eight rules of inference to derive a conclusion of an argument via deduction:

  1. Modus Ponens: p ⊃ q … p… .:q
  2. Modus Tollens: p ⊃ q … ~q … .: ~p
  3. Pure Hypothetical Syllogism: p ⊃ q … q ⊃ r … .: p ⊃ r
  4. Disjunctive Syllogism: p v q … ~q … .:p
  5. Constructive Dilemma: (p ⊃ q) & (r ⊃ s) … p v r … .: q v s
  6. Simplification: p & q… .: p
  7. Conjunction: p … q … .: p & q
  8. Addition: p … .: p v q