**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:

- Modus Ponens: p ⊃ q … p… .:q
- Modus Tollens: p ⊃ q … ~q … .: ~p
- Pure Hypothetical Syllogism: p ⊃ q … q ⊃ r … .: p ⊃ r
- Disjunctive Syllogism: p v q … ~q … .:p
- Constructive Dilemma: (p ⊃ q) & (r ⊃ s) … p v r … .: q v s
- Simplification: p & q… .: p
- Conjunction: p … q … .: p & q
- Addition: p … .: p v q

As long as an existential quantifier is attached to a line of argument the above actions cannot be done.

**Example of use**: All professors are college graduates. Some professors are logicians. Therefore, some logicians are college graduates.

- (x) (Px ⊃ Cx)
- (∃x) (Px & Lx)
- .: (∃x) (Lx & Cx)

This is how we can get to this conclusion by removing the universal and existential quantifiers (let’s let x become m for Max).

- (x) (Px ⊃ Cx)
- (∃x) (Px & Lx)
- Pm & Lm 2, EI
- Pm ⊃ Cm 1, UI
- Pm 3, Simp
- Cm 4, 5, MP
- Lm & Pm 3, Commutativity (not discussed here but you can see how it works)
- Lm 7, Simp
- Lm & Cm 8, Conj
- (∃x) (Lx & Cx) 9, EG

For more on logic and existential instantiation see any edition of Patrick Hurley’s *Introduction to Logic*.

January 27, 2012 at 16:03

“entitites”? Sounds like alien beings! (Check your disclaimer.)

January 27, 2012 at 17:52

Well, it’s to include individuals, institutions, etc. 🙂 Categorically broad.