Quantifier Rules
(Pt. II)

 

 

All men can see these tactics whereby I conquer, but what none can see is the strategy out of which victory is evolved.

~Sun Tzu

Strategies

 

Quantifier Negation (QN)

QN rounds out PD+ for us. This is the last technical concept you'll be learning. QN is a replacement rule, which means that it goes both ways (much like DM, Imp, DN, etc.). Here it is:

Quantifier Negation (QN)

~(∀x)P ←→ (∃x)~P

~(∃x)P ←→ (∀x)~P

The variable is bold to signify that it is a metavariable; i.e., it could stand for variables w-z (with or without subscripts). The "P" is also bolded since it can stand for any truth-functionally compound sentence, another quantified sentence, or an atomic sentence of PL. You'll see this rule at work in the Getting Started (Pt. V) video below; see also The Logic Book, pages 521-24.

Getting Started (Pt. V)

 

 

 

FYI

Homework— The Logic Book (6e), Chapter 10

  • Read p. 492-500, 521-24.
  • Do 10.2E #1-2, p. 518-19.
    • Here is the portion of the student solutions manual for the relevant chapter.