Department

PhilosophyCourse Code

PHIL 10Professor

Rick GrushChapter

4This

**preview**shows half of the first page. to view the full**2 pages of the document.**PHIL 10 – Textbook Notes – Chapter 4: Replacement Rules, Indirect Proof, and

Tautologies

4.2 Replacement Rules: CE

Inference rules go from one or more statements to one new statement that is implied by

them

o Embody implications

Replacement rules go from one statement to one equivalent statement

o Embody equivalences

o Anything that is equivalent is an implication as well

Inference rules can be used in the same way as replacement rules, and

vice versa

Conditional Exchange (CE)

(X ⸧ Y) :: (~X v Y)

(X v Y) :: (~X ⸧ Y)

Can apply replacement rules to parts of lines

o Rest of the line stays intact

Replacement rules are truth-preserving

4.3 DN and Comm

Double Negation (DN)

X :: ~~X

Commutation (Comm)

(X v Y) :: (Y v X)

(X • Y) :: (Y • X)

4.4 Last Three Replacement Rules: DeM, Contra, Assoc

DeMorgan’s (DeM)

~(X v Y) :: ~X • ~Y

~(X • Y) :: ~X v ~Y

Contraposition (Cont)

(X v Y) v Z :: X v (Y v Z)

(X • Y) • Z :: X • (Y • Z)

1. A • ~(B v ~C) / ∴ ~(C ⸧ ~A)

2. A • (~B • C) 1 DeM

3. A • (C • ~B) 2 Comm

4. (A • C) • ~B 3 Assoc

5. A • C 4 Simp

6. ~(~A v ~C) 5 DeM

7. ~(A ⸧ ~C) 6 CE

8. ~(C ⸧ ~A) 7 Contra

4.5 Why You Can Use Replacement Rules on Parts of a Line

Implication does not guarantee truth preservation if used on parts of a statement, but

equivalence does

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