Class Notes (837,488)
United States (325,081)
Philosophy (46)
1002 (23)
Lecture

# philosophy note

3 Pages
128 Views

School
Department
Philosophy
Course
1002
Professor
James Hildebrand
Semester
Spring

Description
1. a. A set of sentences of SL is truth-functionally consistent if and only if there is at least one truth-value assignment on which all of the members of the set are true. b. A sentence P of SL is truth-functionally true if and only if P is true on every truth-value assignment. 2. P ~P P Q P v Q P & Q P ⊃ Q P ≡ Q T F T T T T T T F T T F T F F F F T T F T F F F F F T T ~ rule : A negation, ~P, receives the opposite truth value of its immediate component, P. v rule: A disjunction, P v Q, is true if and only if at least one of P or Q is true; otherwise it is false. & rule: A conjunction, P & Q, is true if and only if both P and Q are true; otherwise it is false. ⊃ rule: A conditional, P ⊃ Q, is true if and only if either its antecedent, P, is false or it consequent, Q, is true; otherwise it is false. ≡ rule: A biconditional, P ≡ Q, is true if and only if P and Q have the same truth value; otherwise it is false. 3. a. F b. F c. T d. F e. F 4. a. Truth-functionally indeterminate because there is at least one line (truth value assignment) that assigns T to the main connective and at least one that assigns F. ↓ F H J ~ [F & (H ≡ J)] (~ H v J) ⊃ T T T F T T T T T T F T T T T T F T T F T F F F F T F F T F T T T F F F T T T F T T T F F F T T F T F T T F T F F T T T F F T T T T F T T T F T F T F F T F F F F T F F F F T T F F F F T T T F T T F F F T F F F T F T T F T F b. Truth-functionally valid because on every line (truth value assignment) either at least one premise is false or the conclusion is true ↓ ↓ ↓ A C H ~ A ⊃ (C ≡ A) (H v A) ≡ C ~ C ⊃ (A ⊃ H) T T T F T T T T T T T T T T F T T T T T T T F F T T T T T F T T T T F T T T F F T F T F T T F F T T T T F F T F T T T T T F F F T T F F T F T T F F T F F T F F F T T T F F T F F T T F T T F T T F T T F T F T F F T F F F F F F T F T T F T F F F T T F T F T F T T F F F T F T F T T F F F T F T F T F F F F T F T F T F T F 5. a. Truth functional indeterminacy. You need to do two short truth tables, one that starts off with the assignment of T to the main connective and one that starts off with the assignment of F to the main connective. b. Truth functional non-equivalence. You start off by making the assignment of a T to the main connective of one of the sentences and an F to the main connective of the other. As long as that works you are done. However, if contradictions prevent you from arriving at a truth value assignment to the atomic components, you must try a second truth table that reverses these assignments and gives an F to the main connective of the sentence you made true on your first attempt, and a T to the main connective of the one you made false. c. Truth functional invalidity. You start off by making the assignment of a T to the main connective of each premise and an F to the main connective of the conclusi
More Less

Related notes for 1002
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.