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philosophy note

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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
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