Chapter_05_ii - Derivation Strategies Goal Analysis: (1)...

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Derivation Strategies Goal Analysis: (1) Examine the goal sentence. What kind of sentence is it? What is its main connective? What are its component parts? (2) Examine the accessible sentences on earlier lines. Do these sentences have components that are similar to the goal sentence? If the goal sentence can be derived immediately, do so. If not, select a subgoal . (3) Enter a subgoal sentence. A subgoal is a sentence from which you could derive the goal sentence immediately . This is not a mechanical procedure. It is instead a useful system of guidelines that will help you in constructing derivations. 1
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Subgoals from the Introduction Rules If the goal sentence consider this has form: subgoal: P & Q P Q _ , _ P Q P P Q _ I P Q P Q P Q _ - _ I P Q P Q Q P P Q _-_, _-_ I ~ P P * Q * ~Q 2
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~ P 3
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Subgoals from the Elimination Rules If the goal and this is consider this sentence accessible: subgoal: contains: P P _ Q P Q P P Q Q _ , _ E Q P Q P P Q Q _ , _ E P Q P Q P R Q R R _, _-_, _-_ E P ~ P * Q * ~Q P _-_, ~ E 4
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If you know WHY you are starting a subderivation then you will know what assumption to make. ALWAYS have a reason for beginning a subderivation. Ask yourself: What I am doing this for? or What do I want to discharge at the end of this subderivation? Then it should be obvious what assumption to make. See chart “Why Make an Assumption . ..?” Do I really have to discharge all my assumptions? Yes, discharge all but the primary assumptions. Discharge the assumption immediately following a single subderivation (for I, ~I, ~E) or after a pair of subderivations (for I, E).
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Chapter_05_ii - Derivation Strategies Goal Analysis: (1)...

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