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Lecture 5

Phil 279 Week 5 - Symbol Deductions.docx

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PHIL 279
John James Mac Intosh

Philosophy 279 Week 5Symbol DeductionsA deduction is a set of premises from zero to infinity from which we deduce from a set of rules to a conclusionA proof is complete if we get what we needed and the dependence has everything that was given from anything on the left of the turn styleProofs must contain the justification of everything Do NOT leave anything outDerived rules help you with a compactsimple solution Although proofs are not always easy and elegantIn your last line of proof the dependence must have everything that is given to you in the premise to get your conclusion or else youre not finished This is the idea when writing these deductions down Dependence Sentence proved Justification Assumptions on which our proof Every line proves the sentence on the What rule lets us get from earlier depends on line sentences to present new ones Nothing goes in here except things introduced by P Rules A and B can be as complex as wed like theyre just placeholders To get things startedWe can assume at any stage of the proof any wellformed formula we likeDepends on itselfMake assumptionsPA A Rules for conjunctionSimple RulePulling apart a conjunctionDepends on the conjunctionIf fromyou can derive AB you can derive A and justify this move by writing simpPABAB simp AB Dependence Sentence proved Justification P AB 1 ABEx B AB Dependence Sentence proved Justification 2 B 1 P ABThe numbers indicate the line number and which one you useFrom AB we can derive B Given AB it follows AB Conjunction RulePuts conjunctions togetherDepends on the two conjuncts usedDerive the left conjunct followed by the right conjunct then put them together and write conj ABconj AB
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