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Lecture #13

# Lecture #13 - Philosophy 12A Lecture#13 Natural deductions...

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Philosophy 12A Lecture #13 3/2/10 Natural deductions are the most challenging topic of the course Deciding formal validity Truth vs. Proof We will prove sequents The following is a valid LSL argument form: A B C D ( A ) D ! H B H Only seven steps required for natural deduction corresponding to the argument 1) A&B Premise 2) C&D Premise 3) (A&D) H Premise 4) A 1 & E 5) D 2 & E 6) A&D 4, 5 & I 7) H 3, 6 E Rule of Assumptions: Premises of an argument are listed at the start of a proof in the order of which they are given, labeled ‘Premise’ on right and numbered with its own line number on the left J (j) p Premise Rule of & Elimination: if a conjunction p & q occurs at line j, then at any later line k, you may infer either conjunct labeling the line j & E, and writing on the left all numbers that appear on the left of line j. A1,…,An (j) p&q (j) p&q A1,…,An (k) p j&E (k) q j&E Rule of & Introduction: For any p and q, if p occurs at line j and q occurs at line k then the

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Lecture #13 - Philosophy 12A Lecture#13 Natural deductions...

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