Lecture #14 - Branden Fitelson ' Philosophy 12A Notes 1...

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Branden Fitelson Philosophy 12A Notes 1 ' $ % Townes Van Zandt Administrative Stuff – HW #3 resubmissions are due today. + When you turn in resubmissions, make sure that you staple them to your original homework submission . – The Take-Home Mid-Term has been posted. [Discuss.] – A Sample In-Class Mid-Term has been posted. [Discuss.] + The Actual In-Class Mid-term is next Thursday, 3/11. Today: Chapter 4 — Natural Deduction Proofs for LSL Continuing on with the LSL- natural deduction rules for ` . MacLogic — a useful computer program for natural deduction. * See http://fitelson.org/maclogic.htm . + Natural deductions are the most challenging topic of the course. UCB Philosophy Chapter 4 03/04/10 Branden Fitelson Philosophy 12A Notes 2 ' $ % The Rule of Assumptions (Preliminary Version) Rule of Assumptions (preliminary version): The premises of an argument-form are listed at the start of a proof in the order in which they are given, each labeled ‘Premise’ on the right and numbered with its own line number on the left. Schematically: j (j) p Premise UCB Philosophy Chapter 4 03/04/10 Branden Fitelson Philosophy 12A Notes 3 ' $ % The Rule of & -Elimination ( E) Rule of & -Elimination : If a conjunction [ p q ± occurs at line j, then at any later writing on the left all the numbers which appear on the left of line j. Schematically: a 1 ,. . . , a n (j) p q a 1 ,. . . , a n (j) p q . . . OR . . . a 1 ,. . . , a n (k) p a 1 ,. . . , a n (k) q UCB Philosophy Chapter 4 03/04/10 Branden Fitelson Philosophy 12A Notes 4 ' $ % The Rule of & -Introduction ( I) Rule of & -Introduction : For any formulae p and q , if p occurs at line j and q occurs at line k then the formula [ p q ± may be inferred at line appear on the left of line j and all which appear on the left of line k. [ Note: we may have j < k, j > k, or j = k. Why ? ] a 1 ,. . . , a n (j) p . . . b 1 ,. . . , b u (k) q . . . a 1 ,. . . , a n , b 1 ,. . . , b u (m) p q UCB Philosophy Chapter 4 03/04/10
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Branden Fitelson Philosophy 12A Notes 5 ' $ % The Rule of -Elimination ( E) Rule of -Elimination : For any formulae p and q , if [ p q ± occurs at a line j and p occurs at a line k, then q may be inferred at line m, labeling the line ‘j, k E’ and writing on the left all numbers which appear on the left of line j and all numbers which appear on the left of line k. [ Note: We may have either j < k or j > k .] a 1 ,. . . , a n (j) p q . . . b 1 ,. . . , b u (k) p . . . a 1 ,. . . , a n , b 1 ,. . . , b u (m) q j, k E UCB Philosophy Chapter 4 03/04/10 Branden Fitelson Philosophy 12A Notes 6 ' $ % Deduction #3 Using the Rules E, I, and E Let’s do a deduction of: A (B (C D)) C (A B) D 1 (1) A (B (C D)) Premise 2 (2) C (A B) Premise
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This note was uploaded on 04/20/2010 for the course PHIL 63170 taught by Professor Fitelson during the Spring '10 term at University of California, Berkeley.

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Lecture #14 - Branden Fitelson ' Philosophy 12A Notes 1...

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