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Lecture #13

# Lecture #13 - Branden Fitelson Philosophy 12A Notes 1...

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Branden Fitelson Philosophy 12A Notes 1 Announcements & Such Air : La Femme D’Argent Administrative Stuff It is business-as-usual in 12A this week — despite the strike. HW #3 will be returned Today — Resubs due Thursday. When you turn in resubmissions, make sure that you staple them to your original homework submission . – The Take-Home Mid-Term will be posted on Thursday. – A Sample In-Class Mid-Term will be posted on Thursday. The Actual In-Class Mid-term is next Thursday, 3/11. Today: Chapter 4 — Natural Deduction Proofs for LSL Validity ( ) vs Proof ( ), and the LSL 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 , Intro. 03/02/10 Branden Fitelson Philosophy 12A Notes 2 Expressive Completeness: Rewind, and More Extra-Credit Q . How can we define in terms of | ? A . If you naïvely apply the schemes I described last time, then you get a 187 symbol monster : p q A | A , where A is given by the following 93 symbol expression: (((p | (q | q)) | (p | (q | q))) | ((p | (q | q)) | (p | (q | q)))) | (((q | (p | p)) | (q | (p | p))) | ((q | (p | p)) | (q | (p | p)))) There are simpler definitions of using | . E.g. , this 43 symbol answer: p q ((p | (q | q)) | (q | (p | p))) | ((p | (q | q)) | (q | (p | p))) I offered E.C. for a shorter solution. Some students came up with a 19-symbol solution (counting parens), which is the shortest possible . More E.C. Find the shortest possible definitions of (1) p q , (2) p q , and (3) p & q in terms of p , q , and the NAND operator | . If you submit EC, please prove the correctness of your solution, using a truth-table method. You may submit these E.C. solutions to your GSI. UCB Philosophy Chapter 4 , Intro. 03/02/10 Branden Fitelson Philosophy 12A Notes 3 Abstract Argument Logical Form LSL / LMPL / LFOL Symbolization Chapters 2, 5 & 7 English Argument Valid Form? Deciding Formal Validity Chapters 3, 4 , 6 & 8 Valid English Argument? Valid Abstract Argument? Articulation of Argument in English UCB Philosophy Chapter 4 , Intro. 03/02/10 Branden Fitelson Philosophy 12A Notes 4 Chapter 4 Introduction: Truth vs Proof ( vs ) Recall: p q iff it is impossible for p to be true while q is false. We have methods (truth-tables) for establishing and claims. These methods are especially good for claims, but they get very complex for claims. Is there another more “natural” way to prove ’s? Yes! In Chapter 4, we will learn a natural deduction system for LSL. This is a system of rules of inference that will allow us to prove all valid LSL arguments in a purely syntactical way (no appeal to semantics). The notation p q means that there exists a natural deduction proof of q from p in our natural deduction system for sentential logic.

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