This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ' & $ % Announcements and Such Todays Music: The Rolling Stones I have posted my solutions to HW #4 (with the shortest proofs I know). HW #5 is due today @ 4pm. Ive posted a handout entitled Working with LMPL Interpretations, which contains model answers for LMPL semantics problems. HW #6 has been posted, and will be due next Thursday @ 4pm. + The final is in class next Thursday. Youll be given 3 hours to do it. Ive posted two important handouts concerning the final exam: The (Complete) Natural Deduction Rules Handout (provided at final). A sample final exam, which has the same structure as the actual final. This sample will be discussed, in detail, in lecture tomorrow. Today: Chapter 6 Natural deduction proofs in LMPL UCB Philosophy Chapter 6 06/23/10 Branden Fitelson Philosophy 12A Notes 2 ' & The Rule of Introduction Rule of Introduction : For any sentence , if has been inferred at line j in a proof, then at line k we may infer [ ( ) , labeling the line j I and writing on its left the numbers that occur on the left of j. a 1 ,. . . , a n (j) . . . a 1 ,. . . , a n (k) ( ) j I Where [ ( ) is obtained syntactically from by: Replacing one or more occurrences of in by a single variable . Note: the variable must not already occur in the expression . [This prevents doublebinding , e.g. , ( x)( x)(Fx & Gx) .] And, finally, prefixing the quantifier [ ( ) in front of the resulting expression (which may now have both [ s and [ s occurring in it). UCB Philosophy Chapter 6 06/23/10 Branden Fitelson Philosophy 12A Notes 3 ' & $ % The Rule of Elimination Rule of Elimination : For any sentence [ ( ) and constant , if [ ( ) has been inferred at a line j, then at line k we may infer , labeling the line j E and writing on its left the numbers that appear on the left of j. a 1 ,. . . , a n (j) ( ) . . . a 1 ,. . . , a n (k) j E Where is obtained syntactically from [ ( ) by: Deleting the quantifier prefix [ ( ) . Replacing every occurrence of in the open sentence by one and the same constant . [This prevents fallacies , e.g. , ( x)(Fx Gx) Fa Gb .] Note: since means everything , there are no restrictions on which individual constant may be used in an application of E. UCB Philosophy Chapter 6 06/23/10 Branden Fitelson Philosophy 12A Notes 4 ' & The Rule of Introduction: Some Background It is useful to think of a universal claim [ ( ) as a conjunction which asserts that the predicate expression is satisfied by all objects in the domain of discourse ( i.e. , the conjunction [ a & (b & (c & ...)) is true)....
View
Full
Document
This note was uploaded on 11/26/2011 for the course PHILOSOPHY 101 taught by Professor Buechner during the Fall '06 term at Rutgers.
 Fall '06
 Buechner
 Philosophy

Click to edit the document details