********* * TODAY: starting our discussion of DIAGRAMMING ARGUMENTS from Chapter 7; * (you will be practicing this on Homework 9 that comes out AFTER Exam 2, and this will be Final Exam-testable...) * WEDNESDAY: REVIEW for EXAM 2 * NOTE that while the exam will INCLUDE concepts from the whole semester, the FOCUS of most of the questions will be on topics from: * Chapter 9 - a little Categorical logic * Chapter 10 - a little Propositional logic * a little WeScheme/Scheme * FRIDAY: EXAM 2 ********* ********* * CHAPTER 7 - ANALYZING arguments * today: diagramming arguments * after Exam 2: summarizing arguments * to ANALYZE an argument means to BREAK IT DOWN into its various parts, to see hopefully-clearly what CONCLUSION is being defended and on what grounds; ********** * DIAGRAMMING an argument * esp. suitable for "shorter" arguments (roughly a paragraph in length or shorter) * BASIC approach: * STEP 1 - IDENTIFY key connecting words and phrases that commonly separate PREMISES from each other and from the CONCLUSION(s) * e.g., because! since! so that! therefore! thus! and! (and many more!) * we are going to CIRCLE such premise and conclusion indicators * STEP 2 - NUMBER the individual STATEMENTS consecutively as they appear in the argument, using CIRCLED numbers at/near the BEGINNING of each statement (you can ignore bits that aren't statements...) * STEP 3 - arrange the numbers on the page such that the premises' numbers are ABOVE the conclusion's number, (premises on a row above the conclusion, BUT you could have more than 2 rows if a statement supports another statement that helps support the overall conclusion...) OMITTING any logically-irrelevant statement(s)' numbers * STEP 4 - for the premises, determine if each premise provides INDEPENDENT support for a conclusion, OR if it provides LINKED support, dependent upon other premises to provide support for the conclusion * a premise provides INDEPENDENT support for a conclusion if the AMOUNT of support it provides would not be weakened or destroyed by the removal of any other premise the argument * a premise provides LINKED support if it must or should be used with one or more premises to more strongly support the conclusion (the amount of support it provides WOULD be significantly weakened by the removal of other premises...) * for each independent premise, draw an arrow from its circled number to the conclusion number for each linked set of premises, put a + between their circled numbers, underline them, and put an arrow from the underline to the conclusion number * you can see the results of following these steps in class for several example arguments projected along with these notes;