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*   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;