CS 100 - Week 10 Lecture 2 - 10-25-12

Chapter 7, continued:
continuing with DIAGRAMMING arguments:

1. First, READ THROUGH the argument, and UNDERLINE
   any premise or conclusion indicator words
   you see

2. Number the statements consecutively as they
   appear in the argument. (We're using parenthesized
   numbers, circled numbers are fine, too)
   (If something is not a logical statement,
   don't number it.)

3. Arrange the statement numbers on lines,
   numbers for premises above the numbers
   of the conclusion(s) they support,

   OMIT/remove any logically irrelevant statements.
   You can also omit redundant statements.

4. Then, using arrows to mean "is offered as 
   evidence for", create a sort of flowchart  
   that indicates relationships of argumentative
   support, 

   drawing a single arrow FROM a single independent
   premise's number to the number of the conclusion
   number it supports,
   
   and for linked premises,
   underlining them, putting + between them,
   and drawing an arrow from the underline
   to the number of the conclusion supported

EXAMPLES
--------

    (1) The death penalty should be abolished because
                                              -------
    (2) it is racially discriminatory, (3) there's no
    evidence
    that it is a more effective deterrent than life
    imprisonment, and (4) innocent people may be
    executed by mistake.

    (2)  (3)  (4)
     \    |   /
      v   v  v
         (1)

*   we say that a premise provides INDEPENDENT support
    when it provides a separate, freestanding reason for
    accepting the conclusion;

    OR, more precisely,
    a premise provides independent support for a
    conclusion when the amount of support it provides
    would not be weakened or destroyed by the removal
    of any other premise in the argument

    *   we draw an arrow from each independent premise
        number to the conclusion number it supports

*   so -- here's another argument:

    (1) Every member of the Applewood Association is more
    than 50 years old. (2) Bob is a member of the Applewood
    Association. So, (3) Bob is more than 50 years old.
                 __

    (1) + (2)
    ---------
         |
         v
        (3)

    *   a premise provides LINKED support for a conclusion
        when the amount of support it provides would
	be WEAKENED or DESTROYED by the removal of some
	other premise in the argument.
 
    *   (linked premises work in combination to support
        the conclusion)

    *   put + between the numbers of linked premises,
        underline them, and draw an arrow from the
	underline to the number of the supported
	conclusion

EXAMPLE:
    (1) If Amy runs marathons, then she's probably very
    fit. (2) Amy does run marathons. (3) She's also
    a B student. So, (4) Amy is probably very fit.
                 --

    *   omitting (3) below, because it isn't relevant
        to the conclusion

      (1) + (2)
      ---------
           |
           v
          (4)

EXAMPLE:

(1) The competition employs a sliding mechanism in their door. 
(2) A hinged door is lighter and easier to operate. (3) A 
hinged door ensures a better fit and seal with the body than a 
sliding mechanism, thus (4) keeping the cabin's interior noise 
                   ----
level to a minimum. (5) A hinged door allows for greater freedom 
in the shape of the vehicle. (6) A hinged door is better 
than a sliding door.

(2)  (3)  (5)  
 |    |    |
 |    v    |
 |   (4)   |
 \    |   /
  v   v  v
     (6)

...after class, thinking about this, I think the following 
would be a better diagram:

     (3)    
      |   
      v   
(2)  (4)  (5)
 \    |   /
  v   v  v
     (6)

EXAMPLE
*   (1) Jim is a senior citizen. So, (2) Jim probably doesn't like
                                 --
    hip-hop music. So, (3) Jim probably won't be going to
                   --
    the Jay-Z concert this weekend.

    (1)
     | 
     v
    (2)
     |
     v
    (3)

EXAMPLE:
(1) A is the murderer. THIS IS EVIDENT BECAUSE (2) his 
                       -----------------------
fingerprints are on the murder weapon. IN ADDITION, (3) all 
                                       -----------
people who wear hockey masks 24 hours a day are murderers, 
and (4) A wears a hockey mask 24 hours a day.

(2)   (3) + (4)
 \    ---------
  \     |
   v    v
     (1)

TIPS for diagramming arguments:
1. Find the main conclusion first.
   ...then you can work through the passage to
      see how the argument as a whole supports
      the main conclusion
2. Pay close attention to premise and conclusion
   indicators
3. Remember that sentences containing the word
   AND often contain two or more separate statements
4. Treat a conditional (if-then) statement as a single
   statement, and treat a disjunctive (either-or)
   statement as a single statement.
5. Don't number or diagram any sentence that is not
   a statement.
6. Don't diagram irrelevant statements (number them,
   but don't put them in the diagram with the arrows.)
7. Don't diagram redundant statements.
   (number them, but don't put them in the diagram with
   the arrows)