CS 100 - Week 6 Lecture 1 - 9-25-12

NOW -- getting more to EVALUATING these
arguments that we have determined are
deductive or inductive....

DEDUCTIVE arguments...
*   text gives the opinion that THE most
    important concept in deductive logic
    IS deductive VALIDITY

*   IF the conclusion in a deductive argument
    REALLY DOES follow NECESSARILY from the
    premises, then that deductive argument
    is called a VALID DEDUCTIVE ARGUMENT

*   more formally:
    a VALID deductive argument is one in which
    it is IMPOSSIBLE for all the premises to
    be true and the conclusion false.

*   put another way:
    a deductive argument is VALID IF the following
    conditions apply:
    *   IF the premises are true, the conclusion
        MUST be true
    *   the conclusion follows NECESSARILY from
        the premises
    *   the premises provide logically CONCLUSIVE
        grounds for the truth of the conclusion
    *   It is logically INCONSISTENT to assert
        that all the premises are true and then
        DENY the conclusion.

*   NOTE -- it is NOT necessary to KNOW
    WHETHER an argument's premises are true
    to know whether the argument is VALID...

*   SO --
    it IS possible to have a VALID argument
    with FALSE premises and a FALSE
    conclusion (as long as, IF the premises WERE
    true, they WOULD *HAVE* to lead that 
    conclusion)

    and you can have a VALID argument with
    FALSE premises and a TRUE conclusion,
    and of course one with TRUE premises
    and a TRUE conclusion --

    BUT!!! you CANNOT have a VALID argument 
    with ALL TRUE premises and a FALSE conclusion!

*   A deductive argument in which the
    conclusion does NOT necessarily follow
    from the premises is said to be 
    an INVALID deductive argument.

*   note:
    an INVALID argument can HAPPEN to have
    any combination of truth and falsity in
    its premises and conclusion;

    a VALID argument can HAPPEN to have
    most combinations, EXCEPT it CANNOT have
    true premises and a false conclusion;

*   AND: a deductive arugment,
    it is EITHER valid OR invalid --
    100% one or the other!
    no "partly", no "somewhat" no "degrees"

*   REMEMBER - DON'T assume that VALID means TRUE

*   why is validity important?
    ...amongst other things, validity
    can be said to PRESERVE the truth, IF ANY,
    contained in the premises;

*   a DEDUCTIVE argument that is BOTH 
    VALID AND has ALL TRUE PREMISES
    is called a SOUND DEDUCTIVE ARGUMENT

    ...deductive arguments that are EITHER
    INVALID OR have at least ONE false premise
    are said to be UNSOUND deductive arguments.

WHAT about INDUCTIVE arguments?
-------------------------------
...we DON'T use the terms valid/invalid for
   INDUCTIVE arguments.
...we DON'T use the terms sound/unsound for
   INDUCTIVE arguments.

We use STRONG/WEAK for inductive arguments,
   and COGENT/UNCOGENT for inductive arguments.

*   A well-reasoned inductive argument
    is called a STRONG inductive argument.

    more precisely...
    in a STRONG inductive argument,
    the conclusion follows PROBABLY from the 
    premise

    or, another way of looking at it:
    an inductive argument is a STRONG inductive
    argument IF the following conditions apply:
    *   IF the premises are true, the conclusion
        is PROBABLY true.
    *   The premises provide PROBABLE, but NOT
        logically conclusive, grounds for
        the truth of the conclusion.
    *   The premises, IF true, make the
        conclusion LIKELY.

*   if an inductive argument is not strong,
    it is WEAK
    (the conclusion does NOT follow probably
    from the premises)

*   AND -- you CAN have a STRONG inductive
    argument with false premises and a probably-
    false conclusion,
    ...with false premises and a probably-true
    conclusion,
    ...and with true premises and a probably-true
    conclusion

    BUT!! NO STRONG inductive argument
    can have all-TRUE premises and a probably-FALSE
    conclusion!

*   (weak inductive arguments can have ANY combo)

*   one important difference on the inductive
    side:
    ...strength DOES come in degrees;
    inductive arguments CAN be more strong,
    more weak, less strong, less weak,
    etc.!

*   IF an inductive argument is STRONG
    AND has ALL-TRUE premises, it is said
    to be a COGENT inductive argument.
    IF it is EITHER weak OR does not have all-true
    premises (or both), it is an UNCOGENT argument

                      Argument!!!
                     /          \
                    /            \
              Deductive        Inductive
              /      \         /        \
            Valid   Invalid   Strong   Weak
            /   \    /       /     \     /
          Sound Unsound    Cogent  Uncogent