With this lesson, we will begin to learn how to deduce statements
from other statements.  Consider the following two statements:

        If Bart is in Hell, then Bart is dead.
        Bart is in Hell.

        If these two statements are true, then we know that another one is
as well.  And that statement is

        Bart is dead.

        When we derive a statement from other statements, as we have done
here, what we have is called an *argument*.  As the word is commonly used,
an argument means a verbal dispute.  That is *not* what argument means
here.  In this context, an argument is a set of statements, one of which is
claimed to follow from the others.  That statement is called the
*conclusion* of the argument.  The statements it is said to follow from are
called the *reasons* or *premises* of the argument.  Please note that the
conclusion does not actually have to follow from the premises for there to
be an argument.  An argument is any series of statements for which the
speaker claims some are reasons for believing another.  For instance,

        Fireflies are neat.  Therefore, Rick Wakeman is 47.

is an argument--though a terribly bad one.

        Getting back to the argument about Bart Simpson, the important
thing to note about it is that it has a particular form.  If we symbolize
it (using P for "Bart is in Hell." and Q for "Bart is dead."), we get

        P -> Q
        P
        ------
        Q

        If we substitute any other statements for P and Q, Q will be true
whenever both (P -> Q) and P are true.  For instance, we could argue

        If Clark Kent works for the Daily Planet, then he is a reporter.
        Clark Kent does work for the Daily Planet.
        ----------------------------------------------------------------
        Clark Kent is a reporter.

        As long as the two premises of this argument are true, it
necessarily follows that the conclusion is true.  Any argument whose
conclusion necessarily follows from the premises is called a *valid*
argument.  So, any argument whose form parallels the form of this argument
is a valid argument.  In the nomenclature of symbolic logic, the form of
this particular argument is called Modus Ponens.