In order to work with
anything in symbolic logic, we need
to begin with the idea of truth-functional propositions. The word
"truth" may actually be misleading. All we need to
think of would be things that can be in more than one state, as
when we think of the power being ON or OFF, or a binary digit
being 1 or 0. To understand this concept better, let's look at
the panel above this one (assuming you are working with a
frames-enabled browser). Presently the color is RED, which we will take as an
initial state equivalent to being "true," but it can
change to BLUE, which
will be an alternate state equivalent to being "false."
The colors are reciprocal: we can only change RED
to BLUE
and BLUE to RED.
To see what we mean by truth functions, let's imagine we have two individuals playing a game that calls on each of them to choose between RED and BLUE in order to decide what color will appear in the panel. There are also four switches that link their choices. We will represent these as buttons, and by pushing one or another button you can see the effect on the panel given particular combinations chosen by the players.
There are sixteen options in the game as played. Each of these could be thought of as being a function of the two players' choices. If we represent them symbolically --for instance, as (P & Q) for the conjunction of the two choices--we can then think of each expression as truth-functional. All this means is that its value (red or blue, true or false) depends on the values of its components as linked in a particular way.Go ahead and experiment
with the options below. Try to get used to the results of combining "P"
and "Q" different ways. Look at the panel above for the
results.