Notes 6.1
So we should have gotten the point now that the validity of a deductive argument
depends entirely on the form of an argument.
But language, of course, can obscure the
form of argument—and this is why we’ve been analyzing more normal language stuff
into logically useful statements (like categorical propositions).
Now, we’re moving on to
look at symbolic logic, where, you guessed it, we’re only dealing with symbols and
operators (connectives)
, instead of just using terms as the focal point of analysis.
So,
here’s a look at some
simple statements:
Fast foods tend to be unhealthy
James Joyce wrote
Ulysses
.
Parakeets are colorful birds.
The monk seal is threatened with extinction.
Any upper-case letter you like (typically, you’d pick a letter which will help remind you
what proposition you’re symbolizing) will represent these whole propositions.
Like, say,
F for the first, J for the second, P for the third, and M for the fourth.
Now, you can also have
compound statements
with at least one simple statement as a
component.
Here are some:
It is not the case that Al-Qaeda is a humanitarian organization.
Dianne Reeves sings jazz, and Christina Aguilera sings pop.
Either people get serious about conservation or energy prices will skyrocket.
If the world’s nations spurn international law, then future wars are guaranteed.
The Broncos will win if and only if they run the ball.
Let’s bring in some letters to symbolize the content of these propositions:
It is not the case that A.
D and C.
Either P or E.
If W then F.
B if and only if R.
Here, then, comes the idea of the
operator (or connective)
.
When you say ‘
it is not the
case that
’ or ‘
and
’, or ‘
or
’, or ‘
if . . . then . .
.’, or ‘
if and only if
’, we can introduce these
operators to symbolize these relations.
Operator
Name
Logical Function
Used to translate
~
tilde
negation
not, it is not the case that
·
dot
conjunction
and, also, moreover, but
v
wedge
disjunction
or, unless
horseshoe
implication
if . . . then . . .; only if
≡
triple bar
equivalence
if and only if