Notes 8.1
Symbols and Translation
So, up to now, we’ve studied Categorical Logic and Symbolic Logic.
But that leaves one
more type of logic to go.
Predicate Logic is just like the others, ultimately, in that it
provides us with a method for analyzing the validity of arguments.
Remember, this is
really the point of the whole course: to understand why good arguments are good and
why bad arguments are bad.
Predicate Logic is important because it’s even more
powerful than the Categorical and Symbolic Logic for analyzing arguments.
Consider
the following categorical syllogism (taken from the book, I swear!):
All student hookups are quickie sexual encounters.
No quickie sexual encounters are committed relationships.
Therefore, no student hookups are committed relationships.
What’s important here, of course, is the
term
(remember the major, minor, and middle
terms??).
The arrangement of the terms is what eventually becomes the important thing
for categorical logic (remember the forms of categorical syllogisms—AAA-2, etc.—and
how we knew whether an argument was valid simply by appealing to those?).
Next was Symbolic Logic—here’s an argument you could symbolize:
If chronic stress is reduced, then relaxation increases and health improves.
If health improves, then people live longer.
Therefore, if chronic stress is reduced, then people live longer.
Here what’s important is not the term, but the whole statement (proposition).
That is, the
statement is taken as the most fundamental unit (rather than the term).
From there, the
arrangement of the propositions will tell you all you need to know about validity—thus
the reduction to symbols, the connectives, and the truth tables.
But consider the following argument (again, taken from the book—I don’t have anything
for Julia Roberts, I swear):
Julia Roberts is rich and beautiful.
If a woman is either rich or famous, she is happy.
Therefore, Julia Roberts is happy.
Categorical Logic isn’t going to help us much here in determining validity.
I don’t know
how you would translate the two premises into a categorical proposition—remember,
categorical propositions are comparing two classes, but the premises are talking about
lots of classes of things (Julia Roberts, rich things, beautiful things, famous things, happy