WORKING WITH SYLLOGISMS
The traditional syllogism
comes
down to us from Aristotle and was the standard for formal logic down to
this century. To work with syllogisms you will need to be able to do
two
things:
(1) Restate information
in
the simplest way possible in order to show whether you have--
-
an A statement
(universal positive),
such as "All students are ambitious"
-
an E statement
(universal negative),
such as "No students are lazy"
-
an I statement
(particular positive),
such as "Some tests are easy"
-
an O statement
(particular negative),
such as "Some students are not ready"
In doing this keep in
mind the impact of the word "only" since it indicates a need to reverse
the order of the terms in thinking through the statement. For
instance,
"Only fun things are easy" has to be rephrased as "All easy things are
fun." Knowing that something is fun does not mean it is easy, but
if we do have something easy it is in the class of things that are fun.
PRACTICE
TEST ON CHANGING TO THE CLASSIC TYPE OF SENTENCE
(2) Organize your
statements
in standard form so that you have the middle (connecting) term as the
first
part of the top premise but the second part of the bottom premise, as
in
this example:
We want to prove that
"Some
tests are hard" by showing the linkage between the idea that anything
long
is hard and the idea that some tests are long.
Anything long is hard.
("being
long" is the middle term)
Some tests are long.
.:Some tests
are
hard.
PRACTICE
TEST ON SETTING UP STATEMENTS AS SYLLOGISMS
There are several
ways
to recognize whether what you have is a valid form (meaning, one in
which
true premises could not give you a false conclusion).
(1) For an invalid form
it is possible to set up a parallel example with different terms so
that
you definitely have true premises but there is an obviously false
conclusion.
(2) For an invalid form
you can imagine a counterexample--a story in which the premises stay
the
same but the conclusion is the opposite, and you supply some
explanation
for how this is possible.
(3) You can work with Venn
diagrams.
(4) You can do what are
called Euler circles--diagrams in which again you keep the premises the
same but try to show a false conclusion.
(5) You can apply a
mechanical
list, such as the "BARBARA CELARENT" type of thing from the Middle Ages.
(6) You can run through
the following checklist.
Rule 1: A syllogism
works with
only three terms used with exactly the same meaning throughout.
Example: "Anything light
can be lifted up, but the sun is light, so the sun can be lifted up."
We
are not using "light" the same way (the fallacy of ambiguity).
Rule 2: Nothing follows
from
two negative premises.
Rule 3: Nothing follows
from
two particular premises.
Rule 4: Any negative
premise
calls for a negative conclusion.
Rule 5: Any particular
premise
calls for a particular conclusion.
Rule 6: The middle term
must
be distributed (meaning, it is used universally at least once in the
premises).
Example: "All
mathematicians
are smart, and all geniuses are smart, so all mathematicians are
geniuses."
In both premises we talk only about
some of those who are smart
(the fallacy of an undistributed middle).
Rule 7: There cannot be
a universal
subject or predicate in a conclusion if the term was not used
universally
in the premises.
Example: "No woman has
been president, but all presidents have lived in the White House, so no
woman
has lived in the White House."
We know the conclusion
is
wrong even though the premises are correct (if we don't count George
Washington, who was president
before the White House was built), so we know the pattern is invalid.
To
see why, we look at the way in which we move from the idea of being some
of the people living in the White House (particular) to being none of
the
people living in the White House.
PRACTICE
TEST ON RECOGNIZING VALID AND INVALID ARGUMENTS
Use
your back button to return to your original site.