The traditional syllogism
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
(1) Restate information
the simplest way possible in order to show whether you have--
an A statement
such as "All students are ambitious"
an E statement
such as "No students are lazy"
an I statement
such as "Some tests are easy"
an O statement
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
"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.
(2) Organize your
in standard form so that you have the middle (connecting) term as the
part of the top premise but the second part of the bottom premise, as
We want to prove that
tests are hard" by showing the linkage between the idea that anything
is hard and the idea that some tests are long.
Anything long is hard.
long" is the middle term)
Some tests are long.
There are several
to recognize whether what you have is a valid form (meaning, one in
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
you definitely have true premises but there is an obviously false
(2) For an invalid form
you can imagine a counterexample--a story in which the premises stay
same but the conclusion is the opposite, and you supply some
for how this is possible.
(3) You can work with Venn
(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
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
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."
are not using "light" the same way (the fallacy of ambiguity).
Rule 2: Nothing
two negative premises.
Rule 3: Nothing
two particular premises.
Rule 4: Any negative
calls for a negative conclusion.
Rule 5: Any
calls for a particular conclusion.
Rule 6: The middle
be distributed (meaning, it is used universally at least once in the
are smart, and all geniuses are smart, so all mathematicians are
In both premises we talk only about some of those who are smart
(the fallacy of an undistributed middle).
Rule 7: There cannot
subject or predicate in a conclusion if the term was not used
in the premises.
Example: "No woman has
been president, but all presidents have lived in the White House, so no
has lived in the White House."
We know the conclusion
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.
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
people living in the White House.