A syllogism can go wrong in many ways. It may have four terms (QUATERNIO TERMINORUM), but even with three, out of 256 possible types, only 24 are valid in classical logic, and just 15 in modern logic. Using the vowels for the four types of proposition in the Table of Opposites (see previous page), medieval logicians devised mnemonics to learn these by heart:
BARBARA AAA1 CELARENT EAE1
DARII AII1 FERIO E101 BARBARI AAIT CELARONT EA01
CESARE EAE2 CAMESTRES AEE2 FESTINO WIO2 BAROCO A002
CESARO EAO2 CAMESTROS AE02
DATISI AII3 DISAMIS IAI3 FERISON EIO3 BOCARDO OAO3 FELAPTON EA03 DARAPTI AA13
CALEMES AEE4 DIMATIS IA14 FRESISON E104 CALEMOS AE04 FESAPO EA04 BAMALIP AA14
Syllogistic formal fallacies can be hard to spot. Here are three Invalid Combinations of Positive and Negative Statements:
EXCLUSIVE PREMISES: If both premises are negative, no connection is
established between the major and minor terms.
- No aliens are human. [E] 2. No humans have three eyes. [E] ~ :. AU aliens have three eyes. [A] x
AFFIRMATIVE CONCLUSION FROM A NEGATIVE PREMISE: If either premise is negative,
the conclusion must also be negative.
- Al fights are trouble. [A] 2. No trouble is worth dying for. [E] .:. Al fights are worth dying for. [A] *
worth dying for
The correct conclusion should be: No fight is worth dying for.