Leonardowerkstatt

194 SYLLOGISTIC FALLACIES

SYLLOGISTIC FALLACIES

misdeductions

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.

three eyes

  1. No aliens are human. [E] 2. No humans have three eyes. [E] ~ :. AU aliens have three eyes. [A] x

humans

aliens

AFFIRMATIVE CONCLUSION FROM A NEGATIVE PREMISE: If either premise is negative,

the conclusion must also be negative.

  1. Al fights are trouble. [A] 2. No trouble is worth dying for. [E] .:. Al fights are worth dying for. [A] *

trouble

fights

worth dying for

The correct conclusion should be: No fight is worth dying for.

194 LOGIC