There are 15 valid ways to structure categorical syllogisms using 3 terms in the standard form of major premise, minor premise, and conclusion. The validity depends on the figure and mood based on the ordering of the terms. Figures 1-4 are unconditionally valid if they match one of the 4 moods: AAA, EAE, AII, EIO. Some additional forms are conditionally valid if the terms refer to existing things. An example valid syllogism uses the terms: shopaholics, consumers with credit cards, and impulse buyers.

1. CREATING
CATEGORICAL
SYLLOGISMS

2. First things first
■ 256 possible ways to put them together
■ Only 15 ways to create them that are unconditionally valid
■ There are another 9 ways that are conditionally valid, but the
condition is that either the subject, predicate, or middle term
names something that actually exists.
■ What matters are the standard form, figure, and mood

3. There are four types of Categorical
syllogism
■ "Those that assert that the whole subject class is included in the predicate
class“ All S are P
■ "Those that assert that part of the subject class is included in the predicate
class“ Some S are P
■ "Those that assert that the whole subject class is excluded from the
predicate class“ No S are P
■ "Those that assert that part of the subject class is excluded from the
predicate class“ Some S are not P
■ Hurley, 2012, p. 198

4. Standard Form
■ In a categorical syllogism, there are two premises and one conclusion,
always, no exceptions
■ Each contains a proposition, a statement that makes sense and they
must be presented in what is called the standard form where each
proposition contains one “term”
■ In the syllogism, each term occurs exactly twice, no more, no less
■ There are three terms:
– There is a MajorTerm, which is also the Predicate
– A MinorTerm, which is also the Subject
– And a Middle term, which serves as a connector or bridge between the two premises

5. Standard Form
All categorical syllogisms must be put into standard form FIRST
1. All three statements are standard-form categorical
propositions.
2. The two occurrences of each term are identical.
3. Each term is used in the same sense throughout the argument
4. The major premise is listed first, the minor second, and the
conclusion last.
(“Categorical Syllogisms,” n.d.)

6. Last thing on Standard Form
■ Every predicate must have one and only one qualifier
– All
– Some
– None (or No)
■ Every predicate must have one copula (are, or are not)

7. Mood and Figure
■ Whether a syllogism is valid or invalid depends solely on the mood and figure (assuming you are
using a proper standard form)
■ In the diagram below, M = Middle term, P = Predicate, S = Subject
■ If the placement of your terms are not in one of these moods, they cannot be valid
(“Categorical Syllogisms,” n.d.)

8. Unconditionally valid Figures
■ Mood is not enough, you
must also have the right
“figure” based on a naming
system first articulated in the
Middle Ages
■ A – All S are P
■ E – No S are P
■ I – Some S are P
■ O – Some S are not P
(“Categorical Syllogisms,” n.d.)

9. Some conditionally valid moods and
figures
■ Aristotle held that some forms were valid if some component named an existing thing.
The more modern Boolean interpretation sees only those on the last slide as
unconditionally valid.
(“Categorical Syllogisms,” n.d.)

10. Creating valid ones in reverse
■ You can follow the steps listed at the bottom of this webpage
http://faculty.bsc.edu/bmyers/CategoricalSyllogisms.htm
■ OR you can do the following:
1. Using the three propositions determine the subject and predicate in your conclusion.
2. Then use the list of unconditionally valid figures and moods to find the ones you want to
use determine the qualifiers.This will take some thinking and perhaps some trial and
error. Ex, and EAE statement must be in figure 2 to work
3. Create the premises and conclusion following the mood and figure and it should work
4. Walk through the premises and reason your way to the conclusion. If you picked a listed
mood and figure, the logic should be apparent and the conclusion absolutely true if the
premises are true

11. Example
■ This comes from an example in Hurley (2012, p. 217)
■ Impulse buyers, shopaholics, consumers with credit cards
■ S – Impulse buyers, P – consumers with credit cards, M – shopaholics
■ Picking an AAA mood, I need to have this in figure 1 to work
M P
S M
S P
All shopaholics are consumers with credit cards
All Impulse buyers are shopaholics
All Impulse buyers are consumers with credit cards

12. Reference
■ Categorical Syllogisms, (n.d.) Retrieved from
http://faculty.bsc.edu/bmyers/CategoricalSyllogisms.htm
■ Hurley, P.J. (2012) Logic: A concise introduction. (11th ed). Boston, MA:Wadsworth
Cengage Learning.