1. Aristotelian Logic

2. Aristotle’s Syllogisms
Aristotle’s Logic began with two premises (a major and a minor) and a conclusion.
For example:
Major: All men are mortals
Minor: Socrates is a man
Concl: Socrates is a mortal

3. Labeling Syllogisms
The parts within a syllogism can also be labeled. In the example:
Major: Men are mortals
Minor: Socrates is a man
Concl: Socrates is a mortal
Looking at the conclusion, Socrates is called the “subject,” and mortal is called the “predicate.” Men is called the “middle term” because it links the premises.

4. Labeling Syllogisms The syllogism becomes:
Major: Men are mortals M are P
Minor: Socrates is a man S is M
Concl: Socrates is a mortal S is P
But not all syllogisms follow the same written order as the example.

5. Figures of Syllogisms
There are four variations in the possible wording of the two premises which are called figures.
Fig. 1
M-P
S-M
S-P
Fig. 2
P-M
S-M
S-P
Fig. 3
M-P
M-S
S-P
Fig. 4
P-M
M-S
S-P
Major:
Minor:
Concl: .

6. Wording of Syllogisms
The wording of the syllogism plays a role is the conclusion.
There are four types of modifiers:
Universal Affirmatives (All)
Universal Negatives (No)
Particular Affirmatives (Some)
Particular Negatives (Some, not)

7. Wording of Syllogisms
The modifiers can be given letters to make it easier to write.
Universal Affirmatives (A)
Universal Negatives (E)
Particular Affirmatives (I)
Particular Negatives (O)

8. Shorthand Syllogism
Using the figures and the modifiers it is possible to create a shorthand notation for all syllogisms.
For example:
Major: All Squinkies are Winkies
Minor: No Winkies are Dinkies
Concl: No Dinkies are Squinkies

9. Shorthand Syllogism
First one must change the syllogism into its terms.
Major: All Squinkies are Winkies
Minor: No Winkies are Dinkies
Concl: No Dinkies are Squinkies
All P are M
No M are S
No S are P
Because of the pattern of the subject, predicate, and middle term, it can be determined that the syllogism is a variation on figure 4.

10. Shorthand Syllogism
Next one examine the modifiers, replacing them with letters.
Major: All P are MA
Minor: No M are SE
Concl: No S are PE
Because of the modifiers and the figure, the syllogism can be notated AEE-4.
It does not matter what the words of the syllogism are, the logic is always the same.

11. Variations of Syllogisms
There are 256 total possible variations of syllogisms; however, only 19 of them make logical sense. The logical variations are:
AAI-3
IAI-3
AII-3
EAO-3
OAO-3
EIO-3
AAI-4
AEE-4
IAI-4
EAO-4
EIO-4
AAA-1
EAE-1
AII-1
EIO-1
EAE-2
AEE-2
EIO-2
AOO-2

12. Mnemonics of Syllogisms
During Medieval times, a system of mnemonics was developed to make it easier to remember the structure of syllogisms that worked logically.
For example for Figure 1:
AAA-1 Barbara
EAE-1Celarent
AII-1Darii
EIO-1Ferio

13. Mnemonics of Syllogisms
The mnemonics for the other figures are:
Figure 2
EAE-2Cesare
AEE-2Camestres
EIO-2Festino
AOO-2Baroco
Figure 4
AAI-4Bramantip
AEE-4Camenes
IAI-4Dimaris
EAO-4Fesapo
EIO-4Fresison
Figure 3
AAI-3Darapti
IAI-3Disamis
AII-3Datisi
EAO-3Felapton
OAO-3Bocardo
EIO-3Ferison

14. In-class Activity
In groups, you will create 25 syllogisms that make logical sense.
After you have created them, convert your syllogisms into shorthand.
Then use Aristotle’s system of classification to check the logic your work.
Try to see if you can find an example which runs contrary to these syllogistic rules.