## Lecture 8: The Principles and Varieties of Syllogism

Supplementary Text

I.    Introduction.

A. We know definitions of syllogism and its parts.
B. we need to make and identify the syllogism.

II.    Perfect and imperfect syllogisms.
A. Difference between perfect and imperfect syllogisms.
B. Examples of both perfect and imperfect: triangles and metal books.

III.    Principles of syllogism.
A. Principles of all syllogisms.
1. First principle of syllogism: said of all.
2. What "said of all/none" means.
B. Principles for imperfect syllogisms: rules of conversion.
1. What conversion is.
2. Argument for the first rule of conversion.
3. Argument for the second rule.
a. Warning about conversion of universal affirmation.
4. Third rule briefly.
5. Fourth rule and instances.

IV.    Varieties of perfect syllogisms.
A. Order of treatment of perfect.
B. Process in general: all possibilities.
1. How he shows that they work and do not work.
a. An example of one that works.
b. An example of one that does not work.
C. Transition to labeling parts and naming syllogisms. First chart.
1. Labels of parts applies to Barbara and example of Barbara.
2. How the names work.
D. Notion of figure: transition to imperfect syllogisms.

V.   Varieties of imperfect syllogisms.
A. Summary of second chart.
B. Good and bad in imperfect, how names work.
1. Shows that some are good by reduction to first figure.
a. Reduction of Cesare to Celarent by conversion.