Question: Give an example of a valid categorical syllogism and identify the form (mood + figure) of the syllogism. Then, give an example of a categorical syllogism that is not valid and identify which rule or rules from 5.3 it breaks.
All professors are doctors.
All mathematicians are professors.
Therefore, all mathematicians are doctors.
Some Star Trek fans are not fans of Star Wars.
No Dr. Who fans are Star Trek fans.
Therefore, all Dr. Who fans are fans of Star Wars.
Mood and Form: OEA – 1
This categorical syllogism is invalid because it violates rules three and four. It uses two negative premises which do not conclusively provide enough evidence to support the conclusion. It is also drawing an affirmative conclusion from a negative premise, which violates rule four.