Ferio Syllogism

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A valid syllogism: No A are B, Some C are A, therefore Some C are not B.

Ferio is the fourth 'perfect' syllogism of the first figure. It combines a universal negative (E) major premise with a particular affirmative (I) minor premise to derive a particular negative (O) conclusion. The name 'Ferio' uses vowels E-I-O to indicate proposition types. It allows us to conclude that some members of a category lack a property based on their membership in an excluded class.

No M are P, Some S are M ⊢ Some S are not P

• No reptiles are warm-blooded. Some pets are reptiles. Therefore, some pets are not warm-blooded.
• No vegetables contain cholesterol. Some foods I eat are vegetables. Therefore, some foods I eat do not contain cholesterol.
• No beginners pass the advanced test. Some students are beginners. Therefore, some students do not pass the advanced test.

How to recognize it

• Major premise uses 'No' (universal negative)
• Minor premise uses 'Some' (particular affirmative)
• Conclusion uses 'Some...not' (particular negative)

Common mistakes

• Concluding 'No C are B' instead of 'Some C are not B' - over-generalizing from partial evidence
• Misreading 'Some C are not B' as 'Some C are B' (opposite meaning)

Practice guidance

Logical Deduction