Celarent Syllogism

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A valid syllogism with negative conclusion: No A are B, All C are A, therefore No C are B.

Celarent is the second of the 'perfect' syllogisms in Aristotle's first figure. It combines a universal negative (E) premise with a universal affirmative (A) premise to derive a universal negative conclusion. The name 'Celarent' uses vowels E-A-E to indicate the proposition types: universal negative, universal affirmative, universal negative.

No M are P, All S are M ⊢ No S are P

• No reptiles are mammals. All snakes are reptiles. Therefore, no snakes are mammals.
• No even numbers are odd. All multiples of 4 are even. Therefore, no multiples of 4 are odd.
• No fish can breathe air. All salmon are fish. Therefore, no salmon can breathe air.

How to recognize it

• One premise uses 'No' (universal negative) and one uses 'All' (universal affirmative)
• The conclusion is always 'No' (universal negative)
• The middle term connects the chain through negation

Common mistakes

• Confusing the direction: 'No A are B' is not the same as 'No B are A' in context
• Missing that both terms in the conclusion inherit the negative relationship

Practice guidance

Logical Deduction