All P are M. No M is S. [and there exists at least one S]* ∴ Some S are not P.
All squares are rectangles. No rectangle is a circle. [and there exists at least one circle]* ∴ Some circles are not squares.
* Note: When an existential conclusion is inferred from universal premisses, this requires an (implicit or explicit) existential import, i.e. it must be proven that what the term refers to actually exists. In case of the Modus Calemos it is sufficient to prove the existence of the minor term (S), as the conclusion does not actually imply the existence of M and/or P.
The Modus Calemos is a weaker form of the Modus Calemes, in which the conclusion is an existential rather than a universal statement. Since every universal quantification that does not refer to an empty extension set always implies an existential quantification, this variation is possible, but this is of course also a weaker statement than the universal conclusion of the Modus Calemes.
The name “Calemos” is a mnemonic term that helps to remember the most important characteristics of this mode: The “C” at the beginning indicates that it is related to the Modus Celarent, the “a” and “e” indicates the affirmative and negative universal premisses, and the “o” that there is a negative existential conclusion.
- Modus Calemop