# Modus Calemos

Form of a syllogism based on the Modus Celarent, in which a negative existential proposition is inferred from positive and negative universal premisses.

All P are M.

No M is S.

[and there exists at least oneS]*

Therefore, some S are not P.

For example:

Allsquaresarerectangles.

Norectangleis acircle.

[and there exists at least onecircle]*

Therefore, somecirclesare notsquares.

The *Modus Calemos* is a weaker form of the Modus Calemes, in which the conclusion is an existential rather than a universal statement. This is possible since every universal quantification that does not refer to an *empty extension set* always implies an *existential quantification*, but this is of course also a weaker statement than the universal conclusion of the *Modus Calemes*.

## Name

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.

### Alternative name

- Modus Calemop