Modus Fesapo

Form of a syllogism based on the Modus Ferio, in which a negative existential proposition is inferred from each negative and affirmative universal premisses. This form has an additional existential requirement.

No P is M.

All M are S.

[and there exists at least one M]*

∴ Some S are not P.

For example:

No circle is a square.

All squares are rectangles.

[and there exists at least one square]*

∴ Some rectangles are not circles.

* 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 Fesapo it is sufficient to prove existence for the middle term (M), as this also implies existence for S, whereas, in this particular case, actual existence for P is not implied.

The name “Fesapo” is a mnemonic term that helps to remember the most important characteristics of this mode: The “F” at the beginning indicates that it is related to the Modus Ferio, while the vowels indicate the types of statements used in the form: “e” and “a” stand for a negative and affirmative universal premisses and the “o” for a negative existential conclusion.

• Existential import
• Existential quantification
• Modus Ferio
• Syllogism
• Universal quantification