Deductive Logic/Categorical Sentence Schemata/Example Modus Festino (EIO-2) syllogisms

Understanding Modus Festino (EIO-2)

Role	Quantity–Quality	Logical Form
Major Premise (E)	Universal Negative	No P are M
Minor Premise (I)	Particular Affirmative	Some S are M
Conclusion (O)	Particular Negative	∴ Some S are not P

Figure 2 rule: the middle term (M) is predicate in both premises.

The reasoning excludes from P those S that share M, because P is wholly outside M.

---

Ten Valid Modus Festino (EIO-2) Syllogisms

#	Major Premise (E)	Minor Premise (I)	Conclusion (O)
1	No mammals are cold-blooded.	Some reptiles are cold-blooded.	∴ Some reptiles are not mammals.
2	No machines are living beings.	Some computers are machines.	∴ Some computers are not living beings.
3	No rectangles are circles.	Some wheels are circles.	∴ Some wheels are not rectangles.
4	No poets are mathematicians.	Some artists are poets.	∴ Some artists are not mathematicians.
5	No liars are trustworthy people.	Some politicians are liars.	∴ Some politicians are not trustworthy people.
6	No birds are mammals.	Some sparrows are birds.	∴ Some sparrows are not mammals.
7	No laws are emotions.	Some feelings are emotions.	∴ Some feelings are not laws.
8	No metals are plants.	Some trees are plants.	∴ Some trees are not metals.
9	No oceans are deserts.	Some ecosystems are deserts.	∴ Some ecosystems are not oceans.
10	No fools are wise men.	Some humans are fools.	∴ Some humans are not wise men.

All ten conform to: No P are M ; Some S are M ; ∴ Some S are not P.

---

Valid vs. Invalid Festino Comparisons

#	Valid Example	Invalid Example	Why Invalid
1	No mammals are cold-blooded. Some reptiles are cold-blooded. ∴ Some reptiles are not mammals.	No cold-blooded creatures are mammals. Some reptiles are cold-blooded. ∴ Some reptiles are not mammals.	Reverses major premise → M not predicate in both premises → wrong figure.
2	No machines are living beings. Some computers are machines. ∴ Some computers are not living beings.	All machines are living beings. Some computers are machines. ∴ Some computers are not living beings.	Major affirmative (A) → wrong mood (A I O).
3	No rectangles are circles. Some wheels are circles. ∴ Some wheels are not rectangles.	No circles are rectangles. Some wheels are circles. ∴ Some wheels are not rectangles.	Major reversed → M subject once only → figure 3.
4	No poets are mathematicians. Some artists are poets. ∴ Some artists are not mathematicians.	No mathematicians are poets. Some artists are poets. ∴ Some artists are not mathematicians.	Major reversed → M subject not predicate in major.
5	No liars are trustworthy people. Some politicians are liars. ∴ Some politicians are not trustworthy people.	All liars are untrustworthy. Some politicians are liars. ∴ Some politicians are not trustworthy.	Major affirmative → no negative premise to justify negative conclusion.
6	No birds are mammals. Some sparrows are birds. ∴ Some sparrows are not mammals.	No mammals are birds. Some sparrows are birds. ∴ Some sparrows are not mammals.	Reversed major → M subject not predicate.
7	No laws are emotions. Some feelings are emotions. ∴ Some feelings are not laws.	No emotions are laws. Some feelings are emotions. ∴ Some feelings are not laws.	Major reversed → violates 2nd-figure structure.
8	No metals are plants. Some trees are plants. ∴Some trees are not metals.	No plants are metals. Some trees are plants. ∴Some trees are not metals.	Middle term not predicate in both premises → wrong figure.
9	No oceans are deserts. Some ecosystems are deserts. ∴ Some ecosystems are not oceans.	All oceans are water bodies. Some ecosystems are deserts. ∴ Some ecosystems are not oceans.	Major affirmative → mood A I O invalid.
10	No fools are wise men. Some humans are fools. ∴ Some humans are not wise men.	No wise men are fools. Some humans are fools. ∴ Some humans are not wise men.	Major reversed → figure 3 instead of 2.

---

Typical Errors in Invalid Festino Forms

Fallacy	Explanation
Wrong Figure	In Festino, M must be predicate in both premises; many invalid examples break this rule.
Wrong Mood (A I O)	If the major is affirmative (A), there is no negative premise to support a negative conclusion.
Reversed Major Premise	Switching “No P are M” to “No M are P” changes the figure (usually to 3rd).
Illicit Middle Term	Middle term not distributed in either premise, so S and P remain unconnected.
Illicit Process of Term	A term distributed in the conclusion but undistributed in its premise.

---

Summary of Modus Festino (EIO-2)

Property	Description
Mood	E I O (Universal Negative + Particular Affirmative → Particular Negative)
Figure	2 (M predicate in both premises)
Form	No P are M; Some S are M; ∴ Some S are not P
Conclusion Type	Particular Negative (O)
Essence of Validity	Some S share M that is excluded from P; therefore those S cannot be P.