Deductive Logic/Categorical Sentence Schemata/Example Modus Ferio (EIO-1) syllogisms

Understanding Modus Ferio (EIO-1)

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

Figure 1 rule: the middle term (M) is subject of the major and predicate of the minor.

The reasoning excludes from P those S that are connected to M.

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Ten Valid Modus Ferio (EIO-1) Syllogisms

#	Major Premise (E)	Minor Premise (I)	Conclusion (O)
1	No mammals are cold-blooded.	Some dogs are mammals.	∴ Some dogs are not cold-blooded.
2	No machines are conscious beings.	Some computers are machines.	∴ Some computers are not conscious beings.
3	No rectangles are circles.	Some squares are rectangles.	∴ Some squares are not circles.
4	No liars are trustworthy people.	Some politicians are liars.	∴ Some politicians are not trustworthy people.
5	No poisons are safe foods.	Some mushrooms are poisons.	∴ Some mushrooms are not safe foods.
6	No birds are mammals.	Some sparrows are birds.	∴ Some sparrows are not mammals.
7	No laws are unjust acts.	Some statutes are laws.	∴ Some statutes are not unjust acts.
8	No metals are organic compounds.	Some coins are metals.	∴ Some coins are not organic compounds.
9	No oceans are fresh-water bodies.	Some seas are oceans.	∴ Some seas are not fresh-water bodies.
10	No fools are wise people.	Some humans are fools.	∴ Some humans are not wise people.

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

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Valid vs. Invalid Ferio Syllogisms Comparison

#	Valid Example	Invalid Example	Why Invalid
1	No mammals are cold-blooded. Some dogs are mammals. ∴ Some dogs are not cold-blooded.	No cold-blooded creatures are mammals. Some dogs are mammals. ∴ Some dogs are not cold-blooded.	Reverses major premise → M no longer subject in major → wrong figure.
2	No machines are conscious beings. Some computers are machines. ∴ Some computers are not conscious beings.	All machines are conscious beings. Some computers are machines. ∴ Some computers are not conscious beings.	Major affirmative (A) → mood A I O invalid in figure 1.
3	No rectangles are circles. Some squares are rectangles. ∴ Some squares are not circles.	No circles are rectangles. Some squares are rectangles. ∴ Some squares are not circles.	Major reversed → M predicate in major → figure 2, not 1.
4	No liars are trustworthy people. Some politicians are liars. ∴ Some politicians are not trustworthy people.	No trustworthy people are liars. Some politicians are liars. ∴ Some politicians are not trustworthy people.	Middle term predicate in major → wrong figure.
5	No poisons are safe foods. Some mushrooms are poisons. ∴ Some mushrooms are not safe foods.	All poisons are unsafe foods. Some mushrooms are poisons. ∴ Some mushrooms are not safe foods.	Major affirmative (A) → mood A I O invalid.
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.	Major reversed → middle term predicate in major.
7	No laws are unjust acts. Some statutes are laws. ∴ Some statutes are not unjust acts.	No unjust acts are laws. Some statutes are laws. ∴ Some statutes are not unjust acts.	Improper figure → M predicate in major.
8	No metals are organic compounds. Some coins are metals. ∴ Some coins are not organic compounds.	No organic compounds are metals. Some coins are metals. ∴ Some coins are not organic compounds.	Major reversed → figure error.
9	No oceans are fresh-water bodies. Some seas are oceans. ∴ Some seas are not fresh-water bodies.	All oceans are salt-water bodies. Some seas are oceans. ∴ Some seas are not fresh-water bodies.	Major affirmative → invalid mood.
10	No fools are wise people. Some humans are fools. ∴ Some humans are not wise people.	No wise people are fools. Some humans are fools. ∴ Some humans are not wise people.	Major reversed → middle term predicate in major.

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Frequent Invalidity Causes in “Ferio” Mistakes

Fallacy	Explanation
Wrong Figure	M must be subject in the major and predicate in the minor (1st figure). Reversing breaks the link between S and P.
Wrong Mood (A I O)	Major must be negative (E); if affirmative (A), no exclusion is asserted.
Illicit Middle Term	Middle term undistributed or not linked to both S and P.
Illicit Process of Term	Term distributed in conclusion but not in premise.
Existential Fallacy	All-universal premises cannot yield a particular conclusion (but Ferio avoids this by having a particular minor).

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Summary of Modus Ferio (EIO-1)

Property	Description
Mood	E I O (Universal Negative + Particular Affirmative → Particular Negative)
Figure	1
Form	No M are P; Some S are M; ∴ Some S are not P.
Middle Term Placement	Subject in major, predicate in minor.
Conclusion Type	Particular Negative (O).
Essence of Validity	The subset of S that belongs to M is excluded from P because M is excluded from P.