Header

© 2010 Jay B Krasner, MD, FACP

Categorical Propositions Immediate inferences Blah

Categorical Proposition Types
Code	Quantity	Quality	Exposition	Distribution
A	Universal	Affirmative	All S are P	Subject
E	Universal	Negative	No S are P	Subject Predicate
I	Particular	Affirmative	Some S are P	-
O	Particular	Negative	Some S are not P	Predicate (No P is in the class referred to by "some S")

Immediate Inferences: Eduction
Inference	Process	Validity
		A	E	I	O
		All S is P	No S is P	Some S is P	Some S is not P
Simple ConvErsIon	Interchange subject and predicate	No All P is S	Yes No P is S	Yes Some P is S	No (Some P is not S)
per AccidEns Conversion	Interchange subject and predicate Invert quantity	Yes Some P is S	Yes Some P is not S	No	No
Obversion	Change quality, invert predicate	Yes No S is non-P	Yes All S is non-P	Yes Some S is not non-P	Yes Some S is non-P
ContrApOsition	Invert subject and predicate, Exchange subject and predicate	Yes All non-P is non-S	By limitation Some non-P is non-S	No (Some non-P is non-S)	Yes Some non-P is not non-S

Syllogism Validity Rules

1. Relating to structure
   1. There are only three terms in a syllogism (by definition).
   2. The middle term is not in the conclusion (by definition).
   3. The major premise contains the predicate (major term) of the conclusion (by definition).
   4. The minor premise containes the subject (minor term) of the conclusion (by definition).
2. Relating to premises irrespective of conclusion or figure
   1. No inference can be made from two negative premises, i.e., at least one premise must be affirmative. (Fallacy of Exclusive Premises)
   2. No inference can be made from two particular premises, i.e., at least one premise must be universal.
3. Relating to propositions irrespective of figure
   1. If one premise is negative, the conclusion must be negative. (Fallacy of Drawing an Affirmative Conclusion from a Negative Premise)
   2. In extensional logic, if both premises are universal, the conclusion must be universal. (Existential Fallacy)
      This is not a necessary condition for validity if empty classes are disallowed
   3. If both premises are affirmative, the conclusion must be affirmative -
      A negative conclusion requires a negative premise (Fallacy of Drawing a Negative Conclusion from Affirmative Premises)
   4. If one premise is particular, the conclusion must be particular.
4. Relating to the distribution of terms
   1. The middle term must be distributed in at least one premise (Fallacy of the Undistributed Middle)
   2. A predicate distributed in the conclusion must be distributed in the major premise. (Fallacy of the Illicit Major)
   3. A subject distributed in the conclusion must be distributed in the minor premise. (Fallacy of the Illicit Minor)
   4. The quantity of a term cannot become greater in the conclusion.

Figure	1	2	3	4
Major Premise	M - P	P - M	M - P	P - M
Minor Premise	S - M	S - M	M - S	M - S
Conclusion	S - P	S - P	S - P	S - P

Mood Figure	Explication	Distributed terms Premises : Conclusion	Rules violated	Validity
AAA1	All M are P All S are M All S are P	2 : 1	-	Valid 1
AAE1	All M are P All S are M No S are P	2 : 2	Affirmative premises, Negative conclusion Illicit Major	Invalid
AAI1	All M are P All S are M Some S are P	2 : 0	Existential Fallacy	Conditionally Valid 2
AAO1	All M are P All S are M Some S are not P	2 : 1	Affirmative premises, Negative conclusion Illicit Major Existential Fallacy	Invalid
AEA1	All M are P No S are M All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
AEE1	All M are P No S are M No S are P	3 : 2	Illicit Major	Invalid
AEI1	All M are P No S are M Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
AEO1	All M are P No S are M Some S are not P	3 : 1	Illicit Major Existential Fallacy	Invalid
AIA1	All M are P Some S are M All S are P	1 : 1	Illicit Minor	Invalid
AIE1	All M are P Some S are M No S are P	1 : 2	Affirmative premises, Negative conclusion Illicit Major Illicit Minor	Invalid
AII1	All M are P Some S are M Some S are P	1 : 0	-	Valid 3
AIO1	All M are P Some S are M Some S are not P	1 : 1	Affirmative premises, Negative conclusion Illicit Major	Invalid
AOA1	All M are P Some S are not M All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
AOE1	All M are P Some S are not M No S are P	2 : 2	Illicit Major Illicit Minor	Invalid
AOI1	All M are P Some S are not M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
AOO1	All M are P Some S are not M Some S are not P	2 : 1	Illicit Major	Invalid
EAA1	No M are P All S are M All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
EAE1	No M are P All S are M No S are P	3 : 2	-	Valid 4
EAI1	No M are P All S are M Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
EAO1	No M are P All S are M Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 5
EEA1	No M are P No S are M All S are P	4 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EEE1	No M are P No S are M No S are P	4 : 2	2 negative premises	Invalid
EEI1	No M are P No S are M Some S are P	4 : 0	2 negative premises Negative premise, affirmative conclusion Existential Fallacy	Invalid
EEO1	No M are P No S are M Some S are not P	4 : 1	2 negative premises Existential Fallacy	Invalid
EIA1	No M are P Some S are M All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EIE1	No M are P Some S are M No S are P	2 : 2	Illicit Minor	Invalid
EII1	No M are P Some S are M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
EIO1	No M are P Some S are M Some S are not P	2 : 1	-	Valid 6
EOA1	No M are P Some S are not M All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion Illicit Minor	Invalid
EOE1	No M are P Some S are not M No S are P	3 : 2	2 negative premises Illicit Minor	Invalid
EOI1	No M are P Some S are not M Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
EOO1	No M are P Some S are not M Some S are not P	3 : 1	2 negative premises	Invalid
IAA1	Some M are P All S are M All S are P	1 : 1	Undistributed Middle	Invalid
IAE1	Some M are P All S are M No S are P	1 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IAI1	Some M are P All S are M Some S are P	1 : 0	Undistributed Middle	Invalid
IAO1	Some M are P All S are M Some S are not P	1 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IEA1	Some M are P No S are M All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
IEE1	Some M are P No S are M No S are P	2 : 2	Illicit Major	Invalid
IEI1	Some M are P No S are M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
IEO1	Some M are P No S are M Some S are not P	2 : 1	Illicit Major	Invalid
IIA1	Some M are P Some S are M All S are P	0 : 1	Undistributed Middle Illicit Minor	Invalid
IIE1	Some M are P Some S are M No S are P	0 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major Illicit Minor	Invalid
III1	Some M are P Some S are M Some S are P	0 : 0	Undistributed Middle	Invalid
IIO1	Some M are P Some S are M Some S are not P	0 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IOA1	Some M are P Some S are not M All S are P	1 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
IOE1	Some M are P Some S are not M No S are P	1 : 2	Illicit Major Illicit Minor	Invalid
IOI1	Some M are P Some S are not M Some S are P	1 : 0	Negative premise, affirmative conclusion	Invalid
IOO1	Some M are P Some S are not M Some S are not P	1 : 1	Illicit Major	Invalid
OAA1	Some M are not P All S are M All S are P	2 : 1	Negative premise, affirmative conclusion Undistributed Middle	Invalid
OAE1	Some M are not P All S are M No S are P	2 : 2	Undistributed Middle	Invalid
OAI1	Some M are not P All S are M Some S are P	2 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
OAO1	Some M are not P All S are M Some S are not P	2 : 1	Undistributed Middle	Invalid
OEA1	Some M are not P No S are M All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
OEE1	Some M are not P No S are M No S are P	3 : 2	2 negative premises	Invalid
OEI1	Some M are not P No S are M Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OEO1	Some M are not P No S are M Some S are not P	3 : 1	2 negative premises	Invalid
OIA1	Some M are not P Some S are M All S are P	1 : 1	Negative premise, affirmative conclusion Undistributed Middle Illicit Minor	Invalid
OIE1	Some M are not P Some S are M No S are P	1 : 2	Undistributed Middle Illicit Minor	Invalid
OII1	Some M are not P Some S are M Some S are P	1 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
OIO1	Some M are not P Some S are M Some S are not P	1 : 1	Undistributed Middle	Invalid
OOA1	Some M are not P Some S are not M All S are P	2 : 1	2 negative premises Negative premise, affirmative conclusion Illicit Minor	Invalid
OOE1	Some M are not P Some S are not M No S are P	2 : 2	2 negative premises Illicit Minor	Invalid
OOI1	Some M are not P Some S are not M Some S are P	2 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OOO1	Some M are not P Some S are not M Some S are not P	2 : 1	2 negative premises	Invalid
AAA2	All P are M All S are M All S are P	2 : 1	Undistributed Middle	Invalid
AAE2	All P are M All S are M No S are P	2 : 2	Affirmative premises, Negative conclusion Undistributed Middle	Invalid
AAI2	All P are M All S are M Some S are P	2 : 0	Undistributed Middle Existential Fallacy	Invalid
AAO2	All P are M All S are M Some S are not P	2 : 1	Affirmative premises, Negative conclusion Undistributed Middle Existential Fallacy	Invalid
AEA2	All P are M No S are M All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
AEE2	All P are M No S are M No S are P	3 : 2	-	Valid 7
AEI2	All P are M No S are M Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
AEO2	All P are M No S are M Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 8
AIA2	All P are M Some S are M All S are P	1 : 1	Undistributed Middle Illicit Minor	Invalid
AIE2	All P are M Some S are M No S are P	1 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Minor	Invalid
AII2	All P are M Some S are M Some S are P	1 : 0	Undistributed Middle	Invalid
AIO2	All P are M Some S are M Some S are not P	1 : 1	Affirmative premises, Negative conclusion Undistributed Middle	Invalid
AOA2	All P are M Some S are not M All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
AOE2	All P are M Some S are not M No S are P	2 : 2	Illicit Minor	Invalid
AOI2	All P are M Some S are not M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
AOO2	All P are M Some S are not M Some S are not P	2 : 1	-	Valid 9
EAA2	No P are M All S are M All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
EAE2	No P are M All S are M No S are P	3 : 2	-	Valid 10
EAI2	No P are M All S are M Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
EAO2	No P are M All S are M Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 11
EEA2	No P are M No S are M All S are P	4 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EEE2	No P are M No S are M No S are P	4 : 2	2 negative premises	Invalid
EEI2	No P are M No S are M Some S are P	4 : 0	2 negative premises Negative premise, affirmative conclusion Existential Fallacy	Invalid
EEO2	No P are M No S are M Some S are not P	4 : 1	2 negative premises Existential Fallacy	Invalid
EIA2	No P are M Some S are M All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EIE2	No P are M Some S are M No S are P	2 : 2	Illicit Minor	Invalid
EII2	No P are M Some S are M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
EIO2	No P are M Some S are M Some S are not P	2 : 1	-	Valid 12
EOA2	No P are M Some S are not M All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion Illicit Minor	Invalid
EOE2	No P are M Some S are not M No S are P	3 : 2	2 negative premises Illicit Minor	Invalid
EOI2	No P are M Some S are not M Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
EOO2	No P are M Some S are not M Some S are not P	3 : 1	2 negative premises	Invalid
IAA2	Some P are M All S are M All S are P	1 : 1	Undistributed Middle	Invalid
IAE2	Some P are M All S are M No S are P	1 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IAI2	Some P are M All S are M Some S are P	1 : 0	Undistributed Middle	Invalid
IAO2	Some P are M All S are M Some S are not P	1 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IEA2	Some P are M No S are M All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
IEE2	Some P are M No S are M No S are P	2 : 2	Illicit Major	Invalid
IEI2	Some P are M No S are M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
IEO2	Some P are M No S are M Some S are not P	2 : 1	Illicit Major	Invalid
IIA2	Some P are M Some S are M All S are P	0 : 1	Undistributed Middle Illicit Minor	Invalid
IIE2	Some P are M Some S are M No S are P	0 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major Illicit Minor	Invalid
III2	Some P are M Some S are M Some S are P	0 : 0	Undistributed Middle	Invalid
IIO2	Some P are M Some S are M Some S are not P	0 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IOA2	Some P are M Some S are not M All S are P	1 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
IOE2	Some P are M Some S are not M No S are P	1 : 2	Illicit Major Illicit Minor	Invalid
IOI2	Some P are M Some S are not M Some S are P	1 : 0	Negative premise, affirmative conclusion	Invalid
IOO2	Some P are M Some S are not M Some S are not P	1 : 1	Illicit Major	Invalid
OAA2	Some P are not M All S are M All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
OAE2	Some P are not M All S are M No S are P	2 : 2	Illicit Major	Invalid
OAI2	Some P are not M All S are M Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
OAO2	Some P are not M All S are M Some S are not P	2 : 1	Illicit Major	Invalid
OEA2	Some P are not M No S are M All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
OEE2	Some P are not M No S are M No S are P	3 : 2	2 negative premises Illicit Major	Invalid
OEI2	Some P are not M No S are M Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OEO2	Some P are not M No S are M Some S are not P	3 : 1	2 negative premises Illicit Major	Invalid
OIA2	Some P are not M Some S are M All S are P	1 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
OIE2	Some P are not M Some S are M No S are P	1 : 2	Illicit Major Illicit Minor	Invalid
OII2	Some P are not M Some S are M Some S are P	1 : 0	Negative premise, affirmative conclusion	Invalid
OIO2	Some P are not M Some S are M Some S are not P	1 : 1	Illicit Major	Invalid
OOA2	Some P are not M Some S are not M All S are P	2 : 1	2 negative premises Negative premise, affirmative conclusion Illicit Minor	Invalid
OOE2	Some P are not M Some S are not M No S are P	2 : 2	2 negative premises Illicit Major Illicit Minor	Invalid
OOI2	Some P are not M Some S are not M Some S are P	2 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OOO2	Some P are not M Some S are not M Some S are not P	2 : 1	2 negative premises Illicit Major	Invalid
AAA3	All M are P All M are S All S are P	2 : 1	Illicit Minor	Invalid
AAE3	All M are P All M are S No S are P	2 : 2	Affirmative premises, Negative conclusion Illicit Major Illicit Minor	Invalid
AAI3	All M are P All M are S Some S are P	2 : 0	Existential Fallacy	Conditionally Valid 13
AAO3	All M are P All M are S Some S are not P	2 : 1	Affirmative premises, Negative conclusion Illicit Major Existential Fallacy	Invalid
AEA3	All M are P No M are S All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
AEE3	All M are P No M are S No S are P	3 : 2	Illicit Major	Invalid
AEI3	All M are P No M are S Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
AEO3	All M are P No M are S Some S are not P	3 : 1	Illicit Major Existential Fallacy	Invalid
AIA3	All M are P Some M are S All S are P	1 : 1	Illicit Minor	Invalid
AIE3	All M are P Some M are S No S are P	1 : 2	Affirmative premises, Negative conclusion Illicit Major Illicit Minor	Invalid
AII3	All M are P Some M are S Some S are P	1 : 0	-	Valid 14
AIO3	All M are P Some M are S Some S are not P	1 : 1	Affirmative premises, Negative conclusion Illicit Major	Invalid
AOA3	All M are P Some M are not S All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
AOE3	All M are P Some M are not S No S are P	2 : 2	Illicit Major	Invalid
AOI3	All M are P Some M are not S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
AOO3	All M are P Some M are not S Some S are not P	2 : 1	Illicit Major	Invalid
EAA3	No M are P All M are S All S are P	3 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EAE3	No M are P All M are S No S are P	3 : 2	Illicit Minor	Invalid
EAI3	No M are P All M are S Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
EAO3	No M are P All M are S Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 15
EEA3	No M are P No M are S All S are P	4 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EEE3	No M are P No M are S No S are P	4 : 2	2 negative premises	Invalid
EEI3	No M are P No M are S Some S are P	4 : 0	2 negative premises Negative premise, affirmative conclusion Existential Fallacy	Invalid
EEO3	No M are P No M are S Some S are not P	4 : 1	2 negative premises Existential Fallacy	Invalid
EIA3	No M are P Some M are S All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EIE3	No M are P Some M are S No S are P	2 : 2	Illicit Minor	Invalid
EII3	No M are P Some M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
EIO3	No M are P Some M are S Some S are not P	2 : 1	-	Valid 16
EOA3	No M are P Some M are not S All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EOE3	No M are P Some M are not S No S are P	3 : 2	2 negative premises	Invalid
EOI3	No M are P Some M are not S Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
EOO3	No M are P Some M are not S Some S are not P	3 : 1	2 negative premises	Invalid
IAA3	Some M are P All M are S All S are P	1 : 1	Illicit Minor	Invalid
IAE3	Some M are P All M are S No S are P	1 : 2	Affirmative premises, Negative conclusion Illicit Major Illicit Minor	Invalid
IAI3	Some M are P All M are S Some S are P	1 : 0	-	Valid 17
IAO3	Some M are P All M are S Some S are not P	1 : 1	Affirmative premises, Negative conclusion Illicit Major	Invalid
IEA3	Some M are P No M are S All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
IEE3	Some M are P No M are S No S are P	2 : 2	Illicit Major	Invalid
IEI3	Some M are P No M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
IEO3	Some M are P No M are S Some S are not P	2 : 1	Illicit Major	Invalid
IIA3	Some M are P Some M are S All S are P	0 : 1	Undistributed Middle Illicit Minor	Invalid
IIE3	Some M are P Some M are S No S are P	0 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major Illicit Minor	Invalid
III3	Some M are P Some M are S Some S are P	0 : 0	Undistributed Middle	Invalid
IIO3	Some M are P Some M are S Some S are not P	0 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IOA3	Some M are P Some M are not S All S are P	1 : 1	Negative premise, affirmative conclusion Undistributed Middle	Invalid
IOE3	Some M are P Some M are not S No S are P	1 : 2	Undistributed Middle Illicit Major	Invalid
IOI3	Some M are P Some M are not S Some S are P	1 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
IOO3	Some M are P Some M are not S Some S are not P	1 : 1	Undistributed Middle Illicit Major	Invalid
OAA3	Some M are not P All M are S All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
OAE3	Some M are not P All M are S No S are P	2 : 2	Illicit Minor	Invalid
OAI3	Some M are not P All M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
OAO3	Some M are not P All M are S Some S are not P	2 : 1	-	Valid 18
OEA3	Some M are not P No M are S All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
OEE3	Some M are not P No M are S No S are P	3 : 2	2 negative premises	Invalid
OEI3	Some M are not P No M are S Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OEO3	Some M are not P No M are S Some S are not P	3 : 1	2 negative premises	Invalid
OIA3	Some M are not P Some M are S All S are P	1 : 1	Negative premise, affirmative conclusion Undistributed Middle Illicit Minor	Invalid
OIE3	Some M are not P Some M are S No S are P	1 : 2	Undistributed Middle Illicit Minor	Invalid
OII3	Some M are not P Some M are S Some S are P	1 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
OIO3	Some M are not P Some M are S Some S are not P	1 : 1	Undistributed Middle	Invalid
OOA3	Some M are not P Some M are not S All S are P	2 : 1	2 negative premises Negative premise, affirmative conclusion Undistributed Middle	Invalid
OOE3	Some M are not P Some M are not S No S are P	2 : 2	2 negative premises Undistributed Middle	Invalid
OOI3	Some M are not P Some M are not S Some S are P	2 : 0	2 negative premises Negative premise, affirmative conclusion Undistributed Middle	Invalid
OOO3	Some M are not P Some M are not S Some S are not P	2 : 1	2 negative premises Undistributed Middle	Invalid
AAA4	All P are M All M are S All S are P	2 : 1	Illicit Minor	Invalid
AAE4	All P are M All M are S No S are P	2 : 2	Affirmative premises, Negative conclusion Illicit Minor	Invalid
AAI4	All P are M All M are S Some S are P	2 : 0	Existential Fallacy	Conditionally Valid 19
AAO4	All P are M All M are S Some S are not P	2 : 1	Affirmative premises, Negative conclusion Existential Fallacy	Invalid
AEA4	All P are M No M are S All S are P	3 : 1	Negative premise, affirmative conclusion	Invalid
AEE4	All P are M No M are S No S are P	3 : 2	-	Valid 20
AEI4	All P are M No M are S Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
AEO4	All P are M No M are S Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 21
AIA4	All P are M Some M are S All S are P	1 : 1	Undistributed Middle Illicit Minor	Invalid
AIE4	All P are M Some M are S No S are P	1 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Minor	Invalid
AII4	All P are M Some M are S Some S are P	1 : 0	Undistributed Middle	Invalid
AIO4	All P are M Some M are S Some S are not P	1 : 1	Affirmative premises, Negative conclusion Undistributed Middle	Invalid
AOA4	All P are M Some M are not S All S are P	2 : 1	Negative premise, affirmative conclusion Undistributed Middle	Invalid
AOE4	All P are M Some M are not S No S are P	2 : 2	Undistributed Middle	Invalid
AOI4	All P are M Some M are not S Some S are P	2 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
AOO4	All P are M Some M are not S Some S are not P	2 : 1	Undistributed Middle	Invalid
EAA4	No P are M All M are S All S are P	3 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EAE4	No P are M All M are S No S are P	3 : 2	Illicit Minor	Invalid
EAI4	No P are M All M are S Some S are P	3 : 0	Negative premise, affirmative conclusion Existential Fallacy	Invalid
EAO4	No P are M All M are S Some S are not P	3 : 1	Existential Fallacy	Conditionally Valid 22
EEA4	No P are M No M are S All S are P	4 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EEE4	No P are M No M are S No S are P	4 : 2	2 negative premises	Invalid
EEI4	No P are M No M are S Some S are P	4 : 0	2 negative premises Negative premise, affirmative conclusion Existential Fallacy	Invalid
EEO4	No P are M No M are S Some S are not P	4 : 1	2 negative premises Existential Fallacy	Invalid
EIA4	No P are M Some M are S All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
EIE4	No P are M Some M are S No S are P	2 : 2	Illicit Minor	Invalid
EII4	No P are M Some M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
EIO4	No P are M Some M are S Some S are not P	2 : 1	-	Valid 23
EOA4	No P are M Some M are not S All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
EOE4	No P are M Some M are not S No S are P	3 : 2	2 negative premises	Invalid
EOI4	No P are M Some M are not S Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
EOO4	No P are M Some M are not S Some S are not P	3 : 1	2 negative premises	Invalid
IAA4	Some P are M All M are S All S are P	1 : 1	Illicit Minor	Invalid
IAE4	Some P are M All M are S No S are P	1 : 2	Affirmative premises, Negative conclusion Illicit Major Illicit Minor	Invalid
IAI4	Some P are M All M are S Some S are P	1 : 0	-	Valid 24
IAO4	Some P are M All M are S Some S are not P	1 : 1	Affirmative premises, Negative conclusion Illicit Major	Invalid
IEA4	Some P are M No M are S All S are P	2 : 1	Negative premise, affirmative conclusion	Invalid
IEE4	Some P are M No M are S No S are P	2 : 2	Illicit Major	Invalid
IEI4	Some P are M No M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
IEO4	Some P are M No M are S Some S are not P	2 : 1	Illicit Major	Invalid
IIA4	Some P are M Some M are S All S are P	0 : 1	Undistributed Middle Illicit Minor	Invalid
IIE4	Some P are M Some M are S No S are P	0 : 2	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major Illicit Minor	Invalid
III4	Some P are M Some M are S Some S are P	0 : 0	Undistributed Middle	Invalid
IIO4	Some P are M Some M are S Some S are not P	0 : 1	Affirmative premises, Negative conclusion Undistributed Middle Illicit Major	Invalid
IOA4	Some P are M Some M are not S All S are P	1 : 1	Negative premise, affirmative conclusion Undistributed Middle	Invalid
IOE4	Some P are M Some M are not S No S are P	1 : 2	Undistributed Middle Illicit Major	Invalid
IOI4	Some P are M Some M are not S Some S are P	1 : 0	Negative premise, affirmative conclusion Undistributed Middle	Invalid
IOO4	Some P are M Some M are not S Some S are not P	1 : 1	Undistributed Middle Illicit Major	Invalid
OAA4	Some P are not M All M are S All S are P	2 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
OAE4	Some P are not M All M are S No S are P	2 : 2	Illicit Major Illicit Minor	Invalid
OAI4	Some P are not M All M are S Some S are P	2 : 0	Negative premise, affirmative conclusion	Invalid
OAO4	Some P are not M All M are S Some S are not P	2 : 1	Illicit Major	Invalid
OEA4	Some P are not M No M are S All S are P	3 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
OEE4	Some P are not M No M are S No S are P	3 : 2	2 negative premises Illicit Major	Invalid
OEI4	Some P are not M No M are S Some S are P	3 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OEO4	Some P are not M No M are S Some S are not P	3 : 1	2 negative premises Illicit Major	Invalid
OIA4	Some P are not M Some M are S All S are P	1 : 1	Negative premise, affirmative conclusion Illicit Minor	Invalid
OIE4	Some P are not M Some M are S No S are P	1 : 2	Illicit Major Illicit Minor	Invalid
OII4	Some P are not M Some M are S Some S are P	1 : 0	Negative premise, affirmative conclusion	Invalid
OIO4	Some P are not M Some M are S Some S are not P	1 : 1	Illicit Major	Invalid
OOA4	Some P are not M Some M are not S All S are P	2 : 1	2 negative premises Negative premise, affirmative conclusion	Invalid
OOE4	Some P are not M Some M are not S No S are P	2 : 2	2 negative premises Illicit Major	Invalid
OOI4	Some P are not M Some M are not S Some S are P	2 : 0	2 negative premises Negative premise, affirmative conclusion	Invalid
OOO4	Some P are not M Some M are not S Some S are not P	2 : 1	2 negative premises Illicit Major	Invalid