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A Standard Form Categorical Syllogism is an argument containing two premises and one conclusion. There are four types of arguments: an Universal and a Particular Affirmative, and an universal and particular Negative. These arguments are named the A, E, I, and O arguments, respectively. Within the two premises there are the middle term, major term, and a minor term (N.B. in standard form the major term is always the Predicate and the minor term is always the Subject in the conclusion). Additionally, there are 4 positions in which the middle terms can be arranged (see the respective tables below).

Because there are four possible arguments in premise one, four possible arguments in premise two, and four possible arguments in the conclusion, as well as four possible arrangements of the middle term, there are exactly two-hundred and fifty-six possible forms of categorical syllogisms. A list of them follows.

Syllogistic Fallacies

There are traditionally five rules that determine validity of an argument, and six rules in modern logic. If a syllogism breaks any one of these rules it is inherently invalid and commits the associated fallacy. They are:

Fallacy of equivocation
Fallacy of the undistributed middle
Illicit major or Illicit minor
Fallacy of exclusive premises
Affirmative conclusion from a negative premise or Negative conclusion from affirmative premises
Existential fallacy (n.b. this fallacy is only present in Boolean logic and not in Aristotelian logic; rule six should not be considered unless rules 1 through 5 have passed. Additionally, the box labeled "6" cannot be determined valid or invalid based solely on the form of the argument: the Existential import must be determined. Thus, all of the boxes labeled "6" are filled with a "?")

In this list, rule one is not included because all syllogisms in the list meet the criteria for rule one.

First Position Middle Term

Premise 1	Argument Type	Middle Term	Copula	Major Term
Premise 2	Argument Type	Minor Term	Copula	Middle Term
Conclusion	Argument Type	Minor Term	Copula	Major Term

AAA-1 through OOA-1

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAA	1
AEA	1
AIA	1
AOA	1
EAA	1
EEA	1
EIA	1
EOA	1
IAA	1
IEA	1
IIA	1
IOA	1
OAA	1
OEA	1
OIA	1
OOA	1

AAE-1 through OOE-1

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAE	1
AEE	1
AIE	1
AOE	1
EAE	1
EEE	1
EIE	1
EOE	1
IAE	1
IEE	1
IIE	1
IOE	1
OAE	1
OEE	1
OIE	1
OOE	1

AAI-1 through OOI-1

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAI	1
AEI	1
AII	1
AOI	1
EAI	1
EEI	1
EII	1
EOI	1
IAI	1
IEI	1
III	1
IOI	1
OAI	1
OEI	1
OII	1
OOI	1

AAO-1 through OOO-1

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAO	1
AEO	1
AIO	1
AOO	1
EAO	1
EEO	1
EIO	1
EOO	1
IAO	1
IEO	1
IIO	1
IOO	1
OAO	1
OEO	1
OIO	1
OOO	1

Second Position Middle Term

Premise 1	Argument Type	Major Term	Copula	Middle Term
Premise 2	Argument Type	Minor Term	Copula	Middle Term
Conclusion	Argument Type	Minor Term	Copula	Major Term

AAA-2 through OOA-2

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAA	2	Example	Example	Example	Example	Example	Example
AEA	2	Example	Example	Example	Example	Example	Example
AIA	2	Example	Example	Example	Example	Example	Example
AOA	2	Example	Example	Example	Example	Example	Example
EAA	2	Example	Example	Example	Example	Example	Example
EEA	2	Example	Example	Example	Example	Example	Example
EIA	2	Example	Example	Example	Example	Example	Example
EOA	2	Example	Example	Example	Example	Example	Example
IAA	2	Example	Example	Example	Example	Example	Example
IEA	2	Example	Example	Example	Example	Example	Example
IIA	2	Example	Example	Example	Example	Example	Example
IOA	2	Example	Example	Example	Example	Example	Example
OAA	2	Example	Example	Example	Example	Example	Example
OEA	2	Example	Example	Example	Example	Example	Example
OIA	2	Example	Example	Example	Example	Example	Example
OOA	2	Example	Example	Example	Example	Example	Example

AAE-2 through OOE-2

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAE	2	Example	Example	Example	Example	Example	Example
AEE	2	Example	Example	Example	Example	Example	Example
AIE	2	Example	Example	Example	Example	Example	Example
AOE	2	Example	Example	Example	Example	Example	Example
EAE	2	Example	Example	Example	Example	Example	Example
EEE	2	Example	Example	Example	Example	Example	Example
EIE	2	Example	Example	Example	Example	Example	Example
EOE	2	Example	Example	Example	Example	Example	Example
IAE	2	Example	Example	Example	Example	Example	Example
IEE	2	Example	Example	Example	Example	Example	Example
IIE	2	Example	Example	Example	Example	Example	Example
IOE	2	Example	Example	Example	Example	Example	Example
OAE	2	Example	Example	Example	Example	Example	Example
OEE	2	Example	Example	Example	Example	Example	Example
OIE	2	Example	Example	Example	Example	Example	Example
OOE	2	Example	Example	Example	Example	Example	Example

AAI-2 through OOI-2

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAI	2	Example	Example	Example	Example	Example	Example
AEI	2	Example	Example	Example	Example	Example	Example
AII	2	Example	Example	Example	Example	Example	Example
AOI	2	Example	Example	Example	Example	Example	Example
EAI	2	Example	Example	Example	Example	Example	Example
EEI	2	Example	Example	Example	Example	Example	Example
EII	2	Example	Example	Example	Example	Example	Example
EOI	2	Example	Example	Example	Example	Example	Example
IAI	2	Example	Example	Example	Example	Example	Example
IEI	2	Example	Example	Example	Example	Example	Example
III	2	Example	Example	Example	Example	Example	Example
IOI	2	Example	Example	Example	Example	Example	Example
OAI	2	Example	Example	Example	Example	Example	Example
OEI	2	Example	Example	Example	Example	Example	Example
OII	2	Example	Example	Example	Example	Example	Example
OOI	2	Example	Example	Example	Example	Example	Example

AAO-2 through OOO-2

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAO	2	Example	Example	Example	Example	Example	Example
AEO	2	Example	Example	Example	Example	Example	Example
AIO	2	Example	Example	Example	Example	Example	Example
AOO	2	Example	Example	Example	Example	Example	Example
EAO	2	Example	Example	Example	Example	Example	Example
EEO	2	Example	Example	Example	Example	Example	Example
EIO	2	Example	Example	Example	Example	Example	Example
EOO	2	Example	Example	Example	Example	Example	Example
IAO	2	Example	Example	Example	Example	Example	Example
IEO	2	Example	Example	Example	Example	Example	Example
IIO	2	Example	Example	Example	Example	Example	Example
IOO	2	Example	Example	Example	Example	Example	Example
OAO	2	Example	Example	Example	Example	Example	Example
OEO	2	Example	Example	Example	Example	Example	Example
OIO	2	Example	Example	Example	Example	Example	Example
OOO	2	Example	Example	Example	Example	Example	Example

Third Position Middle Term

Premise 1	Argument Type	Middle Term	Copula	Major Term
Premise 2	Argument Type	Middle Term	Copula	Minor Term
Conclusion	Argument Type	Minor Term	Copula	Major Term

AAA-3 through OOA-3

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAA	3	Example	Example	Example	Example	Example	Example
AEA	3	Example	Example	Example	Example	Example	Example
AIA	3	Example	Example	Example	Example	Example	Example
AOA	3	Example	Example	Example	Example	Example	Example
EAA	3	Example	Example	Example	Example	Example	Example
EEA	3	Example	Example	Example	Example	Example	Example
EIA	3	Example	Example	Example	Example	Example	Example
EOA	3	Example	Example	Example	Example	Example	Example
IAA	3	Example	Example	Example	Example	Example	Example
IEA	3	Example	Example	Example	Example	Example	Example
IIA	3	Example	Example	Example	Example	Example	Example
IOA	3	Example	Example	Example	Example	Example	Example
OAA	3	Example	Example	Example	Example	Example	Example
OEA	3	Example	Example	Example	Example	Example	Example
OIA	3	Example	Example	Example	Example	Example	Example
OOA	3	Example	Example	Example	Example	Example	Example

AAE-3 through OOE-3

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAE	3	Example	Example	Example	Example	Example	Example
AEE	3	Example	Example	Example	Example	Example	Example
AIE	3	Example	Example	Example	Example	Example	Example
AOE	3	Example	Example	Example	Example	Example	Example
EAE	3	Example	Example	Example	Example	Example	Example
EEE	3	Example	Example	Example	Example	Example	Example
EIE	3	Example	Example	Example	Example	Example	Example
EOE	3	Example	Example	Example	Example	Example	Example
IAE	3	Example	Example	Example	Example	Example	Example
IEE	3	Example	Example	Example	Example	Example	Example
IIE	3	Example	Example	Example	Example	Example	Example
IOE	3	Example	Example	Example	Example	Example	Example
OAE	3	Example	Example	Example	Example	Example	Example
OEE	3	Example	Example	Example	Example	Example	Example
OIE	3	Example	Example	Example	Example	Example	Example
OOE	3	Example	Example	Example	Example	Example	Example

AAI-3 through OOI-3

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAI	3	Example	Example	Example	Example	Example	Example
AEI	3	Example	Example	Example	Example	Example	Example
AII	3	Example	Example	Example	Example	Example	Example
AOI	3	Example	Example	Example	Example	Example	Example
EAI	3	Example	Example	Example	Example	Example	Example
EEI	3	Example	Example	Example	Example	Example	Example
EII	3	Example	Example	Example	Example	Example	Example
EOI	3	Example	Example	Example	Example	Example	Example
IAI	3	Example	Example	Example	Example	Example	Example
IEI	3	Example	Example	Example	Example	Example	Example
III	3	Example	Example	Example	Example	Example	Example
IOI	3	Example	Example	Example	Example	Example	Example
OAI	3	Example	Example	Example	Example	Example	Example
OEI	3	Example	Example	Example	Example	Example	Example
OII	3	Example	Example	Example	Example	Example	Example
OOI	3	Example	Example	Example	Example	Example	Example

AAO-3 through OOO-3

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAO	3	Example	Example	Example	Example	Example	Example
AEO	3	Example	Example	Example	Example	Example	Example
AIO	3	Example	Example	Example	Example	Example	Example
AOO	3	Example	Example	Example	Example	Example	Example
EAO	3	Example	Example	Example	Example	Example	Example
EEO	3	Example	Example	Example	Example	Example	Example
EIO	3	Example	Example	Example	Example	Example	Example
EOO	3	Example	Example	Example	Example	Example	Example
IAO	3	Example	Example	Example	Example	Example	Example
IEO	3	Example	Example	Example	Example	Example	Example
IIO	3	Example	Example	Example	Example	Example	Example
IOO	3	Example	Example	Example	Example	Example	Example
OAO	3	Example	Example	Example	Example	Example	Example
OEO	3	Example	Example	Example	Example	Example	Example
OIO	3	Example	Example	Example	Example	Example	Example
OOO	3	Example	Example	Example	Example	Example	Example

Fourth Position Middle Term

Premise 1	Argument Type	Major Term	Copula	Middle Term
Premise 2	Argument Type	Middle Term	Copula	Minor Term
Conclusion	Argument Type	Minor Term	Copula	Major Term

AAA-4 through OOA-4

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAA	4	Example	Example	Example	Example	Example	Example
AEA	4	Example	Example	Example	Example	Example	Example
AIA	4	Example	Example	Example	Example	Example	Example
AOA	4	Example	Example	Example	Example	Example	Example
EAA	4	Example	Example	Example	Example	Example	Example
EEA	4	Example	Example	Example	Example	Example	Example
EIA	4	Example	Example	Example	Example	Example	Example
EOA	4	Example	Example	Example	Example	Example	Example
IAA	4	Example	Example	Example	Example	Example	Example
IEA	4	Example	Example	Example	Example	Example	Example
IIA	4	Example	Example	Example	Example	Example	Example
IOA	4	Example	Example	Example	Example	Example	Example
OAA	4	Example	Example	Example	Example	Example	Example
OEA	4	Example	Example	Example	Example	Example	Example
OIA	4	Example	Example	Example	Example	Example	Example
OOA	4	Example	Example	Example	Example	Example	Example

AAE-4 through OOE-4

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAE	4	Example	Example	Example	Example	Example	Example
AEE	4	Example	Example	Example	Example	Example	Example
AIE	4	Example	Example	Example	Example	Example	Example
AOE	4	Example	Example	Example	Example	Example	Example
EAE	4	Example	Example	Example	Example	Example	Example
EEE	4	Example	Example	Example	Example	Example	Example
EIE	4	Example	Example	Example	Example	Example	Example
EOE	4	Example	Example	Example	Example	Example	Example
IAE	4	Example	Example	Example	Example	Example	Example
IEE	4	Example	Example	Example	Example	Example	Example
IIE	4	Example	Example	Example	Example	Example	Example
IOE	4	Example	Example	Example	Example	Example	Example
OAE	4	Example	Example	Example	Example	Example	Example
OEE	4	Example	Example	Example	Example	Example	Example
OIE	4	Example	Example	Example	Example	Example	Example
OOE	4	Example	Example	Example	Example	Example	Example

AAI-4 through OOI-4

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAI	4	Example	Example	Example	Example	Example	Example
AEI	4	Example	Example	Example	Example	Example	Example
AII	4	Example	Example	Example	Example	Example	Example
AOI	4	Example	Example	Example	Example	Example	Example
EAI	4	Example	Example	Example	Example	Example	Example
EEI	4	Example	Example	Example	Example	Example	Example
EII	4	Example	Example	Example	Example	Example	Example
EOI	4	Example	Example	Example	Example	Example	Example
IAI	4	Example	Example	Example	Example	Example	Example
IEI	4	Example	Example	Example	Example	Example	Example
III	4	Example	Example	Example	Example	Example	Example
IOI	4	Example	Example	Example	Example	Example	Example
OAI	4	Example	Example	Example	Example	Example	Example
OEI	4	Example	Example	Example	Example	Example	Example
OII	4	Example	Example	Example	Example	Example	Example
OOI	4	Example	Example	Example	Example	Example	Example

AAO-4 through OOO-4

(Form)			Rule broken
Figure	Mood	Validity	2	3	4	5	6
AAO	4	Example	Example	Example	Example	Example	Example
AEO	4	Example	Example	Example	Example	Example	Example
AIO	4	Example	Example	Example	Example	Example	Example
AOO	4	Example	Example	Example	Example	Example	Example
EAO	4	Example	Example	Example	Example	Example	Example
EEO	4	Example	Example	Example	Example	Example	Example
EIO	4	Example	Example	Example	Example	Example	Example
EOO	4	Example	Example	Example	Example	Example	Example
IAO	4	Example	Example	Example	Example	Example	Example
IEO	4	Example	Example	Example	Example	Example	Example
IIO	4	Example	Example	Example	Example	Example	Example
IOO	4	Example	Example	Example	Example	Example	Example
OAO	4	Example	Example	Example	Example	Example	Example
OEO	4	Example	Example	Example	Example	Example	Example
OIO	4	Example	Example	Example	Example	Example	Example
OOO	4	Example	Example	Example	Example	Example	Example