Overview of Examples & Types of Syllogisms

Syllogisms are today’s most commonly accepted form of logical reasoning in >aptitude tests, however they are closer related to mathematical reasoning.

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Within the syllogisms three different types can be distinguished:

Conditional syllogisms

Conditional syllogisms are better known as hypothetical syllogisms, because the arguments used here are not always valid. The basic of this syllogism type is: if A is true then B is true as well. An example will follow to elucidate the former.

This conclusion is invalid because it is possible that Johnny does not eat sweats every day but does eats cake every day what also puts him at risk for diabetes.

Disjunctive syllogisms

These syllogism types do not actually state that a certain premise (major or minor) is correct, but is does states that one of the premises is correct. The basic type for this syllogism is: Either A or B is true, but they can’t be true at the same time. Example:

The conclusion of the syllogism type may be given, however most of the times the conclusion can be drawn based up on own conclusions.

Categorical syllogisms

The third and most commonly used type of syllogisms are the categorical syllogisms. The basic for this syllogism type is: if A is a part of C, then B is a part of C (A and B are members of C). An example of this syllogism type will clarify the above:

Both premises are known to be valid, by observation or historical facts. Because the two premises are valid, the conclusion must be valid as well. Be aware that this conclusion is based on logical reasoning and thus it doesn’t have to represent the “truth” always.

Next, these categorical syllogisms can be divided into 4 kinds of categorical propositions which will be explained separately:

Propositions

1. A: Universal Affirmative
   This is a syllogism of the form: All X are Y, like the example: all woman are shopaholic.
2. E: Universal Negative
   This is the negative form of universal affirmative, which is a syllogism of the form: No X is Y, or as example: No humans are perfect. This syllogism type is exactly the opposite of proposition “A” explained above.
3. I: Particular Affimitive
   Another syllogism type is the “particular form” which only influences some people and not the whole population. This syllogism is of the form: Some X are Y.
4. O: Particular Negative
   The opposite of proposition “I” is proposition “O” which is of the form: Some X are not Y. an example of this would be: some cars are not green.

By explaining these 4 kinds of categorical syllogism types each syllogism can be identified, which is also called “stating the mood of an argument”. We know syllogisms always consist out of a major and minor premise and a conclusion. In standard form, as shown on this page, the major premise is always shown first, after which the minor premise and the conclusion follow. An example of a mood of a categorical syllogism could be: AEO. We now know that the major premise is of type A (all A are B), the minor premise is of type E (No A is B) and the conclusion is of type O (some S is no P).

	1st figure	2nd figure	3rd figure	4th figure
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

 
Next to the mood of a syllogism also the figure of a syllogism if of importance. We know a syllogism always contains a subject (S), a predicate (P) and a middle term (M) of the conclusion which are linked in a specific way in order to obtain a valid statement. Depending on the configuration of the middle terms in the premises (major / minor) different figures (1 to 4) are obtained. The following table will clarify the concept of figures:

1st figure	2nd figure	3rd figure	4th figure
Barbara AAA-1	Cesare EAE-2	Darapti AAI-3	Bramantip AAI-4
Celarent EAE-1	Camestres AEE-2	Disamis IAI-3	Camenes AEE-4
Darii ALL-1	Festino EIO-2	Datisi ALL-3	Dimaris IAI-4
Ferio EIO-1	Baroco AOO-2	Felapton EAO-3	Fesapo EAO-4
		Bocardo OAO-3	Fresison EIO-4
		Ferison EIO-3

 
Using the mood and figure of a syllogism 256 different types of distinct categorical syllogisms exist, resulting from 4 kinds of major premises, 4 kinds of minor premises, 4 kinds of conclusions and 4 positions of the middle term. These 256 valid categorical syllogism forms are divided into the 4 figures which using specific rules can be converted into each other and represented by names as follows:

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