 the major premise is universal and the minor particular, but this need not be so. For example:
- Major premise: All mortal things die.
- Minor premise: All men are mortal things.
- Conclusion: All men die.
Here, the major term is "die", the minor term is "men," and the middle term is "[being] mortal things." Both of the premises are universal.
A sorites is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, if one argues that a given number of grains of sand does not make a heap and that an additional grain does not either, then to conclude that no additional amount of sand will make a heap is to construct a sorites argument.
Types of syllogismEdit
Although there are infinitely many possible syllogisms, there are only a finite number of logically distinct types. We shall classify and enumerate them below. Note that the syllogisms above share the same abstract form:
- Major premise: All M are P.
- Minor premise: All S are M.
- Conclusion: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labelled by letters as follows.
|1):||A||All||S||are||P||universal affirmatives||All humans are mortal.|
|2):||E||All||S||are not||P||universal negatives||All humans are not perfect / No humans are perfect.|
|3):||I||Some||S||are||P||particular affirmatives||Some humans are healthy.|
|4):||O||Some||S||are not||P||particular negatives||Some humans are not clever.|
(See Square of opposition for a discussion of the logical relationships between these types of propositions.)
By definition, S is the subject of the conclusion, P is the predicate of the conclusion, M is the middle term, the major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise that it appears in. This gives rise to another classification of syllogisms known as the figure. The four figures are:
|Figure 1||Figure 2||Figure 3||Figure 4|
Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, although this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogisms above are AAA-1.
Of course, the vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). The table below shows the valid forms of syllogism. Even some of these are sometimes considered to commit the existential fallacy, thus invalid. These controversial patterns are marked in italics.
|Figure 1||Figure 2||Figure 3||Figure 4|
A sample syllogism of each type follows.
- All men are animals.
- All animals are mortal.
- All men are mortal.
- No reptiles have fur.
- All snakes are reptiles.
- No snakes have fur.
- All kittens are playful.
- Some pets are kittens.
- Some pets are playful.
- No homework is fun.
- Some reading is homework.
- Some reading is not fun.
- No healthy food is fattening.
- All cakes are fattening.
- No cakes are healthy.
- All horses have hooves.
- No humans have hooves.
- No humans are horses.
- No lazy people pass exams.
- Some students pass exams.
- Some students are not lazy.
- All informative things are useful.
- Some websites are not useful.
- Some websites are not informative.
- A note to the reader; be careful here, the third statement does not follow from the first two unless there exists a fruit.
- All fruit is nutritious.
- All fruit is tasty.
- Some tasty things are nutritious.
- Some mugs are beautiful.
- All mugs are useful.
- Some useful things are beautiful.
- All the industrious boys in this school have red hair.
- Some of the industrious boys in this school are boarders.
- Some 