llogisms 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 boarders in this school have red hair.
- A note to the reader; be careful here, the third statement does not follow from the first two unless there exists a jug.
- No jug in this cupboard is new.
- All jugs in this cupboard are cracked.
- Some of the cracked items in this cupboard are not new.
- Some cats have no tails.
- All cats are mammals.
- Some mammals have no tails.
- No tree is edible.
- Some trees are green.
- Some green things are not edible.
- A note to the reader; be careful here, the third statement does not follow from the first two unless there exists an apple in the garden.
- All apples in my garden are wholesome.
- All wholesome fruit is ripe.
- Some ripe fruit is in my garden.
- All coloured flowers are scented.
- No scented flowers are grown indoors.
- No flowers grown indoors are coloured.
- Some small birds live on honey.
- All birds that live on honey are colourful.
- Some colourful birds are small.
- A note to the reader; the following is simply false; consider the scenario of humans are the only mythical creatures (note, this does not contradict all perfect creatures are mythical, rather it implies that there are no perfect creatures, mythical or otherwise).
- No humans are perfect.
- All perfect creatures are mythical.
- Some mythical creatures are not human.
- No competent people are people who always make mistakes.
- Some people who always make mistakes are people who work here.
- Some people who work here are not competent people.
Forms can be converted to other forms, following certain rules, and all forms can be converted into one of the first-figure forms.
The syllogism in the history of logicEdit
- Main article: History of Logic
Syllogism dominated Western philosophical thought until The Age of Enlightenment in the 17th Century. At that time, Sir Francis Bacon rejected the idea of syllogism and deductive reasoning by asserting that it was fallible and illogical. Bacon offered a more inductive approach to logic in which experiments were conducted and axioms were drawn from the obser