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 observations discovered in them.
In the 19th Century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Kant famously claimed that logic was the one completed science, and that Aristotelian logic more or less included everything about logic there was to know. Though there were alternative systems of logic such as Avicennian logic or Indian logic elsewhere, Kant's opinion stood unchallenged in the West until Frege invented first-order logic.
Still, it was cumbersome and very limited in its ability to reveal the logical structure of complex sentences. For example, it was unable to express the claim that the real line is a dense order. In the late 19th century, Charles Peirce's discovery of second-order logic revolutionized the field and the Aristotelian system has since been left to introductory material and historical study.
Everyday syllogistic mistakesEdit
People often make mistakes when reasoning syllogistically.
For instance, given the following parameters: some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C. However, this does not follow. For instance, while some cats (A) are black (B), and some black things (B) are televisions (C), it is false that some cats (A) are televisions (C). This is because first, the mood of the syllogism invoked is illicit (III), and second, the supposition of the middle term is variable between that of the middle term in the major premise, and that of the middle term in the minor premise (not all "some" cats are by necessity of logic the same "some black things").
Determining the validity of a syllogism involves determining the distribution of each term in each statement, meaning whether all members of that term are accounted for.
In simple syllogistic patterns, the fallacies of invalid patterns are:
- Undistributed middle - Neither of the premises accounts for all members of the middle term, which consequently fails to link the major and minor term.
- Illicit t