The doppelganger of the fallacy of composition is that of division. When we attribute to the individuals in a group something which is only true of the group as a unit, we fall into the fallacy of division:
Welsh-speakers are disappearing. Dafydd Williams is a Welsh-speaker, therefore Dafydd Williams is disappearing.
(No such luck. Only the class of Welsh-speakers is disappearing, not the individuals who make it up.)
We commit the fallacy by sliding our adjectives to describe the whole over onto the individuals who comprise it:
The Icelanders are the oldest nation on earth. This means that Bjork must be older than other pop stars.
(And before you go to her house, remember that the Icelandic people live surrounded by hot mud and active volcanoes.)
As with composition, the source of the error in the fallacy of division lies in the ambiguity of collective nouns. Both of these are a form of the fallacy of equivocation, in that it is the different meanings of the noun which upset the validity of the argument. It would only be valid if the same meaning were retained throughout. (The gospels are four in number. St Mark’s is a gospel, so St Mark’s is four in number.)
Division is often used fallaciously to confer upon an individual some of the prestige attached to the group or class to which he belongs.
The French are tops at rugby; Marcel is French; obviously he must be tops at rugby.
(But, since the French produce a lot of low-fat milk, Marcel probably has some other strange qualities.)
California is a very wealthy state; so if he comes from there he must be worth quite a bit.
We often commit the fallacy unconsciously, typecasting people according to the groups from which they emanate. This can work to their advantage: The teaching at Edinburgh University is brilliant; Johnson lectures there, so he must be really first-class, or to their disadvantage: Switzerland is a very passive nation, so I don’t think we can expect too much initiative from our Swiss directors.
An entertaining version of the fallacy is called the fallacy of complex division, and assumes that subclasses of the whole share the same properties as the entire class. In this version, we meet the average British couple with their 2.2 children, out walking their 0.7 of a cat with a quarter of a dog. They have 1.15 cars, which they somehow manage to fit into only a third of a garage.
In the world of complex division, an expectant couple with two children are very nervous, because they know that every third child born is Chinese. In the real world, of course, it is different subclasses which produce the overall figures for the class as a whole. (‘Test-pilots occasionally get killed, so I imagine that Flight-Lieutenant Robinson will get killed now and again himself.’)
Division can be used to bring unearned credit upon yourself by virtue of your membership of meritorious classes:
Let me settle this. We British have a longer experience of settling disputes than anyone else in the world.
(Most of it acquired long before any of us were born.)
It can also be used to heap odium upon adversaries by pointing similarly to their involvement in groups which command no respect.
My opponent comes from Glasgow, not a city noted for high intelligence.
(If it were true, it would probably be because the bright ones had, like your opponent, come from it.)
The above article is from the book How To Win Every Argument by Madsen Pirie. The article is only for educational and informative purposes to explain and understand formal logic and logical fallacies. It is a great book, definitely worth a read!