How to Win Every Argument: The Use and Abuse of Logic (2006)

False conversion 75

1. All are


2. Some are


3. None are


4. Some are not

The rule is that only types 2 and 3 give valid conversions. If you
exchange subject and predicate for types 1 and 4 you commit
the fallacy of false conversion. The reason for the fallacy is that
you cannot swap a distributed term (covering the whole of its
class) for an undistributed one. In type 2, both subject and
predicate cover only part of the class, and in type 3 they both
cover all of it. Types 1 and 4 cannot be swapped around because
they mix distributed with undistributed terms. What the rule
means in practice is that you can swap around statements of the
form

Some As are Bs and

No As are Bs

but you cannot swap those which tell us

All As are Bs or

Some As are not Bs

If we know that no innovative people are bureaucrats, we can
deduce perfectly correctly that no bureaucrats are innovative
people. What we cannot do is deduce from the knowledge that
some journalists are not drunks the alternative statement that
some drunks are not journalists. It may happen to be true, but we
cannot deduce it from a false conversion.
In practice, most people can spot the obvious falsity of
converting statements about all animals or all cats. The fallacy