False conversion takes place when we deduce from the fact that
all cats are animals the additional information that all animals are
cats. The converse of a statement, made by exchanging the
subject and predicate, is true in some cases, false in others. When
it is performed for one of the invalid cases, it is called false
conversion.
All rats are four-legged animals, so obviously all four-legged animals are
rats.
(This one is obviously false. Others are less so.)
Some mortal beings are not cats, therefore some cats are not mortal
beings.
(It would be remarkable if the existence of beings other than cats
were sufficient to establish the existence of an immortal strain of
cats.)
The rule is intricate, but worth learning. We can make statements
about all or some, and we can make positive or negative
assertions. This gives us four types of statement:
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.
Like an old Folger's Coffee commercial from 1959, the U.S. Federal District Court, of the Central District of California, has secretly replaced the Bill Of Rightswith aset of the entitlements. (.pdf)
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