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What is False Conversion?

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. 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 tends to be more common, and more deceptive, when it appears in the ‘some are not’ form.

 

Since we know that some Marxists are not school-teachers, it follows some school-teachers are not Marxists.

(No it doesn’t.)

 

Your own wilful use of this fallacy requires careful planning. It is a short-range tactical fallacy, and is best concealed by not letting the audience know if you are talking about ‘some’ or ‘all’. The claim that ‘Texas rabbits are animals which grow to more than a metre long’ is skilfully ambiguous. It is not clear whether it refers to some Texas rabbits or all of them. Your surreptitious false conversion would then leave your audience convinced that any animal in Texas more than a metre in length must be a rabbit. It would also leave any Texans hopping mad.