Tag Archives: fallacy of the converse

Can does not imply ought

‘Ought implies can’ is an ethical principle ascribed to the 18th century philosopher Immanuel Kant which claims that if a person is morally obliged to perform a certain action, then logically that person must be able to perform it. It makes no sense to say that somebody ought to do something that it is impossible for them to do. As a corollary, a person cannot be held responsible for something outside their control.

On the other hand, the converse relationship ‘Can implies ought’ does not apply. Just because a person can do something, it does not logically follow that they ought to do it.

When the Australian Governor-General Sir John Kerr dismissed the Whitlam Government in 1975, a common argument in favour was that he had the power to do it. However, this was an irrelevant red herring – hardly anybody disputed the power of the Governor-General to dismiss the Prime Minister. What they did dispute was whether he ought to have done it.

To give another example, in most cases it is lawful to tell lies, and it is often possible to get away with lying. But that does not mean that lying is acceptable behaviour (except for ‘white lies’ to avoid hurting somebody’s feelings or to otherwise minimise harm).  

In terms of logic, this reverse relationship is a logical fallacy known as ‘Affirming the consequent’ (sometimes called the fallacy of the converse) which consists of invalidly inferring the converse from the original statement. This fallacy takes the following form:

Premise 1: If P, then Q.

Premise 2: Q.

Conclusion: Therefore, P. 

Applying this form to the current case:

Premise 1: If you ought to do something, then you can do it.

Premise 2: You can do it.

Conclusion: Therefore, you ought to do it.

I realise that this is not a very common fallacy, and pointing it out might just seem like common sense, but it does have relevance for critical thinking and logical argument.

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Affirming the Consequent

Affirming the consequent, sometimes called converse error or fallacy of the converse, is a logical fallacy of inferring the converse from the original statement.  For instance, consider the following argument:

Premise 1: If Fiona won the lottery last night, she’ll be driving a red Ferrari today.

Premise 2: Fiona is driving a red Ferrari today.

Conclusion: Therefore, Fiona won the lottery last night.

An argument of this form is invalid, that is, the conclusion can be false even when the premises are true.  Since Premise 1 was never asserted as the only sufficient condition for Premise 2, other factors could account for Premise 2, such as:

  • Fiona could have inherited a large amount of money; or
  • She might just be borrowing the car; or
  • Perhaps she even stole it.

The fallacious argument has the general form:

Premise 1: If P, then Q.

Premise 2: Q.

Conclusion: Therefore, P.

Arguments of this form can sometimes seem superficially convincing, as in the following example:

Premise 1: If I have the flu, then I have a sore throat.

Premise 2: I have a sore throat.

Conclusion: Therefore, I have the flu.

But having the flu is not the only cause of a sore throat since many illnesses cause sore throat, such as the common cold or strep throat.

In contrast, a logically valid form of a similar argument would be:

Premise 1: If P, then Q.

Premise 2: P.

Conclusion: Therefore, Q.

This valid form of argument is a classical logical form known as modus ponens, with a history going back to antiquity.

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