Affirming The Consequent (also called Asserting The Consequent) refers to the fallacy of using an argument of the form:
- If A then B
- B
- Therefore A
An argument of this form is most convincing when the statement 'if B then A' seems plausible.
Equivalence to Denying The Antecedent
Affirming The Consequent is equivalent to the fallacy of Denying The Antecedent, as the above argument can be rewritten:
- If not B then not A
- B
- Therefore A
Examples
Both sides of the terrorism debate in Britain before the 7th July 2005 bombings employed this fallacy:
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Some members of the British government argued that effective anti-terrorism laws prevent terrorist attacks, and, as there had been no terrorist attacks on Britain, the laws introduced since the 11th September 2001 attacks on America were therefore effective. More formally:
- If the anti-terrorism laws are effective then there will be no terrorist attacks
- There have been no terrorist attacks
- Therefore the anti-terrorism laws are effective
The first part of the argument is true by the definition of 'effective' in this context, and the observed lack of attacks was also accurate. The conclusion, however, was an example of Affirming The Consequent, and was demonstrated to be false on 7th July 2005.
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Some civil liberties campaigners argued that the laws were not needed as the terrorists were only interesting in attacking America. The justification for this statement was that if terrorists were interesting in attacking Britain there would have been terrorist attacks, but there had been none. More formally:
- If the terrorists aren't interested in Britain then there will be no terrorist attacks
- There have been no terrorist attacks
- Therefore the terrorists aren't interested in Britain
The first part of the argument is true by the definition of 'interested' in this context, and the observed lack of attacks was also accurate. The conclusion, however, was an example of Affirming The Consequent, and was demonstrated to be false on 7th July 2005.
A note on Bayes' Theorem and the scientific method
Bayes' Theorem can be seen as a probabilistic variation on Affirming The Consequent in which the argument is valid. It tells us that the probability of A given B is equal to the probability of A and B divided by the probability of B. If A implies B, then the probability of A and B equals the probability of A. Therefore, as long as B was not certain to be true, the discovery of the truth of B increases our assessment of the probability of the truth of A.
Some philosophers have argured that this is the basis of the scientific method - if a scientific theory A makes correct predictions B, our assessed probability of that theory being true increases. (Another philosophical argument is that the scientific method relies on the principle of falsification.)
Further reading
For a comprehensive reference on logical fallacies and the principles of good argument, see Attacking Faulty Reasoning: A Practical Guide To Fallacy-Free Arguments:
- Attacking Faulty Reasoning... at Amazon.com
- Attacking Faulty Reasoning... at Amazon.co.uk (for British readers)