Affirming the Consequent
Sibling Fallacy: Denying the Antecedent
- Asserting the Consequent
- Affirmation of the Consequent
Never has a book been subjected to such pitiless search for error as the Holy Bible. Both reverent and agnostic critics have ploughed and harrowed its passages; but through it all God's word has stood supreme…. This is proof…that here we have a revelation from God; for…if God reveals himself to man…, he will preserve a record of that revelation in order that men who follow may know his way and will.1
|If it's raining then the streets are wet.
The streets are wet.
Therefore, it's raining.
|If it's snowing then the streets will be covered with snow.
The streets are covered with snow.
Therefore, it's snowing.
|If p then q.
|Modus Ponens||Modus Tollens|
|If p then q.
|If p then q.
The consequent of a conditional statement is the part that usually follows "then". The part that usually follows "if" is called the "antecedent". I write "usually" here because there are many different ways to make a conditional statement, but we needn't go into them now. So, in the Form given above, the consequent is "q".
For example, in the statement "if today is Tuesday, then I have logic class", "I have logic class" is the consequent. To affirm the consequent is, of course, to claim that the consequent is true. Thus, affirming the consequent in the example would be to claim that I have logic class. In committing the fallacy of affirming the consequent, one makes a conditional statement, affirms the consequent, and concludes that the antecedent is true. Thus to commit the fallacy one would conclude that today is Tuesday.
Affirming the antecedent of a conditional and concluding its consequent is a validating form of argument, usually called "modus ponens" in propositional logic. It is possible that a source of the fallacy is confusion of the Form of affirming the consequent with the similar, validating form for modus ponens―see the Similar Validating Forms, above. Another validating form is modus tollens―shown above―which is similar to the fallacy except that the consequent is denied instead of affirmed, and the conclusion is the denial of the antecedent rather than its affirmation.
In contrast, affirming the consequent is a non-validating form of argument; for instance, let "p" be false and "q" be true, then there is no inconsistency in supposing that the conditional premiss is true, which makes the premisses true and the conclusion false. This can also be seen by means of the Counter-Example given above: this argument has the Form of affirming the consequent, but there is no inconsistency in supposing that its premisses are true and its conclusion false.
Also, suppose that I have logic class on Tuesday and Thursday. Then, it would be true that if today is Tuesday, then I have logic class. Now, suppose that I do have logic class today. It would be fallacious to conclude that today is Tuesday from these two facts alone, since it could just as well be Thursday.2
As mentioned in the Exposition section, above, the form of Affirming the Consequent is non-validating, which means that not every argument of that form is valid. This doesn't mean that every argument that affirms the consequent is invalid; rather, it means that some arguments of that form are invalid. There are arguments of that form that are formally valid, but all of them are such that the second premiss alone implies the conclusion, that is, the immediate inference from the second premiss to the conclusion is valid. Therefore, before pronouncing an instance of affirming the consequent invalid, check to see whether the second premiss implies the conclusion.
Together with its similar sibling fallacy, Denying the Antecedent, instances of Affirming the Consequent are most likely to seem valid when we assume the converse of the argument's conditional premiss. In the Example, for instance, we may assume:
Suppressed Premiss: If the streets are wet then it's raining.
Since wet streets usually dry rapidly, it is a good rule of thumb that wet streets indicate rain. With this suppressed premiss, the argument in the Example is valid. So, in general, in an instance of the form Affirming the Consequent, if it is reasonable to consider the converse of the conditional premiss to be a suppressed premiss, then the argument is not fallacious, but a valid enthymeme.
In contrast, it would not be reasonable to consider the Counter-Example, above, to be an enthymeme, since the converse of its conditional premiss is not plausible, namely:
If the streets are covered with snow then it's snowing.
Unlike rain, we know, at cold temperatures it takes snow a very long time to evaporate or melt. So that, while snow on the ground is a good sign of past snowing, it's a bad sign of present snowing. Thus, the Counter-Example is a fallacious instance of Affirming the Consequent.
The phrase "this is proof that" is an argument indicator, indicating that this passage contains an argument. Specifically, "this is proof that" is a conclusion indicator, which means that the proposition it occurs in is a conclusion: "here [in the Bible] we have a revelation from God". Moreover, the use of the word "proof" also means that the author is claiming that the argument is deductive, that is, that it is the strongest type of reasoning. The word "this" in the conclusion indicator refers back to the preceding proposition, so it is a premiss supporting the conclusion: "Both reverent and agnostic critics have ploughed and harrowed [the Bible's] passages; but through it all God's word has stood supreme." In other words, the author is claiming that the Bible has withstood all criticism. Finally, the word "for" following the conclusion is a premiss indicator, meaning that the proposition it occurs in is a further premiss: "if God reveals himself to man, he will preserve a record of that revelation in order that men who follow may know his way and will." Putting these together and simplifying their wording produces the following argument:
Premiss: If God reveals himself in the Bible, he will preserve a record of that revelation.
Premiss: God has preserved a record of his revelation.
Conclusion: God has revealed himself in the Bible.
Therefore, the second premiss affirms the consequent of the first premiss, and the conclusion is the antecedent of the first premiss, which means that the argument commits the fallacy of affirming the consequent.
Acknowledgment: Thanks to Antoine Leonard Van Gelder for pointing out a mix-up between "antecedent" and "consequent" in the Exposition section that has now been fixed.