Affirming 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.5
|If p then q.
|If it's snowing then the streets will be covered with snow.
The streets are covered with snow.
Therefore, it's snowing.
|Modus Ponens||Modus Tollens|
|If p then q.
|If p then q.
"Conditional statement" is another name for an "if-then" statement, that is, a true-or-false statement that can be expressed in the if-then form. For instance, "If today is Tuesday then this must be Belgium" is a conditional statement. 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" because there are many different ways to make a conditional statement, but we needn't go into them here. So, in the Form given above, the consequent is "q". For example, in the statement "if today is Tuesday then this must be Belgium", "This must be Belgium" is the consequent.
To affirm the consequent of a conditional statement is, of course, to assert or claim that the consequent is true. Thus, to affirm the consequent using the example statement you would claim that this must be Belgium. To commit the fallacy of affirming the consequent, assert a conditional statement, affirm the consequent, and conclude 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―see the Similar Validating Forms, above. A possible source of the fallacy is confusion of the form of affirming the consequent with the similar, validating form of modus ponens. 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 arrive in Belgium on Tuesday but don't leave until Friday. Then, it would be true that if today is Tuesday, then this must be Belgium. Now, suppose that I am in Belgium today. It would be fallacious to conclude that today is Tuesday from these two facts alone, since it could just as well be Wednesday or Thursday. Thus, affirming the consequent is fallacious.
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 valid9. 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. For instance, if I'll only be in Belgium on Tuesday, then I assume that if I look out the window and it's obviously Belgium, then this must be Tuesday. So, in general, in an instance of the form Affirming the Consequent, if it's 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. 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.
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. In addition, it also begs the question, since the second premiss can only be true if God has in fact made a revelation of some sort. Since Straton is claiming that the Bible has withstood all criticism, it is clearly the revelation he has in mind. Of course, the Bible has been subjected to a great deal of criticism, but it's at least dubious to say that it has withstood it all. Believers in the inerrancy of the Bible may be convinced by this argument, but no one who doubted it would be.
- See the Taxonomy of Logical Fallacies, available from the Main Menu in the sidebar to your left.
- A "sibling fallacy" is a closely-related one.
- An "alias" is another name by which a fallacy is known.
- Alonzo Church, in A Dictionary of Philosophy, edited by Dagobert D. Runes (1942).
- Hillyer Straton, Baptists: Their Message and Mission (1941), p. 49, quoted from Howard Pospesel, Introduction to Logic: Propositional Logic (Third Edition) (Prentice Hall, 1998), p. 16, ellipses added.
- A "counter-example" to an argument form is an obviously invalid instance of the form that shows it is not a validating form.
- These are validating forms of argument that are superficially similar to the fallacy and may be confused with it.
- Thanks to Antoine Leonard Van Gelder for pointing out a mix-up between "antecedent" and "consequent" in this section that has now been fixed.
- This is easy to see: Suppose that an argument of the form of affirming the consequent―that is, an argument of the form: p → q, q ∴ p― is valid. Then suppose that all we have is the second premiss, that is, q. From q, using the propositional law q → (p → q), we can infer the conditional premiss by modus ponens. Then, we can validly infer q, by hypothesis. Therefore, the argument from q alone is valid.
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