Translation: Spanish (Traducción en español)
Alias:
- Asserting the Consequent
- Affirmation of the Consequent
Example:
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.
Source: Hillyer Straton, Baptists: Their Message and Mission
| Example | Counter-Example |
|---|---|
| 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. |
| Form |
|---|
| If p then q.
q. Therefore, p. |
| Modus Ponens | Modus Tollens |
|---|---|
| If p then q.
p. Therefore, q. |
If p then q.
Not-q. Therefore, not-p. |
Exposition:
Affirming the Consequent is a non-validating form of argument in propositional logic; for instance, let "p" be false and "q" be true, then there is no inconsistency in supposing that the first, conditional premiss is true, which makes the premisses true and the conclusion false.
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 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. 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.
Sibling Fallacy: Denying the Antecedent
Source:
A. R. Lacey, A Dictionary of Philosophy (Third Revised Edition) (Barnes & Noble, 1996)
Analysis of the Example:
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.
Source: Howard Pospesel, Introduction to Logic: Propositional Logic (Third Edition) (Prentice Hall, 1998), p. 16, ellipses added.
