Affirming the Consequent Overview, Fallacy & Examples
What is an example of affirming the consequent?
If you eat your vegetables, then you will lose weight. You are losing weight. Therefore, you must be eating your vegetables. This is an example of affirming the consequent, and it ignores the possibility that a person might be doing additional exercise, or cutting calories in a different way.
What is an example of affirming the consequent?
An example of affirming the consequent is, if the corn is delicious, then someone spent a lot of time cooking it. Someone spent a lot of time cooking this corn. Therefore, the corn must be delicious.
Can affirming the consequent be valid?
Affirming the consequent can never be valid, meaning that the conclusion will not follow necessarily from the premises. It may just so happen that consequent is true and the antecedent is true independently of that. But again, the inference remains invalid, and their relationship remains accidental rather than logical.
What is an example of affirming the consequent?
An example of affirming the consequent is, if you pet my dog, then she will wag her tail. My dog's tail is wagging. Therefore, you must have petted my dog.
Recommended lessons and courses for you
Logic study rules of inference, and part of that study includes identifying fallacies. A fallacy is an error in reasoning. This means that in the process of making inferences, the reasoner makes an error in drawing conclusions. Identifying fallacies is important because one could perform a fallacy in everyday life and think their reasoning is valid. A rigorous study of logic and fallacies allows one to see through the appearance of validity and establish whether an inference is warranted.
The fallacy of affirming the consequent is a formal fallacy in which a reasoner makes an unwarranted inference from an if-then statement. It is also called the converse error and fallacy of the converse. It can be easy to slip into this fallacy because it looks like a valid argument form, modus ponens, which involves affirming the antecedent of an if-then statement. Understanding what makes affirming the consequent invalid and what makes affirming the antecedent valid requires understanding if-then statements, which are called conditional statements.
Conditional statements are statements in which two propositions are connected by an if-then relationship. For instance, "if you perform a full day of work, then you will get a full day's pay," is a conditional statement. In essence, this statement is claiming that completing a full day of work is sufficient to guarantee a full day's pay. The proposition that follows the if, is called the sufficient condition or antecedent. The proposition that follows the then, is called the necessary condition or the consequent.
Assuming that a conditional is true, then one can infer that the consequent is true as long as one can establish that the antecedent is true. For example, assume that "if you perform a full day of work, then you you will get a full day's pay," is true. When you perform a full day of work, then it follows that you will receive a full day's pay. The form of this argument is as follows:
- Premise 1: If A then B
- Premise 2: A
- Conclusion: Therefore B
Any argument that takes this form is valid, meaning that the conclusion will always be true as long as both premises are true. Of course, the argument is valid even if the premises are false. Further, the premises are logically independent from each other. Thus, the claim "if you perform a full day of work, then you will get a full day's pay" can be true, but you may or may not perform a full day of work. And assuming that you do not perform a full day of work, then we can draw no further inferences. The first premise says nothing about what is true if you don't work, and nothing is logically entailed by it.
In conditional statements, the antecedent is sufficient to guarantee the truth of the consequent. But the consequent does not necessarily imply the truth of the antecedent. In other words, conditional statements have a unidirectional relationship where the antecedent leads to the consequent, but not vice versa. In keeping with the example, assume that if you perform a full day of work, then you will get a full day's pay. Now imagine that you receive that you have received a full day's pay. If you make the inference that you must have done a full day of work, then you have performed the fallacy of affirming the consequent. This fallacy has the following form:
Premise 1: If A then B
Premise 2: B
Conclusion: Therefore A
This form is fallacious, meaning that the conclusion is not warranted. The reason that it is not warranted is because there may be other reasons for why the consequent is true that are independent of the antecedent. In keeping with the example, you might receive a full day's pay from royalty payments or perhaps a tax refund. Alternatively, you might get a bonus or a gift roughly equivalent to a day's pay. In short, there may be multiple ways to make the consequent of a conditional statement true. Again, all a conditional statement guarantees is that the consequent will necessarily follow from the antecedent.
Affirming the consequent examples will always have the same form. They may appear in different contexts. Examples include:
- If you practice basketball every day, then you will be able to dunk. You can dunk. Therefore, you must have practiced every day.
- If everyone pays their taxes, then there will be fewer arrests tomorrow. There are fewer arrests tomorrow. Therefore, everyone must have paid their taxes.
- If someone uses an air freshener, then the room will smell pleasant. The room smells pleasant. Therefore, someone must have used an air freshener.
Each of these examples follows the form "If A then B. B. Therefore A." Further, each example ignores other possible reasons why B could be true. In each case, the antecedent would guarantee the consequent, but the consequent could also be guaranteed through other means.
A fallacy is an error in reasoning, in which a conclusion is faultily drawn from premises. The fallacy of affirming the consequent is a formal fallacy that occurs in arguments that use conditional statements. Conditional statements are if-then statements. The antecedent is the proposition that follows the if; the consequent is the proposition that follows the then. The form of the fallacy of affirming the consequent is "If A then B. B. Therefore A." The main problem with this fallacy is that it ignores the possibility that other conditions might be sufficient to guarantee the truth of the consequent. While a conditional statement asserts that the truth of the antecedent is sufficient to guarantee the truth of the consequent, the conditional statement does not state that the truth of the antecedent is the only condition that will lead to the truth of the consequent. Thus, the consequent might be true while the antecedent is false, and this would not falsify the conditional statement as a whole.
The fallacy of affirming the consequent resembles the valid argument form modus ponens. In this argument form, which affirms the antecedent, the form is "If A then B. A. Therefore B." This argument form is always valid, because as long as both premises are true, then the conclusion will always be true. The only way to have the conclusion be false would be if at least one of the premises was false.
Video Transcript
Up All Night
Carla is very sensitive to caffeine. One cup of coffee in the evening and she'll be up all night long, unable to sleep. She always orders caffeine-free tea and soda. Plenty of times, she's ordered a caffeine-free drink and found herself jittery and lying awake in bed. When this happens, she concludes, 'They got my order wrong. It must be the caffeine keeping me up.'
In this lesson, we'll look at Carla's conclusion and consider whether she has reason to believe what she does about why she's up all night. We'll focus on the affirming the consequent fallacy and how to avoid confusing it with logic that is correctly used.
Conditionals and Consequents
Here's how Carla began her argument. She said, 'If I have caffeine in the evening, then I'm awake all night.' The format of her sentence is known as a conditional statement, an if-then statement which includes two parts: an antecedent and a consequent. The antecedent is the 'if' part of a conditional statement, and the consequent is the 'then' part of a conditional statement. Sometimes 'then' won't be used in the sentence, but the format is still basically 'If A is true, then C is true.'
There's nothing faulty in saying the statement that if she has caffeine, she'll be up all night. But then Carla goes on to say, 'I'm awake all night. Therefore, I must have had caffeine this evening.'
What's wrong with her logic? She's awake all night, so that's simply a fact she's reporting. Can Carla reasonably conclude that this means someone gave her a caffeinated beverage by mistake?
Affirming the Consequent
When Carla says, 'I'm awake all night,' she affirms the consequent has happened. She's awake. The fallacy of affirming the consequent occurs when a person draws a conclusion that if the consequent is true, then the antecedent must also be true.
Written in letters where the antecedent is represented by A, and the consequent is C, this argument looks like this: 'If A, then C.' 'C, therefore, A.' 'If I have caffeine' (antecedent), 'I will be awake all night' (consequent). 'I'm awake all night' (consequent). 'Therefore, I must have had caffeine' (affirms the consequent, concluding that the antecedent must have occurred).
This is not to be confused with the logical argument a person could make that goes like this: 'If I have caffeine' (antecedent), 'I will be awake all night' (consequent). 'I had caffeine. I will be awake all night.' In this case, it's okay to affirm the antecedent and then affirm that the consequent will then be true. This is because an if-then statement is designed to describe just such situations and gives you a logical argument to use. The problem is when the reverse occurs. Then a faulty conclusion could be made.
The conclusion can be faulty because it could miss other reasons why Carla is awake all night. Her own worries and thoughts could keep her up. Noises might be keeping her awake. Perhaps she took an extra long nap earlier in the day, and that's preventing her from sleeping well that night. It could be the caffeine, but it could also be other variables she hasn't considered.
That said, sometimes a person will come to the correct conclusion, but their logic is still considered faulty. For instance, there's plenty of times that Carla lies in her bed awake as a result of someone mistakenly giving her caffeine. But she would need to rule out other possibilities to know for sure, which is not how she makes this argument. Instead, she jumps from: 'I was awake all night. Therefore, I must have had caffeine.'
Lesson Summary
The fallacy of affirming the consequent occurs when a person draws a conclusion that if the consequent is true, then the antecedent must also be true. The consequent is the 'then' part of a conditional statement, though at times you won't see the word 'then' used.
Affirming the consequent is problematic because you might miss possibilities that explain the consequent that have little or nothing to do with the antecedent. For instance, if Carla had a different reason for why she was awake all night, she would miss this. Sometimes, the conclusion drawn when affirming the consequent results in a true statement, such as when Carla really did get caffeine when she asked for caffeine free. The logic is still faulty, regardless of whether the conclusion drawn turns out to be true or false.
Learning Outcomes
You'll have the ability to do the following after this lesson:
- Define conditional statement, antecedent and consequent
- Describe the fallacy of affirming the consequent
- Explain how affirming the consequent can lead to faulty logic
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