Affirming the Consequent | Examples & Definition
Affirming the consequent is the logical fallacy of assuming a particular cause must be true just because its expected outcome is true.
The formula for affirming the consequent is as follows:
- If P, then Q.
- Q.
- Therefore, P.
- If I am sick, then I will feel fatigued.
- I feel fatigued.
- Therefore, I am sick.
The fallacy of affirming the consequent is typically found in contexts such as formal logic, law, and mathematics.
What is the affirming the consequent fallacy?
Affirming the consequent is the mistake of assuming that if an outcome is true, then a specific cause must also be true.
Affirming the consequent is defined by the following formula:
- If P, then Q.
- Q.
- Therefore, P.
This fallacy occurs in hypothetical syllogisms (or “conditional syllogisms”), which include an “if–then” proposition (i.e., “If P, then Q”). The mistake is affirming Q, the consequent, instead of P, the antecedent.
- If my phone is off (P), then it will not ring (Q).
- My phone is not ringing (Q).
- Therefore, my phone is off (P).
It is a mistake to affirm the consequent (Q) when you should be affirming the antecedent (P). In this case, the phone might not be ringing simply because no one is calling.
In this syllogism, even if the premises are true, the conclusion does not necessarily follow. Q might be true for reasons other than P. This means the argument is invalid and commits a formal logical fallacy.
Affirming the consequent vs modus ponens
The valid way to affirm a hypothetical syllogism is modus ponens. Also known as “affirming the antecedent,” modus ponens takes the following form:
- If P, then Q.
- P.
- Therefore, Q.
Modus ponens is always valid, meaning that if the premises are true, it logically follows that the conclusion must also be true.
Affirming the consequent examples
The fallacy of affirming the consequent can be found in scientific reasoning, particularly on questions of causes and conditions.
- If a planet supports life, then it must have liquid water.
- Planet Y has liquid water.
- Therefore, Planet Y supports life.
This example commits the affirming the consequent fallacy by assuming that because Planet Y has liquid water (the consequent), this automatically means the planet supports life (the antecedent). However, additional factors are necessary for supporting life, such as a stable atmosphere and suitable temperatures.
In legal reasoning, the fallacy of affirming the consequent often occurs in inferences
- If the defendant is guilty, then they have a motive.
- The defendant has a motive.
- Therefore, the defendant is guilty.
This argument commits the affirming the consequent fallacy by assuming that because the defendant has a motive (the consequent), they must be guilty (the antecedent).
Affirming the consequent vs post hoc ergo propter hoc
Both affirming the consequent and post hoc ergo propter hoc involve flawed reasoning about causation, but they differ in their structure and implications.
- Affirming the consequent is a formal fallacy that assumes a specific cause based on an observed effect, without considering other potential causes.
- Example: “If it’s nighttime, the sky is dark. The sky is dark. Therefore, it’s nighttime.” (This conclusion is invalid because the sky is also dark at other times, such as during thunderstorms.)
- Post hoc ergo propter hoc is an informal fallacy that assumes a causal relationship between two events based solely on their sequential occurrence. It is also called the post hoc fallacy.
- Example: “A new mayor took office. Shortly after, crime rates decreased. Therefore, the new mayor’s policies caused the decrease in crime.” (This argument is weak because correlation does not imply causation. The decrease in crime could have been a coincidence.)
Frequently asked questions about affirming the consequent
- How can affirming the consequent be avoided?
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You can avoid committing the affirming the consequent fallacy by remembering that in hypothetical syllogisms, the antecedent should be affirmed instead.
The correct way to form a valid affirmative hypothetical syllogism is:
- If P, then Q.
- P.
- Therefore, Q.
In this correct form of the syllogism, called modus ponens (or “affirming the antecedent”), the fact that the antecedent (P) is true logically requires that the consequent (Q) is also true.
- What is the difference between affirming the consequent and denying the antecedent?
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Affirming the consequent and denying the antecedent are both logical fallacies that occur in hypothetical syllogisms, but the two fallacies have different forms.
Affirming the consequent takes the following form:
- If P, then Q.
- Q.
- Therefore, P.
Affirming the consequent example - If it’s summer, then the temperature will be high.
- The temperature is high.
- Therefore, it is summer.
Denying the antecedent takes the following form:
- If P, then Q.
- Not P.
- Therefore, not Q.
Denying the antecedent example - If I study hard, then I’ll pass the exam.
- I didn’t study hard.
- Therefore, I won’t pass the exam.
- Why is affirming the consequent invalid?
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Affirming the consequent is invalid because it assumes a specific cause for an outcome that can have multiple causes. Consider the formula for affirming the consequent:
- If P, then Q.
- Q.
- Therefore, P.
The above syllogism is fallacious because Q can be true for reasons other than P. The mistake lies in assuming a single cause for an effect or trait.
For example:
- If a number is a perfect square, then it is positive.
- The number 14 is positive.
- Therefore, the number 14 is a perfect square.
