Affirming the consequent
Encyclopedia
Affirming the consequent, sometimes called converse error, is a formal fallacy
, committed by reasoning in the form:
An argument of this form is invalid
, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).
The name affirming the consequent derives from the premise Q, which affirms the "then" clause
of the conditional
premise.
Owning Fort Knox is not the only way to be rich. There are any number of other ways to be rich.
Arguments of the same form can sometimes seem superficially convincing, as in the following example:
But having the flu is not the only cause of a sore throat since many illnesses cause sore throat, such as the common cold
or strep throat
.
The following is a more subtle version of the fallacy embedded into conversation.
B attempts to falsify A's conditional statement ("if Republican then against gun control") by providing evidence he believes would contradict its implication. However, B's example of his uncle does not contradict A's statement, which says nothing about non-Republicans. What would be needed to disprove A's assertion are examples of Republicans who support gun control.
Formal fallacy
In philosophy, a formal fallacy is a pattern of reasoning that is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid...
, committed by reasoning in the form:
- If P, then Q.
- Q.
- Therefore, P.
An argument of this form is invalid
Validity
In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....
, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).
The name affirming the consequent derives from the premise Q, which affirms the "then" clause
Consequent
A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then".Examples:* If P, then Q.Q is the consequent of this hypothetical proposition....
of the conditional
Indicative conditional
In natural languages, an indicative conditional is the logical operation given by statements of the form "If A then B". Unlike the material conditional, an indicative conditional does not have a stipulated definition...
premise.
Examples
One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:- If Bill GatesBill GatesWilliam Henry "Bill" Gates III is an American business magnate, investor, philanthropist, and author. Gates is the former CEO and current chairman of Microsoft, the software company he founded with Paul Allen...
owns Fort KnoxUnited States Bullion DepositoryThe United States Bullion Depository, often known as Fort Knox, is a fortified vault building located adjacent to Fort Knox, Kentucky, used to store a large portion of United States official gold reserves and occasionally other precious items belonging or entrusted to the federal government.The...
, then he is rich. - Bill Gates is rich.
- Therefore, Bill Gates owns Fort Knox.
Owning Fort Knox is not the only way to be rich. There are any number of other ways to be rich.
Arguments of the same form can sometimes seem superficially convincing, as in the following example:
- If I have the flu, then I have a sore throatSore throatA sore throat or throat pain is a common physical symptom usually caused by acute pharyngitis, or throat inflammation, though it also occurs in a number of other situations, such as post trauma and in diphtheria. It can cause mild to extreme pain....
. - I have a sore throat.
- Therefore, I have the flu.
But having the flu is not the only cause of a sore throat since many illnesses cause sore throat, such as the common cold
Common cold
The common cold is a viral infectious disease of the upper respiratory system, caused primarily by rhinoviruses and coronaviruses. Common symptoms include a cough, sore throat, runny nose, and fever...
or strep throat
Strep throat
Streptococcal pharyngitis, streptococcal tonsillitis, or streptococcal sore throat is a type of pharyngitis caused by a group A streptococcal infection. It affects the pharynx including the tonsils and possibly the larynx. Common symptoms include fever, sore throat, and enlarged lymph nodes...
.
The following is a more subtle version of the fallacy embedded into conversation.
- A: All RepublicansRepublican Party (United States)The Republican Party is one of the two major contemporary political parties in the United States, along with the Democratic Party. Founded by anti-slavery expansion activists in 1854, it is often called the GOP . The party's platform generally reflects American conservatism in the U.S...
are against gun controlGun controlGun control is any law, policy, practice, or proposal designed to restrict or limit the possession, production, importation, shipment, sale, and/or use of guns or other firearms by private citizens...
. - B: That's not true. My uncle's against gun control and he's not a Republican.
B attempts to falsify A's conditional statement ("if Republican then against gun control") by providing evidence he believes would contradict its implication. However, B's example of his uncle does not contradict A's statement, which says nothing about non-Republicans. What would be needed to disprove A's assertion are examples of Republicans who support gun control.
See also
- Modus ponensModus ponensIn classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...
- Modus tollensModus tollensIn classical logic, modus tollens has the following argument form:- Formal notation :...
- Post hoc ergo propter hocPost hoc ergo propter hocPost hoc ergo propter hoc, Latin for "after this, therefore because of this," is a logical fallacy that states, "Since that event followed this one, that event must have been caused by this one." It is often shortened to simply post hoc and is also sometimes referred to as false cause,...
- Denying the antecedentDenying the antecedentDenying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:The name denying the antecedent derives from the premise "not P", which denies the "if" clause of the conditional premise....
- Fallacy of the undistributed middleFallacy of the undistributed middleThe fallacy of the undistributed middle is a logical fallacy, and more specifically a formal fallacy, that is committed when the middle term in a categorical syllogism is not distributed in the major premise...
- Inference to the best explanation
- ELIZA effectELIZA effectThe ELIZA effect, in computer science, is the tendency to unconsciously assume computer behaviors are analogous to human behaviors.In its specific form, the ELIZA effect refers only to "the susceptibility of people to read far more understanding than is warranted into strings of symbols —...