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Affirming the consequent, sometimes called converse error, is a formal fallacy
Formal fallacy

In Philosophical logic, a formal fallacy or a logical fallacy is a pattern of reasoning which is always wrong. This is due to a flaw in the structure of the logical argument which renders the argument validity....
, committed by reasoning in the form
Argument form

In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables....
:

If P, then Q.
Q.
Therefore, P.


Arguments of this form are invalid
Validity

The term Validity in logic applies to Argument or statements....
, in that arguments of this form do not always give good reason to establish their conclusions, even if their premises are true.

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"....
 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.

One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion.






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Affirming the consequent, sometimes called converse error, is a formal fallacy
Formal fallacy

In Philosophical logic, a formal fallacy or a logical fallacy is a pattern of reasoning which is always wrong. This is due to a flaw in the structure of the logical argument which renders the argument validity....
, committed by reasoning in the form
Argument form

In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables....
:

If P, then Q.
Q.
Therefore, P.


Arguments of this form are invalid
Validity

The term Validity in logic applies to Argument or statements....
, in that arguments of this form do not always give good reason to establish their conclusions, even if their premises are true.

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"....
 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.

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 Gates
Bill Gates

William Henry "Bill" Gates III is an United States business magnate, philanthropist, author, the List of the 100 wealthiest people , and chairman of the board of Microsoft, the software company he founded with Paul Allen....
 owns Fort Knox
Fort Knox

Fort Knox is a United States United States Army post in Kentucky south of Louisville, Kentucky and north of Elizabethtown, Kentucky. The base, , covers parts of Bullitt County, Kentucky, Hardin County, Kentucky, and Meade County, Kentucky counties, with Hardin county receiving the largest benefit, economically....
, then he is rich.
Bill Gates is rich.
Therefore, Bill Gates owns Fort Knox.


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 throat
Sore Throat

Sore Throat were a United Kingdom crust punk / grindcore band, formed in Yorkshire in 1987. They are known for being one of the earliest exponents of the grindcore subgenre known as "noisecore", as well launching the careers of several prominent members of the British heavy metal music community....
.
I have a sore throat.
Therefore, I have the flu.


But many illnesses cause sore throat, such as the common cold
Common cold

Acute viral rhinopharyngitis, or acute coryza, usually known as the common cold, is a highly contagious, virus infectious disease of the upper respiratory system, primarily caused by picornaviruses or coronaviruses....
 or strep throat
Strep throat

Streptoccal pharyngitis or streptococcal sore throat is a form of group A streptococcal infection that affects the pharynx and possibly the larynx and tonsils....
.

However, it is possible that an argument that affirms the consequent could be valid, if the argument instantiates some other valid form. For example, if claims P and Q express the same proposition, then the argument would be trivially valid, as it would beg the question
Begging the question

In logic, begging the question has traditionally described a type of logical fallacy in which the proposition to be proved is assumed implicitly or explicitly in one of the premises....
.

If P, then P.
P.
Therefore, P.


In everyday discourse, however, such cases are rare, typically only occurring when the "if-then" premise is actually an "if and only if
If and only if

If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a biconditional logical connective between statements....
" claim (i.e., a biconditional
Logical biconditional

In logic and mathematics, logical biconditional is a logical operator connecting two statements to assert, p Iff q where p is a hypothesis and q is a logical consequence ....
). For example:

If he's not inside, then he's outside.
He's outside.
Therefore, he's not inside.


The above argument may be valid, but only if the claim "if he's outside, then he's not inside" follows from the first premise. More to the point, the validity of the argument stems not from affirming the consequent, but affirming the antecedent.

Although affirming the consequent is an invalid inference, it is defended by some as a type of inductive reasoning
Inductive reasoning

Induction or inductive reasoning, sometimes called inductive logic, is reasoning which takes us "beyond the confines of our current evidence or knowledge to conclusions about the unknown." The premises of an inductive logical argument support the conclusion but do not entailment it; i.e....
, sometimes under the name "inference to the best explanation". That is, in some cases, reasoners argue that the antecedent is the best explanation, given the truth of the consequent. The strength of such inferences, however, depends on the likelihood of alternative hypotheses
Bayesian inference

Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true....
, which shows that such inferences are based on additional premises, not merely on the affirmation of the consequent.

See also

  • Modus ponens
    Modus ponens

    In classical logic, modus ponendo ponens is a valid, simple argument form sometimes referred to as affirming the antecedent or the law of detachment....
  • Modus tollens
    Modus tollens

    In classical logic, modus tollens has the following argument form:Modus tollens is sometimes confused with indirect proof or proof by contrapositive ....
  • Denying the antecedent
    Denying the antecedent

    Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the argument form:The name denying the antecedent derives from the premise "not P", which denies antecedent of the indicative conditional premise....
  • Fallacy of the undistributed middle
    Fallacy of the undistributed middle

    The fallacy of the undistributed middle is a logical fallacy that is committed when the middle term in a categorical syllogism isn't distribution of terms....
  • Inference to the best explanation
  • ELIZA effect
    ELIZA effect

    The 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 — especially words — strung together by com...