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Information about Affirming The Consequent

Affirming the consequent is a formal fallacy, committed by reasoning in the form:

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


Arguments of this form are invalid (except in the rare cases where such an argument also instantiates some other, valid, form). Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true. The name affirming the consequent derives from the term for the "then" clause of a conditional claim.

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 owns Fort Knox, 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.
I have a sore throat.
Therefore, I have the flu.


But many illnesses cause sore throat, such as the common cold or strep throat. Thus this argument is weak at best.

As noted above, 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. In everyday discourse, however, such valid cases of affirming the consequent are rare, typically only occurring when the "if-then" premise is actually an "if and only if" claim (i.e., a biconditional). 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. But even in such a case, the validity stems not from affirming the consequent, but from the form modus ponens.

Although affirming the consequent is an invalid inference, it is defended by some as an acceptable type of inductive reasoning, sometimes under the name "inference to the best explanation".

See also

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Formal fallacies
Argument from fallacy • Fallacy of modal logic • Masked man fallacy • Appeal to probability • Bare assertion fallacy
Fallacy of propositional logic:Affirming a disjunct • Affirming the consequent • Commutation of Conditionals • False dilemma • Denying the antecedent • Improper Transition
Fallacy of quantificational logic:Existential fallacy • Illicit Conversion • Quantifier shift • Unwarranted contrast
Syllogistic fallacy:Affirmative conclusion from a negative premise • Negative conclusion from an affirmative premise • Exclusive premises • Necessity • Four-term Fallacy • Illicit major • Illicit minor • Undistributed middle
In philosophy, 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 argument which renders the argument invalid.
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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.
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validity as it occurs in logic refers generally to a property of deductive arguments, although many logic texts apply the term to statements as well (a statement is a sentence that “has a truth value,” i.e., that is either true or false).
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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.
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The indicative conditional is the logical operation given by statements of the form "If A then B" in ordinary English (or similar natural languages). The indicative conditional, unlike the material conditional, does not have a stipulated definition.
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William Henry Gates III (born October 28, 1955[1]) is an American entrepreneur, philanthropist and chairman of Microsoft, the software company he founded with Paul Allen.
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Fort Knox is a United States Army post and census-designated place in Kentucky south of Louisville and north of Elizabethtown. The base covers parts of Bullitt, Hardin, and Meade Counties. It holds the U.S. Army Armor Center, the U.S. Army Armor School and the U.S.
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Influenza
Classification & external resources

TEM of negatively stained influenza virons, magnified approximately 70,000 times
ICD-10 J 10. , J 11.
ICD-9 487

DiseasesDB 6791
MedlinePlus 000080
eMedicine med/1170   ped/3006
MeSH
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Acute nasopharyngitis
Classification & external resources

ICD-10 J 00.0
ICD-9 460

DiseasesDB 31088
MedlinePlus 000678
eMedicine med/2339  
MeSH D003139 Acute viral nasopharyngitis, or acute coryza
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Strep throat
Classification & external resources

Strep throat
ICD-10 J 02.0
ICD-9 034.0

Strep throat (or "Streptococcal pharyngitis", or "Streptococcal Sore Throat") is a form of Group A streptococcal infection that affects the pharynx.
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since October 2007.
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“Iff” redirects here. For other uses, see IFF.
If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a logical connective between statements which means that the truth of either one of the statements
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In logic and mathematics, logical biconditional (sometimes also known as the material biconditional) is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and
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In logic, modus ponendo ponens (Latin: mode that affirms by affirming; often abbreviated MP) is a valid, simple argument form. It is a very common rule of inference, and takes the following form:

If P, then Q.
P.

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Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.
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Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence.
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In logic, modus ponendo ponens (Latin: mode that affirms by affirming; often abbreviated MP) is a valid, simple argument form. It is a very common rule of inference, and takes the following form:

If P, then Q.
P.

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In logic, Modus ponendo tollens (Latin for "mode that affirms by denying") is the formal name for indirect proof or proof by contraposition (contrapositive inference), often abbreviated to MT.
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Denying the antecedent is a logical fallacy, committed by reasoning in the form:

If P, then Q.
Not P.
Therefore, not Q.

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The fallacy of the undistributed middle is a logical fallacy that is committed when the middle term in a categorical syllogism isn't distributed. It is thus a syllogistic fallacy.
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Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence.
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The ELIZA effect, in computer science, is the tendency to unconsciously assume computer behaviors are analogous to human behaviors, despite conscious knowledge to the contrary.
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In philosophy, 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 argument which renders the argument invalid.
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The argument from fallacy, also known as argumentum ad logicam or fallacy fallacy, is a logical fallacy which assumes that if an argument is fallacious, its conclusion must be false.

It has the general argument form:
If P, then Q.

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In formal logic, a modal logic is any logic for handling modalities: concepts like possibility, existence, and necessity. Logics for handling a number of other ideas, such as eventually, formerly, can, could
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The masked man fallacy is a fallacy of formal logic in which substitution of identical designators in a true statement can lead to a false one. The name comes from the example "I do not know who the masked man is", which can be true even though the masked man is Jones, and I know
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The appeal to probability is a logical fallacy, often used in conjunction with other fallacies. It assumes that because something could happen, it is inevitable that it will happen. This is flawed logic, regardless of the likelihood of the event in question.
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The bare assertion fallacy is fallacy in formal logic where a premise in an argument is assumed to be true merely because it says that it is true.

One form of the fallacy may be summarized as follows:
  • Fact 1: X claims statement A.

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In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
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The logical fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct occurs when a deductive argument takes either of the two following forms:

A or B
A
Therefore, it is not the case that B

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