Argument
Affirming the consequent
Overview
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the antecedent is true. It takes on the following form:
If P, then Q.
Q.
Therefore, P.
which may also be phrased as
P
→
Q
{\displaystyle P\rightarrow Q}
(P implies Q)
∴
Q
→
P
{\displaystyle \therefore Q\rightarrow P}
(therefore, Q implies P)
For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source), or the lamp might be functional but switched off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not.
Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes.
A related fallacy is denying the antecedent. Two related valid forms of logical argument include modus tollens (denying the consequent) and modus ponens (affirming the antecedent).
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
The copula is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition, The earth is round, the Predicate is the word _round_, which denotes the quality affirmed, or (as the phrase is) predicated: _the earth_, words denoting the object which that quality is affirmed of, compose the…
John Stuart Mill, A System of Logic
States what Affirming the consequent is.
And from those conclusions which I have mentioned above, the former is called by the dialecticians the fourth mood, and the latter the fifth. Then they add a negation of conjunctive propositions; as, "It is not both this and that; but it is this; therefore it is not that." This is the sixth mood.
Marcus Tullius Cicero, The Orations of Marcus Tullius Cicero, Volume 4
States what Affirming the consequent is.
Examples of the latter are: 'The mind is no elephant:' 'A lion is no table;' propositions which are correct but absurd, exactly like the identical propositions: 'A lion is a lion;' 'Mind is mind.' Propositions like these are undoubtedly the truth of the immediate, or, as it is called, Qualitative judgment. But they are not judgments at all, and can only occur in a subjective thought where even an untrue abstraction…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Affirming the consequent is.
Related ideas
- Propositional logic
- Modus ponens
- Modus tollens
- Validity (logic)
- Q.E.D.
- Formal fallacy
- Antecedent (logic)
- Consequent
- Contraposition
Place in the tradition
Part of Hypothetico-deductive model.