TY - JOUR

T1 - The conjunction fallacy and the many meanings of and

AU - Hertwig, Ralph

AU - Benz, Björn

AU - Krauss, Stefan

PY - 2008/9/1

Y1 - 2008/9/1

N2 - According to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator ∧, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language "and" can convey a wide range of relationships between conjuncts such as temporal order ("I went to the store and bought some whisky"), causal relationships ("Smile and the world smiles with you"), and can indicate a collection of sets rather than their intersection (as in "He invited friends and colleagues to the party"). When "and" is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator ∧, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people's understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator ∧. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.

AB - According to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator ∧, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language "and" can convey a wide range of relationships between conjuncts such as temporal order ("I went to the store and bought some whisky"), causal relationships ("Smile and the world smiles with you"), and can indicate a collection of sets rather than their intersection (as in "He invited friends and colleagues to the party"). When "and" is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator ∧, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people's understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator ∧. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.

KW - Conjunction fallacy

KW - Pragmatic and semantic inferences

KW - Rationality

KW - Educational science

UR - http://www.scopus.com/inward/record.url?scp=51249108858&partnerID=8YFLogxK

U2 - 10.1016/j.cognition.2008.06.008

DO - 10.1016/j.cognition.2008.06.008

M3 - Journal articles

C2 - 18723167

AN - SCOPUS:51249108858

VL - 108

SP - 740

EP - 753

JO - Cognition

JF - Cognition

SN - 0010-0277

IS - 3

ER -