The conjunction fallacy and the many meanings of and

Abstract

a b s t r a c tAccording 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.Ó 2008 Elsevier B.V. All rights reserved.. . .it is a mistake to analyze natural language words like and as being identical to entities of the man-made logical terminology which so clearly derives from natural language (rather than the other way around) and so clearly has needs and purposes distinct from those of natural language (Sweetser, 1990, p. 92).One of the most frequent words in the English language is and. In Leech, Rayson, and Wilson's (2001) analysis of word frequencies in a 100 million word collection of samples of written and spoken language (the British National Corpus) the unremarkable three-letter word ''and" is the third most frequent word. Its commonness and plainness, however, do not mean that the most general connective in the English language lacks the ability to convey a wide range of relationships between the states of affairs described by the conjuncts. In fact, one reason for linguists' enduring fascination with and is that among all coordinating conjunctions (e.g., or, but, nor) it has the least semantic and syntactic limits, the least specific meaning, and the highest context dependency (Lang, 1991).Take, for instance, the use of and in (1): (1) Her husband is in hospital and she is seeing other men.As Kitis (2000) pointed out, the and in (1) does much more than conjoin the two clauses. Rather, it functions as an ''emotional device" that communicates the speaker's emotional attitude, surprise, or even outrage.The notion of and's context dependency stands in stark contrast with the highly constrained meaning of the logical and operator (^). The logical^represents the Boolean intersection of two sets. For illustration, if set A contains all even numbers (mu...

Fast and Frugal Heuristics: Tools of Social Rationality

“…(p. 92) In natural language, terms such as and and probability often have multiple meanings and meanings that are different from mathematical probability and the logi-cal and. If, in addition, conversational maxims (Grice, 1989) employed to disambiguate lexical and pragmatic ambiguities suggest that probability does not mean mathematical probability and and does not mean the logical operator, then violations of the conjunctions would be a reflection of sound and intelligent semantic and pragmatic inferences (see Hertwig, Benz, & Krauss, 2008;Hertwig & Gigerenzer, 1999; but see also Mellers, Hertwig, & Kahneman, 2001;Sides, Osherson, Bonini, & Viale, 2002). On this view, the conjunction fallacy, and possibly several other cognitive illusions (Hilton, 1995) are not due to cognitive limits.…”

Quantum-like models cannot account for the conjunction fallacy

“…Kahneman 1982, 1983;Gigerenzer 1996;Kahneman and Tversky 1996;Hertwig 1997;Hertwig and Chase 1998;Hertwig and Gigerenzer 1999;Mellers et al 2001;Stolarz-Fantino et al 2003;Bonini et al 2004;Tentori et al 2004;Hertwig et al 2008;Moro 2009;Kahneman 2011;Erceg and Galic 2014; for a review, cf. Moro 2009).…”

Walter the Banker: The Conjunction Fallacy Reconsidered

“…In Hertwig et al (2008), an overview is given of different arguments that attempt to show that the use of the 'AND' operator in ordinary language is different from the 'AND' operator used in propositional logic. Such arguments would lead us to conclude that the 'and' in 'Linda is a bank teller and a feminist' would be different from the corresponding logical operator and so no fallacy arises.…”