title: Comparing the meanings of "if" and "all".
abstract: In this study, we compared the everyday meanings of conditionals ("if p then q") and universally quantified statements ("all p are q") when applied to sets of elements. The interpretation of conditionals was predicted to be directly related to the conditional probability, such that P("if p then q") = P(q|p). Quantified statements were assumed to have two interpretations. According to an instance-focused interpretation, quantified statements are equivalent to conditionals, such that P("all p are q") = P(q|p). According to a set-focused interpretation, "all p are q" is true if and only if every instance in set p is an instance of q, so that the statement would be accepted when P(q|p) = 1 and rejected when this probability was below 1. We predicted an instance-focused interpretation of "all" when the relation between p and q expressed a general law for an infinite set of elements. A set-focused interpretation of "all" was predicted when the relation between p and q expressed a coincidence among the elements of a finite set. Participants were given short context stories providing information about the frequency of co-occurrence of cases of p, q, not-p, and not-q in a population. They were then asked to estimate the probability that a statement (conditional or quantified) would be true for a random sample taken from that population. The probability estimates for conditionals were in accordance with an instance-focused interpretation, whereas the estimates for quantified statements showed features of a set-focused interpretation. The type of the relation between p and q had no effect on this outcome.
authors.affiliation: University of Marburg, Marburg, Germany, ncruzd01@mail.bbk.ac.uk.
authors.forename: Nicole
authors.initials: N
authors.lastname: Cruz
authors.forename: Klaus
authors.initials: K
authors.lastname: Oberauer
mesh_terms: D000293:Adolescent; D000328:Adult; D006801:Humans; D008128:Logic; D011336:Probability; D013850:Thinking / Q000502:physiology*; D055815:Young Adult