Issues in Reasoning about Iffy Propositions: The Development of Deductive Rationality in Conditional Reasoning

Issues in Reasoning about iffy Propositions: The Development of Deductive Rationality in Conditional Reasoning. Walter J. Schroyens (Walter.Schroyens@psy.kuleuven.be), and Walter Schaeken (Walter.Schaeken@psy.kuleuven.be) R.A. T. Research Group, Laboratory of Experimental Psychology, University of Leuven Tiensestraat 102, Leuven, B-3000, Belgium Deductively rational reasoning performance is Table 1: Logic indices across high school grade. characterised as performance that is in accordance with the strictures of logic. Judging performance as such Grade implies neither that people should reason deductively Problem set F a Mse nor that they would always have the goal of establishing Exp. 1: n logically valid inferences. Indeed, a rational analysis Abstract (Anderson, 1990) distinguishes normative from Causal adaptive rationality. That is, there is no absolute norm Exp. 2 : n against which to measure human reasoning Un-Logical . 033 . 032 . 053 . 056 . 078 . 073 17.6 . 012 performance. Sometimes deductively rational behaviour Logical is appropriate, and sometimes probabilistically rational Exp. 3: n behaviour is appropriate. Neither logic nor probability Un-logical . 020 . 009 . 041 . 033 . 041 . 047 5.9 . 013 theory provides an absolute standard of human Logical rationality. Rational behaviour is adapted to the Note. a. F value of linear contrasts defined over grade. environment; it is flexible behaviour marked by responsiveness to the environmental demands, whether 100°, then it will boil”, and you know that “Water is heated to it is the environment of evolutionary adaptation or our 100°” then it would follow that “the water would boil”. In technologically evolved modern day cultural environment. Experiment 3 the conclusions in both the open and logic Table 1 presents logic indices computed over four conditions were evaluated on a 7 point rating scale marking arguments about conditionals of the form . The respectively the certainty that the conclusion “follows” or Modus Ponens (MP) and Modus Tollens “would follow if one assumes that the rule is true”. argument are logically valid. The The results of three experiments presented in Table 1 Affirmation of the Consequent (AC) argument and Denial of the Antecedent argument are logically invalid. The logic index is computed as contrasts over grade were significant beyond α = . 01. Second, the difference between the mean acceptance rates of logically the propensity to exhibit deductively rational behaviour is valid vs. invalid arguments. In Experiment 1, participants first positively related to measures of general aptitude. In solved the four arguments about an abstract rule (e.g. “if the Experiment 1 participants completed the Standard Raven letter is an A then the number is a 7”). Participants selected Progressive Matrices (RPM), and the sum scores correlated the conclusion among three alternatives: e.g. a) The number is significantly with the logic index on the two problem sets (r = a 7, b) The number is not a 7 and c) The number is possibly a . 152, p subscale of the Rational-Experiential Inventory (r = .116, p cases explicate the rules of the “game” of logic (and the relation and counter the logically valid arguments. In Experiment 2 with general aptitude shows it is not just a game in the and 3 participants received two sets of causal inference common sense meaning of the word) as in Experiment 3, problems. In Experiment 2 participants first evaluated the logic indices are generally higher, F(1,637) = 71.8, Mse = conclusions on a five point rating scale (“very uncertain” to .011, p < .01 and the developmental effects are more “very certain” that the conclusion follows). In the second set pronounced, F(1,637) = 10.3, Mse = . 011, p < . 01. of “logical problems” they evaluated the conclusions as either “yes, it follows” or “no, it does not follow necessarily”. References This condition also stressed the truth-assumption that is Anderson, J. R. (1990). The adaptive character of thought. inherent to the notion of logically validity. They read as Hillsdale, NJ: Lawrence Erlbaum. follows: If it were always true that: “if water is heated to