New normative standards of conditional reasoning and the dual-source model.

Henrik Singmann,David Over,Karl Christoph Klauer

doi:10.3389/fpsyg.2014.00316

Henrik Singmann, David Over + Show 1 more

Open Access

https://doi.org/10.3389/fpsyg.2014.00316

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Abstract

There has been a major shift in research on human reasoning toward Bayesian and probabilistic approaches, which has been called a new paradigm. The new paradigm sees most everyday and scientific reasoning as taking place in a context of uncertainty, and inference is from uncertain beliefs and not from arbitrary assumptions. In this manuscript we present an empirical test of normative standards in the new paradigm using a novel probabilized conditional reasoning task. Our results indicated that for everyday conditional with at least a weak causal connection between antecedent and consequent only the conditional probability of the consequent given antecedent contributes unique variance to predicting the probability of conditional, but not the probability of the conjunction, nor the probability of the material conditional. Regarding normative accounts of reasoning, we found significant evidence that participants' responses were confidence preserving (i.e., p-valid in the sense of Adams, 1998) for MP inferences, but not for MT inferences. Additionally, only for MP inferences and to a lesser degree for DA inferences did the rate of responses inside the coherence intervals defined by mental probability logic (Pfeifer and Kleiter, 2005, 2010) exceed chance levels. In contrast to the normative accounts, the dual-source model (Klauer et al., 2010) is a descriptive model. It posits that participants integrate their background knowledge (i.e., the type of information primary to the normative approaches) and their subjective probability that a conclusion is seen as warranted based on its logical form. Model fits showed that the dual-source model, which employed participants' responses to a deductive task with abstract contents to estimate the form-based component, provided as good an account of the data as a model that solely used data from the probabilized conditional reasoning task.

Highlights

The most influential work in the psychology of conditional reasoning long presupposed as its normative standard the binary and extensional logic of the propositional calculus (Johnson-Laird and Byrne, 1991 see especially pp. 7 and 74)
It can be seen that, as predicted, the conditional probability P(q|p) and the conjunction P(p ∧ q) are correlated with P(if p q) but not the other variables. These results have to be interpreted cautiously as responses were nested within participants and within conditionals which violates the assumptions for standard correlation or multiple regression (Judd et al, 2012)
We entered the four assumed predictors and inference (MP, Modus Tollens (MT), Affirmation of the Consequent (AC), and Denial of the Antecedent (DA)) simultaneously as fixed effects and estimated random intercepts for participants and items plus random inference slopes and correlations among the random inference slopes for the random item effect

Summary

Introduction

The most influential work in the psychology of conditional reasoning long presupposed as its normative standard the binary and extensional logic of the propositional calculus (Johnson-Laird and Byrne, 1991 see especially pp. 7 and 74). There are, many problems with holding that the natural language conditionals that people reason with are equivalent to material conditionals (Evans and Over, 2004). Prominent among these problems are the “paradoxes” of the material conditional. Consider a conditional about a coin we know to be fair, “If we spin the coin 100 times we will get 100 heads.” It would be absurd if our subjective probability for this conditional increased to ever higher levels as it became more and more likely that we would not go to the trouble of spinning the coin that many times Consider a conditional about a coin we know to be fair, “If we spin the coin 100 times we will get 100 heads.” It would be absurd if our subjective probability for this conditional increased to ever higher levels as it became more and more likely that we would not go to the trouble of spinning the coin that many times

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