Linguistic barriers to logical reasoning: a new perspective on Aristotelian syllogisms

Andreas Haida,Luka Crnič,Yosef Grodzinsky

doi:10.21248/zaspil.60.2018.476

Abstract

Experimental studies investigating logical reasoning performance show very high errorrates of up to 80% and more. Previous research identified scalar inferences of the sentencesof logical arguments as a major error source. We present new analytical tools to quantify theimpact of scalar inferences on syllogistic reasoning. Our proposal builds on a new classificationof Aristotelian syllogisms and a closely linked classification of reasoning behaviors/strategies.We argue that the variation in error rates across syllogistic reasoning tasks is in part due toindividual variation: reasoners follow different reasoning strategies and these strategies playout differently for syllogisms of different classes.Keywords: syllogisms, reasoning errors, individual variation, scalar inferences.

Highlights

Our paper investigates the impact of so-called scalar inferences on logical reasoning performance
24Note that we excluded syllogisms whosevalidity is affected by illicit conversion (IC) inferences. 25Recall that all syllogisms with two universal premises and an existential conclusion, such as AE4O and EA3O, are invalid in predicate logic (PL) and that all syllogisms that are valid in PL are valid in Aristotelian logic (AL). 26We did not collect the information whether a participant had training in formal logic
The data set of Rips (1994) suggests that a syllogism’s validity in PL is a relevant factor for the acceptance rates within class [+v −v]: syllogisms in [+v −v] that are valid in both AL and PL were accepted 68% of all times and syllogisms in [+v −v] that are only valid in AL 51% of all times. 27One might think that this result is expected since Rips (1994) already notes that “subjects gave 85.8% “follows”

Summary

Introduction

Our paper investigates the impact of so-called scalar inferences on logical reasoning performance. (1) some Ms are Ks SI not all Ms are Ks. To see how commonly the SI in (1) seems to be drawn in logical reasoning tasks, consider the argument in (2), from the premise (I) to the putative conclusion (O).. Since the reasoning task targeted logical inferences,7 94% of all subjects erred in their judgment. A possible explanation for this high error rate is that the vast majority of subjects considered the logical entailments of the I-premise and its SI.. The conjunction of the I-premise and its SI logically entails the O-conclusion.. The conjunction of the I-premise and its SI logically entails the O-conclusion.9 This observation suggests that the errors observed in the I-to-O inference task are due to the SI of the I-premise (as already concluded by N&G). The magnitude of the error rate suggests that almost all reasoners computed (and took it into account) the SI of the I-premise

Objectives

Findings

Discussion

Conclusion