Confidence judgments in syllogistic reasoning: the role of consistency and response cardinality

ABSTRACT

In two experiments, we examined the resolution of confidence judgments in syllogistic reasoning and their heuristic bases. Based on the assumptions of Koriat's Self-Consistency Model of confidence, we expected the confidence judgments to be related to conclusion consensuality, reflecting the role of consistency as a heuristic cue to confidence. In Experiment 1, the participants evaluated 24 syllogisms with conclusions that varied with respect to validity and consensuality. In Experiment 2, the participants produced conclusions to 64 pairs of premises. The correlation between confidence and reasoning accuracy was low. In both experiments confidence was related to the consensuality of the responses. For consensually correct items, correlation between confidence and accuracy was positive; however, for consensually incorrect items it was negative. In Experiment 2, confidence was lower for syllogisms with higher response cardinality, or syllogisms that elicited a greater variety of conclusions.

KEYWORDS:

• Syllogistic reasoning
• meta-reasoning
• confidence
• self-consistency
• response cardinality

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Categorical syllogisms contain two categorical propositions that can appear in four moods: affirmative-universal (All A are B), affirmative-particular (Some A are B), negative-universal (No A are B) or negative-particular (Some A are not B), which are labelled as A, I, E and O, respectively. Each pair of premises (e.g., Some A are B; No B are C) includes three terms: two end terms (A and C) and a middle term (B). The distributions of the three terms in the premises are referred to as figures: A-B, B-C (Figure 1); B-A, C-B (Figure 2); A-B, C-B (Figure 3); B-A, B-C (Figure 4). In the text below, the following notation will be used: AE1 will designate the pairs of premises in Figure 1, with the first premise in the affirmative-universal mood, and the second premise in the negative-universal mood. The number of possible pairs of premises for every figure is 16, resulting in a total of 64 pairs of premises. Furthermore, there are eight possible conclusions to the 64 pairs of premises: four ac moods and four ca moods, resulting in a total of 512 syllogisms. When the conclusion necessarily follows from the premises, the syllogism is valid. In instances when a conclusion derived from the premises does not necessarily follow, the syllogism is invalid. Of the 64 pairs of premises, 27 yield at least one valid conclusion, whereas the remaining 37 syllogistic forms are invalid (Khemlani & Johnson-Laird, 2012).

Additional information

Funding

This work was supported by the Croatian Science Foundation (Hrvatska Zaklada za Znanost) [grant number 4139], [grant number 2408]; University of Rijeka Research Grant [grant number 13.04.1.3.11].