Getting one step closer to deduction: Introducing an alternative paradigm for transitive inference

Abstract

Transitive inference is claimed to be "deductive". Yet every group/species ever reported apparently uses it. We asked 58 adults to solve 5-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible.response-accuracy and RT (non-discriminative nRT) were measured as typically done. We also measured RT confined to correct responses (cRT). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was not at all evident for nRT; suggesting the use of non-deductive end-anchor strategies. For overall performance and particularly the critical B?D inference, our findings indicate deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings, suggests at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a "Dual Process" conception of reasoning. Finally, our differing findings for nRT versus cRT, suggests researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held. Inference (Goel, Makale & Grafman, 2004;Goodwin & Johnson-Laird, 2005;Martin & Alsop, 2004). Consider the following example. During your lunch break yesterday, you might have gone out running with one friend (say Jane), and noted that you really struggled to keep up with her.We can term the above information a premise, where A and B are entities and there is some comparison made between them (i.e. premise A:B). Now, during today's lunch break you ran the same route with Kerry, and noted she was really struggling to keep up with you (premise B:C). At the end of the day, Kerry tells you Jane has asked her to go running during tomorrow's lunch break, asking you whether you think she will struggle or not (A?C). A transitive inference allows you to work out that, exceptional circumstances aside, Kerry will struggle running with Jane. The beauty is that you can infer such an outcome, without having already experienced it directly.Many argue that the capacity for transitive inference is logical (i.e., deductive), partly because the conclusion necessarily follows as long as the relation used is a linear comparative term (e.g., "runs faster than"), and partly because we can deduce the conclusion upon simply being told the two premises, rather than having to directly perceive and verify them as true for ourselves.Transitive inference may lay at the heart of a plethora of cognitive and sub-cognitive competencies, from spatial navigation through to predicting where to find food; and from placing oneself within a social network through to scientific thinking (Allen, 2006;Archie et al., 2006;Bond, Kamil & Bolda, 2003;Hummel & Holyoak, 2001;Markovits...

Transitivity for height versus speed: To what extent do the under-7s really have a transitive capacity?

“…Relevant to this issue, Goodwin and Johnson-Laird (2006) found that even by the end of adolescence, deductive-transitive-inference has still not fully matured (see also Reyna & Farley, 2006;Wright & Howells, 2008). Goodwin and Johnson-Laird's participants' mean performance never exceeded around 89%, although admittedly their task was very demanding, using transitive problems having two premise-pairs but housing four integrated items (i.e., four-term series) and also using a double-relational comparative (e.g., one premise was of the form John is taller than Peter to a greater extent than Robert is taller than Mike).…”

“…(Klaczynski, 2009, pp.286). It is therefore unsurprising that recent researchers have sought to explain transitivity development from a Dual-Process perspective (Ameel et al, 2007;Bouwmeester et al, 2007;Wright & Howells, 2008).…”

“…Clearly it is time to revisit the performance particularly of 4 year-olds. But in order to avoid unduly loading our young participants, we restricted the task to three-term series.2, Should our findings differ either from those of Bryant and colleagues or Markovits and colleagues, we also aimed to evaluate our methodological improvements to three-term tasks and place our findings in the context of a conception of human reasoning (i.e., Dual-Process theory) that has already been noted as capable of accepting the classical three-term findings but also simultaneously the findings from the Extensive-Training-Paradigm (e.g., see Bouwmeester, Vermunt & Sijtsma, 2007;Evans, 2003;Wright & Howells, 2008).3, Extending Kallio (1988), we aimed to present arguably the first study that made a direct comparison of a three-term height task with a more classical three-term task using dynamic motion. This was also relevant to the issue of whether different transitive tasks (here, height v racing) tend to lead to very different response profiles (e.g., see the location v length tasks of Russell et al, 1996).…”

“…2, Should our findings differ either from those of Bryant and colleagues or Markovits and colleagues, we also aimed to evaluate our methodological improvements to three-term tasks and place our findings in the context of a conception of human reasoning (i.e., Dual-Process theory) that has already been noted as capable of accepting the classical three-term findings but also simultaneously the findings from the Extensive-Training-Paradigm (e.g., see Bouwmeester, Vermunt & Sijtsma, 2007;Evans, 2003;Wright & Howells, 2008).…”

“…First, he presented a total of six items all at one time, so that all were simultaneously in view. Thus, here was a task using even more than five items, yet it had no need for training (see also Wright & Howells, 2008). Second, Kallio used an experimental procedure that allowed children to focus on only three items out of the six on display.…”