Leaping to Conclusions: Why Premise Relevance Affects Argument Strength

Abstract

Everyday reasoning requires more evidence than raw data alone can provide. We explore the idea that people can go beyond this data by reasoning about how the data was sampled. This idea is investigated through an examination of premise non-monotonicity, in which adding premises to a category-based argument weakens rather than strengthens it. Relevance theories explain this phenomenon in terms of people's sensitivity to the relationships among premise items. We show that a Bayesian model of category-based induction taking premise sampling assumptions and category similarity into account complements such theories and yields two important predictions: First, that sensitivity to premise relationships can be violated by inducing a weak sampling assumption; and second, that premise monotonicity should be restored as a result. We test these predictions with an experiment that manipulates people's assumptions in this regard, showing that people draw qualitatively different conclusions in each case.

Sample size, number of categories and sampling assumptions: Exploring some differences between categorization and generalization

“…In contrast, the Twelve Helpful condition is designed to induce a strong sampling assumption by encouraging the belief that items are chosen from a specific category by a helpful teacher. Experimentally manipulating sampling assumptions has been applied fruitfully in a number of inductive generalization tasks including word learning (Xu & Tenenbaum, 2007a), property induction tasks (Ransom, Perfors, & Navarro, 2016;Hayes, Navarro, Stephens, Ransom, & Dilevski, 2019) and single category generalization tasks (Ransom, Hendrickson, Perfors, & Navarro, 2018;Ransom & Perfors, submitted). The consistent finding in these studies is that experimentally manipulating the sampling assumption does have an effect on generalization.…”

Adding types, but not tokens, affects property induction

“…Conditions falling along the diagonal correspond to cases where the total number of observations is held constant: for example, the 2 TYPE AND TOKEN EFFECTS IN INDUCTION 14 condition and 11 condition both contain a total of two instances, but in the 11 condition these observations comprise two different types, whereas in the 2 condition, a single type is presented twice (i.e., there are two tokens). By necessity, a design such as this that includes all possible partitions of k or fewer tokens into k or fewer types will not be a fully factorial design with respect to the number of types and tokens, but such designs are not uncommon in the literature on categorization and inductive reasoning (e.g., Navarro & Kemp, 2017;Osherson et al, 1990;Ransom et al, 2016;Tenenbaum & Griffiths, 2001).…”

“…Tightening has also been observed with more complex, multidimensional categories (Ransom et al, 2016;Sanjana & Tenenbaum, 2003). For example, Ransom et al (2016) told participants about an animal that possessed a property (e.g., grizzly bears produce the TH-L2 hormone) and then asked participants whether the property generalized to a new animal (e.g., lions). Participants then learnt about a second animal that also possessed the property (e.g., black bears), and the generalization question was repeated.…”

“…However, the predictions from Bayesian models about how additional types would affect generalization also apply to cases where the training instances are less similar to one another. For example, finding that a property was shared by parrots, turkeys and robins, rather than just parrots, would increase property generalization to other birds (monotonicity) but decrease or "tighten" generalization to other categories at the same level of abstraction as birds (e.g., mammals, fish) (see Ransom et al, 2016 for a demonstration of tightening with these kinds of stimuli).…”

“…induction (Navarro et al, 2012;Ransom et al, 2016;Sanjana & Tenenbaum, 2003;Tenenbaum & Griffiths, 2001). Tenenbaum and Griffiths (2001) for example, found that adding instances within a particular numerical range (presented as values that indicate "healthy hormone levels") reduced generalization to more distant values.…”