Notes on discounting

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (D), may enter into the hyperbolic equation as kD. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (kDS in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility     

Rate, Probability and Matching: Comments on ��The Identities Hidden in the Matching Laws, and Their Uses�� by David Thorne

David Thorne's (2010) article, “The Identities Hidden In The Matching Laws, And Their Uses” performs a valuable service in pointing out alternative expressions of matching. However, some identities tend to obscure rather than illuminate empirical relationships. Three such problematic instances are discussed: interresponse time as a function of interval and ratio schedule parameters; probability equality as implying rate matching; the apparent simplicity of probabilistic functions, as opposed to response rate functions, of reinforcement rate.     

Embedding irony and the semantics/pragmatics distinction

This paper argues that we need to re-think the semantics/pragmatics distinction in the light of new evidence from embedding of irony. This raises a new version of the old problem of ‘embedded implicatures’. I argue that embedded irony isn’t fully explained by solutions proposed for other embedded implicatures. I first consider two strategies: weak pragmatics and strong pragmatics. These explain embedded irony as truth-conditional content. However, by trying to shoehorn irony into said-content, they raise problems of their own. I conclude by considering how a modified Gricean model can explain that irony embeds qua implicature. This leads us to prefer a local implicature model. This has important consequences for how we draw the semantics/pragmatics distinction.     

Signs in their times: introducing a review symposium on Robert Yelle's Semiotics of Religion

This essay introduces a review symposium on Robert Yelle's Semiotics of Religion: Signs of the Sacred in History (2013). It first reviews the book's argument, then offers a selective review of the six contributions to the symposium, along with aspects of Yelle's responses to these.     

How Do Children Restrict Their Linguistic Generalizations? An (Un‐)Grammaticality Judgment Study

A paradox at the heart of language acquisition research is that, to achieve adult‐like competence, children must acquire the ability to generalize verbs into non‐attested structures, while avoiding utterances that are deemed ungrammatical by native speakers. For example, children must learn that, to denote the reversal of an action, un‐ can be added to many verbs, but not all (e.g., roll/unroll; close/*unclose). This study compared theoretical accounts of how this is done. Children aged 5–6 (N = 18), 9–10 (N = 18), and adults (N = 18) rated the acceptability of un‐ prefixed forms of 48 verbs (and, as a control, bare forms). Across verbs, a negative correlation was observed between the acceptability of ungrammatical un‐ prefixed forms (e.g., *unclose) and the frequency of (a) the bare form and (b) alternative forms (e.g., open), supporting the entrenchment and pre‐emption hypotheses, respectively. Independent ratings of the extent to which verbs instantiate the semantic properties characteristic of a hypothesized semantic cryptotype for un‐ prefixation were a significant positive predictor of acceptability, for all age groups. The relative importance of each factor differed for attested and unattested un‐ forms and also varied with age. The findings are interpreted in the context of a new hybrid account designed to incorporate the three factors of entrenchment, pre‐emption, and verb semantics.     

Imprecise Epistemic Values and Imprecise Credences

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential and alethic epistemic norms. In the first part of the paper, I claim that these arguments fail if we understand imprecise credences as indeterminate credences. In the second part, I explore why agents with entirely alethic epistemic values can end up in an indeterminate credal state. Following William James, I argue that there are many distinct alethic values that a rational agent can have. Furthermore, such an agent is rationally permitted not to have settled on one fully precise value function. This indeterminacy in value will sometimes result in indeterminacy in epistemic behaviour—that is, because the agent’s values aren’t settled, what she believes might not be.     

Can membership-functions capture the directionality of verbal probabilities?

Verbal probabilities are a common mean for communicating risk and uncertainties in many decision-making settings (e.g., finance, medicine, military). They are considered directional because they elicit a focus on either the outcome occurrence (e.g., there is a chance) or on its non-occurrence (e.g., it is unlikely). According to a quantitative perspective, directionality is dependent on the vague probabilistic meaning conveyed by verbal probabilities—e.g., p(outcome) > .50 = > focus on outcome occurrence. In contrast a more qualitative perspective suggests that directionality depends on contextual factors. The present study tested whether the directionality of verbal probabilities was determined by their vague probabilistic meaning, by contextually manipulated variables (i.e., representativeness and base rate), or by a combination of both. Participants provided their own expressions to describe the guilt of a suspect and then assessed the vague probabilistic meaning and directionality associated with those expressions. Results showed that directionality was mainly determined by the vague probabilistic meaning but also by the base rate of guilt. Although attention focus on the occurrence or the non-occurrence of the target outcome is dependent on vague probabilistic meaning, it cannot be fully accounted for by it.     

The effectiveness of feedback in multiple-cue probability learning

How effective are different types of feedback in helping us to learn multiple contingencies? This article attempts to resolve a paradox whereby, in comparison to simple outcome feedback, additional feedback either fails to enhance or is actually detrimental to performance in nonmetric multiple-cue probability learning (MCPL), while in contrast the majority of studies of metric MCPL reveal improvements at least with some forms of feedback. In three experiments we demonstrate that if feedback assists participants to infer cue polarity then it can in fact be effective in nonmetric MCPL. Participants appeared to use cue polarity information to adopt a linear judgement strategy, even though the environment was nonlinear. The results reconcile the paradoxical contrast between metric and nonmetric MCPL and support previous findings of people's tendency to assume linearity and additivity in probabilistic cue learning.