The matching law

The matching law may be viewed either as an empirical generalization, and therby subject to disproof, or as part of a system of equations used to define the utility (“value”) of a reinforcer. In the latter case it is tautologous, and not subject to disproof within the defining context. A failure to obtain matching will most often be a signal that the independent variables have not been properly scaled. If, however, the proper transformations have been made on the independent variables, and matching is not obtained, the experimental paradigm may be outside the purview of the matching law. At that point, reinterpretations or revisions of the law are called for. The theoretical matching law is but one of many possible ways to define utility, and it may eventually be rejected in favor of a more useful definition.     

The matching problem

Tables of the exact distributions of number of matches are given for small decks having the same number of cards in each suit. Several approximate distributions are considered for use with larger decks, and some indication of the goodness of the approximations is given.The calculations for this paper were done while the writer was working on a project sponsored by funds from the Ford Foundation. The writer wishes to express his gratitude to Dr. Frederick Mosteller for his constant help and encouragement during the writing of this paper.     

How to do things with things

J.L. Austin has demonstrated that people can do things—bring about social facts — with words. Here we describe how some people do things with things. This is a study of the symbolic use and situated history of material objects during a business negotiation between two German entrepreneurs: of the practical transformation of things-at-hand from objects of use into exemplars, or into forms-at-hand that can be used for the construction of transitory symbolic artifacts. Arranging boxes in a particular fashion can be the equivalent of an illocutionary act, but unlike words things remain on the scene as indexical monuments to prior interactional arrangements.

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The peculiar longevity of things not so bad

Abstract— Intense hedonic states trigger psychological processes that are designed to attenuate them, and thus intense states may abate more quickly than mild states. Because people are unaware of these psychological processes, they may mistakenly expect intense states to last longer than mild ones. In Study 1, participants predicted that the more they initially disliked a transgressor, the longer their dislike would last. In Study 2, participants predicted that their dislike for a transgressor who hurt them a lot would last longer than their dislike for a transgressor who hurt them a little, but precisely the opposite was the case. In Study 3, participants predicted that their dislike for a transgressor who hurt them a lot would last longer than their dislike for a transgressor who hurt someone else a lot, but precisely the opposite was the case. These errors of prediction are discussed as instances of a more general phenomenon known as the region-β paradox.     

The matching game: Testing for the generality of the matching law

The matching law suggests that animals will allocate responses as a function of reinforcer availability; that is, if one choice produces more reinforcement, a greater proportion of total responding will be allocated to that choice. Indeed, there tends to be a match between response allocation and proportions of reinforcers delivered, given each of those choices. A computer game that delivers simulated coins of experimenter-selected denominations for responding on either of two keys was developed to test the generality of the matching law. The data suggest that even within a single 10-min session, matching functions may be obtained (although undermatching was the rule in the present results). This program may also be used to test various accounts of the matching law.     

Visual similarity is greater for line drawings of nonliving than living things: the importance of musical instruments and body parts

It has been argued that greater intra-category structural similarity for living things, and the subsequent "visual crowding," makes them more difficult to recognize and name for neurologically damaged individuals and normal subjects (Humphreys et al., 1988). Nevertheless, the precise meaning and quantification of structural similarity remains unclear, as does the rationale for why it necessarily should be greater for living things. We derived a new measure of visual overlap from the Snodgrass and Vanderwart corpus of line drawings: the degree of pixel overlap within subcategories (Euclidean distance: ED). Contrary to existing notions of visual crowding and extant measures of contour overlap, within-category ED indicated less within-category visual overlap for living things. Furthermore, musical instruments clustered with living things (having low overlap), while body parts clustered with nonliving things (having high overlap). These counter-intuitive findings accord with patient data and thus, provide evidence for the psychological reality and utility of ED.     

The dynamics of intermodal matching: Seven- and 12-month-olds' intermodal matching of affect

The purpose of this experiment was to examine whether and how a common methodological difference frequently employed within the intermodal matching procedure affects infants' intermodal matching. Specifically we examined the effects of incorporating or excluding silent control trials on seven- and 12-month-olds' intermodal matching of affect. Results revealed that seven-month-olds showed reliable matching when presented all in-sound trials whereas 12-month-olds showed reliable matching when half of the trials were presented silently and half of the trials were presented in-sound. Results are discussed in terms of the dynamics of infant attention and those conditions where the inclusion of silent trials may be appropriate.     

Reminiscences of things past

A personalistic and selective view of the history of school psychology is offered. A brief biographical sketch, and some of the early personal encounters and major professional preoccupations of the author, are presented first. This is followed by an exposition centered on the development of school psychology as a specialty. Two historical streams of intellectual thought, intervention methods, and professional affiliation, along with their consequences for school psychology, are then described. Finally, some observations on the future of school psychology are made.     

Hallucinating real things

No particular dagger was the object of Macbeth’s hallucination of a dagger. In contrast, when he hallucinated his former comrade Banquo, Banquo himself was the object of the hallucination. Although philosophers have had much to say about the nature and philosophical import of hallucinations (e.g. Macpherson and Platchias, Hallucination, 2013) and object-involving attitudes (e.g. Jeshion, New essays on singular thought, 2010), their intersection has largely been neglected. Yet, object-involving hallucinations raise interesting questions about memory, perception, and the ways in which we have knowledge of the world around us. In this paper, I offer an account of object-involving hallucinations. Specifically, I argue that they are an unusual species of perceptual remembering.     

Reevaluation of things past

The ability of rats to reevaluate previously presented information in light of subsequently provided information was evaluated using a CER (conditioned emotional response) procedure. In Experiment 1, rats suppressed responding to a compound light + tone stimulus that was repeatedly paired with shock. Groups of rats were then presented with only one element of the compound (the tone), either presented alone or paired with shock, for 15 days. During this 15-day period, two control groups received trials with the shock alone or neither stimulus nor shock. All of the rats were then tested with the other element of the compound (the light). Rats that had received the tone paired with shock during the intervening training continued to suppress to the light, whereas rats that had received the tone alone showed rapid extinction of the CER to light. The control groups showed that this effect was not due to the number of shock presentations received. A subsequent experiment also demonstrated that these results were not due to nonspecific stimulus effects. Apparently, a subsequent change in the associative strength of one element results in a similar change to the other element of a previously established compound stimulus.     

Logic in general philosophy of science: old things and new things

This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments.     

The problem of evil and the suffering of creeping things

Even philosophers of religion working on the problem of non-human animal suffering have ignored the suffering of creatures like insects. Sensible as this seems, it’s mistaken. I am not sure whether creatures like these can suffer, but it is plausible, on both commonsensical and scientific and philosophical grounds, that many of them can. If they do, their suffering makes the problem of evil much worse: their vast numbers mean the amount of evil in the world will almost certainly be increased by many, many orders of magnitude, the fact that disproportionately many of them live lives which are nasty, brutish, and short means that the proportion of good to evil in the world will be drastically worsened, and their relative lack of cognitive sophistication means that many theodicies, including many specifically designed to address animal suffering, would apply to their suffering only with much greater difficulty, if at all. Philosophers of religion should therefore more seriously investigate whether these beings can suffer and what, if anything, could justify God in allowing as much.