Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism

Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends on a false view of how abductive considerations mediate the transfer of empirical support. More specifically, I argue that even if inference to the best explanation is cogent, and claims about mathematical entities play an essential explanatory role in some of our best scientific explanations, it doesn’t follow that the empirical phenomena that license those explanations also provide empirical support for the claim that mathematical entities exist.

     

Externalizing and Internalizing Problems: Associations with Family Adversity and Young Children’s Adrenocortical and Autonomic Functioning

Research on Child and Adolescent Psychopathology - The development of child mental health problems has been associated with experiences of adversity and dysregulation of stress response systems;...     

Mathematical surrealism as an alternative to easy-road fictionalism

Philosophical Studies - Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories...     

The Social Relations Model: How to Understand Dyadic Processes

The social relations model (SRM) is an intriguing tool both to conceptualize and to analyze dyadic processes. We begin with explaining why interpersonal phenomena in everyday life are more complex than often considered. We then show how the SRM accounts for these complexities by decomposing interpersonal perceptions and behaviors into three independent components and describe the designs required to investigate these components. We then provide a step-by-step introduction into social relations analyses, thereby showing how the SRM can be used to investigate a multitude of exciting research questions. Finally, we summarize the existing software solutions for conducting social relations analyses. Resources for further information are suggested.     

Learning times for large lexicons through cross-situational learning

Cross-situational learning is a mechanism for learning the meaning of words across multiple exposures, despite exposure-by-exposure uncertainty as to a word's true meaning. Doubts have been expressed regarding the plausibility of cross-situational learning as a mechanism for learning human-scale lexicons in reasonable timescales under the levels of referential uncertainty likely to confront real word learners. We demonstrate mathematically that cross-situational learning facilitates the acquisition of large vocabularies despite significant levels of referential uncertainty at each exposure, and we provide estimates of lexicon learning times for several cross-situational learning strategies. This model suggests that cross-situational word learning cannot be ruled out on the basis that it predicts unreasonably long lexicon learning times. More generally, these results indicate that there is no necessary link between the ability to learn individual words rapidly and the capacity to acquire a large lexicon.     

The Cultural Evolution of Structured Languages in an Open‐Ended,Continuous World

Language maps signals onto meanings through the use of two distinct types of structure. First, the space of meanings is discretized into categories that are shared by all users of the language. Second, the signals employed by the language are compositional: The meaning of the whole is a function of its parts and the way in which those parts are combined. In three iterated learning experiments using a vast, continuous, open‐ended meaning space, we explore the conditions under which both structured categories and structured signals emerge ex nihilo. While previous experiments have been limited to either categorical structure in meanings or compositional structure in signals, these experiments demonstrate that when the meaning space lacks clear preexisting boundaries, more subtle morphological structure that lacks straightforward compositionality—as found in natural languages—may evolve as a solution to joint pressures from learning and communication.     

Reflections on the actor–partner interdependence model

The actor–partner interdependence model (APIM) has been widely successful and has become the default method for analyses of dyadic data in which both members of the pair have the same measurements. This article reviews the history of the development of the APIM, focusing on the original presentation of the model, a 1979 article by Kraemer and Jacklin. Also discussed are the topics of APIM patterns, whether the APIM is a dyadic model, and the automation of APIM analyses. Although the APIM is the most popular method for dyadic analysis, it should be recognized there are alternatives that should also be considered.