Direct and converse applications: Two sides of the same coin?

In this paper I present two cases, taken from the history of science, in which mathematics and physics successfully interplay. These cases provide, respectively, an example of the successful application of mathematics in astronomy and an example of the successful application of mechanics in mathematics. I claim that an illustration of these cases has a twofold value in the context of the applicability debate. First, it enriches the debate with an historical perspective which is largely omitted in the contemporary discussion. Second, it reveals a component of the applicability problem that has received little attention. This component concerns the successful application of physical principles in mathematical practice. With the help of the two examples, in the final part of the paper I address the following question: are successful applications of mathematics to physics (direct applications) and successful applications of physics to mathematics (converse applications) two sides of the same problem

Exploring the Effect of Early Motor Delay and Physical Therapy Interventions on the Parent-Child Relationship

Emotional availability (EA) or the ability of the parent-child dyad to engage emotionally and partake in congruent and mutually enjoyable interactions, is essential for familial health and well-being. EA is considered the “connective tissue” of healthy parent-child relationships and is associated with secure attachment, maternal mental health, and children’s adaptive development. Most evidence supporting the integral role of EA on healthy outcomes is supported by typically developing populations in which adults present with a social or biological risk factor such as experiencing past traumas of adversities with mental health. In line with the transactional model of development, children are equal members of the dyad and play and active and integral role in dyadic interactions. Caregivers’ actions are rarely spontaneous but rather they are in response to children’s actions. EA is hypothesized to be 80-90% non-verbal highlighting the importance of children’s motor abilities in establishing the dyadic reciprocity of the relationship. Children with delayed or atypical motor skills are surmised to have difficulties with EA. This dissertation aimed to understand the relationship between emotional availability, children’s development, and early physical therapy interventions in young children with motor delays. Specifically, we were addressing gaps in knowledge on the relationship between early motor delays and the developmental change in emotional availability (Chapter 2), the bidirectional relationship between adult EA and children’s gross motor and problem-solving development (Chapter 3), and the effect of early physical therapy interventions on EA in young children with motor delays and their caregivers (Chapter 4). Our findings in Chapter 2 suggests that dyads with motor delay have different developmental trajectories of emotional availability than dyads with children with typical motor development. Chapter 3 highlights that in our young sample, Adult EA and child development influenced future performance within each domain respectively, but there were no current or future associations between the two variables. Lastly, results from Chapter 4 propose that early physical therapy interventions may uniquely affect dyadic emotional availability depending on how the intervention was delivered. Taken together, these studies provide critical information for the urgency to measure and treat qualities of the parent-child relationship as part of routine early therapy services in children with motor delay. We will discuss clinical implications for our findings as well opportunities for future translational research opportunities

Deductive nomological model and mathematics: making dissatisfaction more satisfactory

El debate sobre la explicación matemática ha heredado el mismo sentimiento de insatisfacción que los filósofos de la ciencia expresaron, en el contexto de la explicación científica, hacia el modelo nomológico deductivo. Este modelo se considera incapaz de cubrir casos de explicaciones matemáticas genuinas y, además, continúa siendo ignorado en gran medida en la literatura relevante. Sorprendentemente, las razones de este ostracismo no son suficientemente manifiestas. En este artículo exploro una posible extensión del modelo al caso de las explicaciones matemáticas y sostengo que hay por lo menos dos razones para juzgar la imagen nomológico deductiva de la explicación como inadecuada en este contexto

Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism

Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory

The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context

Evidence, explanation and enhanced indispensability

International audienceIn this paper I shall adopt a possible reading of the notions of ‘explanatory indispensability’ and ‘genuine mathematical explanation in science’ on which the Enhanced Indispensability Argument (EIA) proposed by Alan Baker is based. Furthermore, I shall propose two examples of mathematical explanation in science and I shall show that, whether the EIA-partisans accept the reading I suggest, they are easily caught in a dilemma. To escape this dilemma they need to adopt some account of explanation and offer a plausible answer to the following ‘question of evidence’: What is a genuine mathematical explanation in empirical science and on what basis do we consider it as such? Finally, I shall suggest how a possible answer to the question of evidence might be given through a specific account of mathematical explanation in science. Nevertheless, the price of adopting this standpoint is that the genuineness of mathematical explanations of scientific facts turns out to be dependent on pragmatic constraints and therefore cannot be plugged in EIA and used to establish existential claims about mathematical objects

What’s the Matter with the Deductive Nomological Model?

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