Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...) potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...) Langford find themselves in conflict with mathematical and scientific practice. (shrink)

According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...) what is picked out by the mathematics are structural facts that go beyond any specific physical facts. (shrink)

Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...) Mark Steiner), according to which a genuine MES incorporates an explanatory proof of the mathematical result being used. The central case study involves an explanation for why bees build the cells of their honeycombs in the shape of hexagons. I make a distinction between two kinds of MES, mathematics-driven explanation in science and science-driven mathematical explanation, and argue that it is the second category which is both scientifically and philosophical more central. I conclude that the explanatory relation involved in MES is genuinely scientific and hence that the phenomenon of MES poses a challenge to general accounts of scientific explanation. (shrink)

The desire to minimize the number of individual new entities postulated is often referred to as quantitative parsimony. Its influence on the default hypotheses formulated by scientists seems undeniable. I argue that there is a wide class of cases for which the preference for quantitatively parsimonious hypotheses is demonstrably rational. The justification, in a nutshell, is that such hypotheses have greater explanatory power than less parsimonious alternatives. My analysis is restricted to a class of cases I shall refer to as (...) additive. Such cases involve the postulation of a collection of qualitatively identical individual objects which collectively explain some particular observed phenomenon. Especially clear examples of this sort occur in particle physics.1Introduction2Particle physics: a case study3Three kinds of simplicity4Explanatory power5Explanation and non‐observation6Parsimony and scientific methodology7Conclusions. (shrink)

Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's (...) first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively. (shrink)

The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...) the property that cicada period lengths are expressible as the sum of two perfect squares. I argue that mathematical spandrels pose a particular problem for nominalism because of the way in which they are entangled with scientific explanations. (shrink)

Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the (...) stronger mathematics, and this poses a challenge for the nominalist position. (shrink)

The rise of the field of “ experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is (...) considered according to which experimental mathematics involves calculating instances of some general hypothesis. The paper concludes with the examination of some philosophical implications of this characterization. (shrink)

This book outlines the realist and pluralist philosophy of John Anderson, Australia's most original thinker. His teaching at Sydney University and his arti6es have deeply influenced Australian intellectual life. Several main themes run through his work, but Anderson never gave an overall account of his views. This is remedied here: exhibiting the range of Anderson's thought from logic, epistemology and theory of mind, to language and social theory, this volume sketches realism as a systematic philosophical position, while showing something of (...) the history of ideas in Australia. (shrink)

In this paper I examine a strategy which aims to bypass the technicalities of the indispensability debate and to offer a direct route to nominalism. The starting-point for this alternative nominalist strategy is the claim that--according to the platonist picture--the existence of mathematical objects makes no difference to the concrete, physical world. My principal goal is to show that the 'Makes No Difference' (MND) Argument does not succeed in undermining platonism. The basic reason why not is that the makes-no-difference claim (...) which the argument is based on is problematic. Arguments both for and against this claim can be found in the literature; I examine three such arguments, uncovering flaws in each one. In the second half of the paper, I take a more direct approach and present an analysis of the counterfactual which underpins the makes-no-difference claim. What this analysis reveals is that indispensability considerations are in fact crucial to the proper evaluation of the MND Argument, contrary to the claims of its supporters. (shrink)

One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is (...) that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects. (shrink)

I. INTRODUCTIONIs Jesus the perfect human being? An affirmative response seems unavoidable for classical Christology. Indeed, at the Council of Chalcedon in 451, the gathered bishops and representatives of the church across Africa, Asia, and Europe agreed that Jesus Christ was “perfect in divinity and perfect in humanity”: teleion…en Theótæti kai teleion…en anthropótæti.Theologians and patristics scholars alike often sort through the second part of this formula in the way that the remainder of the conciliar definition itself seems to indicate, interpreting (...) it to mean that nothing that belongs to the humanity we share can be lacking in the humanity of Jesus, and nothing belongs to Him that would compromise the human form. He does not, for instance, have a body animated by a divine spirit in place of a human will, or a superhuman ability to translocate. This is theologically appropriate as far as it goes, but it does not go far enough. (shrink)

Background:New graduate transition into the workforce is challenging and can involve managing ethical tensions. Ethical tensions cause new graduates to doubt their capabilities due to their lack of experience. To support new graduates, we need to know what these ethical tensions are.Objectives:To explore the ethical tensions perceived to occur in practice for new graduate health professionals.Research design:This qualitative systematic review involved a search of five databases (Medline, EMBASE, AMED, CINAHL and Scopus) which resulted in the retrieval of 3554 papers. After (...) the two-phased screening process, eight studies were identified that met the inclusion criteria and had rich data on the review question. Articles were read several times, critically appraised and analysed through thematic analysis.Ethical considerations:No ethical approval was required for the systematic review. The review was conducted following well-established reporting guidelines enabling transparency and rigour.Findings:Studies originated from Australia, United States, Iran and China. One study included speech pathologists and seven were with nurses. Four themes included the following: (1) enduring an unknown workplace culture that generates uncertainty without support for new graduates; (2) being vulnerable because of distress from bullying, exclusion and being a scapegoat; (3) constraining systems and institutional restrictions that cause dilemmas; and (4) experiencing disillusionment from lost ideals about ethical practice.Discussion:This review has brought to light the vulnerability of new graduates to negative workplace culture and collegial incivility. In addition, new graduates are subjected to ethical tensions created by institutional constraints which can create dilemmas and uncertainties through practice that does not align with what they anticipated.Conclusion:Understanding ethical tensions experienced by new graduates enables provision of informed support. There needs to be considerable cultural change for orientation and socialisation of new graduates to enable them to learn and manage ethical tensions. (shrink)

The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I (...) argue that this sort of naïve realism about structure is not a coherent or plausible position, especially given the multiplicity of types of entities and relations that can feature as nodes and links in complex networks. (shrink)

This paper traces an expanded ethical perspective for youth and community work (YCW) practice in response to the climate and biodiversity crises. Discussing ecological ethics, we problematise the liberal humanist emphasis on utilitarianism and reject it as inappropriate for YCW in these times. Instead, we argue for an ecocentric practice ethic which intrinsically values the non-human world. To advance an ecocentric ethical perspective for YCW we draw on decolonial and posthuman theory. Inspired by a Freirean dialogical approach, we apply these (...) theoretical domains as lenses to problematise YCW practice, seeking a generative dialogue between perspectives. Through this, we identify three emergent tasks for ecocentric YCW: (a) thinking and acting beyond the individual; (b) cultivating reciprocal care and connection and (c) practicing critical pedagogies of place. This third element builds on YCW's social pedagogic tradition and provides a practical means to incorporate ecocentric ideas into practice. We conclude that, given the unprecedented implications of climate crises and biodiversity collapse, a YCW ethics that does not consider these implications for young people is insufficient for the context of practice today. Enacting an ecocentric YCW ethics requires ongoing collective praxis and dialogue between young people, practitioners, educators, managers and students. (shrink)

Theological language has always faced a fundamental dilemma: it seeks to put the divine reality into limited human language. While this dilemma can obfuscate our theological pathways, it can also generate a new awareness of the task and possibilities of the discipline. New testimonials, or uniquely accented human experiential utterances, have emerged in theological discourse in the past decades, greatly increasing our vision of the expansiveness of theology. The tools for integration into systematic or discursive development are still, however, lacking. (...) This article suggests that an extension of the innovative methodology of Thomas Aquinas, beginning and ending with ‘what seems’ to be the case, putting testimony into discursive forms, and testing for a fittingness with the mysterious and excessive mystery of the divine reality, offers a promising path for discerning common and trustworthy theological language. (shrink)

Defenders of the enhanced indispensability argument argue that the most effective route to platonism is via the explanatory role of mathematical posits in science. Various compelling cases of mathematical explanation in science have been proposed, but a satisfactory general philosophical account of such explanations is lacking. In this paper, I lay out the framework for such an account based on the notion of “the mathematical stance.” This is developed by analogy with Dennett’s well-known concept of “the intentional stance.” Roughly, adopting (...) the mathematical stance towards a particular physical phenomenon involves treating it as an abstract mathematical structure for the purposes of prediction and explanation. Interestingly, Dennett himself frequently draws analogies between his intentional stance towards beliefs and desires and scientists’ stance towards centers of gravity. I explore the theoretical role played by centers of gravity within science and discuss how an indispensabilist platonist ought to categorize the ontological status of this type of posit. I conclude with some thoughts on how an approach based on the mathematical stance might be developed into a more general philosophical account of the application of mathematics in science. (shrink)

Objective: There is a demonstrated link between the mental health and substance use comorbidities experienced by young adults, however the vast majority of psychological interventions are disorder specific. Novel psychological approaches that adequately acknowledge the psychosocial complexity and transdiagnostic needs of vulnerable young people are urgently needed. A modular skills-based program for emotion regulation and impulse control addresses this gap. The current one armed open trial was designed to evaluate the impact that 12 weeks exposure to ERIC alongside usual care (...) had on young people's ability to regulate emotions, as well as examine potential moderating mechanisms.Methods: Seventy nine young people were enrolled to the 12 week intervention period. Twenty one practitioners from youth and community health services delivered relevant ERIC modules adjunct to usual care. Linear mixed effects regression was used to examine change over time across the primary outcome of emotion dysregulation and secondary outcomes of depression, anxiety, stress, experiential avoidance and mindfulness. Moderation analyses were conducted to test whether the magnitude of change in emotion dysregulation moderated change over time in secondary outcomes.Results: Analyses revealed significant improvement in the primary outcome of emotion dysregulation with a moderate effect size, in addition to decreases in the secondary outcomes of depression, anxiety, stress and experiential avoidance. No improvements in mindfulness were reported. Moderation analyses revealed that the residualised change over time in emotion dysregulation moderated the change over time in symptoms of distress, depression, anxiety, stress, experiential avoidance, and mindfulness.Conclusion: Reductions in the severity of emotion dysregulation, depression, anxiety, stress and experiential avoidance are promising, and were evident despite the complexity of the participants and the diversity of the service setting. The improvements found in each outcome were only observed for those young people whose emotion regulation also improved, providing preliminary evidence for the role of emotion regulation as a key treatment target in this population. (shrink)

In this paper I present a case study of mathematical explanation in science that is new to the philosophical literature, and that arises in the context of estimating the energetic costs of running in bipedal animals. I refer to this as the Bipedal Gait Costs explanation. I argue that it is important for examples of applied mathematics to be driven not just by philosophical and mathematical concerns but also by scientific concerns. After a detailed presentation of the BGC case study, (...) I discuss ways in which it is different from standard examples of MES. One distinctive aspect of BGC is that substantive mathematics occurs at two different levels. I argue for a distinction to be drawn between the mathematical modeling that occurs at one level, which is non-explanatory, and the mathematical theorem which is applied to results gleaned from these models, which is explanatory. I conclude by drawing some connections with broader indispensability-based arguments for platonism in the philosophy of mathematics. (shrink)

This case study extends the findings of Pickering et al. 2009 to the domain of conversational humor. We find that, as was the case in humorous narratives, conversational humor is not marked by higher pitch or volume, increased speech rate, or significant pauses. Unlike narrative humor, conversational humor is not produced at a lower pitch and slower rate than non-humorous parts of the text. We find that smiling and laughter tend to occur with humor.

We agree with Jones & Love (J&L) that much of Bayesian modeling has taken a fundamentalist approach to cognition; but we do not believe in the potential of Bayesianism to provide insights into psychological processes. We discuss the advantages of associative explanations over Bayesian approaches to causal induction, and argue that Bayesian models have added little to our understanding of human causal reasoning.

This book outlines the realist and pluralist philosophy of John Anderson, Australia's most original thinker, whose articles and teaching at Sydney University have deeply influenced Australian intellectual life. Several main themes run though his work, but Anderson never gave an overall account of his views. This is remedied here: in exhibiting the range of Anderson's thought, from logic, epistemology and theory of mind, to language and social theory, Baker's work sketches realism as a systematic philosophical position and shows something of (...) the history of ideas in Australia. This book will be of particular interest to historians of modern philosophy and those studying realism. (shrink)