Explanation in mathematics: Proofs and practice

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do they relate to the sorts of explanation encountered in philosophy of science and metaphysics

It's just a feeling: why economic models do not explain

Julian Reiss correctly identified a trilemma about economic models: we cannot maintain that they are false, but nevertheless explain and that only true accounts explain. In this reply we give reasons to reject the second premise – that economic models explain. Intuitions to the contrary should be distrusted

No one left behind: Using mixed-methods research to identify and learn from socially marginalised adolescents in low- and middle-income countries

This article describes the mixed-methods approach used by the Gender and Adolescence: Global Evidence (GAGE) research programme. It discusses how qualitative and quantitative methods can be used both in isolation and combined to learn about the lives of adolescents in low- and middle-income countries (LMICs), focusing on the methodological and ethical approaches used to reach socially marginalised adolescents (including adolescents with disabilities, adolescents not in school, adolescent refugees, adolescents living in urban slums, adolescents who married as children, and adolescent mothers). We reflect on the implementation of the GAGE conceptual framework, discussing its strengths and weaknesses, and the challenges to promoting inclusive and genuinely mixed-methods research practices. While these methods have been adapted in the countries where research was undertaken, the conceptual framework provides a common methodological approach, utilising an intersectional lens. We show how mixed-methods approaches can contribute to the knowledge base on research with socially marginalised adolescent girls and boys globally, serving as an important resource for future research with young people in LMICs

Mathematical Explanations and Mathematical Applications

One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.Peer reviewe

On the Mathematical Constitution and Explanation of Physical Facts

The mathematical nature of modern physics suggests that mathematics is bound to play some role in explaining physical reality. Yet, there is an ongoing controversy about the prospects of mathematical explanations of physical facts and their nature. A common view has it that mathematics provides a rich and indispensable language for representing physical reality but that, ontologically, physical facts are not mathematical and, accordingly, mathematical facts cannot really explain physical facts. In what follows, I challenge this common view. I argue that, in addition to its representational role, in modern physics mathematics is constitutive of the physical. Granted the mathematical constitution of the physical, I propose an account of explanation in which mathematical frameworks, structures, and facts explain physical facts. In this account, mathematical explanations of physical facts are either species of physical explanations of physical facts in which the mathematical constitution of some physical facts in the explanans are highlighted, or simply explanations in which the mathematical constitution of physical facts are highlighted. In highlighting the mathematical constitution of physical facts, mathematical explanations of physical facts deepen and increase the scope of the understanding of the explained physical facts. I argue that, unlike other accounts of mathematical explanations of physical facts, the proposed account is not subject to the objection that mathematics only represents the physical facts that actually do the explanation. I conclude by briefly considering the implications that the mathematical constitution of the physical has for the question of the unreasonable effectiveness of the use of mathematics in physics

The FIT Model - Fuel-cycle Integration and Tradeoffs

All mass streams from fuel separation and fabrication are products that must meet some set of product criteria – fuel feedstock impurity limits, waste acceptance criteria (WAC), material storage (if any), or recycle material purity requirements such as zirconium for cladding or lanthanides for industrial use. These must be considered in a systematic and comprehensive way. The FIT model and the “system losses study” team that developed it [Shropshire2009, Piet2010] are an initial step by the FCR&D program toward a global analysis that accounts for the requirements and capabilities of each component, as well as major material flows within an integrated fuel cycle. This will help the program identify near-term R&D needs and set longer-term goals. The question originally posed to the “system losses study” was the cost of separation, fuel fabrication, waste management, etc. versus the separation efficiency. In other words, are the costs associated with marginal reductions in separations losses (or improvements in product recovery) justified by the gains in the performance of other systems? We have learned that that is the wrong question. The right question is: how does one adjust the compositions and quantities of all mass streams, given uncertain product criteria, to balance competing objectives including cost? FIT is a method to analyze different fuel cycles using common bases to determine how chemical performance changes in one part of a fuel cycle (say used fuel cooling times or separation efficiencies) affect other parts of the fuel cycle. FIT estimates impurities in fuel and waste via a rough estimate of physics and mass balance for a set of technologies. If feasibility is an issue for a set, as it is for “minimum fuel treatment” approaches such as melt refining and AIROX, it can help to make an estimate of how performances would have to change to achieve feasibility

Voluntary Medical Male Circumcision: Strategies for Meeting the Human Resource Needs of Scale-Up in Southern and Eastern Africa

Kelly Curran and colleagues conducted a program review to identify human resource approaches that are being used to improve voluntary medical male circumcision volume and efficiency, identifying several innovative responses to human resource challenges

Alcohol use as a risk factor for tuberculosis – a systematic review

<p>Abstract</p> <p>Background</p> <p>It has long been evident that there is an association between alcohol use and risk of tuberculosis. It has not been established to what extent this association is confounded by social and other factors related to alcohol use. Nor has the strength of the association been established. The objective of this study was to systematically review the available evidence on the association between alcohol use and the risk of tuberculosis.</p> <p>Methods</p> <p>Based on a systematic literature review, we identified 3 cohort and 18 case control studies. These were further categorized according to definition of exposure, type of tuberculosis used as study outcome, and confounders controlled for. Pooled effect sizes were obtained for each sub-category of studies.</p> <p>Results</p> <p>The pooled relative risk across all studies that used an exposure cut-off level set at 40 g alcohol per day or above, or defined exposure as a clinical diagnosis of an alcohol use disorder, was 3.50 (95% CI: 2.01–5.93). After exclusion of small studies, because of suspected publication bias, the pooled relative risk was 2.94 (95% CI: 1.89–4.59). Subgroup analyses of studies that had controlled for various sets of confounders did not give significantly different results and did not explain the significant heterogeneity that was found across the studies.</p> <p>Conclusion</p> <p>The risk of active tuberculosis is substantially elevated in people who drink more than 40 g alcohol per day, and/or have an alcohol use disorder. This may be due to both increased risk of infection related to specific social mixing patterns associated with alcohol use, as well as influence on the immune system of alcohol itself and of alcohol related conditions.</p

Factive Scientific Understanding Without Accurate Representation

This paper analyzes two ways idealized biological models produce factive scientific understanding. I then argue that models can provide factive scientific understanding of a phenomenon without providing an accurate representation of the (difference-making) features of their real-world target system(s). My analysis of these cases also suggests that the debate over scientific realism needs to investigate the factive scientific understanding produced by scientists’ use of idealized models rather than the accuracy of scientific models themselves