Modality and constitution in distinctively mathematical explanations

Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, but not in their “reversals,” the empirical fact appealed to in the explanation is “understood to be constitutive of the physical task or arrangement at issue” in the explanandum. I argue that Lange’s reply is unsatisfactory because it leaves the crucial notion of being “understood to be constitutive of the physical task or arrangement” obscure in ways that fail to block “reversals” except by an apparent ad hoc stipulation or by abandoning the reliance on understanding and instead accepting a strong realism about essence

The directionality of distinctively mathematical explanations

In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each case by appeal to ontic facts that account for why the explanation is acceptable in one direction and unacceptable in the other direction. The mathematics involved in these examples cannot play this crucial normative role. While Lange's examples fail to demonstrate the existence of distinctively mathematical explanations, they help to emphasize that many superficially natural scientific explanations rely for their explanatory force on relations of stronger-than-natural necessity. These are not opposing kinds of scientific explanations; they are different aspects of scientific explanation

Mechanistic Levels, Reduction, and Emergence

We sketch the mechanistic approach to levels, contrast it with other senses of “level,” and explore some of its metaphysical implications. This perspective allows us to articulate what it means for things to be at different levels, to distinguish mechanistic levels from realization relations, and to describe the structure of multilevel explanations, the evidence by which they are evaluated, and the scientific unity that results from them. This approach is not intended to solve all metaphysical problems surrounding physicalism. Yet it provides a framework for thinking about how the macroscopic phenomena of our world are or might be related to its most fundamental entities and activities

Overlooked and Underpaid: Number of Low-Income Working Families Increases to 10.2 Million

Highlights 2007-10 trends in the number and percentage of working families with incomes below 200 percent of the poverty line by state and race/ethnicity, as well as the number of children affected. Examines income inequality by quintile and implications

Great Recession Hit Hard at America's Working Poor: Nearly 1 in 3 Working Families in United States Are Low-Income

Highlights findings on the 2009 increase in the number of low-income working families and their children, proportion of low-income working families by parents' race/ethnicity, and the growth of income inequality. Discusses policy implications

Low-Income Working Mothers and State Policy: Investing for a Better Economic Future

In 2012, there were more than 10 million low-income working families with children in the United States,and 39 percent were headed by working mothers. The economic conditions for these families have worsened since the onset of the recession; between 2007 and 2012, there was a four percentage-point increase in the share of female-headed working families that are low-income. Addressing challenges specific to these families will increase their economic opportunity, boost the economy and strengthen the fabric of communities across the nation.Public policy can play a critical role in our future prosperity by reversing this trend and improving outcomes for low-income working mothers. Of particular interest is how state governments can best invest in helping working mothers gain the education, skills and supports necessary to become economically secure and provide a strong economic future for their children. In this brief, we highlight the latest data from the Census Bureau's American Community Survey and recommend state government policies and actions that would facilitate the economic advancement of female-headed, low-income working families with children under age 18

Model and World: Generalizing the Ontic Conception of Scientific Explanation

Model and World defends a theory of scientific explanation that I call the “Generalized Ontic Conception” (GOC), according to which a model explains when and only when it provides (approximately) veridical information about the ontic structures on which the explanandum phenomenon depends. Causal and mechanistic explanations are species of GOC in which the ontic structures on which the explanandum phenomenon depends are causes and mechanisms, respectively, and the kinds of dependence involved are causal and constitutive/mechanistic, respectively. The kind of dependence relation about which information is provided determines the species of the explanation. This provides an intuitive typology of explanations and opens the possibility for non-causal, non-mechanistic explanations that provide information about noncausal, non-mechanistic kinds of dependence (Pincock 2015; Povich forthcoming a). What unites all these forms of explanation is that, by providing information about the ontic structures on which the explanandum phenomenon depends, they all can answer what-if-things-had-beendifferent questions (w-questions) about the explanandum phenomenon. This is what makes causal explanations, mechanistic explanations, and non-causal, non-mechanistic explanations all explanations. Furthermore, GOC is a generalized ontic conception of scientific explanation (Salmon 1984, 1989; Craver 2014). It is consistent with Craver\u27s claim that (2014), according to the ontic conception, commitments to ontic structures (like causes or mechanisms) are required to demarcate explanation from other scientific achievements. GOC demarcates explanatory from non-explanatory models in terms of ontic structures. For example, the distinction between explanatory and phenomenal models is cashed out in terms of the ontic structures about which information is conveyed: A phenomenal model provides information about the explanandum phenomenon, but not the ontic structures on which it depends. GOC is generalized because it says that commitments to more of the ontic than just the causal-mechanical – the traditional focus of the ontic conception – are required adequately to achieve this demarcation; attention to all ontic structures on which the explanandum depends is required. The relation between model and world required for explanation is elaborated in terms of information rather than mapping, reference, description, or similarity (Craver and Kaplan 2011; Kaplan 2011; Weisberg 2013). The latter concepts prove too strong, so will not count models as explanatory that in fact are. Take Kaplan and Craver\u27s (2011) model-to-mechanism-mapping (3M) principle. According to 3M, the variables in a mechanistic explanatory model must map to specific structural components and causal interactions of the explanandum phenomenon\u27s mechanism. However, you can mechanistically explain without referring to the explanandum\u27s mechanism or its components and their activities, for example, by describing what the mechanism is not like. This is a way of constraining or conveying information about a mechanism without actually mapping to, referring to, describing, representing, or being similar to it

Model-based Cognitive Neuroscience: Multifield Mechanistic Integration in Practice

Autonomist accounts of cognitive science suggest that cognitive model building and theory construction (can or should) proceed independently of findings in neuroscience. Common functionalist justifications of autonomy rely on there being relatively few constraints between neural structure and cognitive function (e.g., Weiskopf, 2011). In contrast, an integrative mechanistic perspective stresses the mutual constraining of structure and function (e.g., Piccinini & Craver, 2011; Povich, 2015). In this paper, I show how model-based cognitive neuroscience (MBCN) epitomizes the integrative mechanistic perspective and concentrates the most revolutionary elements of the cognitive neuroscience revolution (Boone & Piccinini, 2016). I also show how the prominent subset account of functional realization supports the integrative mechanistic perspective I take on MBCN and use it to clarify the intralevel and interlevel components of integration

The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation

An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory