Psychologists have had very little to say about things. Things are one thing, people are another. There is now, however, a growing recognition of the importance of things within human psychology. But, in cognitive theory, the meanings of things are usually radically subjectivized. ‘Their’ meanings are really ‘our’ meanings that we mentally project upon them. James Gibson’s concept of affordances was an attempt to avoid subject–object dualism by defining the meanings of things-what we can do with them-as properties of the (...) object but defined relative to the agent. Critics have rightly objected that Gibson himself, nevertheless, overly objectified or reified affordances. Yet the affordances of many objects in the human world are objective, or, better, impersonal. The present chapter, however, is concerned with such ‘canonical affordances’-the things that things are for. But, as it argues, this kind of ‘objectivity’ must itself be understood in relation to other objects and events, and other people. (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)

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. 1 Introduction 2 Particle physics: a case study 3 Three kinds of simplicity 4 Explanatory power 5 Explanation and non-observation 6 Parsimony and scientific methodology 7 Conclusions. (shrink)

Philosophical theories of counterfactuals have had relatively little to say about counterfactual reasoning in mathematics. Partly this is because most mathematical counterfactuals seem also to be counterpossibles, in that their antecedents deny some necessary truth. In this chapter, I delineate several different categories of mathematical counterfactual (or “countermathematical”) and then examine in detail a case study from mathematical practice that features counterfactual reasoning about “spoof perfect” numbers. I argue that reasoning about spoof perfect numbers presents both a challenge to philosophical (...) analyses of counterfactuals and a resource for thinking more productively about the role of counterfactual reasoning in mathematics. (shrink)

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)

This paper examines relationships between accountants’ personal values and their moral reasoning. In particular, we hypothesize that there is an inverse relationship between accountants’ “Conformity” values and principled moral reasoning. This investigation is important because the literature suggests that conformity with rule-based standards may be one reason for professional accountants’ relatively lower scores on measures of moral reasoning (Abdolmohammadi et al. J Bus Ethics 16 (1997) 1717). We administered the Rokeach Values Survey (RVS) (Rokeach: 1973, The Nature of Human Values (...) (The Free Press, New York)) and the Defining Issues Test (DIT) (Rest: 1979, Development in Judgment Moral Issues (University of Minnesota Press, Minneapolis, MN)) to164 graduating accounting students enrolled in capstone courses at two universities in the Northeastern United States. As potential entrants into the accounting profession, these subjects bring their values and moral reasoning to bear on attitudes and behaviors in the workplace. We find a highly significant inverse relationship between “Conformity” values and principled moral reasoning (i.e., those who prefer Conformity values have lower levels of moral reasoning). However, we also find that accounting students as a group do not prefer Conformity values above other values such as Self-actualization and Idealism, and we find positive relationships between Self-actualization and Idealism values and moral reasoning. Implications for values and ethics research are discussed. (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)

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)

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)

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)

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)

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)

Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. Fitch on (...) consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)

When I started the book, I thought that if there are beliefs, then they are brain states. I still believe that. I express three caveats about the book.

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)

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)

In 'Philosophy and the Mirror of Nature' Richard Rorty presented his provocation and influential vision of the post-philosophical culture, calling upon professional philosophers to accept that epistemology is dead, that the analytic method is a myth, and that philosophy and science are merely forms of literature.

Robin Donkin was an exceptional scholar in the field of historical geography, particularly concerning Latin America and the domestication of plants and animals globally. His early research was on the effect of the Cistercians on medieval landscape, and he held posts at the University of Edinburgh and the University of Brimingham. Donkin then lectured in Latin American geography at the University of Cambridge. He was a Fellow of Jesus College, Cambridge and was elected as a Fellow of the British Academy (...) in 1985. Obituary by Alan R. H. Baker FBA. (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 core thesis of Malebranche’s doctrine of occasionalism is that God is the sole true cause, where a true cause is one that has the power to initiate change and for which the mind perceives a necessary connection between it and its effects. Malebranche gives two separate arguments for his core thesis, T, based on necessary connection and on divine power respectively. The standard view is that these two arguments are necessary to establish T. I argue for a reinterpretation of (...) Malebranche’s strategy, according to which the Necessary Connection Argument alone is sufficient to establish T. The Divine Power Argument, which is anyway weaker, is needed not to support T but to bridge the gap between T and full-fledged occasionalism. Specifically, it is needed to rule out the existence of causal powers in nature, a scenario which is consistent with T but inconsistent with occasionalism. (shrink)

The core thesis of Malebranche’s doctrine of occasionalism is that God is the sole true cause, where a true cause is one that has the power to initiate change and for which the mind perceives a necessary connection between it and its effects. Malebranche gives two separate arguments for his core thesis, T, based on necessary connection and on divine power respectively. The standard view is that these two arguments are necessary to establish T. I argue for a reinterpretation of (...) Malebranche’s strategy, according to which the Necessary Connection Argument alone is sufficient to establish T. The Divine Power Argument, which is anyway weaker, is needed not to support T but to bridge the gap between T and full-fledged occasionalism. Specifically, it is needed to rule out the existence of causal powers in nature, a scenario which is consistent with T but inconsistent with occasionalism. (shrink)

Book Information The Foundations of Mathematics in the Theory of Sets. The Foundations of Mathematics in the Theory of Sets J. P. Mayberry Cambridge Cambridge University Press 2000 xx + 424 Hardback US$80.00 By J. P. Mayberry. Cambridge University Press. Cambridge. Pp. xx + 424. Hardback:US$80.00.

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)

In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness of the overall argument. In this discussion (...) I offer a defense of the Burgess-Rosen argument against Liggins’s objection. I show how plausible versions of the argument can be constructed based on either of two interpretations of mathematical acceptability, and I locate the argument in the space of contemporary anti-nominalist views. (shrink)

In their paper, “Vexing Expectations,” Nover and Hájek (2004) present an allegedly paradoxical betting scenario which they call the Pasadena Game (PG). They argue that the silence of standard decision theory concerning the value of playing PG poses a serious problem. This paper provides a threefold response. First, I argue that the real problem is not that decision theory is “silent” concerning PG, but that it delivers multiple conflicting verdicts. Second, I offer a diagnosis of the problem based on the (...) insight that standard decision theory is, rightly, sensitive to order. Third, I describe a new betting scenario—the Alternating St. Petersburg Game—which is genuinely paradoxical. Standard decision theory is silent on the value of playing this game even if restrictions are placed on the order in which the various alternative payoffs are summed. †To contact the author, please write to: Department of Philosophy, Swarthmore College, Swarthmore, PA 19081; e-mail: [email protected]. (shrink)

According to Malebranche’s occasionalism, all cases of causation in the world are due to the action of God’s will. These actions are divided into "particular volitions" and "general volitions". There has been sharp disagreement in the secondary literature concerning the nature of general volitions, for Malebranche. One side claims that general volitions are volitions of wide scope which cover a multiplicity of potential situations. The other side claims that general volitions are specific but fall under the scope of broader laws (...) of nature. I draw on the quantifier apparatus of modern predicate logic to highlight the differences between the two views, which I refer to as the Universality view and the Regularity view respectively. I also outline a third ‘Hybrid’ view that borrows elements of each. I conclude that there is a fundamental ambiguity in Malebranche’s account of general volitions which prevents any one account from fully fitting with Malebranche’s remarks. (shrink)