Understanding the relationship between adult fish populations (the "stock") and the number of new fish entering the population (the "recruits") is essential for effective fisheries management. Traditionally, this relationship is represented by a stock-recruitment (SR) function, which is a simplified mathematical model that directly links stock size to recruitment. However, fish populations pass through several life stages, each stage influenced by unique population dynamic factors. Current SR functions often overlook these complexities, assuming that recruitment depends solely on the adult population (...) size. In this study, we use a multi-stage, age-structured discrete-time population dynamic model that accounts for all life stages and the transitions between them. We demonstrate that, in general, a closed-form, univariate SR function may not accurately represent the recruitment process when these life stages are considered. Instead, we identify specific mathematical conditions under which a SR function is equivalent to our multi-stage model. Our findings suggest a re-evaluation of conventional SR models, advocating for multi-stage approaches to support fisheries management decisions. (shrink)

It is a common criticism of presentism – the view according to which only the present exists – that it errs against truthmaker theory. Recent attempts to resolve the truthmaker objection against presentism proceed by restricting truthmaker maximalism (the view that all truths have truthmakers), maintaining that propositions concerning the past are not made true by anything, but are true nonetheless. Support for this view is typically garnered from the case for negative existential propositions, which some philosophers contend are exceptions (...) to truthmaker maximalism. In this article, we argue that a ‘no truthmakers’ approach to the truthmaker objection is critically flawed. (shrink)

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a σ₁-supremum (...) principle 'up-to-infinitesimals', and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is 'too strong' for finitism by reconsidering Rössler and Jeřábek's conclusions. (shrink)

윤리의 근본 참뜻을 공자.맹자의 사상과 저술, 삶의 일화를 인용하며 알기 쉽게 엮었다.

001. 성인, 이땅에 오다 002. 효의 참뜻 003. 오직 한 가지로 004. 나루터 005. 공자와 섭공의 대결 006. 고민하는 사마우 007. 광에서의 봉변 008. 모략받는 중궁 009. 은자의 독설 010. 인은 인이다 011. 노자를 찾아서 012. 광야를 헤매며 013. 재여의 낮잠 014. 천성을 전하는 목탁 015. 공자의 음악론은 곧 인생론 016. 하늘은 진리의 어머니 017. 외교상의 승리 018. 영원히 흐르는 것 019. 성인에의 길.

Although recent research suggests that women are underrepresented in philosophy after initial philosophy courses, there have been relatively few empirical investigations into the factors that lead to this early drop-off in women’s representation. In this paper, we present the results of empirical investigations at a large American public university that explore various factors contributing to women’s underrepresentation in philosophy at the undergraduate level. We administered climate surveys to hundreds of students completing their Introduction to Philosophy course and examined differences in (...) women’s and men’s feelings of belonging, comfort, and confidence in the philosophy classroom. We present findings suggesting various factors that contribute to women’s lower willingness to continue in philosophy compared to men’s, including perceptions about intuition-based methods in philosophy, the usefulness of the philosophy major, philosophy as a male discipline, and philosophical abilities as innate talents. We conclude by providing some suggestions for improving undergraduate philosophy courses in ways that would increase women’s willingness to continue in philosophy and may improve the courses for all students. (shrink)

The study of intellectual humility is still in its early stages and issues of definition and measurement are only now being explored. To inform and guide the process of defining and measuring this important intellectual virtue, we conducted a series of studies into the implicit theory – or ‘folk’ understanding – of an intellectually humble person, a wise person, and an intellectually arrogant person. In Study 1, 350 adults used a free-listing procedure to generate a list of descriptors, one for (...) each person-concept. In Study 2, 335 adults rated the previously generated descriptors by how characteristic each was of the target person-concept. In Study 3, 344 adults sorted the descriptors by similarity for each person-concept. By comparing and contrasting the three person-concepts, a complex portrait of an intellectually humble person emerges with particular epistemic, self-oriented, and other-oriented dimensions. (shrink)

Theories of consciousness have a long and controversial history. One well-known proposal — integrated information theory — has recently been labeled as ‘pseudoscience’, which has caused a heated open debate. Here we discuss the case and argue that the theory is indeed unscientific because its core claims are untestable even in principle.

Cheating in the undergraduate classroom is not a new problem, and it is recognized as one that is endemic to the education system. This paper examines the highly normative behavior of using unauthorized assistance (e.g., a solutions manual or a friend) on an individual assignment within the context of an upper division undergraduate course in engineering mechanics. The findings indicate that there are varying levels of accepting responsibility among the students (from denial to tempered to full) and that acceptance of (...) responsibility can lead to identification of learning and necessary behavioral changes. The findings have implications for institutions and engineering faculty, in particular the need for consistent academic integrity education and the teaching of professional integrity and ethics. (shrink)

In this enlightening book, Sam Harris argues that free will is an illusion but that this truth should not undermine morality or diminish the importance of social and political freedom; indeed, this truth can and should change the way we think about some of the most important questions in life.

Sam Harris dismantles the most common justification for religious faith--that a moral system cannot be based on science.

This article explores the process of teaching Christian theological ethics beyond the common focus on European and North American sources. In conversation with moves to decolonise university curricula, the article proposes a theology of listening, an example of a research seminar for master’s and doctoral students at the University of Aberdeen on Christian ethics beyond Europe and North America, and an exploration of broader challenges for the formation of the theologian. The article asks, what can we learn when we give (...) up power and control when teaching and learning theology? How can we shift our methods of knowing and practising theology? We write as theologians from India, Mexico, and the United States living in the United Kingdom. We reflect on forms of exclusion in theological method and formation that arise from colonising, systemic violence, and inequalities. The article considers intercultural challenges when encountering different methods of reflection on the Christian experience. In a search for a more profoundly theological approach, we propose listening to the other as integral to doing theology. In an intercultural move, we draw on Dietrich Bonhoeffer's theology of listening, proposing that theology must be an advent of voices from beyond our usual places and methods. (shrink)

Medical students lack opportunities to have authentic conversations with patients with cancer in busy hospitals. An improved understanding of what such communication might look like may provide a framework for end-of-life curricula. The authors performed thematic analysis using written correspondence between patient and student participants in the University of California, San Francisco’s Firefly Program whose letters discussed death or dying. Four themes emerged: (1) turmoil, (2) grief, (3) making peace, and (4) past, present, and future. Medical students expressed a fifth (...) theme: unmet student expectations. The study provides educators with a unique perspective to help inform curriculum development and patient care. (shrink)

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

This paper, co-authored by undergraduate students and their instructor part of an educational psychology seminar, describes a participatory curriculum design approach for preservice teacher education that focuses on the use of the principles of second-order cybernetics to teach about teaching and learning. Using elements of an Open Source Educational Processes framework, our Spring ESEPSY2309 section created project-based collective hive minds of preservice teachers, relying on a cybernetic approach at the crossroads of Gregory Bateson and Gordon Pask's theories. The classroom community (...) used four innovative tool-mediated pillars to guide collaborative activity: 1) Live-chatting using the Reddit social media platform, 2) observation of the lives, strategies, and practices used by teachers and students in their own social networks through Soundcloud podcasting to expand their own perceptions of pedagogies and best practices that they could employ in their careers, 3) open-ended paper writing, exploring sources beyond the object language provided by the textbook through extensive dyadic conversations with the instructor, and 4) training in the use of the Alice 3 game creation tool for block programming enabling the accumulation of competence in designing classroom systems that may treat students these undergraduates would soon teach as active historical agents in learning environments, combining skills from varied subjects into transdisciplinary educational experiences. We showcase outcomes of our class projects using a narrative inquiry to describe podcast episodes, a topic network analysis to illustrate the expansive nature of Open Source writing activity, and a visual depiction of our class Alice 3 games. (shrink)

In conversation, we often do not acknowledge what we jointly know to be true. My aim in this paper is to identify a distinctive kind of non-acknowledgment norm, open secrecy, and analyze how such norms constrain our speech. I argue that open secrecy norms are structurally different from other everyday non-acknowledgment norms. Open secrecy norms iterate: when p is an open secret, then there’s a norm not to acknowledge that p, and this norm is itself an open secret. The non-acknowledgment (...) at issue in open secrecy norms, I argue, motivates a more complex understanding of discourse. When interlocutors are conforming to open secrecy norms, they rely on at least two disjoint common grounds, one of which has a privileged status. To understand why and how it is privileged, I develop Erving Goffman’s notion of defining a social interaction. Finally, I show how strategic speakers can exploit the structure of open secrecy in order to both communicate about the open secret and shield themselves from retaliation for what they communicate. (shrink)

The distinction between perception and cognition frames countless debates in philosophy and cognitive science. But what, if anything, does this distinction actually amount to? In this introductory article, we summarize recent work on this question. We first briefly consider the possibility that a perception-cognition border should be eliminated from our scientific ontology, and then introduce and critically examine five positive approaches to marking a perception–cognition border, framed in terms of phenomenology, revisability, modularity, format, and stimulus-dependence.

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

This paper develops an analysis of non-epistemic deniability. On my analysis, a speaker has non-epistemic deniability for G-ing when non-acknowledgment social norms make it impermissible for others to retaliate against the speaker for G-ing. I identify two kinds of non-acknowledgment norms that generate non-epistemic deniability: two-tracking norms, which function to contain conflict within a group, and open secrecy norms, which function to inhibit the group from acting on shared knowledge. Narrowly, this paper builds on Alexander Dinges and Julia Zakkou’s recent (...) landmark analysis of deniability. Dinges and Zakkou argue that non-epistemic deniability does not exist. I disagree. But I also use their account of epistemic deniability in order to motivate my own analysis of non-epistemic deniability. Broadly, my paper provides a case study in how speakers strategically leverage non-acknowledgment norms in order to protect their own interests at the expense of others’. (shrink)

Jerry Fodor deemed informational encapsulation ‘the essence’ of a system’s modularity and argued that human perceptual processing comprises modular systems, thus construed. Nowadays, his conclusion is widely challenged. Often, this is because experimental work is seen to somehow demonstrate the cognitive penetrability of perceptual processing, where this is assumed to conflict with the informational encapsulation of perceptual systems. Here, I deny the conflict, proposing that cognitive penetration need not have any straightforward bearing on the conjecture that perceptual processing is composed (...) of nothing but informationally encapsulated modules, the conjecture that each and every perceptual computation is performed by an informationally encapsulated module, and the consequences perceptual encapsulation was traditionally expected to have for a perception-cognition border, the epistemology of perception and cognitive science. With these points in view, I propose that particularly plausible cases of cognitive penetration would actually seem to evince the encapsulation of perceptual systems rather than refute/problematize this conjecture. (shrink)

It is often claimed that pre-attentive vision has an ‘iconic’ format. This is seen to explain pre-attentive vision's characteristically high processing capacity and to make sense of an overlap in the mechanisms of early vision and mental imagery. But what does the iconicity of pre-attentive vision amount to? This paper considers two prominent ways of characterising pre-attentive visual icons and argues that neither is adequate: one approach renders the claim ‘pre-attentive vision is iconic’ empirically false while the other obscures its (...) ability to do the explanatory work, which motivates positing pre-attentive visual icons in the first place. With this noted, I introduce the notion of an ‘Analogue Map’ and argue that it provides a superior characterisation of pre-attentive vision's iconicity. I then argue that this forces a reassessment of debates which have traditionally presupposed the iconicity of pre-attentive vision, emphasising ramifications for the viability of a format-based perception-thought border. (shrink)

According to a number of approaches in theoretical physics, spacetime does not exist fundamentally. Rather, spacetime exists by depending on another, more fundamental, non-spatiotemporal structure. A prevalent opinion in the literature is that this dependence should not be analyzed in terms of composition. We should not say, that is, that spacetime depends on an ontology of non-spatiotemporal entities in virtue of having them as parts. But is that really right? On the contrary, we argue that a mereological approach to dependent (...) spacetime is not only viable, but promises to enhance our understanding of the physical situation. (shrink)

This paper offers a new account of metaphysical explanation. The account is modelled on Kitcher’s unificationist approach to scientific explanation. We begin, in Sect. 2, by briefly introducing the notion of metaphysical explanation and outlining the target of analysis. After that, we introduce a unificationist account of metaphysical explanation before arguing that such an account is capable of capturing four core features of metaphysical explanations: irreflexivity, non-monotonicity, asymmetry and relevance. Since the unificationist theory of metaphysical explanation inherits irreflexivity and non-monotonicity (...) directly from the unificationist theory of scientific explanation that underwrites it, we focus on demonstrating how the account can secure asymmetry and relevance. (shrink)

We develop a new version of the causal theory of spacetime. Whereas traditional versions of the theory seek to identify spatiotemporal relations with causal relations, the version we develop takes causal relations to be the grounds for spatiotemporal relations. Causation is thus distinct from, and more basic than, spacetime. We argue that this non-identity theory, suitably developed, avoids the challenges facing the traditional identity theory.

Inquiry aims at knowledge. Your inquiry into a question succeeds just in case you come to know the answer. However, combined with a common picture on which misleading evidence can lead knowledge to be lost, this view threatens to recommend a novel form of dogmatism. At least in some cases, individuals who know the answer to a question appear required to avoid evidence bearing on it. In this paper, we’ll aim to do two things. First, we’ll present an argument for (...) this novel form of dogmatism and show that it presents a substantive challenge. Second, we’ll consider a way those who take knowledge to be the aim of inquiry can mount a response. In the course of doing so, we’ll try to get clearer on the normative connections between inquiry, knowledge and evidence gathering. (shrink)

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

Taking their motivation from the perceived failure of the reductive physicalist project concerning consciousness, panpsychists ascribe subjectivity to fundamental material entities in order to account for macro-consciousness. But there exists an unresolved tension within the mainstream panpsychist position, the seriousness of which has yet to be appreciated. I capture this tension as a dilemma, and offer advice to panpsychists on how to resolve it. The dilemma is as follows: Panpsychists take the micro-material realm to feature phenomenal properties, plus micro-subjects to (...) whom these properties belong. However, it is impossible to explain the generation of a macro-subject (like one of us) in terms of the assembly of micro-subjects, for, as I show, subjects cannot combine. Therefore the panpsychist explanatory project is derailed by the insistence that the world’s ultimate material constituents are subjects of experience. The panpsychist faces a choice of giving up her explanatory ambitions, or of giving up the claim that the ultimates are subjects. I argue that the latter option is preferable, leading to neutral monism, on which phenomenal qualities are irreducible but subjects are reducible. So panpsychists should be neutral monists. (shrink)

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment of the problems raised (...) by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

The theoretical virtue of parsimony values the minimizing of theoretical commitments, but theoretical commitments come in two kinds : ontological and ideological. While the ontological commitments of a theory are the entities it posits, a theory’s ideological commitments are the primitive concepts it employs. Here, I show how we can extend the distinction between quantitative and qualitative parsimony, commonly drawn regarding ontological commitments, to the domain of ideological commitments. I then argue that qualitative ideological parsimony is a theoretical virtue. My (...) defense proceeds by demonstrating the merits of qualitative ideological parsimony and by showing how the qualitative conception of ideological parsimony undermines two notable arguments from ideological parsimony: David Lewis’ defense of modal realism and Ted Sider’s defense of mereological nihilism. (shrink)

It has been hypothesized that our believing that, or its seeming to us as though, the world is in some way dynamical partially explains (and perhaps rationalizes) future-bias. Recent work has, in turn, found a correlation between future-bias and near-bias, suggesting that there is a common explanation for both. Call the claim that what partially explains our being both future- and near-biased is our believing/it seeming to us as though the world is dynamical, the dynamical explanation. We empirically test two (...) versions of the dynamical explanation. The first is the moving ego explanation—according to which it is our belief that the ego moves, or our phenomenology as of the ego moving, that jointly (partially) explains future- and near-bias. The second is the moving time explanation—according to which it is our belief that time robustly passes, or our phenomenology as of robust passage, which jointly (partially) explain future- and near-bias. We found no evidence in favour of either explanation. (shrink)

In non‐literal uses of language, the content an utterance communicates differs from its literal truth conditions. Loose talk is one example of non‐literal language use (amongst many others). For example, what a loose utterance of (1) communicates differs from what it literally expresses: (1) Lena arrived at 9 o'clock. Loose talk is interesting (or so I will argue). It has certain distinctive features which raise important questions about the connection between literal and non‐literal language use. This paper aims to (i.) (...) introduce a range of novel data demonstrating certain overlooked features of loose talk, and (ii.) develop a new theory of the phenomenon which accounts for these data. In particular, this theory is motivated by the need to explain minimal pairs such as (2)-(3): (2) Lena arrived at 9 o'clock, but she did not arrive at 9 o'clock exactly. (3) ?? Lena did not arrive at 9 o'clock exactly, but she arrived at 9 o'clock. (2) and (3) agree in their truth conditions. Yet they differ in felicity. As such, they constitute a problem for any account which hopes to predict the acceptability of the loose use of a sentence from its truth conditions and the context of utterance alone. Instead, it will be argued, to explain loose talk phenomena we must posit an additional layer of meaning outstripping truth conditions. This layer of meaning is shown to exhibit a range of properties, all of which point to its being semantically encoded. Thus, if correct, the theory provides a new example of how semantic meaning must extend beyond literal, truth‐conditional content. (shrink)

Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.

This paper refines a controversial proposal: that core systems belong to a perceptual kind, marked out by the format of its representational outputs. Following Susan Carey, this proposal has been understood in terms of core representations having an iconic format, like certain paradigmatically perceptual outputs. I argue that they don’t, but suggest that the proposal may be better formulated in terms of a broader analogue format type. Formulated in this way, the proposal accommodates the existence of genuine icons in perception, (...) and avoids otherwise troubling objections. (shrink)

Many philosophers have thought that our folk, or pre-reflective, view of persistence is one on which objects endure. This assumption not only plays a role in disputes about the nature of persistence itself, but is also put to use in several other areas of metaphysics, including debates about the nature of change and temporal passage. In this paper, we empirically test three broad claims. First, that most people (i.e. most non-philosophers) believe that, and it seems to them as though, objects (...) persist by enduring rather than perduring. Second, that most people have a view of change on which enduring but not perduring objects count as changing. Third, that one reason why the folk represent time as dynamical is because it seems to them, and they believe that, they endure through time. We found no evidence to support these claims. While there are certainly plenty of ‘folk’ endurantists in the population we tested, there are also plenty of ‘folk’ perdurantists. We did not find robust evidence that a majority of people believed that, or it seemed to them as though, objects endure rather than perdure. We conclude that many arguments in favour of endurantism that appeal to folk beliefs about, or experiences of, persisting objects and change rest on views about those beliefs and experiences that are empirically unsupported. There is no evidence to suggest that endurantism is the folk friendly view of persistence, and so we should stop treating it as such without argument. (shrink)

Inquiry aims at knowledge. Your inquiry into a question succeeds just in case you come to know the answer. However, combined with a common picture on which misleading evidence can lead knowledge to be lost, this view threatens to recommend a novel form of dogmatism. At least in some cases, individuals who know the answer to a question appear required to avoid evidence bearing on it. In this paper, we’ll aim to do two things. First, we’ll present an argument for (...) this novel form of dogmatism and show that it presents a substantive challenge. Second, we’ll consider a way those who take knowledge to be the aim of inquiry can mount a response. In the course of doing so, we’ll try to get clearer on the normative connections between inquiry, knowledge and evidence gathering. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...) appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)

It has been claimed that naïve realism predicts phenomenological similarities where there are none and, thereby, mischaracterises the phenomenal character of perceptual experience. If true, this undercuts a key motivation for the view. Here, we defend naïve realism against this charge, proposing that such arguments fail (three times over). In so doing, we highlight a more general problem with critiques of naïve realism that target the purported phenomenological predictions of the view. The problem is: naïve realism, broadly construed, doesn’t make (...) phenomenological predictions of the required sort. So, as a result, opponents must resign themselves to attacking specific incarnations of naïve realism, or approach matters quite differently. (shrink)

According to the modal view, essence admits of reductive analysis in exclusively modal terms. Fine (1994) argues that modal view delivers an inadequate analysis of essence. This paper defends the modal view from Fine's challenge. This defense proceeds by examining the disagreement between Finean primitivists and Quinean eliminativists about essence. In order to model this disagreement, a distinction between essence and a separable concept, nature, is required. This distinction is then used to show that Fine's challenge is misdirected and therefore (...) unsuccessful. (shrink)

It is plausible that the models of scientific theories correspond to possibilities. But how do we know which models of which scientific theories so correspond? This paper provides a novel proposal for guiding belief about possibilities via scientific theories. The proposal draws on the notion of an effective theory: a theory that applies very well to a particular, restricted domain. We argue that it is the models of effective theories that we should believe correspond, at least in part, to possibilities. (...) It is thus effective theories that should guide modal reasoning in science. (shrink)

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

This paper develops an account of pluralities based on the following simple claim: some things are nothing over and above the individual things they comprise. For some, this may seem like a mysterious statement, perhaps even meaningless; for others, like a truism, trivial and inferentially inert. I show that neither reaction is correct: the claim is both tractable and has important consequences for a number of debates in philosophy.