• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer (...) has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks.. (shrink)

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure (...) cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Imagination has been assigned an important explanatory role in a multitude of philosophical contexts. This paper examines four such contexts: mindreading, pretense, our engagement with fiction, and modal epistemology. Close attention to each of these contexts suggests that the mental activity of imagining is considerably more heterogeneous than previously realized. In short, no single mental activity can do all the explanatory work that has been assigned to imagining.

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

The modern Everett interpretation of quantum mechanics describes an emergent multiverse. The goal of this paper is to provide a perspicuous characterisation of how the multiverse emerges making use of a recent account of (weak) ontological emergence. This will be cashed out with a case study that identifies decoherence as the mechanism for emergence. The greater metaphysical clarity enables the rebuttal of critiques due to Baker (2007) and Dawid and Th\'ebault (2015) that cast the emergent multiverse ontology as incoherent; responses (...) are also offered to challenges to the Everettian approach from Maudlin (2010) and Monton (2013). (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

The interventionist account of causal explanation, in the version presented by Jim Woodward, has been recently claimed capable of buttressing the widely felt—though poorly understood—hunch that high-level, relatively abstract explanations, of the sort provided by sciences like biology, psychology and economics, are in some cases explanatorily optimal. It is the aim of this paper to show that this is mistaken. Due to a lack of effective constraints on the causal variables at the heart of the interventionist causal-explanatory scheme, as presently (...) formulated it is either unable to prefer high-level explanations to low, or systematically overshoots, recommending explanations at so high of a level as to be virtually vacuous. (shrink)

There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...) options, including their accounts of what X is, the examples supporting each theory, and the reasons for identifying the science of X with (most or all of) mathematics. Some comparison of the options is undertaken, but the main aim is to display the spectrum of viable alternatives to Platonism and nominalism. It is explained how these views answer Frege’s widely accepted argument that arithmetic cannot be about real features of the physical world, and arguments that such mathematical objects as large infinities and perfect geometrical figures cannot be physically realized. (shrink)

What is consciousness and why is it so philosophically and scientifically puzzling? For many years philosophers approached this question assuming a standard physicalist framework on which consciousness can be explained by contemporary physics, biology, neuroscience, and cognitive science. This book is a debate between two philosophers who are united in their rejection of this kind of "standard" physicalism - but who differ sharply in what lesson to draw from this. Amy Kind defends dualism 2.0, a thoroughly modern version of dualism (...) (the theory that there are two fundamentally different kinds of things in the world: those that are physical and those that are mental) decoupled from any religious or non-scientific connotations. Daniel Stoljar defends non-standard physicalism, a kind of physicalism different from both the standard version and dualism 2.0. The book presents a cutting-edge assessment of the philosophy of consciousness and provides a glimpse at what the future study of this area might bring. (shrink)

The puzzle of imaginative desire arises from the difficulty of accounting for the surprising behaviour of desire in imaginative activities such as our engagement with fiction and our games of pretend. Several philosophers have recently attempted to solve this puzzle by introducing a class of novel mental states—what they call desire-like imaginings or i-desires. In this paper, I argue that we should reject the i-desire solution to the puzzle of imaginative desire. The introduction of i-desires is both ontologically profligate and (...) unnecessary, and, most importantly, fails to make sense of what we are doing in the imaginative contexts in question. (shrink)

We often talk of people as being more or less imaginative than one another – as being better or worse at imagining – and we also compare various feats of imagination to one another in terms of how easy or hard they are. Facts such as these might be taken to suggest that imagination is often implicitly understood as a skill. This implicit understanding, however, has rarely (if ever) been made explicit in the philosophical literature. Such is the task of (...) this chapter. I first attempt to flesh out several conditions for an activity to count as a skill. I then attempt to show how imagination can meet such conditions. The chapter concludes with an attempt to answer various worries that might be raised to the claim that imagination should be thought of as a skill. (shrink)

According to representationalism, the phenomenal character of a mental state reduces to its intentional content. Although representationalism seems plausible with respect to ordinary perceptual states, it seems considerably less plausible for states like moods. Here the problem for representationalism arises largely because moods seem to lack intentional content altogether. In this paper, I explore several possible options for identifying the intentional content of moods and suggest that none of them is wholly satisfactory. Importantly, however, I go on to argue that (...) the plausibility of representationalism should not be seen to rest on the question of whether moods have intentional content but rather on the question of whether the intentional content of moods, were there any, would be sufficient to determine their phenomenal character. As I argue, even if we concede to the representationalist that moods have intentional content, their phenomenal character outstrips their intentional content; thus, the representationalist reduction cannot succeed. Ultimately, then, I conclude that moods do indeed pose a serious objection to the representationalist theory. (shrink)

Nearly all defences of the agent-causal theory of free will portray the theory as a distinctively libertarian one — a theory that only libertarians have reason to accept. According to what I call ‘the standard argument for the agent-causal theory of free will’, the reason to embrace agent-causal libertarianism is that libertarians can solve the problem of enhanced control only if they furnish agents with the agent-causal power. In this way it is assumed that there is only reason to accept (...) the agent-causal theory if there is reason to accept libertarianism. I aim to refute this claim. I will argue that the reasons we have for endorsing the agent-causal theory of free will are nonpartisan. The real reason for going agent-causal has nothing to do with determinism or indeterminism, but rather with avoiding reductionism about agency and the self. As we will see, if there is reason for libertarians to accept the agent-causal theory, there is just as much reason for compatibilists to accept it. It is in this sense that I contend that if anyone should be an agent-causalist, then everyone should be an agent-causalist. (shrink)

Multiple realisation prompts the question: how is it that multiple systems all exhibit the same phenomena despite their different underlying properties? In this paper I develop a framework for addressing that question and argue that multiple realisation can be reductively explained. I illustrate this position by applying the framework to a simple example – the multiple realisation of electrical conductivity. I defend my account by addressing potential objections:contra Polger and Shapiro, Batterman, and Sober, I claim that multiple realisation is commonplace, (...) that it can be reductively explained, but that it requires asui generisreductive explanatory strategy. (shrink)

Scientific realists don’t standardly discriminate between, say, biology and fundamental physics when deciding whether the evidence and explanatory power warrant the inclusion of new entities in our ontology. As such, scientific realists are committed to a lush rainforest of special science kinds (Ross, 2000). Viruses certainly inhabit this rainforest – their explanatory power is overwhelming – but viruses’ properties can be explained from the bottom up: reductive explanations involving amino acids are generally available. However, reduction has often been taken to (...) lead to a metaphysical downgrading, so how can viruses keep their place in the rainforest? In this paper, we show how the inhabitants of the rainforest can be inoculated against the eliminative threat of reduction: by demonstrating that they are emergent. According to our account, emergence involves a screening off condition as well as novelty. We go on to demonstrate that this account of emergence, which is compatible with theoretical reducibility, satisfies common intuitions concerning what should and shouldn’t count as real: viruses are emergent, as are trout and turkeys, but philosophically gerrymandered objects like trout-turkeys do not qualify. (shrink)

Both realist and anti-realist accounts of natural kinds possess prima facie virtues: realists can straightforwardly make sense of the apparent objectivity of the natural kinds, and anti-realists, their knowability. This paper formulates a properly anti-realist account designed to capture both merits. In particular, it recommends understanding natural kinds as ‘categorical bottlenecks,’ those categories that not only best serve us, with our idiosyncratic aims and cognitive capacities, but also those of a wide range of alternative agents. By endorsing an ultimately subjective (...) categorical principle, this view sidesteps epistemological difficulties facing realist views. Yet, it nevertheless identifies natural kinds that are fairly, though not completely, stance-independent or objective. (shrink)

The universality of critical phenomena is best explained by appeal to the Renormalisation Group (RG). Batterman and Morrison, among others, have claimed that this explanation is irreducible. I argue that the RG account is reducible, but that the higher-level explanation ought not to be eliminated. I demonstrate that the key assumption on which the explanation relies – the scale invariance of critical systems – can be explained in lower-level terms; however, we should not replace the RG explanation with a bottom-up (...) account, rather we should acknowledge that the explanation appeals to dependencies which may be traced down to lower levels. (shrink)

Journal of Applied Philosophy, EarlyView.

Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.

David Lewis has argued that “having an experience is the best way or perhaps the only way, of coming to know what that experience is like”; when an experience is of a sufficiently new sort, mere science lessons are not enough. Developing this Lewisian line, L.A. Paul has suggested that some experiences are epistemically transformative. Until an individual has such an experience it remains epistemically inaccessible to her. No amount of stories and theories and testimony from others can teach her (...) what it is like to have it, nor is she able to achieve this knowledge by way of imaginative projection. It’s this last claim that is the focus of this paper. In particular, I explore the case for the claim that some experiences are in principle imaginatively inaccessible to someone who has not undergone the experience itself or one relevantly similar. As I will suggest, this case is not as strong as is often thought. Close attention to the mechanisms of imagination, and in particular, to cases of skilled imaginers, suggests how techniques of imaginative scaffolding can sometimes be used to give us epistemic access to experiences we have not had, even ones that are radically different from any that we have had before. As a result, considerably fewer experiences remain imaginatively out of reach than proponents of transformative experience would have us believe. Experience may well be the best teacher, but this paper aims to show that imagination comes in a close second. (shrink)

Can one have imaginative access to experiential perspectives vastly different from one’s own? Can one successfully imagine what it’s like to live a life very different from one’s own? These questions are particularly pressing in contemporary society as we try to bridge racial, ethnic, and gender divides. Yet philosophers have often expressed considerable pessimism in this regard. It is often thought that the gulf between vastly different experiential perspectives cannot be bridged. This chapter explores the case for this pessimism. Though (...) the case is often less implicit, the chapter identifies two different arguments that can be found in the literature: the Epistemic Arrogance argument and the Too Big a Gulf argument. Both arguments are found to be considerably weaker than is usually thought. But even if the case for pessimism is unsuccessful, discussion of that case suggests the importance of treading carefully in taking up imaginative explorations of different experiential perspectives. The chapter thus concludes with a cautionary note in this regard. (shrink)

Underlying much current work in philosophy of imagination is the assumption that imagination is a skill. This assumption seems to entail not only that facility with imagining will vary from one person to another, but also that people can improve their own imaginative capacities and learn to be better imaginers. This paper takes up this issue. After showing why this is properly understood as a philosophical question, I discuss what it means to say that one imagining is better than another (...) and then discuss the kinds of imagination training and techniques that might be employed in an effort to get better at imagining. The discussion of these techniques draws insight from consideration of other skills-based activities, as well as from consideration of the creation of art and our engagement with literature and poetry. Over the course of this discussion, we also gain further insight into the nature of imagination. (shrink)

How are we to understand the phenomenology of imagining? Attempts to answer this question often invoke descriptors concerning the “vivacity” or “vividness” of our imaginative states. Not only are particular imaginings often phenomenologically compared and contrasted with other imaginings on grounds of how vivid they are, but such imaginings are also often compared and contrasted with perceptions and memories on similar grounds. Yet however natural it may be to use “vividness” and cognate terms in discussions of imagination, it does not (...) take much reflection to see that these terms are ill understood. In this paper, I review both some relevant empirical literature as well as the philosophical literature attempt to get a handle on what it could mean, in an imaginative context, to talk of vividness. As I suggest, this notion ultimately proves to be so problematic as to be philosophically untenable. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

This paper critiques the new mechanistic explanatory program on grounds that, even when applied to the kinds of examples that it was originally designed to treat, it does not distinguish correct explanations from those that blunder. First, I offer a systematization of the explanatory account, one according to which explanations are mechanistic models that satisfy three desiderata: they must 1) represent causal relations, 2) describe the proper parts, and 3) depict the system at the right ‘level.’ Second, I argue that (...) even the most developed attempts to fulfill these desiderata fall short by failing to appropriately constrain explanatorily apt mechanistic models. -/- *This paper used to be called "The Emperor's New Mechanisms". (shrink)

In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. It offers a semipopular introduction to an objective Bayesian/logical probabilist account of scientific reasoning, arguing that inductive reasoning is logically justified (though actually existing science sometimes falls short). Its account of mathematics is Aristotelian realist.

According to representationalism, the qualitative character of our phenomenal mental states supervenes on the intentional content of such states. Strong representationalism makes a further claim: the qualitative character of our phenomenal mental states _consists in_ the intentional content of such states. Although strong representationalism has greatly increased in popularity over the last decade, I find the view deeply implausible. In what follows, I will attempt to argue against strong representationalism by a two-step argument. First, I suggest that strong representationalism must (...) be _unrestricted_ in order to serve as an adequate theory of qualia, i.e., it must apply to all qualitative mental states. Second, I present considerations to show that an unrestricted form of strong representationalism is problematic. (shrink)

In this essay, the focus is not on what imagination is but rather on what it is like. Rather than exploring the various accounts of imagination on offer in the philosophical literature, we will instead be exploring the various accounts of imaginative experience on offer in that literature. In particular, our focus in what follows will be on three different sorts of accounts that have played an especially prominent role in philosophical thinking about these issues: the impoverishment view (often associated (...) with Hume), the will-dependence view (often associated with Wittgenstein), and the nonexistence view (often associated with Sartre). While there are important insights to be drawn from each of these views, each seems to me to be importantly flawed in various ways. As I will suggest, close examination reveals that none of them gives us an adequate account of the character of imaginative experience. Ultimately, in the final section of this paper, I briefly explore what their failure teaches us about the project of giving an account of imaginative experience. (shrink)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...) is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (shrink)

What is it about a person's becoming an adult that makes it generally inappropriate to treat that person paternalistically any longer? The Standard View holds that a mere difference in age or stage of life cannot in itself be morally relevant, but only matters insofar as it is correlated with the development of capacities for mature practical reasoning. This paper defends the contrary view: two people can have all the same general psychological attributes and yet the mere fact that one (...) person is at the beginning of a life and another in the middle of one can justify treating the younger person more paternalistically than the older one. Recognising the moral relevance of age, moreover, is crucial if one is to accommodate both the liberal moral ideal of respect for autonomy and our demanding educational aims, given that these otherwise come into conflict with one another. (shrink)

A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...) and the ethical realism of Rai Gaita and Catholic philosophers. In addition to strict philosophy, the book treats non-religious moral traditions to train virtue, such as Freemasonry, civics education and the Greek and Roman classics. (shrink)

Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...) a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

This paper sketches a causal account of scientific explanation designed to sustain the judgment that high-level, detail-sparse explanations—particularly those offered in biology—can be at least as explanatorily valuable as lower-level counterparts. The motivating idea is that complete explanations maximize causal economy: they cite those aspects of an event’s causal run-up that offer the biggest-bang-for-your-buck, by costing less (in virtue of being abstract) and delivering more (in virtue making the event stable or robust).

Antitheodicy objects to all attempts to solve the problem of evil. Its objections are almost all on moral grounds—it argues that the whole project of theodicy is morally offensive. Trying to excuse God’s permission of evil is said to deny the reality of evil, to exhibit gross insensitivity to suffering, and to insult the victims of grave evils. Since antitheodicists urge the avoidance of theodicies for moral reasons, it is desirable to evaluate the moral reasons against theodicies in abstraction from (...) the intellectual reasons for and against them. It is argued that the best known theodicies such as those based on soul-making and free will are guilty of moral faults as alleged. But Leibniz’s best of all possible worlds theory, often thought to be the most morally offensive ‘Panglossian’ theodicy, is morally blameless because it excuses God by the absolute impossibility of his choosing any world better than the present one. Theodicy should not be conceived of as a search for greater goods which may excuse God’s permitting evils. From the divine point of view, creation is an upfront choice between scenarios—in modern parlance, a Trolley problem rather than a Transplant problem. In cases of forced choice among scenarios, it is morally improper to criticize one who chooses the best. (shrink)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...) the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

Narrativists about well-being claim that our lives go better for us if they make good stories—if they exhibit cohesion, thematic consistency, and narrative arc. Yet narrativism leads to mistaken assessments of well-being: prioritizing narrative makes it harder to balance and change pursuits, pushes us toward one-dimensionality, and can’t make sense of the diversity of good lives. Some ways of softening key narrativist claims mean that the view can’t tell us very much about how to live a good life that we (...) can’t find in other theories of well-being; while there are smaller-scale ways we can incorporate narrativist insights into our views of well-being, narrativism should not be a universal organizing principle for our lives. (shrink)

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...) explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)

Our ordinary conception of imagination takes it to be essentially a conscious phenomenon, and traditionally that’s how it had been treated in the philosophical literature. In fact, this claim had often been taken to be so obvious as not to need any argumentative support. But lately in the philosophical literature on imagination we see increasing support for the view that imagining need not occur consciously. In this paper, I examine the case for unconscious imagination. I’ll consider four different arguments that (...) we can find in the recent literature—three of which are based on cases and one that is based on considerations relating to action guidance. To my mind, none of these arguments is successful. I conclude that the case for postulating unconscious imagining has not yet been well motivated. (shrink)

The effective altruism movement (EA) is one of the most influential philosophically savvy movements to emerge in recent years. Effective Altruism has historically been dedicated to finding out what charitable giving is the most overall-effective, that is, the most effective at promoting or maximizing the impartial good. But some members of EA want the movement to be more inclusive, allowing its members to give in the way that most effectively promotes their values, even when doing so isn’t overall-effective. When we (...) examine what it means to give according to one’s values, I argue, we will see that this is both inconsistent with what EA is like now and inconsistent with its central philosophical commitment to an objective standard that can be used to critically analyze one’s giving. While EA is not merely synonymous with act utilitarianism, it cannot be much more inclusive than it is right now. (shrink)

Philosophical discussions of species have focused on multicellular, sexual animals and have often neglected to consider unicellular organisms like bacteria. This article begins to fill this gap by considering what species concepts, if any, apply neatly to the bacterial world. First, I argue that the biological species concept cannot be applied to bacteria because of the variable rates of genetic transfer between populations, depending in part on which gene type is prioritized. Second, I present a critique of phylogenetic bacterial species, (...) arguing that phylogenetic bacterial classification requires a questionable metaphysical commitment to the existence of essential genes. I conclude by considering how microbiologists have dealt with these biological complexities by using more pragmatic and not exclusively evolutionary accounts of species. I argue that this pragmatism is not borne of laziness but rather of the substantial conceptual problems in classifying bacteria based on any evolutionary standard. (shrink)

Among the factors necessary for the occurrence of some event, which of these are selectively highlighted in its explanation and labeled as causes — and which are explanatorily omitted, or relegated to the status of background conditions? Following J. S. Mill, most have thought that only a pragmatic answer to this question was possible. In this paper I suggest we understand this ‘causal selection problem’ in causal-explanatory terms, and propose that explanatory trade-offs between abstraction and stability can provide a principled (...) solution to it. After sketching that solution, it is applied to a few biological examples, including to a debate concerning the ‘causal democracy’ of organismal development, with an anti-democratic (though not a gene-centric) moral. (shrink)

Though biologists identify individuals as ‘male’ or ‘female’ across a broad range of animal species, the particular traits exhibited by males and females can vary tremendously. This diversity has led some to conclude that cross-animal sexes (males, or females, of whatever animal species) have “little or no explanatory power” (Dupré 1986: 447) and, thus, are not natural kinds in any traditional sense. This essay will explore considerations for and against this conclusion, ultimately arguing that the animal sexes, properly understood, are (...) “historical explanatory kinds”: groupings that can be scientifically significant even while their members differ radically in their current properties and particular histories. Whether this makes them full-fledged natural kinds is a question I take up at the very end. (shrink)

The relationship between the phenomenology of imagination and the phenomenology of memory is an interestingly complicated one. On the one hand, there seem to be important similarities between the two, and there are even occasions in which we mistake an imagining for a memory or vice versa. On the other hand, there seem to be important differences between the two, and we can typically tell them apart. This paper explores various attempts to delineate a phenomenological marker differentiating imagination and memory, (...) with a special focus on two proposed markers that have generated considerable philosophical discussion: the feeling of pastness and the feeling of familiarity. As we will find, neither of them proves to be up to the task at hand. However, by way of a deeper exploration of the feeling of familiarity, we are able to tease out some important morals for efforts to differentiate imagination and memory on phenomenological grounds and, more generally, for efforts to engage in a descriptive phenomenological enterprise. (shrink)

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.

Comparative valuation of different policy interventions often requires interpersonal comparability of benefit. In the field of health economics, the metric commonly used for such comparison, quality adjusted life years (QALYs) gained, has been criticized for failing to respect the equality of all persons’ intrinsic worth, including particularly those with disabilities. A methodology is proposed that interprets ‘full quality of life’ as the best health prospect that is achievable for the particular individual within the relevant budget constraint. This calibration is challenging (...) both conceptually and operationally as it shifts dramatically when technology or budget developments alter what can be achieved for incapacitated individuals. The proposal nevertheless ensures that the maximal achievable satisfaction of one person’s preferences can carry no more intrinsic value than that of another. This approach, which can be applied to other domains of social valuation, thus prevents implicit discrimination against the elderly and those with irremediable incapacities. (shrink)

Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the few (...) who have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeley and Hume. All of these assert not only that space and time might be atomic, but that they must be. Infinite divisibility is, they say, impossible on purely conceptual grounds. (shrink)

Blaming (construed broadly to include both blaming-attitudes and blaming-actions) is a puzzling phenomenon. Even when we grant that someone is blameworthy, we can still sensibly wonder whether we ought to blame him. We sometimes choose to forgive and show mercy, even when it is not asked for. We are naturally led to wonder why we shouldn’t always do this. Wouldn’t it be a better to wholly reject the punitive practices of blame, especially in light of their often undesirable effects, and (...) embrace an ethic of unrelenting forgiveness and mercy? In this paper I seek to address these questions by offering an account of blame that provides a rationale for thinking that to wholly forswear blaming blameworthy agents would be deeply mistaken. This is because, as I will argue, blaming is a way of valuing, it is “a mode of valuation.” I will argue that among the minimal standards of respect generated by valuable objects, notably persons, is the requirement to redress disvalue with blame. It is not just that blame is something additional we are required to do in properly valuing, but rather blame is part of what that it is to properly value. Blaming, given the existence of blameworthy agents, is mode of valuation required by the standards of minimal respect. To forswear blame would be to fail value what we ought to value. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

This essay develops a concept of curiotization, through which people are reduced to a curio for the fascination of others. I argue that trans people as they have appeared in media, philosophy, and narratives of history are curiotized as forever fascinating, new, titillating, and controversial. In contrast to the narrative of momentous trans progress in the mid-2010s, I point out that frameworks such as the "Transgender Tipping Point" worked to position its "trans moment" as unprecedented and always on the threshold (...) of arrival. To work through a specific example, I point to decades of renewed fascination over trans women being capable of breastfeeding and the long history of trans fascination in popular music. I conclude by emphasizing the obscured world-historical presence of transsexuality as it coincides with the history of pharmaceuticals, hormone technologies, and birth control. In contrast to a "goldfish memory optics" through which trans people become eternally new, fascinating, and debatable, I stress the importance of restoring the complexity of "trans" and its histories back into an understanding of the present. (shrink)