Visual illusions of number provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces their perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age are affected by the illusion and that the magnitude of the effect increased into adulthood. Moreover, (...) individuals with greater numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning. (shrink)

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)

Hohwy (Hohwy 2016, Hohwy 2017) argues there is a tension between the free energy principle and leading depictions of mind as embodied, enactive, and extended (so-called ‘EEE1 cognition’). The tension is traced to the importance, in free energy formulations, of a conception of mind and agency that depends upon the presence of a ‘Markov blanket’ demarcating the agent from the surrounding world. In what follows I show that the Markov blanket considerations do not, in fact, lead to the kinds of (...) tension that Hohwy depicts. On the contrary, they actively favour the EEE story. This is because the Markov property, as exemplified in biological agents, picks out neither a unique nor a stationary boundary. It is this multiplicity and mutability– rather than the absence of agent-environment boundaries as such - that EEE cognition celebrates. (shrink)

Accounts of moral responsibility commonly focus on responsibility for actions and their consequences. But we can be responsible as well for omitting to act or refraining from acting, and for consequences of these. And since omitting and refraining are not in every case performing an action, an account of responsibility for actions will not apply straightforwardly to these cases. This paper advances proposals concerning responsibility for omitting, refraining, and their consequences. Providing such an account is complicated by the fact that (...) cases of omitting or refraining are quite varied. (shrink)

In “Mathematical Truth,” Paul Benacerraf presented an epistemological problem for mathematical realism.

Elga's presentation of The Sleeping Beauty Problem is often misread, with analyses that impute extra premises and derive false answers to the problem as Elga presented it. Here it is shown that hewing to the text requires that the Sleeping Beauty's degree of belief in a coin flip upon her first awakening is 1/2.

When evaluating theories of causation, intuitions should not play a decisive role, not even intuitions in flawlessly-designed thought experiments. Indeed, no coherent theory of causation can respect the typical person’s intuitions in redundancy (pre-emption) thought experiments, without disrespecting their intuitions in threat-and-saviour (switching/short-circuit) thought experiments. I provide a deductively sound argument for these claims. Amazingly, this argument assumes absolutely nothing about the nature of causation. I also provide a second argument, whose conclusion is even stronger: the typical person’s causal intuitions (...) are thoroughly unreliable. This argument proceeds by raising the neglected question: in what respects is information about intermediate and enabling variables relevant to reliable causal judgment? (shrink)

The visual system adapts to a wide range of visual features, from lower-level features like color and motion to higher-level features like causality and, perhaps, number. According to some, adaptation is a strictly perceptual phenomenon, such that the presence of adaptation licenses the claim that a feature is truly perceptual in nature. Given the theoretical importance of claims about adaptation, then, it is important to understand exactly when the visual system does and does not exhibit adaptation. Here, we take as (...) a case study one specific kind of adaptation: visual adaptation to size. Supported by evidence from four experiments, we argue that, despite robust effects of size adaptation in the lab, (1) size adaptation effects are phenomenologically underwhelming (in some cases, hardly appreciable at all), (2) some effects of size adaptation appear contradictory, and difficult to explain given current theories of size adaptation, and (3) prior studies on size adaptation may have failed to isolate size as the adapted dimension. Ultimately, we argue that while there is evidence to license the claim that size adaptation is genuine, size adaptation is a puzzling and poorly understood phenomenon. (shrink)

Several theories of causation reject causation of or by absences. They thereby clash with much of what we think and say about what causes what. This paper examines a way in which one kind of theory, causal dispositionalism, can be modified so as to accept absence causation, while still retaining a fundamental commitment of dispositionalism. The proposal adopts parts of a strategy described by David Lewis. The paper concludes with a brief discussion of the problem of the proliferation of causes.

Some recent exchanges (Gebharter 2017a,2017b; Baumgartner and Cassini, 2023) concern whether composition can have conditional independence properties analogous to causal relations. If so, composition might sometimes be detectable by the application of causal search algorithms. The discussion has focused on a particular algorithm, PC (Spirtes and Glymour, 1991). PC is but one, and in many circumstances not the best, of a host of causal search algorithms that are candidates for methods of discovering composition provided appropriate statistical relations obtain. The discussion (...) raises two issues: 1. Does the structure of the composition relation entail probability relations such that PC and like algorithms cannot discover composition from frequency data about kinds; and 2. what can be discovered—and how—about the composition of systems by PC or related causal search algorithms that exploit conditional independence relations. Baumgartner and Cassini answer the first question positively: constitution entails probability relations incompatible with discovery by PC. They do not engage the second question, but we will. (shrink)

Some explanations are relatively abstract: they abstract away from the idiosyncratic or messy details of the case in hand. The received wisdom in philosophy is that this is a virtue for any explanation to possess. I argue that the apparent consensus on this point is illusory. When philosophers make this claim, they differ on which of four alternative varieties of abstractness they have in mind. What’s more, for each variety of abstractness there are several alternative reasons to think that the (...) variety of abstractness in question is a virtue. I identify the most promising reasons, and dismiss some others. The paper concludes by relating this discussion to the idea that explanations in biology, psychology and social science cannot be replaced by relatively micro explanations without loss of understanding. (shrink)

Reductionists say things like: all mental properties are physical properties; all normative properties are natural properties. I argue that the only way to resist reductionism is to deny that causation is difference making (thus making the epistemology of causation a mystery) or to deny that properties are individuated by their causal powers (thus making properties a mystery). That is to say, unless one is happy to deny supervenience, or to trivialize the debate over reductionism. To show this, I argue that (...) if properties are individuated by their causal powers then, surprisingly, properties are individuated by necessary co-exemplification. (shrink)

This paper examines the view of abilities to act advanced by Kadri Vihvelin in Causes, Laws, and Free Will. Vihvelin argues that (i) abilities of an important kind are “structurally” like dispositions such as fragility; (ii) ascriptions of dispositions can be analyzed in terms of counterfactual conditionals; (iii) ascriptions of abilities of the kind in question can be analyzed similarly; and (iv) we have the free will we think we have by having abilities of this kind and being in circumstances (...) that are propitious for their exercise. I raise doubt about each of these claims. Further, I argue that even if abilities of the kind in question are dispositions, and even if determinism is compatible with our commonly having unexercised abilities of this kind, the compatibility of determinism and free will remains in question. (shrink)

This chapter is a contribution to an exchange with Carolina Sartorio about intentional omissions.

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

Biological theory demands a clear organism concept, but at present biologists cannot agree on one. They know that counting particular units, and not counting others, allows them to generate explanatory and predictive descriptions of evolutionary processes. Yet they lack a unified theory telling them which units to count. In this paper, I offer a novel account of biological individuality, which reconciles conflicting definitions of ‘organism’ by interpreting them as describing alternative realisers of a common functional role, and then defines individual (...) organisms as essentially possessing some mechanisms that play this role. (shrink)

In his précis of a recent book, Richard Joyce writes, “My contention…is that…any epistemological benefit-of-the-doubt that might have been extended to moral beliefs…will be neutralized by the availability of an empirically confirmed moral genealogy that nowhere…presupposes their truth.” Such reasoning – falling under the heading “Genealogical Debunking Arguments” – is now commonplace. But how might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs “neutralize” whatever “epistemological benefit-of-the-doubt that might have been extended (...) to” them? In this article, I argue that there appears to be no satisfactory answer to this question. The problem is quite general, applying to all arguments with the structure of Genealogical Debunking Arguments aimed at realism about a domain meeting two conditions. The Benacerraf-Field Challenge for mathematical realism affords an important special case. (shrink)

Many philosophical theories of causation are egalitarian, rejecting a distinction between causes and mere causal conditions. We sought to determine the extent to which people's causal judgments discriminate, selecting as causes counternormal events—those that violate norms of some kind—while rejecting non-violators. We found significant selectivity of this sort. Moreover, priming that encouraged more egalitarian judgments had little effect on subjects. We also found that omissions are as likely as actions to be judged as causes, and that counternormative selectivity appears to (...) apply equally to actions and omissions. (shrink)

The problem of plant individuality is something which has vexed botanists throughout the ages, with fashion swinging back and forth from treating plants as communities of individuals (Darwin 1800 ; Braun and Stone 1853 ; Münch 1938 ) to treating them as organisms in their own right, and although the latter view has dominated mainstream thought most recently (Harper 1977 ; Cook 1985 ; Ariew and Lewontin 2004 ), a lively debate conducted mostly in Scandinavian journals proves that the issues (...) are far from being resolved (Tuomi and Vuorisalo 1989b ; Fagerström 1992 ; Pan and Price 2001 ). In this paper I settle the matter once and for all, by showing which elements of each side are correct. (shrink)

Consider the idea that suffering of some specific kind is deserved by those who are guilty of moral wrongdoing. Feeling guilty is a prime example. It might be said that it is noninstrumentally good that one who is guilty feel guilty (at the right time and to the right degree), or that feeling guilty (at the right time and to the right degree) is apt or fitting for one who is guilty. Each of these claims constitutes an interesting thesis about (...) desert, given certain understandings of what desert is. After examining these claims, the paper briefly explores the idea that an offender might deserve certain forms of treatment by others. The paper concludes by contrasting the modest theses on which it focuses with a far bolder one, to the effect that if we are morally responsible, then it makes sense to suppose that some of us might deserve to suffer eternal torment. The more modest theses do not commit one to anything of this sort. (shrink)

I distinguish several doctrines that economic methodologists have found attractive, all of which have a positivist flavour. One of these is the doctrine that preference assignments in economics are just shorthand descriptions of agents' choice behaviour. Although most of these doctrines are problematic, the latter doctrine about preference assignments is a respectable one, I argue. It doesn't entail any of the problematic doctrines, and indeed it is warranted independently of them.

I argue for the usefulness of the evolutionary kind of biological individual.

It is often supposed that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical (...) hypothesis is absolutely undecidable, then it is indeterminate. I shall argue that on no understanding of absolute undecidability could one hope to establish all of (a)–(c). However, I will identify one understanding of absolute undecidability on which one might hope to establish both (a) and (c) to the exclusion of (b). This suggests that a new style of mathematical antirealism deserves attention—one that does not depend on familiar epistemological or ontological concerns. The key idea behind this view is that typical mathematical hypotheses are indeterminate because they are relevantly similar to CH. (shrink)

Often when one omits to do a certain thing, there's no action that is one's omission; one's omission, it seems, is an absence of any action of some type. This paper advances the view that an absence of an action--and, in general, any absence--is nothing at all: there is nothing that is an absence. Nevertheless, it can result from prior events that one omits to do a certain thing, and there can be results of the fact that one omits to (...) do something. This is so even if absences cannot be causes or causal effects. (shrink)

A growing number of philosophers now hold that agent causation is required for agency, or free will, or moral responsibility. To clarify what is at issue, this paper begins with a distinction between agent causation that is ontologically fundamental and agent causation that is reducible to or realized in causation by events or states. It is widely accepted that agency presents us with the latter; the view in question claims a need for the former. The paper then examines a “disappearing (...) agent” argument from Derk Pereboom that is aimed at showing that free will requires agent causation that is ontologically fundamental. It is argued that the argument fails. Further, it is argued that, contrary to Pereboom’s claim, the issue raised by his disappearing agent argument is distinct from the problem of present luck that libertarian theories of free will face. The paper concludes with an assessment of the prospects for success of a disappearing agent argument showing that agent causation that is ontologically fundamental is required for agency tout court. (shrink)

The preface paradox does not show that it can be rational to have inconsistent beliefs, because preface writers do not have inconsistent beliefs. I argue, first, that a fully satisfactory solution to the preface paradox would have it that the preface writer's beliefs are consistent. The case here is on basic intuitive grounds, not the consequence of a theory of rationality or of belief. Second, I point out that there is an independently motivated theory of belief – sensitivism – which (...) allows such a solution. I sketch a sensitivist account of the preface writer's doxastic state. (shrink)

It is widely held that one can be responsible for doing something that one was unable to avoid doing. This paper focuses primarily on the question of whether one can be responsible for not doing something that one was unable to do. The paper begins with an examination of the account of responsibility for omissions offered by John Martin Fischer and Mark Ravizza, arguing that in many cases it yields mistaken verdicts. An alternative account is sketched that jibes with and (...) explains judgments about a variety of omissions cases, including intentional omissions as well as simple failures to act. (shrink)

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.

This paper argues for a treatment of belief as essentially sensitive to certain features of context. The first part gives an argument that we must take belief to be context-sensitive in the same way that assertion is, if we are to preserve appealing principles tying belief to sincere assertion. In particular, whether an agent counts as believing that p in a context depends on the space of alternative possibilities the agent is considering in that context. One and the same doxastic (...) state may amount to belief that p in one context but not another. The second part of the paper gives a formal treatment of doxastic states, according to which belief is context-sensitive along just these lines. The model is applied to characterize (but not to refute) skeptical arguments. (shrink)

In this thesis, I give a metascientific account of causality in medicine. I begin with two historical cases of causal discovery. These are the discovery of the causation of Burkitt’s lymphoma by the Epstein-Barr virus, and of the various viral causes suggested for cervical cancer. These historical cases then support a philosophical discussion of causality in medicine. This begins with an introduction to the Russo- Williamson thesis (RWT), and discussion of a range of counter-arguments against it. Despite these, I argue (...) that the RWT is historically workable, given a small number of modifications. I then expand Russo and Williamson’s account. I first develop their suggestion that causal relationships in medicine require some kind of evidence of mechanism. I begin with a number of accounts of mechanisms and produce a range of consensus features of them. I then develop this consensus position by reference to the two historical case studies with an eye to their operational competence. In particular, I suggest that it is mechanistic models and their representations which we are concerned with in medicine, rather than the mechanism as it exists in the world. -/- I then employ these mechanistic models to give an account of the sorts of evidence used in formulating and evaluating causal claims. Again, I use the two human viral oncogenesis cases to give this account. I characterise and distinguish evidence of mechanism from evidence of difference-making, and relate this to mechanistic models. I then suggest the relationship between types of evidence presents us with a means of tackling the reference-class problem. This sets the scene for the final chapter. Here, I suggest the manner in which these two different classes of evidence become integrated is also reflected in the way that developing research programmes change as their associated causal claims develop. (shrink)

Free will is often said—by compatibilists and incompatibilists alike—to be a power (or complex of powers) of agents. This paper offers proposals for, and examines the prospects of, a powers-conception of free will that takes the powers in question to be causal dispositions. A difficulty for such an account stems from the idea that when one exercises free will, it is up to oneself whether one wills to do this or that. The paper also briefly considers whether a powers-conception that (...) invokes powers of a different kind, such as agent-causal or noncausal powers, might fare better with respect to this problem. (shrink)

I develop the foundation for cosmopolitan care, an underexplored variety of moral cosmopolitanism. I begin by offering a characterization of contemporary cosmopolitanism from the justice tradition. Rather than discussing the political, economic or cultural aspects of cosmopolitanism, I instead address its moral dimensions. I then employ a feminist philosophical perspective to provide a critical evaluation of the moral foundations of cosmopolitan justice, with an eye toward demonstrating the need for an alternative account of moral cosmopolitanism as cosmopolitan care. After providing (...) an explanation of how care ethics in connection with Kantian ethics generates a duty to care, I consider one main feature of cosmopolitan care, namely the theory of obligation it endorses. In developing this account, I place special emphasis on the practical ramifications of the theory by using it to analyze gender violence in conflict zones. (shrink)

This paper is a study about Philadelphia’s comprehensive user engagement sites (CUESs) as the authors address and examine issues related to the upcoming implementation of a CUES while seeking solutions for its disputed questions and plans. Beginning with the federal drug schedules, the authors visit some of the medical and public health issues vis-à-vis safe injection facilities (SIFs). Insite, a successful Canadian SIF, has been thoroughly researched as it represents a paradigm for which a Philadelphia CUES can expand upon. Also, (...) the existing criticisms against SIFs are revisited while critically unpackaged and responded to in favor of the establishment. In the main section, the authors propose the layout and services of the upcoming CUES, much of which would be in congruent to Vancouver’s Insite. On the other hand, the CUES would be distinct from Insite, as the authors emphasize, in that it will offer an information center run by individuals in recovery and place additional emphasis on early education for young healthcare professionals by providing them a platform to work at the site. The paper will also briefly investigate the implementation of a CUES site under an ethical scope of the Harm Reduction Theory. Lastly, the authors recommend some strategic plans that the Philadelphia City government may consider employing at this crucial stage. (shrink)

A large chorus of voices has grown around the claim that theistic belief is epistemically suspect since, as some cognitive scientists have hypothesized, such beliefs are a byproduct of cognitive mechanisms which evolved for rather different adaptive purposes. This paper begins with an overview of the pertinent cognitive science followed by a short discussion of some relevant epistemic concepts. Working from within a largely Williamsonian framework, we then present two different ways in which this research can be formulated into an (...) argument against theistic belief. We argue that neither version works. (shrink)

Neuroeconomics is a research programme founded on the thesis that cognitive and neurobiological data constitute evidence for answering economic questions. I employ confirmation theory in order to reject arguments both for and against neuroeconomics. I also emphasize that some arguments for neuroeconomics will not convince the skeptics because these arguments make a contentious assumption: economics aims for predictions and deep explanations of choices in general. I then argue for neuroeconomics by appealing to a much more restrictive (and thereby skeptic-friendly) characterization (...) of the aims of economics. (shrink)

It is often assumed that adaptation — a temporary change in sensitivity to a perceptual dimension following exposure to that dimension — is a litmus test for what is and is not a “primary visual attribute”. Thus, papers purporting to find evidence of number adaptation motivate a claim of great philosophical significance: That number is something that can be seen in much the way that canonical visual features, like color, contrast, size, and speed, can. Fifteen years after its reported discovery, (...) number adaptation’s existence seems to be nearly undisputed, with dozens of papers documenting support for the phenomenon. The aim of this paper is to offer a counterweight — to critically assess the evidence for and against number adaptation. After surveying the many reasons for thinking that number adaptation exists, we introduce several lesser-known reasons to be skeptical. We then advance an alternative account — the old news hypothesis — which can accommodate previously published findings while explaining various (otherwise unexplained) anomalies in the existing literature. Next, we describe the results of eight pre-registered experiments which pit our novel old news hypothesis against the received number adaptation hypothesis. Collectively, the results of these experiments undermine the number adaptation hypothesis on several fronts, whilst consistently supporting the old news hypothesis. More broadly our work raises questions about the status of adaptation itself as a means of discerning what is and is not a visual attribute. (shrink)

A recent empirical study claims to show that the answer to Molyneux’s question is negative, but, as John Schwenkler points out, its findings are inconclusive: Subjects tested in this study probably lacked the visual acuity required for a fair assessment of the question. Schwenkler is undeterred. He argues that the study could be improved by lowering the visual demands placed on subjects, a suggestion later endorsed and developed by Kevin Connolly. I suggest that Connolly and Schwenkler both underestimate the difficulties (...) involved in rectifying the study they seek to fix. The problem is that the experimental paradigm under consideration fails to account for the role that rational inference plays in newly sighted subjects’ ability or inability to recognize spatial properties across modalities. Since answering Molyneux’s question requires establishing whether spatial properties can be recognized, across modalities, by newly sighted subjects without recourse to rational inference, this is a problem. Indeed, it is a problem that may be worsened by Schwenkler and Connolly’s suggestions regarding the lowering of visual demands on subjects in cross-modal matching tasks. (shrink)

This paper proposes a novel conception of mental files, aimed at addressing Frege puzzles. Classical Frege puzzles involve ignorance and discovery of identity. These may be addressed by accounting for a more basic way for identity to figure in thought—the treatment of beliefs by the believer as being about the same thing. This manifests itself in rational inferences that presuppose the identity of what the beliefs are about. Mental files help to provide a functional characterization of a mind capable of (...) this presupposition, but more must be said to show how it may be rational. I argue that this can be done by drawing out the way in which mental files interact with a thinker's motivational states and so come to have normative functional properties. I show how this theory works better than some other treatments of mental files. (shrink)

I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...) to doubt that our F-beliefs are modally secure. (shrink)

Some explanations in social science, psychology and biology belong to a higher level than other explanations. And higher explanations possess the virtue of abstracting away from the details of lower explanations, many philosophers argue. As a result, these higher explanations are irreplaceable. And this suggests that there are genuine higher laws or patterns involving social, psychological and biological states. I show that this ‘abstractness argument’ is really an argument schema, not a single argument. This is because the argument uses the (...) ‘is lower than’ relation, and this relation admits of different readings. I then suggest four rigorous definitions of the ‘is lower than’ relation, and show that the abstractness argument’s prospects are much brighter for some of these definitions than for others. To show this, I evaluate the so-called ‘disjunctive threat’ to the abstractness argument. (shrink)

This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on the compatibility of (...) the previously discussed views with dualist and monist interpretations of our mental states and our ways of modeling them. (shrink)

This paper uses readings of two classic autobiographies, Edmund Gosse's Father & Son and John Stuart Mill's Autobiography, to develop a distinctive answer to an old and central question in value theory: What role is played by pleasure in the most successful human life? A first section defends my method. The main body of the paper then defines and rejects voluntarist, stoic, and developmental hedonist lessons to be taken from central crises in my two subjects' autobiographies, and argues for a (...) fourth, diagnostic lesson: Gosse and Mill perceive their individual good through the medium of pleasure. Finally, I offer some speculative moral psychology of human development, as involving the waking, perception, management, and flowering of generic and individual capacities, which I suggest underlies Gosse and Mill's experiences. The acceptance of one's own unchosen nature, discovered by self-perceptive pleasure in the operation of one's nascent capacities, is the beginning of a flourishing adulthood in which that nature is fully developed and expressed. (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)

I argue for a perfectionist reading of Mill’s account of the good life, by using the failures of development recorded in his Autobiography as a way to understand his official account of happiness in Utilitarianism. This work offers both a new perspective on Mill’s thought, and a distinctive account of the role of aesthetic and emotional capacities in the most choiceworthy human life. I consider the philosophical purposes of autobiography, Mill’s disagreements with Bentham, and the nature of competent judges and (...) the pleasure they take in higher culture. I conclude that Millian perfectionism is an attractive and underappreciated option for contemporary value theory. (shrink)

In this article, I begin by giving a brief history of melanoma causation. I then discuss the current manner in which malignant melanoma is classified. In general, these systems of classification do not take account of the manner of tumour causation. Instead, they are based on phenomenological features of the tumour, such as size, spread, and morphology. I go on to suggest that misclassification of melanoma is a major problem in clinical practice. I therefore outline an alternative means of classifying (...) these tumours based on causal factors. By analogy with similar systems that have recently emerged for other cancers, I suggest that this causal classification is likely to be both workable and helpful, even in the absence of a full causal-mechanistic understanding of the aetiology of the tumour. (shrink)