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)

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)

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)

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)

In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an area, D—the (...) challenge to justify our D-beliefs—with the reliability challenge for D-realism—the challenge to explain the reliability of our D-beliefs. Harman’s contrast is relevant to the first, but not, evidently, to the second. One upshot of the discussion is that genealogical debunking arguments are fallacious. Another is that indispensability considerations cannot answer the Benacerraf–Field challenge for mathematical realism. (shrink)

1. We sometimes angrily confront, pointedly ostracize, castigate, or denounce those whom we think have committed moral offences. Conduct of this kind may be called blaming behaviour. When genuine,...

Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be One True Logic is noncognitive. The same may be true of monism about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)

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

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree (...) with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it. (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)

I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

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)

Cognitivists about intention hold that intending to do something entails believing you will do it. Non-cognitivists hold that intentions are conative states with no cognitive component. I argue that both of these claims are true. Intending entails the presence of a belief, even though the intention is not even partly the belief. The result is a form of what Sarah Paul calls Non-Inferential Weak Cognitivism, a view that, as she notes, has no prominent defenders.

Number Nativism is the view that humans innately represent precise natural numbers. Despite a long and venerable history, it is often considered hopelessly out of touch with the empirical record. I argue that this is a mistake. After clarifying Number Nativism and distancing it from related conjectures, I distinguish three arguments which have been seen to refute the view. I argue that, while popular, two of these arguments miss the mark, and fail to place pressure on Number Nativism. Meanwhile, a (...) third argument is best construed as a challenge: rather than refuting Number Nativism, it challenges its proponents to provide positive evidence for their thesis and show that this can be squared with apparent counterevidence. In response, I introduce psycholinguistic work on The Tolerance Principle (not yet considered in this context), propose that it is hard to make sense of without positing precise and innate representations of natural numbers, and argue that there is no obvious reason why these innate representations couldn’t serve as a basis for mature numeric conception. (shrink)

Let F be a fact in virtue of which an agent, S, is blameworthy for performing an act of A-ing. We advance a slightly qualified version of the following thesis: -/- (Reason) F is (at some time) a reason for S to feel guilty (to some extent) for A-ing. -/- Leaving implicit the qualification concerning extent, we claim as well: -/- (Desert) S's having this reason suffices for S’s deserving to feel guilty for A-ing. -/- We also advance a third (...) thesis connecting desert of feeling guilty with the fittingness of this response. -/- In light of our three theses, we address several claims that have been made regarding responsibility and desert. We take issue with the divorce of desert from responsibility. We find acceptable a claim regarding blameworthiness and reason to induce guilt, and we defend the idea that it is noninstrumentally good that one who is blameworthy be subject to a fitting feeling of guilt. We argue against a view on which desert of blame has a teleological dimension. (shrink)

According to what may be called PERMANENT, blameworthiness is forever: once you are blameworthy for something, you are always blameworthy for it. Here a prima facie case for this view is set out, and the view is defended from two lines of attack. On one, you are no longer blameworthy for a past offense if, despite being the person who committed it, you no longer have any of the pertinent psychological states you had at the time of the misdeed. On (...) the other, you can cease to be blameworthy if you sufficiently experience guilt or remorse, suffer enough punishment, or are forgiven for your misdeed. Although several points made in support of the second challenge are accepted, they are entirely consistent with PERMANENT. Neither line of attack, as so far presented, undermines the plausibility of this view stemming from the prima facie case. (shrink)

How seriously should we take the idea that the mind employs mental files? Goodman and Gray (2022) argue that mental filing – a thinker rationally treating her cognitive states as being about the same thing – can be explained without files. Instead, they argue that the standard commitments of mental file theory, as represented by Recanati’s indexical model, are better seen in terms of a relational representational feature of object representations, which in turn is based on the epistemic links a (...) thinker bears to objects. This paper argues that this revision is misguided. Neither the representational property nor any basic role for epistemic links are needed for an adequate explanatory theory that makes use of the image of a mental filing system. A better alternative to the indexical model does posit files, albeit as causal-functional entities. This makes additional representational features redundant, and shows that epistemic links play a secondary 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)

Consider cases in which an agent simply doesn.t think to do a certain thing, or doesn't think of a crucial consideration favoring doing a certain thing, or intends to do a certain thing but forgets to do it. In such a case, is the agent able to do the thing that she fails to do? Assume that commonly we all‐in can do things that we do not do. Here I argue that, given this assumption, in the cases under consideration, too, (...) commonly agents all‐in can do the things they fail to do. (shrink)

Although we are morally responsible for things of various kinds, what we bear direct responsibility for are certain exercises of our agency (and perhaps some omissions of these). Theorists disagree about what kind of agency is in this respect the source of our responsibility. Some hold that it is agency the exercises of which are actions. Others say that it is agency exercised in forming reasons-responsive attitudes on the basis of our take on reasons (or value). With attention to the (...) relation of moral responsibility to moral obligation, I argue for the first of these views. (shrink)

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)

Holly Smith has done more than anyone to explore and defend the importance of usability for moral theories. In Making Morality Work, she develops a moral theory that is almost universally usable. But not quite. In this article, I argue that no moral theory is universally usable, in the sense that is most immediately relevant to action, even by agents who know all the normative facts. There is no moral theory knowledge of which suffices to settle deliberation about what to (...) do. However, this is unsurprising if the question of what to do is not a question of fact. One upshot of the discussion is that the search for a universally usable moral theory is misconceived. Another is that, contra Smith (341), agents who are radically uncertain need not lack autonomy. (shrink)

Negligence and omission are closely related: commonly, in cases of negligent action, the agent has failed to turn her attention to some pertinent fact. But that omission is itself typically unwitting. A sufficient condition for blameworthiness for an unwitting omission is offered, as is an account of blameworthiness for negligent action. It is argued that one can be blameworthy for wrongdoing done from ignorance even if one is not blameworthy for that ignorance.

I am grateful to Sean Carroll, Paul Horwich, and Sarah McGrath for their stimulating responses to Morality and Mathematics (M&M). Their arguments concern the reality of unapplied mathematics, the practical import of moral facts, and the deliberative and explanatory roles of evaluative theories. In what follows, I address their responses, as well as some broader issues.

I discuss methodology in epistemology. I argue that settling the facts, even the epistemic facts, fails to settle the questions of intellectual policy at the center of our epistemic lives. An upshot is that the standard methodology of analyzing concepts like knowledge, justification, rationality, and so on is misconceived. More generally, any epistemic method that seeks to issue in intellectual policy by settling the facts, whether by way of abductive theorizing or empirical investigation, no matter how reliable, is inapt. The (...) argument is a radicalization of Moore’s Open Question Argument. I conclude by considering the ramifications of this conclusion for the debate surrounding “Modal Security”, a proposed necessary condition on undermining defeat. (shrink)

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series (...) of expected gains can the paradox be resolved. (shrink)

Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...) to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

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.

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.

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)

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)

1Department of Philosophy, University of Nottingham, University Park, Nottingham NG7 2RD, UK. [email protected] of Philosophy, University of Nottingham, University Park, Nottingham NG7 2RD, UK. [email protected].

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)

Several philosophers claim that the phenomenology of one’s own agency conflicts with standard causal theories of action, couched in terms of causation by mental events or states. Others say that the phenomenology is prima facie incompatible with such a theory, even if in the end a reconciliation can be worked out. Here it is argued that the type of action theory in question is consistent with what can plausibly be said to be presented to us in our experience of our (...) agency. Several routes to a claim that there is nevertheless a prima facie incompatibility are examined, and all are found wanting. The phenomenology of agency, it is argued, is no threat to a standard causal theory of action. (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)

Disproof of heaven? -- Brain and gods -- The rational stance -- Reason and belief in God -- Against naturalism -- Atheism, inference, and IQ -- Atheism, autism, and intellectual humility -- Googling God -- Inference, intuition, and rationality.

We make the case that scientifically accurate and politically feasible responses to the climate crisis require a complex understanding of human cultural practices of niche construction that moves beyond the adaptive significance of culture. We develop this thesis in two related ways. First, we argue that cumulative cultural practices of niche construction can generate stable equilibria and runaway selection processes that result in long-term existential risks within and across cultural groups. We dub this the back of the invisible hand. Second, (...) we argue that the ability of cultural groups to innovate technological solutions to environmental problems is highly constrained in ways that are exacerbated by sustained intergroup conflict, inequality and by inherently unpredictable cascades in climate change and human migration patterns. After developing these theoretical points about human cultural practices of niche construction in detail, we conclude our discussion with some tentative practical suggestions about the way that cultural evolutionary history can more fruitfully be used in efforts to remit the climate crisis and contribute to sustainable practices of human climate change adaptation. (shrink)

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)

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)

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)

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)

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.

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)

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)