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)

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)

You ought to save a larger group of people rather than a distinct smaller group of people, all else equal. A consequentialist may say that you ought to do so because this produces the most good. If a non-consequentialist rejects this explanation, what alternative can he or she give? This essay defends the following explanation, as a solution to the so-called numbers problem. Its two parts can be roughly summarised as follows. First, you are morally required to want the survival (...) of each stranger for its own sake. Secondly, you are rationally required to achieve as many of these ends as possible, if you have these ends. (shrink)

Cognitive Science, Volume 46, Issue 7, July 2022.

We prove that each countable rooted K4 -frame is a d-morphic image of a subspace of the space $\mathbb{Q}$ of rational numbers. From this we derive that each modal logic over K4 axiomatizable by variable-free formulas is the d-logic of a subspace of $\mathbb{Q}$ . It follows that subspaces of $\mathbb{Q}$ give rise to continuum many d-logics over K4 , continuum many of which are neither finitely axiomatizable nor decidable. In addition, we exhibit several families of modal logics finitely (...) axiomatizable by variable-free formulas over K4 that d-define interesting classes of topological spaces. Each of these logics has the finite model property and is decidable. Finally, we introduce quasi-scattered and semi-scattered spaces as generalizations of scattered spaces, develop their basic properties, axiomatize their corresponding modal logics, and show that they also arise as the d-logics of some subspaces of $\mathbb{Q}$. (shrink)

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities are aligned with addition, whereas certain functional relations between entities are aligned with division. Similarly, discreteness vs. continuity of quantities is aligned with different formats for rational numbers. These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook (...) analyses revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations. (shrink)

For a ring R, Hilbert’s Tenth Problem $HTP$ is the set of polynomial equations over R, in several variables, with solutions in R. We view $HTP$ as an enumeration operator, mapping each set W of prime numbers to $HTP$, which is naturally viewed as a set of polynomials in $\mathbb {Z}[X_1,X_2,\ldots ]$. It is known that for almost all W, the jump $W'$ does not $1$ -reduce to $HTP$. In contrast, we show that every Turing degree contains a set W (...) for which such a $1$ -reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for $W'$ from $HTP$ can succeed uniformly on a set of measure $1$, and regarding the consequences for the boundary sets of the $HTP$ operator in case $\mathbb {Z}$ has an existential definition in $\mathbb {Q}$. (shrink)

Clarke and Beck suggest that the ratio processing system may be a component of the approximate number system, which they suggest represents rational numbers. We argue that available evidence is inconsistent with their account and advocate for a two-systems view. This implies that there may be many access points for numerical cognition – and that privileging the ANS may be a mistake.

The present study examined whether a dissociation among formats for rational numbers can be obtained in tasks that require comparing a number to a non-symbolic quantity. In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude (...) task was performed more quickly using decimals, whereas the relation task was performed more accurately with fractions. The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display. (shrink)

Let ${{\mathcal L}^{\square\circ}}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language ${{\mathcal L}^{\square\circ}}$ by interpreting ${{\mathcal L}^{\square\circ}}$ in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fernández Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete for continuous functions on the rational numbers. (shrink)

The following result is an approximation to the answer of the question of Kokorin about decidability of a quantifier-free theory of field of rational numbers. Let Q0 be a subset of the set of all rational numbers which contains integers 1 and −1. Let be a set containing Q0 and closed by the functions of addition, subtraction and multiplication. For example coincides with Q0 if Q0 is the set of all binary rational numbers or the set of (...) all decimal rational numbers. It is clear that , where Z is the set of all integers and Q is the set of all rational numbers. A negationless theory uses only conjunction and disjunction as logical connectives. Let T be a quantifier-free negationless elementary theory of signature , where Pol is the list of all polynomials with rational coefficients from Q0 in which exponent of the polynomials and rational coefficients are written in binary number system. Theorem 1. Theory T is NP-hard and if is everywhere dense then the theory T is decidable by an algorithm which belongs to EXPTIME. The set of all rational numbers or the set of all binary rational numbers may be taken instead of . The quantifier-free negationless theory of the field of rational numbers may be regarded as a base of constructive mathematics. (shrink)

We agree with Clarke and Beck that the approximate number system represents rational numbers, and we demonstrate our support by highlighting the case of the empty set – the non-symbolic manifestation of zero. It is particularly interesting because of its perceptual and semantic uniqueness, and its exploration reveals fundamental new insights about how numerical information is represented.

The relationship between ideals I of Turing degrees and groups of I-recursive automorphisms of the ordering on rationals is studied. We discuss the differences between such groups and the group of all automorphisms, prove that the isomorphism type of such a group completely defines the ideal I, and outline a general correspondence between principal ideals of Turing degrees and the first-order properties of such groups.

Let ƒ be a real number. It is well known [7] that the set of rational numbers which are less than ƒ is a recursive set if and only if ƒ is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this paper we replace the condition that the set of rational numbers less than ƒ is recursive by the condition that this set is at various points in the Kleene hierarchy, (...) and we replace the recursive, recursively convergent limit by a variety of other recursive limiting processes. (shrink)

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.

The main contribution of this article is to apply Herbert Marcuse’s work in contemporary neoliberal society. Specifically, this article will focus on Marcuse’s critique of advanced industrial society and the role that technology plays in the quantification of the self. In this article, I will argue that in recent years, the development of technology has created the possibility to measure, calculate and quantify even the most trivial aspects of our lives, reducing people to numbers. The quantification of people is done (...) with the specific purpose of enhancing efficacy and productivity. I will unpack this notion by first looking to Marcuse’s critique of an advanced industrial society which he argues has the unique purpose of quantifying people to achieve a universal norm of calculated efficiency. Specifically, I will refer to Marcuse’s critique of industrial rationality as the prevailing rationality in advanced industrial societies which encourages the quantification of people. Secondly, I argue that Marcuse’s critique has evolved in the work of contemporary thinkers such as political economist Wendy Brown and cultural theorist Byung-Chul Han. I argue that Brown expands on Marcuse’s theories and contextualises those theories in contemporary neoliberalism. Specifically, I will focus on the concept of governmentality as a political rationality in neoliberal societies and how it advances a one-dimensional political passivity in neoliberal subjects. Finally, I refer to Han, whose theories explore the influence of new forms of technology in a neoliberal society and the development of the neoliberal subject as a “quantified self”. (shrink)

This article exposes the sophistry inherent in the construction of the "number line," as this continuum is named by mathematicians, and shows how another continuum, one which preserves the properties of the old "number line" but which is based on rational foundations, namely the relations to one another of the ratios that continuous magnitudes have to one another, can be generated to replace it.

Let h : ℕ → ℚ be a computable function. A real number x is called h-monotonically computable if there is a computable sequence of rational numbers which converges to x h-monotonically in the sense that h|x – xn| ≥ |x – xm| for all n andm > n. In this paper we investigate classes h-MC of h-mc real numbers for different computable functions h. Especially, for computable functions h : ℕ → ℚ, we show that the class (...) h-MC coincides with the classes of computable and semi-computable real numbers if and only if Σi∈ℕ) = ∞and the sum Σi∈ℕ) is a computable real number, respectively. On the other hand, if h ≥ 1 and h converges to 1, then h-MC = SC no matter how fast h converges to 1. Furthermore, for any constant c > 1, if h is increasing and converges to c, then h-MC = c-MC. Finally, if h is monotone and unbounded, then h-MC contains all ω-mc real numbers which are g-mc for some computable function g. (shrink)

A number of authors have defended permissivism by appealing to rational supererogation, the thought that some doxastic states might be rationally permissible even though there are other, more rational beliefs available. If this is correct, then there are situations that allow for multiple rational doxastic responses, even if some of those responses are rationally suboptimal. In this paper, I will argue that this is the wrong approach to defending permissivism—there are no doxastic states that are rationally (...) supererogatory. By the lights of contemporary linguistics, ‘rational’ is an absolute gradable adjective, and as such, can only be applied to things that satisfy the top of the scale of rationality. For this reason, it is not possible to believe what is rational while also failing to believe what is rationally optimal. (shrink)

Different people reason differently, which means that sometimes they reach different conclusions from the same evidence. We maintain that this is not only natural, but rational. In this essay we explore the epistemology of that state of affairs. First we will canvass arguments for and against the claim that rational methods of reasoning must always reach the same conclusions from the same evidence. Then we will consider whether the acknowledgment that people have divergent rational reasoning methods should (...) undermine one’s confidence in one’s own reasoning. Finally we will explore how agents who employ distinct yet equally rational methods of reasoning should respond to interactions with the products of each others’ reasoning. We find that the epistemology of multiple reasoning methods has been misunderstood by a number of authors writing on epistemic permissiveness and peer disagreement. (shrink)

This book is about the respective roles of intuition and reasoning in ethics. It responds to a number of well-known philosophers and psychologists, and proposes a new perspective – radical in its moderation. It examines in depth the work of the philosopher Joshua Greene and the psychologist Jonathan Haidt. With the so-called empirical turn in ethics, much work has been done to try to isolate the role of reason and intuition in forming our moral judgements, with Haidt and Greene (...) leading the research programmes and attracting much of the professional and public attention, and many others following. The current view – shared by both camps – is that intuition is largely the driver of our moral judgements – a view summed up in Haidt’s slogan ‘intuition first, strategic reasoning second’. Haidt believes we have to live with this and accept it. Greene does not: he contends that our intuitions, while suitable for the environments in which we evolved, are worthless in the modern, global, technological age, and to avoid ethical disaster we must learn to adopt reason as the arbiter of moral truth. This book steers a middle course between these two positions and is therefore of great interest to philosophers and psychologists alike. (shrink)

In this paper, I explore the question of whether the expected consequences of holding a belief can affect the rationality of doing so. Special attention is given to various ways in which one might attempt to exert some measure of control over what one believes and the normative status of the beliefs that result from the successful execution of such projects. I argue that the lessons which emerge from thinking about the case ofbelief have important implications for the way we (...) should think about the rationality of a number of other propositional attitudes,such as regret, desire, and fear. Finally,I suggest that a lack of clarity with respect to the relevant issues has given rise to a number of rather serious philosophical mistakes. (shrink)

The independence of irrelevant alternatives is a popular and important axiom of decision theory. It states, roughly, that one’s choice from a set of options should not be influenced by the addition or removal of further, unchosen options. In recent debates, a number of authors have given putative counterexamples to it, involving intuitively rational agents who violate IIA. Generally speaking, however, these counterexamples do not tend to move IIA’s proponents. Their strategy tends to be to individuate the options (...) that the agent faces differently, so that the case no longer counts as a violation of IIA. In this paper, we examine whether this strategy succeeds. We argue that the ways of individuating options required to save IIA from the most problematic counterexamples—in particular, cases where agents violate IIA due to nonconsequentialist moral beliefs—do so only at the expense of severely compromising its central function within decision theory. (shrink)

Evolutionary thinking has expanded in the last decades, spreading from its traditional stronghold - the explanation of speciation and adaptation in Biology - to new domains including the human sciences. The essays in this collection attest to the illuminating power of evolutionary thinking when applied to the understanding of the human mind. The contributors to Cognition, Evolution and Rationality use an evolutionary standpoint to approach the nature of the human mind, including both cognitive and behavioral functions. Cognitive science is by (...) its nature an interdisciplinary subject and the essays use a variety of disciplines including the Philosophy of Science, the Philosophy of Mind, Game Theory, Robotics and Computational Neuroanatomy to investigate the workings of the mind. The topics covered by the essays range from general methodological issues to long-standing philosophical problems such as how rational human beings actually are. This book will be of interest across a number of fields, including philosophy, evolutionary theory and cognitive science. (shrink)

Area number x is called k-monotonically computable , for constant k > 0, if there is a computable sequence n ∈ ℕ of rational numbers which converges to x such that the convergence is k-monotonic in the sense that k · |x — xn| ≥ |x — xm| for any m > n and x is monotonically computable if it is k-mc for some k > 0. x is weakly computable if there is a computable sequence s ∈ (...) ℕ of rational numbers converging to x such that the sum equation image|xs — xs + 1| is finite. In this paper we show that a mc real numbers are weakly computable but the converse fails. Furthermore, we show also an infinite hierarchy of mc real numbers. (shrink)

A number of philosophers argue that law enforcement officers may have good reasons to racially profile suspects under certain conditions. Their conclusions rest on a claim of epistemic rationality: if members of some races are at an increased risk of criminality, then it may be rational for law enforcement officers to subject them to increased scrutiny. In this paper I contest the epistemic rationality of racial profiling by appealing to recent work in criminology and the sociology of race (...) and crime. I argue that recent studies indicate that race is a comparatively poor baseline for judging criminality. Law enforcement officers are therefore not making a cognitive error by ignoring race to focus on other correlates of crime but are keeping up with our best social science. (shrink)

Additive theories of rationality, as I use the term, are theories that hold that an account of our capacity to reflect on perceptually-given reasons for belief and desire-based reasons for action can begin with an account of what it is to perceive and desire, in terms that do not presuppose any connection to the capacity to reflect on reasons, and then can add an account of the capacity for rational reflection, conceived as an independent capacity to ‘monitor’ and ‘regulate’ (...) our believing-on-the-basis-of-perception and our acting-on-the-basis-of-desire. I show that a number of recent discussions of human rationality are committed to an additive approach, and I raise two difficulties for this approach, each analogous to a classic problem for Cartesian dualism. The interaction problem concerns how capacities conceived as intrinsically independent of the power of reason can interact with this power in what is intuitively the right way. The unity problem concerns how an additive theorist can explain a rational subject's entitlement to conceive of the animal whose perceptual and desiderative life he or she oversees as ‘I’ rather than ‘it’. I argue that these difficulties motivate a general skepticism about the additive approach, and I sketch an alternative, ‘transformative’ framework in which to think about the cognitive and practical capacities of a rational animal. (shrink)

Rationing in healthcare remains very much a taboo topic. Before COVID-19, it rarely received public attention, even when it occurred in everyday practices, mainly in the form of implicit rationing, as it continues to do today. There are different definitions, types and levels of healthcare rationing, according to different perspectives. With the aim of contributing to a more coherent debate on such a highly emotional healthcare issue as rationing, here are provided a number of reflections from a patient advocate (...) perspective which are specifically focused on bedside rationing, the most troublesome level, both for patients and clinicians, particularly in regard to cancer care. Oncology, with its numerous expensive therapies and increasing number of patients, is undeniably one of the main areas contributing to the increase in healthcare costs. However, the fixed budgets of today's publicly financed health systems cannot allow unlimited access to the potentially beneficial treatments to all patients. Bedside rationing constitutes the last phase of many decision-making processes occurring at different interrelated levels (macro-levels), both inside and outside healthcare systems, which implicitly and inevitably result in a bottleneck determined by the upstream decisions themselves. Shifting from implicit to explicit bedside rationing essentially means moving from a paternalistic to a citizen-before-patient approach; this implies, first of all, a cultural change. Practical bedside rationing is an ethically complex topic, but one that needs to be urgently addressed in a transparent and open debate. In this scenario, the oncological community – patients, patient advocates and clinicians – can and should play an important role. (shrink)

An important area of business ethics research focuses on how otherwise normal and law-abiding individuals can engage in acts of corruption. Key in this literature is the concept of rationalization. This is where individuals attempt to justify past and future corrupt deeds to themselves and others. In this article, we argue that rationalization often entails a process of overcompensation whereby the justification forwarded is excessive in relation to the actual act. Such over-rationalization provides an impetus for further and more serious (...) acts of illegality. Using a number of high profile cases, it is argued that this dynamic gap between the act and excessive rationalization can explain why corruption often escalates in severity and scope in the organization. (shrink)

BackgroundRationing of care in nursing is nurses' inability to complete all care activities for patients because of scarcity in time and resource. Literature suggests that rationing of care is closely related to patient safety and quality of care. The phenomena have been defined and studied from varied perspectives and contexts. A systematic review of studies related to the concept was aimed at identifying and synthesizing the finding.MethodsThe review followed Preferred Reporting Items for Systematic Reviews and Meta‐analysis guidelines, and literature searches (...) were conducted in MEDLINE, CINAHL, PsycInfo, Web of Science and EMBASE databases. Fifty‐seven quantitative studies were included in the review.FindingsThe review observed that nursing activities addressing the emotional, educational, mobility and hygiene needs of the patients were commonly rationed. Antecedents of rationing included resource inadequacy and organizational work environment. Rationing influenced patient satisfaction, mortality and a number of adverse events and was associated with decreased job satisfaction, increased intention to leave and high turnover among nurses.DiscussionsThis review concludes that rationing in nursing is ubiquitous, embedded in the work environment and poses a threat to the professional health and philosophical base of nursing in addition to having serious implications on patients' safety. Strategies to reframe and reconsider organizational traits, and open discussion with other healthcare stakeholders can reduce rationing of nursing care. The review suggests future researchers adopt different methodological layout to study rationing. (shrink)

This is a major contribution to the theory of rational choice which will be of particular interest to philosophers and economists. The author sets out the foundations of rational choice, and then sketches a dynamic choice framework in which principles of ordering and independence follow from a number of apparently plausible conditions. However, there is potential conflict among these conditions, and when they are weakened to avoid it the usual foundations of rational choice no longer prevail. (...) The thrust of the argument is to suggest that the theory of rational choice is less deterministic than many suppose. (shrink)

A number of authors, Including Thomas Schelling and David Lewis, have envisaged a model of the generation of action in coordination problems in which salience plays a crucial role. Empirical studies suggest that human subjects are likely to try for the salient combination of actions, a tendency leading to fortunate results. Does rationality dictate that one aim at the salient combination? Some have thought so, Thus proclaiming that salience is all that is needed to resolve coordination problems for agents (...) who are rational in the sense of game theory. I argue against this position; rational agents will not necessarily aim for the salient. It remains to explain how the salient comes to be chosen by human beings. Various possibilities are noted. One involves a mechanism invoked by Hume and Wittgenstein in other contexts: we may project an unreasoned compulsion onto reason, falsely believing that rationality dictates our choice of the salient. (shrink)

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility (...) theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate. (shrink)

I argue that if a normative theory of practical rationality is to represent an adequate and coherent response to a plurality of incommensurable goods, it cannot be a maximising theory. It will have to be a theory that recognises two responses to goods as morally licit – promotion and respect – and one as morally illicit – violation. This result has a number of interesting corollaries, some of which I indicate. Perhaps the most interesting is that it makes the (...) existence of a plurality of incommensurable goods incompatible with consequentialism. (shrink)

In the United Kingdom, a number of National Health Service Clinical Commissioning Groups have proposed controversial measures to restrict elective surgery for patients who either smoke or are obese. Whilst the nature of these measures varies between NHS authorities, typically, patients above a certain Body Mass Index and smokers are required to lose weight and quit smoking prior to being considered eligible for elective surgery. Patients will be supported and monitored throughout this mandatory period to ensure their clinical needs (...) are appropriately met. Controversy regarding such measures has primarily centred on the perceived unfairness of targeting certain health states and lifestyle choices to save public money. Concerns have also been raised in response to rhetoric from certain NHS authorities, which may be taken to imply that such measures punitively hold people responsible for behaviours affecting their health states, or simply for being in a particular health state. In this paper, we examine the various elective surgery rationing measures presented by NHS authorities. We argue that, where obesity and smoking have significant implications for elective surgical outcomes, bearing on effectiveness, the rationing of this surgery can be justified on prognostic grounds. It is permissible to aim to maximise the benefit provided by limited resources, especially for interventions that are not urgently required. However, we identify gaps in the empirical evidence needed to conclusively demonstrate these prognostic grounds, particularly for obese patients. Furthermore, we argue that appeals to personal responsibility, both in the prospective and retrospective sense, are insufficient in justifying this particular policy. Given the strength of an alternative justification grounded in clinical effectiveness, rhetoric from NHS authorities should avoid explicit statements, which suggest that personal responsibility is the key justificatory basis of proposed rationing measures. (shrink)

To support the claim that the approximate number system represents rational numbers, Clarke and Beck argue that number perception is abstract and characterized by a second-order character. However, converging evidence from visual illusions and psychophysics suggests that perceived number is not abstract, but rather, is perceptually interdependent with other magnitudes. Moreover, number, as a concept, is second-order, but number, as a percept, is not.

Evolutionary thinking has expanded in the last decades, spreading from its traditional stronghold – the explanation of speciation and adaptation in biology - to new domains. Fascinating pieces of work, the essays in this collection attest to the illuminating power of evolutionary thinking when applied to the understanding of the human mind. The contributors to_ Cognition, Evolution and Rationality_ use an evolutionary standpoint to approach the nature of the human mind, including both cognitive and behavioural functions. Cognitive science is by (...) its nature an interdisciplinary subject and the essays in this collection investigate the workings of the mind through a variety of disciplines including the philosophy of science, the philosophy of mind, game theory, robotics and computational neuroanatomy. Topics covered range from general methodological issues to long-standing philosophical problems such as how rational human beings actually are. With contributions from leading experts in the areas involved, this book will be of interest across a number of fields, including philosophy, evolutionary theory and cognitive science. (shrink)

Evolutionary thinking has expanded in the last decades, spreading from its traditional stronghold – the explanation of speciation and adaptation in biology - to new domains. Fascinating pieces of work, the essays in this collection attest to the illuminating power of evolutionary thinking when applied to the understanding of the human mind. The contributors to_ Cognition, Evolution and Rationality_ use an evolutionary standpoint to approach the nature of the human mind, including both cognitive and behavioural functions. Cognitive science is by (...) its nature an interdisciplinary subject and the essays in this collection investigate the workings of the mind through a variety of disciplines including the philosophy of science, the philosophy of mind, game theory, robotics and computational neuroanatomy. Topics covered range from general methodological issues to long-standing philosophical problems such as how rational human beings actually are. With contributions from leading experts in the areas involved, this book will be of interest across a number of fields, including philosophy, evolutionary theory and cognitive science. (shrink)

Against Clarke and Beck's proposal that the approximate number system represents natural and rational numbers, I suggest that the experimental evidence is better accommodated by the thesis that the ANS represents cardinality comparisons. Cardinality comparisons do not stand in arithmetical relations and being able to apply them does not involve basic arithmetical concepts and operations.

The proposal by Clarke and Beck offers a new explanation for the association between the approximate number system and math. Previous explanations have largely relied on developmental arguments, an underspecified notion of the ANS as an “error detection mechanism,” or affective factors. The proposal that the ANS represents rational numbers suggests that it may directly support a broader range of math skills.

Timothy Hsiao argues that animals lack moral status because they lack the capacity for the sort of higher-level rationality required for membership in the moral community. Stijn Bruers and László Erdős have already raised a number of objections to this argument, to which Hsiao has replied with some success. But I think a stronger critique can be made. Here I raise further objections to three aspects of Hsiao's view: his conception of the moral community, his idea of root capacities (...) grounded in one's nature, and his explanation of why cruelty is wrong. I also argue that sentience is a more plausible candidate for the morally salient capacity than rationality. (shrink)

In this paper, I explore the question of whether the expectedconsequences of holding a belief can affect the rationality ofdoing so. Special attention is given to various ways in whichone might attempt to exert some measure of control over whatone believes and the normative status of the beliefs thatresult from the successful execution of such projects. I arguethat the lessons which emerge from thinking about the case ofbelief have important implications for the way we should thinkabout the rationality of a (...) number of other propositional attitudes,such as regret, desire, and fear. Finally,I suggest that a lack of clarity with respect to the relevant issueshas given rise to a number of rather serious philosophical mistakes. (shrink)