In The Border between Seeing and Thinking, Ned Block argues that the distinction between perception and cognition should be grounded in representational format. I object that cognition is multifaceted, and includes representations with the same format as some perceptual representations. We can save Block’s view by interpreting it as concerning the border between one elite species of cognition—namely, propositional thought—and everything below it, including perception. But that leaves the border between perception and cognition in general unexplained. To fill this gap, (...) I recommend my stimulus-dependence account of the border and reply to objections Block raises against it. This brings into relief a category of mind that is crucial to understanding human infants and nonhuman animals—namely, nonpropositional cognition, which sits between perception and propositional thought. (shrink)

A background assumption in much contemporary political philosophy is that justice is the first virtue of social institutions, taking priority over other values such as beneficence. This assumption is typically treated as a methodological starting point, rather than as following from any particular moral or political theory. In this paper, I challenge this assumption. To frame my discussion, I argue, first, that justice doesn’t in principle override beneficence, and second, that justice doesn’t typically outweigh beneficence, since, in institutional contexts, the (...) stakes of beneficence are often extremely high. While there are various ways one might resist this argument, none challenge the core methodological point that political philosophy should abandon its preoccupation with justice and begin to pay considerably more attention to social beneficence—that is, to beneficence understood as a virtue of social institutions. Along the way, I also highlight areas where focusing on social beneficence would lead political philosophers in new and fruitful directions, and where normative ethicists focused on personal beneficence might scale up their thinking to the institutional case. GPI Working Paper No. 11-2022. (shrink)

Medical nihilism is the view that we should have little confidence in the effectiveness of medical interventions. Jacob Stegenga argues persuasively that this is how we should see modern medicine, and suggests that medical research must be modified, clinical practice should be less aggressive, and regulatory standards should be enhanced.

Philosophy, scientific psychology, and common sense all distinguish perception from cognition. While there is little agreement about how the perception–cognition boundary ought to be drawn, one prominent idea is that perceptual states are dependent on a stimulus, or stimulus-dependent, in a way that cognitive states are not. This paper seeks to develop this idea in a way that can accommodate two apparent counterexamples: hallucinations, which are prima facie perceptual yet stimulus-independent; and demonstrative thoughts, which are prima facie cognitive yet stimulus-dependent. (...) The payoff is not only a specific proposal for marking the perception–cognition boundary, but also a deeper understanding of the natures of hallucination and demonstrative thought. (shrink)

I summarize and critically review Block's book, focusing on his format-based account of the border between perception and cognition and his argument for the phenomenal overflow of color perception.

In the 1980s, a number of philosophers argued that perception is analog. In the ensuing years, these arguments were forcefully criticized, leaving the thesis in doubt. This paper draws on Weber’s Law, a well-entrenched finding from psychophysics, to advance a new argument that perception is analog. This new argument is an adaptation of an argument that cognitive scientists have leveraged in support of the contention that primitive numerical representations are analog. But the argument here is extended to the representation of (...) non-numerical magnitudes, such as luminance and distance, and shown to apply to perception and not just cognition. The relevant sense of ‘analog’ is also clarified, and two powerful objections are addressed. Finally, the question whether perception’s analog vehicles are located in conscious experience is explored and related to a well-known controversy within psychophysics. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. However, the most familiar instances of magnetic forces acting in everyday life, such as when bar magnets lift other bar magnets, appear to present manifest evidence of magnetic forces doing work. These sorts of (...) counterexamples are often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)

An astonishing volume and diversity of evidence is available for many hypotheses in the biomedical and social sciences. Some of this evidence—usually from randomized controlled trials (RCTs)—is amalgamated by meta-analysis. Despite the ongoing debate regarding whether or not RCTs are the ‘gold-standard’ of evidence, it is usually meta-analysis which is considered the best source of evidence: meta-analysis is thought by many to be the platinum standard of evidence. However, I argue that meta-analysis falls far short of that standard. Different meta-analyses (...) of the same evidence can reach contradictory conclusions. Meta-analysis fails to provide objective grounds for intersubjective assessments of hypotheses because numerous decisions must be made when performing a meta-analysis which allow wide latitude for subjective idiosyncrasies to influence its outcome. I end by suggesting that an older tradition of evidence in medicine—the plurality of reasoning strategies appealed to by the epidemiologist Sir Bradford Hill—is a superior strategy for assessing a large volume and diversity of evidence. (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

According to the Generality Constraint, mental states with conceptual content must be capable of recombining in certain systematic ways. Drawing on empirical evidence from cognitive science, I argue that so-called analogue magnitude states violate this recombinability condition and thus have nonconceptual content. I further argue that this result has two significant consequences: it demonstrates that nonconceptual content seeps beyond perception and infiltrates cognition; and it shows that whether mental states have nonconceptual content is largely an empirical matter determined by the (...) structure of the neural representations underlying them. (shrink)

Robustness is a common platitude: hypotheses are better supported with evidence generated by multiple techniques that rely on different background assumptions. Robustness has been put to numerous epistemic tasks, including the demarcation of artifacts from real entities, countering the “experimenter’s regress,” and resolving evidential discordance. Despite the frequency of appeals to robustness, the notion itself has received scant critique. Arguments based on robustness can give incorrect conclusions. More worrying is that although robustness may be valuable in ideal evidential circumstances (i.e., (...) when evidence is concordant), often when a variety of evidence is available from multiple techniques, the evidence is discordant. †To contact the author, please write to: Jacob Stegenga, Department of Philosophy, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093; e‐mail: [email protected]. (shrink)

Science and technology are so intertwined that technoscience has been argued to more accurately reflect the progress of science and its impact on society, and most socioscientific issues require technoscientific reasoning. Education policy documents have long noted that the general public lacks sufficient understanding of science and technology necessary for informed decision-making regarding socioscientific/technological issues. The science–technology–society movement and scholarship addressing socioscientific issues in science education reflect efforts in the science education community to promote more informed decision-making regarding such issues. (...) Now Science, Technology, Engineering, Mathematics education has emerged as a major reform movement impacting science education. STEM education efforts emphasize literacy across the disciplines of science, technology, engineering, and mathematics, but with rare exceptions, treat issues of technology superficially and uncritically. Informed decision-making regarding many personal and societal issues requires technological literacy beyond merely becoming an enthusiastic designer or skilled user of technology, but the science education community has given little attention to what such literacy entails. Here, we present results of an extensive review of the literature regarding the nature of technology in order to identify key issues among scholars who study technology. We then provide predominant perspectives among those scholars and suggest which identified NOT issues are most essential to address as part of STEM education efforts that seek to promote informed personal and societal decision-making. (shrink)

Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...) philosophical audience by rehearsing empirical evidence for their existence and analysing their format, their content, and the computations they support. 1 Background1.1 Evidence of analogue magnitude representations1.2 Weber’s law1.3 Scepticism about analogue magnitude representations2 Format2.1 Carey’s analogy2.2 Neural realization2.3 Analogue representation2.4 Analogue magnitude representation components3 Content3.1 Do analogue magnitude representations have representational content?3.2 What do analogue magnitude representations represent?3.3 What content types do analogue magnitude representations have?4 Computations4.1 Arithmetic computation4.2 Practical deliberation5 Conclusion. (shrink)

Matteo Ricci (1552-1610) was an Italian Jesuit and one of the first Christian missionaries to China in the modern era. He was a genuine polymath—a translator, cartographer, mathematician, astronomer, and musician. Above all, Ricci was a missionary for the gospel. As we briefly examine his 1603 seminal work, The True Meaning of the Lord of Heaven, our hope is that we, as evangelical educators, will perceive some of the deeper principles necessary for our own missionary work among unreached people.

Measuring the effectiveness of medical interventions faces three epistemological challenges: the choice of good measuring instruments, the use of appropriate analytic measures, and the use of a reliable method of extrapolating measures from an experimental context to a more general context. In practice each of these challenges contributes to overestimating the effectiveness of medical interventions. These challenges suggest the need for corrective normative principles. The instruments employed in clinical research should measure patient-relevant and disease-specific parameters, and should not be sensitive (...) to parameters that are only indirectly relevant. Effectiveness always should be measured and reported in absolute terms (using measures such as 'absolute risk reduction'), and only sometimes should effectiveness also be measured and reported in relative terms (using measures such as 'relative risk reduction')-employment of relative measures promotes an informal fallacy akin to the base-rate fallacy, which can be exploited to exaggerate claims of effectiveness. Finally, extrapolating from research settings to clinical settings should more rigorously take into account possible ways in which the intervention in question can fail to be effective in a target population. (shrink)

In 1655 La Peyrère was the first to substantially argue for and popularize polygenism—the view that God created multiple original human mating pairs in separate acts of creation with numerous created before Adam. Positing or rejecting polygenism has been central to modern theorizing about human types and origins. Prominent recent interpreters have maintained that La Peyrère’s polygenism does not imply a hierarchy of human types. This paper reconstructs La Peyrère’s account and, in opposition to the dominant view, argues that his (...) polygenism produces a human species hierarchy. The Adamite species is superior to the Pre-Adamite species in virtue of its material composition, mode of creation, and form. The upshot is that La Peyrère’s theological system posits a proto-racialist conception of human types. (shrink)

The tuning-fork model of human social cognition, based on the discovery of mirror neurons (MNs) in the ventral premotor cortex of monkeys, involves the four following assumptions: (1) mirroring processes are processes of resonance or simulation. (2) They can be motor or non-motor. (3) Processes of motor mirroring (or action-mirroring), exemplified by the activity of MNs, constitute instances of third-person mindreading, whereby an observer represents the agent's intention. (4) Non-motor mirroring processes enable humans to represent others' emotions. After questioning all (...) four assumptions, I point out that MNs in an observer's brain could not synchronically resonate with MNs in an agent's brain unless they discharged in a single brain in two distinct tasks at different times. Finally, I sketch a conceptualist alternative to the resonance model according to which a brain mechanism active in both the execution and the perception of e.g., the act of grasping is the neural basis of the concept of e.g., grasping. (shrink)

Building on Christopher Peacocke’s account of analog perceptual contentand my own account of analog perceptual vehicles, I defend three claims: that theperception of magnitudes often has analog contents; that the perception of magni-tudes often has analog vehicles; and that the first claim is true in virtue of the second—that is, the analog vehicles help to ground the analog contents.

David Rosenthal explains conscious mentality in terms of two independent, though complementary, theories—the higher-order thought (“HOT”) theory of consciousness and quality-space theory (“QST”) about mental qualities. It is natural to understand this combination of views as constituting a kind of representationalism about experience—that is, a version of the view that an experience’s conscious character is identical with certain of its representational properties. At times, however, Rosenthal seems to resist this characterization of his view. We explore here whether and to what (...) extent it makes sense to construe Rosenthal’s views as representationalist. Our goal is not merely terminological—discerning how best to use the expression ‘representationalism’. Rather, we argue that understanding Rosenthal’s account as a kind of representationalism permits us not only to make sense of broader debates within the philosophy of mind, but also to extend and clarify aspects of the view itself. (shrink)

John Morrison has argued that confidences are assigned in perceptual experience. For example, when you perceive a figure in the distance, your experience might assign a 55-percent confidence to the figure’s being Isaac. Morrison’s argument leans on the phenomenon of ‘completely trusting your experience’. I argue that Morrison presupposes a problematic ‘importation model’ of this familiar phenomenon, and propose a very different way of thinking about it. While the article’s official topic is whether confidences are assigned in perceptual experience, it (...) is also about two more general issues: how we can determine which properties are assigned in perceptual experience; and how we transition from perception to belief. (shrink)

This book provides a detailed account of the role of property in German Idealism. It puts the concept of property in the center of the philosophical systems of Kant, Fichte, and Hegel and shows how property remains tied to their conceptions of freedom, right, and recognition. The book begins with a critical genealogy of the concept of property in modern legal philosophy, followed by a reconstruction of the theory of property in Kant's Doctrine of Right, Fichte's Foundations of Natural Right, (...) and Hegel's Jena Realphilosophie. By turning to the tradition of German Rechtsphilosophie, as opposed to the more standard libertarian and utilitarian frameworks of property, it explores the metaphysical, normative, political, and material questions that make property intelligible as a social relation. The book formulates a normative theory of property rooted in practical reason, mutual recognition, and social freedom. This relational theory of property, inspired by German Idealism, brings a fresh angle to contemporary property theory. Additionally, it provides crucial philosophical background to 19th century debates on private property, inequality, labor, socialism, capitalism, and the state. The Concept of Property in Kant, Fichte, and Hegel will appeal to scholars and advanced students interested in 19th Century German philosophy, social and political philosophy, philosophy of law, political theory, and political economy. (shrink)

In his classic “Freedom and Resentment,” P. F. Strawson introduces us to an optimist who believes that our moral responsibility practices are justified by their beneficial consequences. Although many see Strawson as a staunch critic of this consequentialist position, his stated view is only that there is a gap in the optimist’s story where the reactive attitudes should be. In this paper, I fill in the gap. I show how optimism can be suitably modified to reflect an appreciation of the (...) reactive attitudes. And I argue that the ensuing position—on which our moral responsibility practices, taken as a whole, are justified both by their regulation of behavior and by their enabling of interpersonal relationships—provides us not only with a plausible justification of our moral responsibility practices, but also with a fruitful framework for evaluating potential reforms. (shrink)

Physicians expressing opinions on medical matters that run contrary to the consensus of experts pose a challenge to licensing bodies and regulatory authorities. While the right to express contrarian views feeds a robust marketplace of ideas that is essential for scientific progress, physicians advocating ineffective or dangerous cures, or actively opposing public health measures, pose a grave threat to societal welfare. Increasingly, a distinction has been made between professional speech that occurs during the physician-patient encounter and public speech that transpires (...) beyond the clinical setting, with physicians being afforded wide latitude to voice empirically false claims outside the context of patient care. This paper argues that such a bifurcated model does not sufficiently address the challenges of an age when mass communications and social media allow dissenting physicians to offer misleading medical advice to the general public on a mass scale. Instead, a three-tiered model that distinguishes between citizen speech, physician speech and clinical speech would best serve authorities when regulating physician expression. (shrink)

We summarize a new realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive (...) picture of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. Our interpretation—which we claim is ultimately compatible with Lorentz invariance—reformulates wave-function collapse in terms of an underlying interpolating dynamics, makes it possible to derive the Born rule from deeper principles, and resolves several open questions regarding ontological stability and dynamics. (shrink)

Resource Bounded Agents Resource bounded agents are persons who have information processing limitations. All persons and other cognitive agents who have bodies are such that their sensory transducers have limited resolution and discriminatory ability; their information processing speed and power is bounded by some threshold; and their memory and … Continue reading Resource Bounded Agents →.

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Robustness arguments hold that hypotheses are more likely to be true when they are confirmed by diverse kinds of evidence. Robustness arguments require the confirming evidence to be independent. We identify two kinds of independence appealed to in robustness arguments: ontic independence —when the multiple lines of evidence depend on different materials, assumptions, or theories—and probabilistic independence. Many assume that OI is sufficient for a robustness argument to be warranted. However, we argue that, as typically construed, OI is not a (...) sufficient independence condition for warranting robustness arguments. We show that OI evidence can collectively confirm a hypothesis to a lower degree than individual lines of evidence, contrary to the standard assumption undergirding usual robustness arguments. We employ Bayesian networks to represent the ideal empirical scenario for a robustness argument and a variety of ways in which empirical scenarios can fall short of this ideal. (shrink)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

Evidence hierarchies are widely used to assess evidence in systematic reviews of medical studies. I give several arguments against the use of evidence hierarchies. The problems with evidence hierarchies are numerous, and include methodological shortcomings, philosophical problems, and formal constraints. I argue that medical science should not employ evidence hierarchies, including even the latest and most-sophisticated of such hierarchies.

Despite a staggering body of research demonstrating sex differences in expressed emotion, very few theoretical models (evolutionary or non-evolutionary) offer a critical examination of the adaptive nature of such differences. From the perspective of a socio-relational framework, emotive behaviors evolved to promote the attraction and aversion of different types of relationships by advertising the two most parsimonious properties ofreciprocity potential, or perceived attractiveness as a prospective social partner. These are the individual's (a)perceived capacityor ability to provide expedient resources, or to (...) inflict immediate harm onto others, and their (b)perceived trustworthinessor probability of actually reciprocating altruism (Vigil 2007). Depending on the unique social demands and relational constraints that each sex evolved, individuals should be sensitive to advertise “capacity” and “trustworthiness” cues through selective displays of dominant versus submissive and masculine versus feminine emotive behaviors, respectively. In this article, I introduce the basic theoretical assumptions and hypotheses of the framework, and show how the models provide a solid scaffold with which to begin to interpret common sex differences in the emotional development literature. I conclude by describing how the framework can be used to predict condition-based and situation-based variation in affect and other forms of expressive behaviors. (shrink)

A platitude that took hold with Kuhn is that there can be several equally good ways of balancing theoretical virtues for theory choice. Okasha recently modelled theory choice using technical apparatus from the domain of social choice: famously, Arrow showed that no method of social choice can jointly satisfy four desiderata, and each of the desiderata in social choice has an analogue in theory choice. Okasha suggested that one can avoid the Arrow analogue for theory choice by employing a strategy (...) used by Sen in social choice, namely, to enhance the information made available to the choice algorithms. I argue here that, despite Okasha’s claims to the contrary, the information-enhancing strategy is not compelling in the domain of theory choice. (shrink)

Much of the work in moral philosophy and the political debate on abortion has focused on when in human development personhood begins. In this article, using a variant of Derek Parfit’s view on personal identity, I instead frame the question as one of victimhood. I argue for what I call the Victim Requirement for the wrongness of killing–killing is wrong only if there is an identifiable victim. An identifiable victim is, temporally speaking, in the midst of a chain of psychological (...) connections in the sense of “Relation R.” I go on to argue for a version of psychological identity which makes consciousness a necessary condition of rational self-interest and numerical identity across time. The implications for the abortion debate, based upon the best neurological evidence, are that abortion cannot be wrong before at least 22 weeks of pregnancy and perhaps significantly later. I then respond to alternatives to my Victim Requirement and argue that they either fail on their own merits or are deeply problematic. Finally, I discuss the role of autonomy and consent in a world where fetal consciousness develops much earlier. (shrink)

The value-free ideal for science holds that values should not influence the core features of scientific reasoning. We defend the difference-to-inference model of value-permeation, which holds that value-permeation in science is problematic when values make a difference to the inferences made about a hypothesis. This view of value-permeation is superior to existing views, and it suggests a corresponding maxim—namely, that scientists should strive to eliminate differences to inference. This maxim is the basis of a novel value-free ideal for science. -/- (...) . (shrink)

Susan Carey's account of Quinean bootstrapping has been heavily criticized. While it purports to explain how important new concepts are learned, many commentators complain that it is unclear just what bootstrapping is supposed to be or how it is supposed to work. Others allege that bootstrapping falls prey to the circularity challenge: it cannot explain how new concepts are learned without presupposing that learners already have those very concepts. Drawing on discussions of concept learning from the philosophical literature, this article (...) develops a detailed interpretation of bootstrapping that can answer the circularity challenge. The key to this interpretation is the recognition of computational constraints, both internal and external to the mind, which can endow empty symbols with new conceptual roles and thus new contents. (shrink)

Close attention to Kant’s comments on animal minds has resulted in radically different readings of key passages in Kant. A major disputed text for understanding Kant on animals is his criticism of G. F. Meier’s view in the 1762 ‘False Subtlety of the Four Syllogistic Figures’. In this article, I argue that Kant’s criticism of Meier should be read as an intervention into an ongoing debate between Meier and H. S. Reimarus on animal minds. Specifically, while broadly aligning himself with (...) Reimarus, Kant distinguishes himself from both Meier and Reimarus on the role of judgement in human consciousness. (shrink)

Realists about animal cognition confront a puzzle. If animals have real, contentful cognitive states, why can’t anyone say precisely what the contents of those states are? I consider several possible resolutions to this puzzle that are open to realists, and argue that the best of these is likely to appeal to differences in the format of animal cognition and human language.

The “Goldwater rule,” a policy adopted by the American Psychiatry Association in 1973, prohibits organization members from diagnosing or offering professional opinions regarding the mental health of public figures without both first-hand evaluation and authorization. Initially developed in response to a controversial survey of APA members during the 1964 Presidential election campaign, the ethics rule faced few large scale challenges until the election of Donald Trump in 2016. Since that time, a significant number of psychiatrists have either violated or criticized (...) the rule openly. This paper argues that whatever the initial merits of the rule, the prohibition has since been rendered obsolete by the combined lack of professional consensus supporting the policy, absence of a meaningful enforcement mechanism, and the credible statements of non-APA members in the mental health professions regarding public figures. (shrink)

I defend a radical interpretation of biological populations—what I call population pluralism—which holds that there are many ways that a particular grouping of individuals can be related such that the grouping satisfies the conditions necessary for those individuals to evolve together. More constraining accounts of biological populations face empirical counter-examples and conceptual difficulties. One of the most intuitive and frequently employed conditions, causal connectivity—itself beset with numerous difficulties—is best construed by considering the relevant causal relations as ‘thick’ causal concepts. I (...) argue that the fine-grained causal relations that could constitute membership in a biological population are huge in number and many are manifested by degree, and thus we can construe population membership as being defined by massively multidimensional constructs, the differences between which are largely arbitrary. I end by showing that positions in two recent debates in theoretical biology depend on a view of biological populations at odds with the pluralism defended here. (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.

Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of “analog” presupposed by these arguments for analog mental representation, and to open avenues for future research.