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.

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)

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)

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.

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)

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 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)

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)

Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent. A natural idea is that there are requirements of "structural rationality" that forbid us from being in these incoherent states. Yet a number of surprisingly difficult challenges arise for this idea. These challenges have recently led many philosophers to attempt to minimize or eliminate structural rationality, arguing that it is just a "shadow" of "substantive rationality"--that is, correctly responding to one's (...) reasons. -/- In *Fitting Things Together*, Alex Worsnip pushes back against this trend--defending the view that structural rationality is a genuine kind of rationality, distinct from and irreducible to substantive rationality, and tackling the most important challenges for this view. In so doing, he gives an original positive theory of the nature of coherence and structural rationality that explains how the diverse range of instances of incoherence can be unified under a general account, and how facts about coherence are normatively significant. He also shows how a failure to focus on coherence requirements as a distinctive phenomenon and distinguish them adequately from requirements of substantive rationality has led to confusion and mistakes in several substantive debates in epistemology and ethics. -/- Taken as a whole, Fitting Things Together provides the first sustained defense of the view that structural rationality is a genuine, autonomous, unified, and normatively significant phenomenon. (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)

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.

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)

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)

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)

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)

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.

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.

Vagueness is often regarded as a kind of defect of our language or of our thinking. This paper portrays vagueness as the natural outcome of applying a number of rationality principles to the cognitive domain. Given our physical and cognitive makeup, and given the way the world is, applying those principles to conceptualization predicts not only the concepts that are actually in use, but also their vagueness, and how and when their vagueness manifests itself.

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)

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)

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)

Belief polarization is said to occur when two people respond to the same evidence by updating their beliefs in opposite directions. This response is considered to be “irrational” because it involves contrary updating, a form of belief updating that appears to violate normatively optimal responding, as for example dictated by Bayes' theorem. In light of much evidence that people are capable of normatively optimal behavior, belief polarization presents a puzzling exception. We show that Bayesian networks, or Bayes nets, can simulate (...) rational belief updating. When fit to experimental data, Bayes nets can help identify the factors that contribute to polarization. We present a study into belief updating concerning the reality of climate change in response to information about the scientific consensus on anthropogenic global warming. The study used representative samples of Australian and U.S. participants. Among Australians, consensus information partially neutralized the influence of worldview, with free-market supporters showing a greater increase in acceptance of human-caused global warming relative to free-market opponents. In contrast, while consensus information overall had a positive effect on perceived consensus among U.S. participants, there was a reduction in perceived consensus and acceptance of human-caused global warming for strong supporters of unregulated free markets. Fitting a Bayes net model to the data indicated that under a Bayesian framework, free-market support is a significant driver of beliefs about climate change and trust in climate scientists. Further, active distrust of climate scientists among a small number of U.S. conservatives drives contrary updating in response to consensus information among this particular group. (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)

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)

This book explores a new approach to understanding the human mind - rational analysis - that regards thinking as a facility adapted to the structure of the world. This approach is most closely associated with the work of John R Anderson, who published the original book on rational analysis in 1990. Since then, a great deal of work has been carried out in a number of laboratories around the world, and the aim of this book is to bring (...) this work together for the benefit of the general psychological audience. The book contains chapters by some of the world's leading researchers in memory, categorisation, reasoning, and search, who show how the power of rational analysis can be applied to the central question of how humans think. It will be of interest to students and researchers in cognitive psychology, cognitive science, and animal behaviour. (shrink)

There is a venerable philosophical tradition that views human beings as intrinsically rational, though even the most ardent defender of this view would admit that under certain circumstances people’s decisions and thought processes can be very irrational indeed. When people are extremely tired, or drunk, or in the grip of rage, they sometimes reason and act in ways that no account of rationality would condone. About thirty years ago, Amos Tversky, Daniel Kahneman and a number of other psychologists began (...) reporting findings suggesting much deeper problems with the traditional idea that human beings are intrinsically rational animals. What these studies demonstrated is that even under quite ordinary circumstances where fatigue, drugs and strong emotions are not factors, people reason and make judgments in ways that systematically violate familiar canons of rationality on a wide array of problems. Those first surprising studies sparked the growth of a major research tradition whose impact has been felt in economics, political theory, medicine and other areas far removed from cognitive science. In Section 2, we will sketch a few of the better known experimental findings in this area. We’ve chosen these particular findings because they will play a role at a later stage of the paper. For readers who would like a deeper and more systematic account of the fascinating and disquieting research on reasoning and judgment, there are now several excellent texts and anthologies available. (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)

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)

The term “synthetic biology” is a popular label of an emerging biotechnological field with strong claims to robustness, modularity, and controlled construction, finally enabling the creation of new organisms. Although the research community is heterogeneous, it advocates a common denominator that seems to define this field: the principles of rational engineering. However, it still remains unclear to what extent rational engineering—rather than “tinkering” or the usage of random based or non-rational processes—actually constitutes the basis for the techniques (...) of synthetic biology. In this article, we present the results of a quantitative bibliometric analysis of the realized extent of rational engineering in synthetic biology. In our analysis, we examine three issues: (1) We evaluate whether work at three levels of synthetic biology (parts, devices, and systems) is consistent with the principles of rational engineering. (2) We estimate the extent of rational engineering in synthetic biology laboratory practice by an evaluation of publications in synthetic biology. (3) We examine the methodological specialization in rational engineering of authors in synthetic biology. Our analysis demonstrates that rational engineering is prevalent in about half of the articles related to synthetic biology. Interestingly, in recent years the relative number of respective publications has decreased. Despite its prominent role among the claims of synthetic biology, rational engineering has not yet entirely replaced biotechnological methods based on “tinkering” and non-rational principles. (shrink)

It is commonly thought that belief in God couldn’t be rational unless it is held on the basis of arguments. But is that right? Could there be rational religious belief without arguments? For the past few decades, a prominent position within the philosophy of religion literature is that belief in God can be rational even if it isn’t based on any arguments. This position is often called ‘Reformed Epistemology’ to signify its roots in the writings of John (...) Calvin (1509-64), the great Protestant theologian and the main source of the Reformed tradition within Christendom. The central thesis of Reformed Epistemology is simply that religious belief, including belief in God, can be rational (sensible, reasonable, justified) even if it is not inferred from any other beliefs—even if it is not held on the basis of any argument at all. In what follows, I will explain this view in greater detail and then consider and respond to a number of objections to it. (shrink)

The project of understanding rationality in non-human animals faces a number of conceptual and methodological difficulties. The present chapter defends the view that it is counterproductive to rely on the human folk psychological idiom in animal cognition studies. Instead, it approaches the subject on the basis of dynamic- evolutionary considerations. Concepts from control theory can be used to frame the problem in the most general terms. The specific selective pressures exerted on agents endowed with information-processing capacities are analysed. It is (...) hypothesized that metacognition offers an evolutionary stable response to the various demands of the internal and external flows of information in a competitive environment. Metacognition provides a form of process-reflexivity that can, but does not have to be redeployed through metarepresentations. Finally the claim that rationality so conceived involves normativity is discussed. (shrink)

This paper provides an account of what it is to have faith in a proposition p, in both religious and mundane contexts. It is argued that faith in p doesn’t require adopting a degree of belief that isn’t supported by one’s evidence but rather it requires terminating one’s search for further evidence and acting on the supposition that p. It is then shown, by responding to a formal result due to I.J. Good, that doing so can be rational in (...) a number of circumstances. If expected utility theory is the correct account of practical rationality, then having faith can be both epistemically and practically rational if the costs associated with gathering further evidence or postponing the decision are high. If a more permissive framework is adopted, then having faith can be rational even when there are no costs associated with gathering further evidence. (shrink)

[Michael Smith] The requirements of instrumental rationality are often thought to be normative conditions on choice or intention, but this is a mistake. Instrumental rationality is best understood as a requirement of coherence on an agent's non-instrumental desires and means-end beliefs. Since only a subset of an agent's means-end beliefs concern possible actions, the connection with intention is thus more oblique. This requirement of coherence can be satisfied either locally or more globally, it may be only one among a number (...) of such requirements on an agent's total set of desires and beliefs, and it has no special connection with reasoning. An appreciation of these facts leads to a better understanding of both the nature and the significance of instrumental rationality. /// [Edward Harcourt] I argue that the incoherence Smith claims to identify in agents who desire that q, believe that p is a necessary means to q, but fail to desire that p is illusory, since it rests on the false assumption that every property I know to be possessed by an object of my desire is an object of my desire. Though the failure of Smith's account of the irrationality of this pattern of attitudes leaves it open that the pattern is indeed irrational, I argue that there are instances of it that are not irrational where the desires are desires for what the agent knows to be impossible for him. This conclusion casts doubt on the overall strategy-that of making a Humean theory of action explanation do duty as a theory of instrumental rationality-which implies that the norms of instrumental rationality apply to desires simply as such. I then try to criticise the strategy in such a way as to leave the Humean theory of action explanation unaffected. (shrink)