While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by their work is (...) significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses of ethics courses for incorporation into mathematics degrees. (shrink)

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...) The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields - some sympathetically, others unsympathetically. (shrink)

This paper extends several themes from recent work on norms of assertion. It does as much by applying those themes to the speech act of asking. In particular, it argues for the view that there is a species of asking which is governed by a certain norm, a norm to the effect that one should ask a question only if one doesn’t know its answer.

What is intellectual humility? In this essay, we aim to answer this question by assessing several contemporary accounts of intellectual humility, developing our own account, offering two reasons for our account, and meeting two objections and solving one puzzle.

When it originated in the late 19th century, psychometrics was a field with both a scientific and a social mission: psychometrics provided new methods for research into individual differences, and at the same time, these psychometric instruments were considered a means to create a new social order. In contrast, contemporary psychometrics - due to its highly technical nature and its limited involvement in substantive psychological research - has created the impression of being a value-free discipline. In this article, we develop (...) a contrasting characterization of contemporary psychometrics as a value-laden discipline. We expose four such values: that individual differences are quantitative (rather than qualitative), that measurement should be objective in a specific sense, that test items should be fair, and that utility of a model is more important than its truth. Our goal is not to criticize psychometrics for employing these values, but rather to bring them into the open and to show that these values are not inevitable and are in need of systematic evaluation. (shrink)

Abstract: Contemporary analytic philosophers of the “reactive attitudes” tend to share a simple conception of guilt as “self-directed blame”—roughly, an “unpleasant affect” felt in combination with, or in response to, the thought that one has violated a moral requirement, evinced substandard “quality of will,” or is blameworthy. I believe that this simple conception is inadequate. As an alternative, I offer my own theory of guilt’s logic and its connection to morality. In doing so, I attempt to articulate guilt’s defining thought (...) or proposition through an extended investigation and analysis of guilt’s many competing metaphors, which I trace from the Hebrew Bible to the New Testament to Shakespeare to contemporary vernacular. My interpretation of this literary genealogy offers a way to understand guilt’s seemingly disparate metaphors in terms of a single master-image that illuminates our self-conceptions and our relationship to morality. I conclude by making a very brief start toward a moral vindication of guilt against the backdrop of Nietzschean and Freudian analyses that explicitly call guilt’s place in a healthy social and personal life into question. I suggest that once guilt’s logic is made explicit, we can see that it makes sense of, honors, and addresses some of our deepest aspirations and needs. (shrink)

This paper explores the nature of curiosity from an epistemological point of view. First it motivates this exploration by explaining why epistemologists do and should care about what curiosity is. Then it surveys the relevant literature and develops a particular approach.

Naturalist views of persons, such as those of the philosophers Annette Baier and Marjorie Grene, emphasize that human persons are cultural animals: We are living, embodied, organic beings, embedded in nature, the product of Darwinian evolution, but dependent on culture. Such naturalist views of persons typically eschew science fiction and look askance at the philosophical fantasies and thought experiments that often populate philosophical treatments of personal identity. Marge Piercy’s dystopian, cyberpunk, science fiction novel He, She and It weaves a complex (...) tale around the debate over the status of its central character Yod, a cyborg created in a lab but humanized through the efforts of two women, Malkah Shipman and her granddaughter Shira Shipman. Is Yod a person, despite having been engineered in a lab for a specific purpose? Piercy’s tale both challenges and ultimately supports a naturalist view of persons while simultaneously forewarning us of possible new styles of persons to come. (shrink)

I argue that recent attempts to vindicate blame have failed to fully face the vengeful feelings and angry outbursts that have led to scepticism about blame’s ethical status. This paper ende...

This study aims to determine the factors that may affect in constructing the contextualized learning activity sheets based on the learners’ results and the teachers’ self-assessment using a descriptive correlation research design. The findings of the study revealed that the teachers have varied levels of competence in terms of cultural knowledge and on average, they were at the Proficient level of competency. In addition, teachers’ self-assessments indicated that they strongly practiced the criteria in constructing contextualized IPED LAS. However, still at (...) the Advanced Beginner level based on the learners’ results. It can be concluded that teachers are competent in handling IPED based on their profile and cultural knowledge yet, Advance Beginners in terms of assessment skills. Teachers with higher educational qualifications improved their assessment skills. It is recommended that the regional and division IPED specialist should conduct quarterly training for teachers on the Indigenous Knowledge System and Practices (IKSP) and other IPED-related topics. Teachers may conduct indigenization mapping as part of the pedagogical strategy of handling IPED to encourage localization and indigenization of content. With the findings and results, the project ETASIP is made to aid teachers in planning for their assessment strategies. (shrink)

This paper argues that questions can be bullshit. First it explores some shallowly interrogative ways in which that can happen. Then it shows how questions can also be bullshit in a way that’s more deeply interrogative.

Explains Aristotle's views on the possibility of continuous variation between biological species. While the Porphyrean/Linnean classification of species by a tree suggests species are distributed discretely, Aristotle admitted continuous variation between species among lower life forms.

Contemporary philosophers of moral responsibility are in widespread agreement that we can only be blamed for actions that express, reflect, or disclose something about us or the quality of our wills. In this paper I reject that thesis and argue that self disclosure is not a necessary condition on moral responsibility and blameworthiness: reactive responses ranging from aretaic appraisals all the way to outbursts of anger and resentment can be morally justified even when the blamed agent’s action expresses or discloses (...) nothing significant about his or her “deep self,” judgments and cares, or the quality of his or her will. I argue that the self-disclosure requirement on responsibility overestimates the extent to which our blaming practices and responsibility judgments are responsive to agents as opposed to actions, and that this mistake has the potential to distort both our reactive responses and our understanding of blamed agents’ characters. (shrink)

Comparative valuation of different policy interventions often requires interpersonal comparability of benefit. In the field of health economics, the metric commonly used for such comparison, quality adjusted life years (QALYs) gained, has been criticized for failing to respect the equality of all persons’ intrinsic worth, including particularly those with disabilities. A methodology is proposed that interprets ‘full quality of life’ as the best health prospect that is achievable for the particular individual within the relevant budget constraint. This calibration is challenging (...) both conceptually and operationally as it shifts dramatically when technology or budget developments alter what can be achieved for incapacitated individuals. The proposal nevertheless ensures that the maximal achievable satisfaction of one person’s preferences can carry no more intrinsic value than that of another. This approach, which can be applied to other domains of social valuation, thus prevents implicit discrimination against the elderly and those with irremediable incapacities. (shrink)

In this paper, I argue that the principle of respect for autonomy can serve as the basis for laws that significantly limit conduct, including orders mandating isolation and quarantine. This thesis is fundamentally at odds with an overwhelming consensus in contemporary bioethics that the principle of respect for autonomy, while important in everyday clinical encounters, must be 'curtailed', 'constrained', or 'overridden' by other principles in times of crisis. I contend that bioethicists have embraced an indefensibly 'thin' notion of autonomy that (...) uproots the concept from its foundations in Kantian ethics. According to this thin conception, respect for autonomy, if unconditioned by competing principles (beneficence, justice, non-maleficence) would give competent adults the right to do anything they desired to do so long as they satisfied certain baseline psychological conditions. I argue that the dominant 'principlist' model of bioethical reasoning depends on this thin view of autonomy and show how it deprives us of powerful analytical tools that would help us to think seriously about the foundations of human rights, justice, and law. Then, I offer a brief sketch of a 'thick', historically grounded notion of autonomy and show what we could gain by taking it seriously. (shrink)

They say that argumentative writing skills are best learned through writing argumentative essays. I say that while this is excellent practice for argumentative writing, an important exercise to practice structuring such essays and build critical thinking skills simultaneously is what I call the four-sentence paper. The exercise has the template They say..., I say..., one might object..., I reply... One might object that the assignment oversimplifies argumentative writing, stifles creativity, promotes an adversarial attitude, or that students can’t consider objections well (...) anyway. I reply that a simplified form of argumentative writing is fine for beginners, especially since the template is ubiquitous in philosophy; that any assignment template has room for creativity; that considering objections is consistent with good manners; and that despite some pitfalls of trying to defend a thesis and consider objections, students are capable of considering objections well with proper instruction and practice. (shrink)

This paper argues that epistemologists should theorize about wisdom and critically examines a number of attempts to do as much. It then builds and argues for a particular theory of what wisdom is.

Aritsotle's hyle is contrasted with Plato's chora and Aquinas's prima materia. It is argued that Plato and Aristotle developed their concepts in response to very different needs, and that Aquinas's theory reflects a conflation of their views by Neoplatonic commentators. Hyle is shown to be an active potential to a determinate form in contrast to Aquinas's prima materia, which is a purely indeterminate passive potential. This gives a point of attachment in Aristotle's philosophy of nature for the later notion of (...) universal laws of nature. (shrink)

This article critically examines numerous attempts to build a knowledge-first ethics of belief. These theories specify a number of potential "knowledge norms for belief".

In this paper, we argue that providers who conscientiously refuse to provide legal and professionally accepted medical care are not always morally required to refer their patients to willing providers. Indeed, we will argue that refusing to refer is morally admirable in certain instances. In making the case, we show that belief in a sweeping moral duty to refer depends on an implicit assumption that the procedures sanctioned by legal and professional norms are ethically permissible. Focusing on examples of female (...) genital cutting, clitoridectomy and ‘normalizing’ surgery for children with intersex traits, we argue that this assumption is untenable and that providers are not morally required to refer when refusing to perform genuinely unethical procedures. The fact that acceptance of our thesis would force us to face the challenge of distinguishing between ethical and unethical medical practices is a virtue. This is the central task of medical ethics, and we must confront it rather than evade it. There are no data in this work. (shrink)

Suppose for reductio that I know a proposition of the form <p and I don’t know p>. Then by the factivity of knowledge and the distribution of knowledge over conjunction, I both know and do not know p ; which is impossible. Propositions of the form <p and I don’t know p> are therefore unknowable. Their particular kind of unknowability has been widely discussed and applied to such issues as the realism debate. It hasn’t been much applied to theories of (...) the nature of knowledge. That is what I’m going to do here. (shrink)

I start with a critical discussion of some attempts to ground epistemic normativity in curiosity. Then I develop three positive proposals. The first of these proposals is more or less purely philosophical; the second two reside at the interdisciplinary borderline between philosophy and psychology. The proposals are independent and rooted in different literatures. Readers uninterested in the first proposal (and the critical discussion preceding it) may nonetheless be interested in the second two proposals, and vice versa. -/- The proposals are (...) as follows. First I argue that, among several ways in which the notion of curiosity might be used to delineate significant truths from trivial ones, a particular way is the most promising. Second, I argue that curiosity has some underappreciated epistemic roles involving memory. Third, I argue that curiosity has some underappreciated epistemic roles involving coherence. (shrink)

Suppose that you are engaging with someone who is your oppressor, or someone who espouses a heinous view like Nazism or a ridiculous view like flat-earthism. In contexts like these, there is a disparity between you and your interlocutor, a dramatic normative difference across which you are in the right and they are in the wrong. As theorists of humility, we find these contexts puzzling. Humility seems like the *last* thing oppressed people need and the *last* thing we need in (...) dealing with those whose views are heinous or ridiculous. Responding to such people via humility seems uncalled for, even inappropriate. But how could this be, given that humility is a *virtue*? The purpose of the paper is to explore this puzzle. We explain what the puzzle is and then attempt to draw some lessons from it: first, the lesson that the importance of humility is limited in several ways, and second, the lesson that humility nonetheless has several important roles to play, even for people who are in the right in contexts of disparity. (shrink)

This chapter argues that adequately facing and responding to medical error requires making space for blame. In vindicating blame as a response to medical error, this essay does not advocate a return to a “bad apple” blame culture in which unlucky practitioners are unfairly scapegoated. It does, however, defend the targeted feeling and expression of angry, and even resentful, blaming attitudes toward health-care providers who make at least certain kinds of mistakes. The chapter makes the case that the angry and (...) resentful feelings associated with blame reflect a conception of oneself as a person worthy of consideration, and that expressing these feelings allows victims and families to fight for their dignity and self-respect. Along the way, it distinguishes between shaming and blaming, explaining that blaming, unlike shaming, characteristically aims to draw offenders into a moral dialogue. As a result, a good blaming practice can provide a logic within which providers who make costly errors may seek forgiveness, reconciliation, and healing. (shrink)

I argue that fitting resentment tracks unacceptable ‘ecological’ imbalances in relative social strength between victims and perpetrators that arise from violations of legitimate moral expectations. It does not respond purely, or even primarily, to offenders’ attitudes, and its proper targets need not be fully developed moral agents. It characteristically involves a wish for the restoration of social equilibrium rather than a demand for moral recognition or good will. To illuminate these contentions, I focus on cases that I believe demonstrate a (...) corollary thesis, namely, that strength, broadly construed, is a necessary condition of resentment-worthiness. I argue that weakness can make resentment unfitting in two ways. First, weakness may prevent a wrongdoer from shifting the balance of social power. Second, a weak wrongdoer may do social damage but be so lowly that resentment, which would represent him as excessively strong, would be inapt. Finally, I consider how accepting the ecological view might affect our theorizing about moral responsibility and the ethics of blame. (shrink)

This is the introduction to the volume Kantian Nonconceptualism (Palgrave 2016).

Epistemology is normative. This normativity has been widely recognized for a long time, but it has recently come into direct focus as a central topic of discussion. The result is a recent and large turn towards focusing on epistemic value. I’ll start by describing some of the history and motivations of this recent value turn. Then I’ll categorize the work within the value turn into three strands, and I’ll discuss the main writings in those strands. Finally, I’ll explore some themes (...) that are ripe for further development. (shrink)

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

:Recently, Allais, Hanna and others have argued that Kant is a nonconceptualist about intuition and that intuitions refer objectively, independently of the functions of the understanding. Kantian conceptualists have responded, which the nonconceptualists also cite as textual evidence for their reading) that this view conflicts with the central goal of Kant’s Transcendental Deduction: to argue that all intuitions are subject to the categories. I argue that the conceptualist reading of KrV, A 89 ff./B 122 ff. is unfounded. Further, I argue (...) that the nonconceptualists are wrong to believe that intuitions as such refer objectively and that they are mistaken about the relation between figurative synthesis and intellectual synthesis. (shrink)

Programs of drug testing welfare recipients are increasingly common in US states and have been considered elsewhere. Though often intensely debated, such programs are complicated to evaluate because their aims are ambiguous – aims like saving money may be in tension with aims like referring people to treatment. We assess such programs using a proportionality approach, which requires that for ethical acceptability a practice must be: reasonably likely to meet its aims, sufficiently important in purpose as to outweigh harms incurred, (...) and lower in costs than feasible alternatives. In the light of empirical findings, we argue that the programs fail the three requirements. Pursuing recreational drug users is not important in the light of costs incurred, while dependent users who may require referral are usually identifiable without testing and typically need a broader approach than one focussing on drugs. Drug testing of welfare recipients is therefore not ethically acceptable policy. (shrink)

Future robots should have common sense about the world in order to handle the problems they will encounter. A large part of this commonsense knowledge must be naive physics knowledge, since carrying out even the simplest everyday chores requires familiarity with physics laws. But how should one start codifying this knowledge? What kind of skills should be elicited from the experts (each and every one of us)? This paper will attempt to provide some hints by studying the mental models of (...) force and motion. (shrink)

In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...) localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics. (shrink)

A physicalist view of qualia labelled non-eliminative reductionism is outlined. If it is true, qualia and physicalism can co-exist without difficulty. First, qualia present no particular problem for reductionist physicalism - they are entirely physical, can be studied and explained using the standard scientific approach, and present no problem any harder than any other scientists face. Second, reductionist physicalism presents no particular problem for qualia – they can be encompassed within an entirely physicalist position without any necessity, either to reduce (...) them to non-existence, or to treat them as new fundamental properties. It is suggested that the position also has sufficient explanatory power to successfully deal with the 'why like anything – why does experience exist at all' question and to counter both Chalmers' Conceivability Argument and Jackson's Knowledge Argument. (shrink)

What is the relationship between knowledge and ethics? Does what we know and the reason that secures knowledge determine ethical responsibility, or might ethical responsibility itself awaken and animate the enterprise of knowing? The dissertation affirms the priority of ethics by juxtaposing two accounts of the relationship between truth and goodness. It critiques Hegel's systematic conception of absolute knowing by showing that this knowing elides the anarchical ethical demand arising from the other person. Hegel's dialectic reconciles the problem of the (...) relation with the other by transposing it to the plane of cognition where it becomes spirit's self-knowing. However, Emmanuel Levinas's phenomenological reduction of the structures of knowing exposes an ethical level of experience that both inspires and interrupts this adventure of knowing. ;After the introduction of this problematic, Chapter 1 examines the challenge that Levinas poses to Hegel, discovering in experience and subjectivity a ground where real dialogue can take place. Chapter 2 traces the reconception of subjectivity by which Hegel brings all exteriority within the experience of self-consciousness and compares this with Levinas's notion of "lived experience." In Chapter 3, I show how Levinas's account of sensibility and enjoyment resists incorporation into Hegel's notion of self-consciousness. Chapter 4 examines the encounter with the other person and explicates why Hegel's and Levinas's accounts cannot be reconciled or made to complement one another, for the non-allergic responsibility incurred in the face to face relation is inassimilable to the antagonism of the same and the other experienced as self-consciousness. Then, in Chapter 5, I trace Hegel's pursuit of a more authentic recognition of otherness through the development of the concept of spirit, paying special attention to the role of language. The ultimate accomplishment of spiritual recognition in Hegel's account is again challenged by Levinas's notion of responsibility, which signifies as an ethical "saying" apart from the "said." Finally, I contest the absoluteness of knowing without denying the dialectic that animates it by suggesting that philosophy can be maintained as a human enterprise, a pursuit of knowing that is ever subject to and interrupted by the face of the other. (shrink)

Shared intentions supporting cooperation and other social practices are often used to describe human social life but not the social lives of nonhuman animals. This difference in description is supported by a lack of evidence for rebuke or stakeholding during collaboration in nonhuman animals. We suggest that rebuke and stakeholding are just two examples of the many and varied forms of social maintenance that can support shared intentions. Drawing on insights about mindshaping in social cognition, we show how apes can (...) be stakeholders of a different sort in joint action. Drawing on pluralistic social maintenance methods of behavior enforcement, we show ape joint action can be supported by different forms of positive and negative social pressures, and not just protest. We explain how diverse relationships, contexts, social structures, and forms of communication may play a role in forming and successfully fulfilling joint commitments for humans, great apes, and other animals. (shrink)

A physicalist view of qualia labelled non-eliminative reductionism is outlined. If it is true, qualia and physicalism can co-exist without difficulty. First, qualia present no particular problem for reductionist physicalism - they are entirely physical, can be studied and explained using the standard scientific approach, and present no problem any harder than any other scientists face. Second, reductionist physicalism presents no particular problem for qualia – they can be encompassed within an entirely physicalist position without any necessity, either to reduce (...) them to non-existence, or to treat them as new fundamental properties. It is suggested that the position also has sufficient explanatory power to successfully deal with the 'why like anything – why does experience exist at all' question and to counter both Chalmers' Conceivability Argument and Jackson's Knowledge Argument. (shrink)

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)

I outline and develop a particular physicalist perspective on qualia, and suggest that it may be the basis of a correct account of the relationship of mental states to the physical world. Assume that a quale is a perspective on a physical state in the organism – the reality as known as distinct from the reality as such – but that the perspective, though it entails irreducible experiential knowledge, has no physical substance over that encompassed in the physical state itself. (...) Assume this physical state is also a brain state. The position is a useful one. First, reductionist physicalism is true, but experiential qualities are irreducible physical knowledge, and a required part of our physical world view. Second, experiences are not additional problems over those addressed externally, but only how these problems seem when known internally – an experience just is the physical state that underlies its external counterpart, and the same standard scientific account suffices to explain both, permitting a science of consciousness to develop by applying the same standard external–observer–based methods adopted in older scientific disciplines. Finally, challenges to physicalism associated with the ‘unbridgeable gap’, Leibniz's Law, Jackson's knowledge argument, and Chalmers' hard problem of consciousness are successfully countered. (shrink)

Talk at University of Turin, 'Kant, oltre Kant, May 5th 2023. --- -/- It is useful, while keeping in mind a holistic approach, to concentrate on a common theme in Kant’s text, which it will turn out is the quintessential element of his novel ‘way of thinking’, as he himself put it in preface of the second edition of the Critique of Pure Reason. This common theme is the idea of synthesis, which is what holds together, and is the entryway (...) to, all the other familiar aspects of Kant’s thought: his concept of self-consciousness or how mind is involved in cognition, his ideas about the role of the imagination, his theory of knowledge and his metaphysics of experience, and not unimportantly, its relation to what is probably the most Kantian element here: the categories of the understanding as the first principles of knowledge. But the meaning of synthesis and its role in its various facets, though frequently the subject of discussion in papers and monographs alike, is hardly understood in contemporary Kant scholarship. Most readings of the text of the Deduction, the part in which Kant elucidates his concept of synthesis, exhibit a shallow, mechanical understanding of it. -/- A compounding factor is that synthesis can’t really be understood independently of the other aforementioned elements of Kant’s thought. Grasping the meaning of synthesis implies coming to grips with his concept of self-consciousness and the way both self-consciousness and the categories are intricately and intimately involved. Most interpretations consider these aspects too much as if they were indeed separable faculties or entities that serve separable functions, undercutting an important feature of Kant’s metaphysics: the possibility of a priori unified cognition, for which an indivisible self-legislating subject is responsible. Rather, they are expressions of various aspects of a singular function of the mind as the ground of possible unified knowledge. -/- One striking example of such a superficial reading of the text is the way the relation between figurative synthesis and intellectual synthesis—or in the case of the A-Deduction the threefold synthesis—is standardly interpreted, as if the two are independent or quasi-independent functions of different faculties of the mind, the imagination and the understanding. In this paper, I focus on the relation between figurative and intellectual synthesis, while arguing that failing to understand this properly, indeed the relation between the imagination and the understanding, leads to a vicious regress in the explanation of the ground of knowledge, for which a priori synthesis is specifically designed. In other words, failing to see the intimate relation between the imagination and the understanding, the very identity that lies at their root, risks losing sight of the primary aim of Kant’s thought: the possibility of a priori unified knowledge. (shrink)

We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an argument that shows that all mathematical artifacts have politics. We conclude by showing the implications for embedding ethics into mathematical curricula. We show how acknowledging that mathematical artifacts have politics can help mathematicians design better exercises for their mathematics students.

In this chapter I advance a moderately conceptualist interpretation of Kant’s account of the threefold synthesis in the A-Deduction. Often the first version of TD, the A-Deduction, is thought to be less conceptualist than the later B-version from 1787 (e.g. Heidegger 1991, 1995). Certainly, it seems that in the B-Deduction Kant puts more emphasis on the role of the understanding in determining the manifold of representations in intuition than he does in the A-Deduction. It also appears that in the A-Deduction (...) the seemingly pre-conceptual aspects of a priori synthesis, namely those of the synthesis of apprehension and the imagination, are more prominently featured than in the B-Deduction. And the fact that in the A-Deduction judgement does not appear to play any significant role reinforces the view that the A-Deduction is less strongly conceptualist. I believe that Kant is a conceptualist also in the A-Deduction (as much as in the B-Deduction) in the sense that all syntheses, which are expounded in the second section of the A-Deduction, must be seen as involving the categories or the understanding as the seat of the categories. However, despite some apparent strong modal claims regarding apperception in the A-Deduction, I argue that Kant is a moderate conceptualist in the sense that he allows for the real possibility that some representations are apprehended that are not subsumed or subsumable under the categories, or determined or determinable by the understanding as the seat of the categories. Not all representations must be synthesised and hence be conceptualised (by means of the categories), nor are all representations necessarily conceptualisable (by means of the categories). Often it is argued that the application of the categories must be seen as separate from or prior to conceptualisation (that is, employment of concepts in a judgement), so that the categories must be considered to apply to representations at least to the extent that the productive imagination or recognitive synthesis is involved, even if no empirical concepts are applied in an actual judgement. But it is difficult to see how categories can apply outside the context of an actual judgement in which ipso facto empirical concepts are employed, because, after all, categories are nothing but logical functions of judgement (e.g. B143). More in particular, I shall argue for the claims that (1) appearances to the contrary, all three levels of syntheses in the A-Deduction, including the synthesis of recognition, are interdependent and are not to be seen as operating singly or independently of each other, and hence of the categories; (2) ‘mere’ apprehension, or ‘mere’ intuition, is not dependent on the understanding and the application or possible application of the categories; and that (3) ‘mere’ apprehension does not even invoke a priori synthesis of apprehension and hence is as such fully lawless in terms of Kantian a priori laws. In this context, I also address Kant’s argument in the A-Deduction about the role of the imagination in the production of spatial objects and explain his apt use of the example of cinnabar to show that the kind of association that is at issue here concerns the possibility of knowledge, not the possibility of mere association, as is often assumed. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

The interventionist account of causal explanation, in the version presented by Jim Woodward, has been recently claimed capable of buttressing the widely felt—though poorly understood—hunch that high-level, relatively abstract explanations, of the sort provided by sciences like biology, psychology and economics, are in some cases explanatorily optimal. It is the aim of this paper to show that this is mistaken. Due to a lack of effective constraints on the causal variables at the heart of the interventionist causal-explanatory scheme, as presently (...) formulated it is either unable to prefer high-level explanations to low, or systematically overshoots, recommending explanations at so high of a level as to be virtually vacuous. (shrink)