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)

• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer (...) has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks.. (shrink)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...) the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

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.

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)

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)

The winning entry in David Stove's Competition to Find the Worst Argument in the World was: “We can know things only as they are related to us/insofar as they fall under our conceptual schemes, etc., so, we cannot know things as they are in themselves.” That argument underpins many recent relativisms, including postmodernism, post-Kuhnian sociological philosophy of science, cultural relativism, sociobiological versions of ethical relativism, and so on. All such arguments have the same form as ‘We have eyes, therefore we (...) cannot see’, and are equally invalid. (shrink)

Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.

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.

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)

Leibniz's best-of-all-possible worlds solution to the problem of evil is defended. Enlightenment misrepresentations are removed. The apparent obviousness of the possibility of better worlds is undermined by the much better understanding achieved in modern mathematical sciences of how global structure constrains local possibilities. It is argued that alternative views, especially standard materialism, fail to make sense of the problem ofevil, by implying that evil does not matter, absolutely speaking. Finally, itis shown how ordinary religious thinking incorporates the essentials of Leibniz's (...) view. (shrink)

The imperviousness of mathematical truth to anti-objectivist attacks has always heartened those who defend objectivism in other areas, such as ethics. It is argued that the parallel between mathematics and ethics is close and does support objectivist theories of ethics. The parallel depends on the foundational role of equality in both disciplines. Despite obvious differences in their subject matter, mathematics and ethics share a status as pure forms of knowledge, distinct from empirical sciences. A pure understanding of principles is possible (...) because of the simplicity of the notion of equality, despite the different origins of our understanding of equality of objects in general and of the equality of the ethical worth of persons. (shrink)

Pascal’s wager and Leibniz’s theory that this is the best of all possible worlds are latecomers in the Faith-and-Reason tradition. They have remained interlopers; they have never been taken as seriously as the older arguments for the existence of God and other themes related to faith and reason.

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.

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.

Elsevier, the world's leading provider of science and health information, published an academic/scientific textbook about a new mathematical discovery discovered in a near-death experience (NDE) that matches the dynamics of living and life-like (social) systems and has applications in general systems theory, universal systems modelling, human clinical molecular genetics modelling, medical informatics, astrobiology, education and other areas of study. This article is about Lynnclaire Dennis and how she brought back perhaps the greatest scientific discovery ever from a NDE. The (...) Mereon Matrix's sequential process generates a coherent link to living and non-living systems whether they are physical, mathematical, philosophical, or social. (shrink)

Philosophical discussions of species have focused on multicellular, sexual animals and have often neglected to consider unicellular organisms like bacteria. This article begins to fill this gap by considering what species concepts, if any, apply neatly to the bacterial world. First, I argue that the biological species concept cannot be applied to bacteria because of the variable rates of genetic transfer between populations, depending in part on which gene type is prioritized. Second, I present a critique of phylogenetic bacterial species, (...) arguing that phylogenetic bacterial classification requires a questionable metaphysical commitment to the existence of essential genes. I conclude by considering how microbiologists have dealt with these biological complexities by using more pragmatic and not exclusively evolutionary accounts of species. I argue that this pragmatism is not borne of laziness but rather of the substantial conceptual problems in classifying bacteria based on any evolutionary standard. (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)

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)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (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...

Some courses achieve existence, some have to create Professional Issues and Ethics in existence thrust upon them. It is normally Mathematics; but if you don’t do it, we will a struggle to create a course on the ethical be.” I accepted. or social aspects of science or mathematics. The gift of a greenfield site and a bull- This is the story of one that was forced to dozer is a happy occasion, undoubtedly. But exist by an unusual confluence of outside (...) cirwhat to do next? It seemed to me I should cumstances. ensure the course satisfied these require- In the mid 1990s, the University of New ments: South Wales instituted a policy that all its • It should look good to students, to staff. (shrink)

Stove's article, 'So you think you are a Darwinian?'[ 1] was essentially an advertisement for his book, Darwinian Fairytales.[ 2] The central argument of the book is that Darwin's theory, in both Darwin's and recent sociobiological versions, asserts many things about the human and other species that are known to be false, but protects itself from refutation by its logical complexity. A great number of ad hoc devices, he claims, are used to protect the theory. If co operation is observed (...) where the theory predicts competition, then competition is referred to the time of the cavemen, or is reinterpreted as competition between some hidden entities like genes or abstract entities like populations. In a characteristic sally, Stove writes of the sociobiologists' oscillation on the meaning of kin altruism: Any discussion of altruism with an inclusive fitness theorist is, in fact, exactly like dealing with a pair of balloons connected by a tube, one balloon being the belief that kin altruism is an illusion, the other being the belief that kin altruism is caused by shared genes. If a critic puts pressure on the illusion balloon - perhaps by ridiculing the selfish theory of human nature - air is forced into the causal balloon. There is then an increased production of earnest causal explanations of why we love our children, why hymenopteran workers look after their sisters, etc., etc. Then, if the critic puts pressure on the causal balloon - perhaps about the weakness of sibling altruism compared with parental, or the absence of sibling altruism in bacteria - then the illusion balloon is forced to expand. There will now be an increased production of cynical scurrilities about parents manipulating their babies for their own advantage, and vice versa, and in general, about the Hobbesian bad times that are had by all. In this way critical pressure, applied to the theory of inclusive fitness at one point, can always be easily absorbed at another point, and the theory as a whole is never endangered.[ 3] Now, it is uncontroversial to assert that Darwinism is a logically complex theory, and that its relation to empirical evidence is distant and multi faceted. One does not directly observe chance genetic variations leading to the development of new species, or even continuous variations in the fossil record, but must rely on subtle arguments to the best explanation, scaling up from varieties to species, and so on.. (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.

If Tahiti suggested to theorists comfortably at home in Europe thoughts of noble savages without clothes, those who paid for and went on voyages there were in pursuit of a quite opposite human ideal. Cook's voyage to observe the transit of Venus in 1769 symbolises the eighteenth century's commitment to numbers and accuracy, and its willingness to spend a lot of public money on acquiring them. The state supported the organisation of quantitative researches, employing surveyors and collecting statistics to..

The late twentieth century saw two long-term trends in popular thinking about ethics. One was an increase in relativist opinions, with the “generation of the Sixties” spearheading a general libertarianism, an insistence on toleration of diverse moral views (for “Who is to say what is right? – it’s only your opinion.”) The other trend was an increasing insistence on rights – the gross violations of rights in the killing fields of the mid-century prompted immense efforts in defence of the “inalienable” (...) rights of the victims of dictators, of oppressed peoples, of refugees. The obvious incompatibility of those ethical stances, one anti-objectivist, the other objectivist in the extreme, proved no obstacle to their both being held passionately, often by the same people. (shrink)

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 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.

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)

To move beyond vague platitudes about the importance of context in legal reasoning or natural language understanding, one must take account of ideas from artificial intelligence on how to represent context formally. Work on topics like prior probabilities, the theory-ladenness of observation, encyclopedic knowledge for disambiguation in language translation and pathology test diagnosis has produced a body of knowledge on how to represent context in artificial intelligence applications.

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)

Australian women who are university graduates have fewer children than non-graduates. In most cases this appears to be the result of circumstantial pressures not preference. Long years of study fill the most fertile years of women students and new graduates need further time to establish their careers. The chance of medical infertility increases with age so, for some, this means that childbearing is not postponed but ruled out. Graduates who do make the transition from university to professional work find that (...) working hours are long and that professional occupations are now both highly demanding and insecure. Women who take time off to care for young children must depend on one insecure income (their partner’s) rather than two, and their return to work is uncertain. These difficulties of time, money and insecurity are compounded by problems in finding a suitable partner. They are magnified by the enduring tendency of women to marry up. Thus it can be more difficult for women graduates to find husbands than it is for women who are non-graduates. (shrink)

Democracy has difficulties with the rights on non-voters (children, the mentally ill, foreigners etc). Democratic leaders have sometimes acted ethically, contrary to the wishes of voters, e.g. in accepting refugees as immigrants. The remarkable story of resettlement of the Displaced Persons of Europe after World War II is a case in point.

The classical arguments for scepticism about the external world are defended, especially the symmetry argument: that there is no reason to prefer the realist hypothesis to, say, the deceitful demon hypothesis. This argument is defended against the various standard objections, such as that the demon hypothesis is only a bare possibility, does not lead to pragmatic success, lacks coherence or simplicity, is ad hoc or parasitic, makes impossible demands for certainty, or contravenes some basic standards for a conceptual or linguistic (...) scheme. Since the conclusion of the sceptical argument is not true, it is concluded that one can only escape the force of the argument through some large premise, such as an aptitude of the intellect for truth, if necessary divinely supported. (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 article critically examines numerous attempts to build a knowledge-first ethics of belief. These theories specify a number of potential "knowledge norms for belief".

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)

When a person commits a testimonial injustice, the unjust thing they do consists in their reaction to an assertion (theorists diverge on the details; paradigmatically the relevant unjust thing consists in prejudicially refraining from believing the assertion). Whatever reactions to questions are analogous to these reactions to assertions, those things are "interrogative injustices". I explore some models of those things and apply them to some non-ideal cases. One of the models appeals to mental states like curiosity and wonder, telling us (...) that interrogative injustice occurs when hearers prejudicially refrain from adopting those mental states. Other models appeal to common conversational goals – these goals including the answering of questions. On these models, interrogative injustice occurs when a person asks a question, and another person prejudicially blocks the answering of that question from joining the common goals. Or, if they don’t block said answering, perhaps they believe that it should be thus blocked. Or perhaps they merely resist the question, not fully blocking its answering from joining the common goals but instead pushing back against it in some other way. Or perhaps they merely believe that they should resist the question. I endorse a pluralism on which each of these things can be an interrogative injustice. (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)

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)

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)

Both realist and anti-realist accounts of natural kinds possess prima facie virtues: realists can straightforwardly make sense of the apparent objectivity of the natural kinds, and anti-realists, their knowability. This paper formulates a properly anti-realist account designed to capture both merits. In particular, it recommends understanding natural kinds as ‘categorical bottlenecks,’ those categories that not only best serve us, with our idiosyncratic aims and cognitive capacities, but also those of a wide range of alternative agents. By endorsing an ultimately subjective (...) categorical principle, this view sidesteps epistemological difficulties facing realist views. Yet, it nevertheless identifies natural kinds that are fairly, though not completely, stance-independent or objective. (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)

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)