Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

Prologue: on the weakness of education -- Creativity -- Communication -- Teaching -- Learning -- Emancipation -- Democracy -- Virtuosity -- Epilogue: for a pedagogy of the event -- Appendix: coming into the world, uniqueness, and the beautiful risk of education: an interview with Gert Biesta by Philip Winter.

Joshua Gert presents an original account of color properties, and of our perception of them. He employs a general philosophical strategy - neo-pragmatism - which challenges an assumption made by virtually all other theories of color: he argues that colors are primitive properties of objects, irreducible to physical or dispositional properties.

In §50 of Philosophical Investigations Wittgenstein wrote the sentence, “There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.” Although some interpreters have claimed that Wittgenstein's statement is mistaken, while others have proposed various explanations showing that this must be correct, none have questioned the fact that he intended to assert that it is impossible to describe the standard (...) meter as being a meter long. Given that Wittgenstein introduces this sentence as analogous to the claim that “existence cannot be attributed to an element,” and that the preceding passages discuss a language‐game the simples of which can be described by their own names, there is good reason to think that Wittgenstein did not intend to assert this infamous sentence. (shrink)

When did the concept of model begin to be used in mathematics? This question appears at first somewhat surprising since “model” is such a standard term now in the discourse on mathematics and “modelling” such a standard activity that it seems to be well established since long. The paper shows that the term— in the intended epistemological meaning—emerged rather recently and tries to reveal in which mathematical contexts it became established. The paper discusses various layers of argumentations and reflections in (...) order to unravel and reach the pertinent kernel of the issue. The specific points of this paper are the difference in the epistemological concept to the usually discussed notions of model and the difference between conceptions implied in mathematical practices and their becoming conscious in proper reflections of mathematicians. (shrink)

In a number of recent publications, Douglas Portmore has defended consequentialism, largely on the basis of a maximizing view of practical rationality. I have criticized such maximizing views, arguing that we need to distinguish two independent dimensions of normative strength: justifying strength and requiring strength. I have also argued that this distinction helps to explain why we typically have so many rational options. Engaging with these arguments, Portmore has (a) developed his own novel maximization-friendly method of explaining the ubiquity of (...) rational options, and (b) criticized one argument in favour of a substantive justifying/requiring distinction in the domain of practical rationality. The present article defends the justifying/requiring distinction, and criticizes Portmore's maximization-friendly strategy for explaining the ubiquity of rational options. (shrink)

An influential view of the nature of the language system is that of an evolved biological system in which a set of rules is combined with a lexicon that contains the words of the language together with a representation of their context. Alternative views, usually based on connectionist modeling, attempt to explain the structure of language on the basis of complex associative processes. Here, I put forward a third view that stresses experience-dependent structural development of the brain circuits supporting language (...) as a core principle of the organization of the language system. In this view, embodied in a recent neuroconstructivist neural network of past tense development and processing, initial domain-general predispositions enable the development of functionally specialized brain structures through interactions between experience-dependent brain development and statistical learning in a structured environment. Together, these processes shape a biological adult language system that appears to separate into distinct mechanism for processing rules and exceptions, whereas in reality those subsystems co-develop and interact closely. This view puts experience-dependent brain development in response to a specific language environment at the heart of understanding not only language development but adult language processing as well. (shrink)

This book presents an account of normative practical reasons and the way in which they contribute to the rationality of action. Rather than simply 'counting in favour of' actions, normative reasons play two logically distinct roles: requiring action and justifying action. The distinction between these two roles explains why some reasons do not seem relevant to the rational status of an action unless the agent cares about them, while other reasons retain all their force regardless of the agent's attitude. It (...) also explains why the class of rationally permissible action is wide enough to contain not only all morally required action, but also much selfish and immoral action. The book will appeal to a range of readers interested in practical reason in particular, and moral theory more generally. (shrink)

In this paper I explore the relationship between teaching and learning. Whereas particularly in the English language the relationship between teaching and learning has become so intimate that it often looks as if ‘teaching and learning’ has become one word, I not only argue for the importance of keeping teaching and learning apart from each other, but also provide a number of arguments for suggesting that learning may not be the one and only option for teaching to aim for. I (...) explore this idea through a discussion of the relationship between teaching and learning, both at a conceptual and at an existential level. I discuss the limitations of the language of learning as an educational language, point at the political work that is being done through the language of learning, and raise epistemological and existential questions about the identity of the learner, particularly with regard to the question what it means to be in and with the world in terms of learning as comprehension and sense making. Through this I seek to suggest that learning is only one possible aim for teaching and that the learner identity and the learning way of engaging with the world puts the learner in a very specific position vis-à-vis the world, one where the learner remains in the centre and the world appears as object for the learner’s acts of learning. That it is possible to teach without requesting from students that they learn, comprehend and make sense, is demonstrated through a brief account of a course in which students were explicitly asked to refrain from learning and were instead asked to adopt a concept. I show how this request opened up very different existential possibilities for the students and argue that if we value such existential possibilities, there may be good reasons for freeing teaching from learning. (shrink)

Thomas Hobbes was the first great English political philosopher. His work excited intense controversy among his contemporaries and continues to do so in our own time. In this masterly introduction to his work, Bernard Gert provides the first account of Hobbes’s political and moral philosophy that makes it clear why he is regarded as one of the best philosophers of all time in both of these fields. In a succinct and engaging analysis the book illustrates that the commonly accepted (...) view of Hobbes as holding psychological egoism is not only incompatible with his account of human nature but is also incompatible with the moral and political theories that he puts forward. It also explains why Hobbes’s contemporaries did not accept his explicit claim to be providing a natural law account of morality. Gert shows that for Hobbes, civil society is established by a free-gift of their right of nature by the citizens; it does not involve a mutual contract between citizens and sovereign. As injustice involves breaking a contract, the sovereign cannot be unjust; however, the sovereign can be guilty of ingratitude, which is immoral. This distinction between injustice and immorality is part of a sophisticated and nuanced political theory that is in stark contrast to the reading often incorrectly attributed to Hobbes that “might makes right”. It illustrates how Hobbes’s goal of avoiding civil war provides the key to understanding his moral and political philosophy. _Hobbes: Prince of Peace_ is likely to become the classic introduction to the work of Thomas Hobbes and will be a valuable resource for scholars and students seeking to understand the importance and relevance of his work today. (shrink)

This article investigates whether different religious (mythological) worldviews can be described as alternative and altered states of consciousness (ASCs). Differences between conscious and unconscious motivations for behaviour are discussed before looking at ASCs, Weltanschauung and symbolic universes. Mythology can be described both as Weltanschauung and symbolic universe, functioning on all levels of consciousness. Different Weltanschauungen constitute alternative states of consciousness. Compared to secular worldviews, religious worldviews may be described as ASCs. Thanks to our globalised modern societies, the issue is even (...) more complex, as alternate modernities lead to a symbolic multiverse, with individuals living in a social multiverse.Keyowrds: mythology; Weltanschauung; worldview; symbolic universe; states of consciousness; altered states of consciousness; alternative states of consciousness; symbolic multiverse; social multiverse. (shrink)

This article discusses the English construction variously known as Locative Inversion or Stylistic Inversion. It shows that the construction displays a unique ensemble of grammatical and usage properties that can be stated but not motivated through purely grammatical means. In search of an explanatory approach, an analysis is presented that draws on concepts of Artificial Intelligence, in particular plans viewed as complex mental attitudes. It is claimed that utterances of Locative Inversion are associated with a particular communicative plan on the (...) speaker's part that motivates the grammatical and usage properties of the construction where grammar alone cannot. The final section of the article presents corpus examples showing that Locative Inversion is indeed used in the contexts predicted by the plan associated with the construction. This result is both theoretically and methodologically significant, insofar as it constitutes a case where the grammatical properties of a syntactic construction are better explained through its typical conditions of use than through grammatical means proper. (shrink)

This paper defends the right not to know personal health information, while it discards the right of research participants to receive individual research results. Disagreement regarding the right not to know stems from two different conceptions of autonomy, leading to opposing normative conclusions. Researchers occasionally have good reason to inform research participants about incidental findings in spite of the absence of a right to know such information. Such decisions have to be made by health care personnel and researchers on a (...) case by case basis, although external support for the decisions may be available. (shrink)

Thomas Hobbes was the first great English political philosopher. His work excited intense controversy among his contemporaries and continues to do so in our own time. In this masterly introduction to his work, Bernard Gert provides the first account of Hobbes’s political and moral philosophy that makes it clear why he is regarded as one of the best philosophers of all time in both of these fields. In a succinct and engaging analysis the book illustrates that the commonly accepted (...) view of Hobbes as holding psychological egoism is not only incompatible with his account of human nature but is also incompatible with the moral and political theories that he puts forward. It also explains why Hobbes’s contemporaries did not accept his explicit claim to be providing a natural law account of morality. Gert shows that for Hobbes, civil society is established by a free-gift of their right of nature by the citizens; it does not involve a mutual contract between citizens and sovereign. As injustice involves breaking a contract, the sovereign cannot be unjust; however, the sovereign can be guilty of ingratitude, which is immoral. This distinction between injustice and immorality is part of a sophisticated and nuanced political theory that is in stark contrast to the reading often incorrectly attributed to Hobbes that “might makes right”. It illustrates how Hobbes’s goal of avoiding civil war provides the key to understanding his moral and political philosophy. _Hobbes: Prince of Peace_ is likely to become the classic introduction to the work of Thomas Hobbes and will be a valuable resource for scholars and students seeking to understand the importance and relevance of his work today. (shrink)

It has been debated for quite some time among bioethicists and others whether or not the distinction between therapy and research in healthcare can and should be maintained. This paper tries to clarify what the disagreement is about, and argues that the distinction can be maintained in most, if not all, situations. However, even if it can be maintained, it does not necessarily follow that it should. It is argued here that there are good reasons to maintain the distinction both (...) for the sake of protecting research interests and the sake of patient safety. In addition, recognizing the distinction provides a barrier against unreasonable prioritization between patients. However, there may be situations, such as innovative last-resort treatment, in which regulatory requirements from both therapy and research should be considered. (shrink)

Bioethicists have for quite some time discussed the right to know and the right not to know personal health information, such as genetic information acquired in health care and incidental health-related findings in research. Several international ethical guidelines explicitly defend these rights.My own interest in these matters stems from my participation in ethics-related research tied to a longitudinal screening study on Type I diabetes involving young children. A few of the participating parents did not want to be informed if the (...) study revealed their child had a high risk of developing diabetes. This response was troublesome, not least since the information would concern the child's and not the parents’ health. Our inclination was that there cannot be a right not to know that should be granted without qualifications. Furthermore, other contextual factors, e.g., that parents experienced pressure to participate and felt concern about some of the personal data handled in the study, gave reason to question whether autonomous decisions were made regarding participation. The autonomy of their expressed desire not to know was therefore questionable. (shrink)

This article seeks to contribute to the process of reconciliation in South Africa. This is achieved by firstly exploring the meaning of ubuntu as a common culture or religion under a large percentage of South Africa’s people over the borders of language and other cultural values. In the second part of the article two concepts that play a major role in Christianity are explored, namely koinonia and diakonia. Again a large percentage of South Africans believe that the Bible is the (...) Word of God in which the right way of living is described. A comparison is made between the core values of ubuntu and the way of living that emerges from the use of the two concepts of koinonia and diakonia in the New Testament. A way that can contribute to reconciliation is suggested from this comparison. (shrink)

We give a historical overview of the development of almost 50 years of empirical research on the affordances in the past and in the present. Defined by James Jerome Gibson in the early development of the Ecological Approach to Perception and Action as the prime of perception and action, affordances have become a rich topic of investigation in the fields of human movement science and experimental psychology. The methodological origins of the empirical research performed on affordances can be traced back (...) to the mid 1980’s and the works of Warren (1984, 1988) and Michaels (1988). Most of the research in Ecological Psychology performed since has focused on the actualization of discretely defined actions, the perception of action boundaries, the calculation of pi-numbers, and the measurement of response times. The research efforts have resulted in advancements in the understanding of the dynamic nature of affordances, affordances in a social context and the importance of calibration for perception of affordances. Although affordances are seen as an instrumental part of the control of action most studies investigating affordances do not pay attention to the control of the action. We conclude that affordances are still primarily treated as a utility to select behaviour, which creates a conceptual barrier that hinders deeper understanding of affordances. A focus on action-boundaries has largely prevented advancement in other aspects of affordances, most notably an integrative understanding of the role of affordances in the control of action. (shrink)

The second volume in Joel Feinberg's series The Moral Limits of the Criminal Law, Offense to Others focuses on the "offense principle," which maintains that preventing shock, disgust, or revulsion is always a morally relevant reason for legal prohibitions. Feinberg clarifies the concept of an "offended mental state" and further contrasts the concept of offense with harm. He also considers the law of nuisance as a model for statutes creating "morals offenses," showing its inadequacy as a model for understanding "profound (...) offenses," and discusses such issues as obscene words and social policy, pornography and the Constitution, and the differences between minor and profound offenses. (shrink)

Despite the urgency of this issue, AI still struggles to represent social life. This article presents a comprehensive agent-based model that investigates status-power dynamics in groups. Kemper’s sociological status–power theory of social relationships, and a literature review on school children in middle youth, is its basis. The model allows us to investigate causation of the near-ubiquitous phenomenon that females have lower social status on average than males. Possible causes included in the model are children’s dispositional traits (kindness, beauty, and physical (...) power), schoolyard culture (social acceptability of fighting), behavioural strategy (amount of rough-and-tumble play) and the balance between public and dyadic sources of status. An agent-based model of a virtual schoolyard was created in which the children assemble in changing groups and mutually confer status. The status conferred upon a child modifies the status it holds. Rough-and-tumble is modelled as ambiguous: it is intended as a status conferral, but may be perceived as a power move. Running many trials of the model we found that in time, depending on the parameter settings, a gender-based status gap emerged. Rough-and-tumble play had more impact on emergent status differences than did physical power differences. Social acceptability of fighting also strongly moderated the resulting status gap. Placing more weight on dyadic relationship could alleviate status loss. All these model behaviours are in line with empirical findings of child behaviour studies at schools. They have face validity for social status issues in the adult world. We conclude from this that this kind of agent-based model merits use in studying the status–power dynamics of other issues in child behaviour, or indeed in social behaviour in general. (shrink)

Fetal alcohol spectrum disorders is an umbrella term covering several conditions for which alcohol consumption during pregnancy is taken to play a causal role. The benefit of individuals being identified with a condition within FASD remains controversial. The objective of the present study was to identify ethical aspects and consequences of diagnostics, interventions, and family support in relation to FASD. Ethical aspects relating to diagnostics, interventions, and family support regarding FASD were compiled and discussed, drawing on a series of discussions (...) with experts in the field, published literature, and medical ethicists. Several advantages and disadvantages in regards of obtaining a diagnosis or description of the condition were identified. For instance, it provides an explanation and potential preparedness for not yet encountered difficulties, which may play an essential role in acquiring much needed help and support from health care, school, and the social services. There are no interventions specifically evaluated for FASD conditions, but training programs and family support for conditions with symptoms overlapping with FASD, e.g. ADHD, autism, and intellectual disability, are likely to be relevant. Stigmatization, blame, and guilt are potential downsides. There might also be unfortunate prioritization if individuals with equal needs are treated differently depending on whether or not they meet the criteria for a specific condition. The value for the concerned individuals of obtaining a FASD-related description of their condition – for instance, in terms of wellbeing – is not established. Nor is it established that allocating resources based on whether individuals fulfil FASD-related criteria is justified, compared to allocations directed to the most prominent specific needs. (shrink)

_Obstinate Education: Reconnecting School and Society_ argues that education is not just there to give individuals, groups and societies what they want from it, but that education has a duty to resist.

This paper calls into question the idea that moral disgust is usefully regarded as a form of genuine disgust. This hypothesis is questionable even if, as some have argued, the spread of moral norms through a community makes use of signaling mechanisms that are central to core disgust. The signaling system is just one part of disgust, and may well be completely separable from it. Moreover, there is plausibly a significant difference between the cognitive scientist’s concept of an emotion and (...) the everyday notion of that emotion. Finally, even if, as this paper contests, some form of disgust were directly elicited by the moral wrongness of certain kinds of behavior, research on the socio-moral elicitors of the disgust mechanism would still be unlikely to shed much direct light on the nature or content of morality. (shrink)

It is a suggestive feature of English and other languages that an indicative sentence such as ‘Premarital sex is wrong’ can be described not only as an expression of the belief that premarital sex is wrong, but also as an expression of disapproval of premarital sex. Disapproval is plausibly regarded as an attitude that is distinct from belief, in that it does not have truth conditions. What sort of attitude, then, should we take ‘Premarital sex is wrong’ to express: disapproval, (...) belief, or perhaps both? One group of contemporary philosophers advocates the first Option. They hold that evaluative claims serve essentially to express positive and negative attitudes that are more like desires than beliefs, and that cannot be said to be true or false — at least in the robust way in which claims about the ages of trees can be true or false. Call these philosophers ‘expressivists.’ Seemingly opposed to expressivists are those who hold that evaluative claims express beliefs, and can be true or false. (shrink)