Definitions are traditionally seen as abbreviations, as tools for notational convenience that do not increase inferential power. From a Philosophy of Mathematical Practice point of view, however, there is much more to definitions. For example, definitions can play a role in problem solving, definitions can contribute to understanding, sometimes equivalent definitions are appreciated differently, and so on. This chapter reviews the literature on definitions and (to a certain extent) concepts in mathematical practice. It is structured according to four themes through (...) which definitions (and concepts) in mathematical practice have been studied. These themes concern (1) the nature of definitions, (2) whether and how concepts evolve, (3) definitions and concepts from a communal perspective, and (4) different values relating to definitions and concepts. (shrink)

In the philosophy of mathematical practice, the aim is to understand the various aspects of this practice. Even though definitions are a central element of mathematical practice, the study of this aspect of mathematical practice is still in its infancy. In particular, there is little empirical evidence to substantiate claims about definitions in practice. In this article, we address this gap by reporting on an empirical investigation on how mathematicians create definitions and which roles and properties they attribute to them. (...) On the basis of interviews with thirteen research mathematicians, we provide a broad range of relevant aspects of definitions. In particular, we address various roles of definitions and show that definitions are not just a product of mathematical factors, but also of social and contingent factors. Furthermore, we provide concrete examples of how mathematicians interact and think about definition. This broad empirical basis with a variety of examples provides an optimal starting point for future investigations into definitions in mathematical practice. (shrink)

The Hiero is an account in Socratic conversational form of a meeting between Simonides the poet and Hiero the tyrant of Syracuse; it was written by Xenophon of Athens in the fourth century b.c., but is set in the fifth, when the historical Simonides and Hiero lived and met. The subject they are portrayed discussing is the relative happiness of the tyrant and private individual. Plato also makes this a topic of discussion in his Republic. However, whereas Plato writes a (...) regular Socratic dialogue, Xenophon does not, for though he represents his characters using Socratic conversation, Socrates himself does not appear; the characteros of the Hiero are Simonides and Hiero, poet and tyrant. This is the problem of the Hiero. It requires explanation. The action of the Hiero is initiated by Simonides and begins in the following way: Simonides the poet once came to the court of Hiero the tyrant. When they were both at leisure, Simonides said, ‘Would you be willing to tell me, Hiero, something you are likely to know better than I?’ And Hiero said, ‘What is it that I should know better than you, who are such a wise man?’ He replied, ‘I know that you were once a private individual and are now a tyrant. Since you have experienced both conditions, you are likely to know better than I how tyrannical life differs from private life in respect of men's pleasures and griefs’ . The identification of Simonides as a wise man who nevertheless seeks wisdom from others establishes his Socratic nature from the start. (shrink)

Case-based, multidisciplinary seminars provided a vehicle for clinicians, philosophers and students to debate current problems in medical ethics in a manner which ensured maximum learning and interest for all participants. Prior training in philosophical medical ethics was an essential prerequisite, giving students the knowledge and skills to take part in the discussions at an appropriate level of sophistication.

Since James defined emotion as consciousness of bodily reactions and Cannon and others detailed the nature of these reactions, there has been an increasing tendency among behaviorists to equate emotions with visceral reactions and to neglect some of the genetic and adaptive aspects of emotion which had been discussed by Darwin.

In Aeneid 7. 1–285 Vergil colours his picture of early Latium with a religious atmosphere which can be fully appreciated only if these verses are read with an attentive awareness of Roman religious beliefs and practices. A detailed exegesis of all 285 verses would hardly be possible here, and I will limit myself to two major points, the account of Latinus' ancestry and the description of the royal palace , both because these passages are interesting in themselves for the way (...) they apparently contradict each other, and because they are good illustrations of how Vergil draws on the data of Roman religion, both its folklore and its cult, to fix in his reader's mind certain definite impressions about Latinus and the Latins. (shrink)

To whom is Aeschinus speaking? Editors in general follow Eugraphius and have Aeschinus address his lines to the psaltria. According to this interpretation, it would be the psaltria who anxiously looks back ; since Sannio is the only person on stage whom the girl would have reason to fear, the leno would have to be standing behind her, and hence must have followed the psaltria on to the stage.

The topic of consent in paediatrics is made more difficult, and at the same time more interesting, by the complexity of the issues involved and the consequent diversity of viewpoints. In a teaching session for senior medical students on consent in paediatrics it proved necessary to reinstate previous learning from a range of disciplines. Philosophical medical ethics, developmental psychology, communication skills and the appropriate legal definitions all contributed to a proper understanding of the cases presented. The two most important additional (...) components appeared to be a) a basic knowledge of cognitive development and how to apply it, and b) an awareness of the need to balance an individual child's rights or best interests, with those of the family unit, as well as the wider society. (shrink)

The use of dialogue in Xenophon's Hellenica is a phenomenon that needs explanation. Among previous historians, Herodotus had used it frequently but Thucydides hardly at all. In Xenophon's own time, Ctesias had used it but not the author of the Hellenica Oxyrhynchia nor Ephorus to any great extent, as far as we can tell. Theopompus had plagiarized one of the Hellenica dialogues as well as adding others of his own. Generally, dialogue occurred less frequently in history writing than the set (...) speech. Yet there have been no serious studies of dialogue in the Hellenica, and where opinions are expressed they often vary. Sordi considered that the purpose of dialogue was decorative and agreed with the estimates of ancient critics about the liveliness of the conversations. Breitenbach also thought they had literary merit but suggested that their purpose was moral and didactic. Henry agreed that their purpose was didactic but thought them flat and lifeless and lacking in literary merit. Bruce thought their purpose was to illustrate personality. These differences of opinion should be settled. Moreover, Sordi's view that the content, style and purpose of dialogue is quite different from that of the set speech, and that this reflects a difference of genre within the Hellenica, dialogue being typical of memoir and the set speech of ‘serious’ history, cannot go unchallenged. Herodotus used dialogue in what was clearly not memoir. Further, there has been no serious attempt to place dialogue in the Hellenica in the tradition of dialogue writing in history or to examine its relationship to dramatic dialogue or the philosophical dialogue. This needs to be attempted. Such are the aims of this paper. (shrink)

This paper presents findings from a longitudinal study of patient refusals (as reported by graduating medical students) to take part in the teaching function of public hospitals. Results from a smaller study of non-patients' attitudes are also reported. Findings are discussed in terms of patients' rights, issues of personal privacy, medical education, and the public good.

Neither the chronology nor the interpretation of the history of the years 375 to 371 BC is yet settled. The date of the peace that followed the Athenian naval victory over Sparta at Alyzeia in Scirophorion 375 is put variously in the second half of 375 or 374 or even in spring 374. The status of the Boeotian cities at the time of the peace as well as the role of the King and the participation of Thebes are controversial, and (...) this affects the interpretation of the peace itself. (shrink)

The death of Socrates gave birth to an industry of biographical literature which often took the form of a defence or prosecution , sometimes purporting to be the actual defence or prosecution conducted at his trial. Plato and Xenophon wrote works in his defence. Among his critics, one Polycrates had a certain notoriety. Lysias, Theodectes and Demetrius of Phalerum, orators and rhetoricians like Polycrates, were credited with further works of apology. There were doubtless many others. The aim of this paper (...) is to show that Xenophon wrote his Defence in the light of the rhetorical theory that required that a speaker utter words and thoughts appropriate πρεποντα to his character. (shrink)