Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on (...) the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on (...) the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on (...) the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)

What are some of the key historical trends in hours of work per worker in US? What economic, social-psychological, organizational and institutional forces determine the length of individuals' working hours? How much of the trend toward longer working hours among so many workers may be attributable to workers' preferences, workplace incentives or employers' constraints? When can work become overwork or workaholism – an unforced addiction to incessant work activity which risk harm to workers, families or even economies? The first part (...) of this article traces the history of the length of working hours and its recent polarization. The second part develops a multi-disciplinary model to identify motivations behind working longer hours. Individuals' desired work hours will stem from the weighted contribution of five sources: (1) current real wage rates; (2) forward-looking, wage trajectories; (3) relative status associated with hours of labor; (4) intrinsic rewards, process benefits or amenities acquired through work; (5) hours demanded by the employer and other structural constraints, to which workers may adapt. Employers and their established conditions of work have influenced the course of long run trends labor supply and in work time structures. The final section suggests policies that might address the persistence of long hours. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:684 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER 1995 "Private I.anguage" and the pivotal paper in the Stoic section, "The Conjunctive Model," bring out a third feature of Brunschwig's method. Many of his essays take their start from a small text or a relatively local problem, one which does not primafacie bear significantly on large philosophical issues. Yet in a rigorously conceived philosophical system, the whole is often (...) reflected in the details; where possible Brunschwig elicits the larger significance. He shows how Epicurean physics provides a normative model for Epicurean psychology without falling into the reductionist error; the Epicurean does extrapolate from physical theory to human experience, but in so doing he does not forget that human beings are not just atomic; they are atomic compounds. Reductionism does not follow from materialism, for Epicurus or for us. Similarly in "The Conjunctive Model" Brunschwig connects, in a manner which is speculative but nevertheless compelling, a important Stoic thesis in logic (that a conjunction is false if even one of its conjuncts is false) with a comprehensive understanding of Stoic ethics and physics, thereby giving definite content to the Stoic claims about the coherence of their system. The other Stoic papers focus on ontology and logic, showing how central these are to Stoicism. The titles speak for themselves: "Remarks on the Stoic Theory of the Proper Noun," "Remarks on the Classification of Simple Propositions in Hellenistic Logics," "The Stoic Theory of the Supreme Genus and Platonic Ontology," and "Did Diogenes of Babylon Invent the Ontological Argument?" (the answer is 'no'). One essay ("On a Stoic Way of Not Being") disguises by its title a crucial contribution to the philosophy of mind. The papers on Scepticism include "The 6oov ~t~ x~ ~.6"f.t 9 Formula in Sextus Empiricus," a definitive treatment of a verbal formula crucial to understanding the precise character of his sceptical stance, and "Sextus Empiricus on the xptxfl0tov," the only paper in the volume which has previously appeared in English. The papers "Once Again on Eusebius on Aristocles on Timon on Pyrrho" and "The Title of Timon's lndalmoi: From Odysseus to Pyrrho" deal with early Pyrrhonism, for which the evidence is so thin that no firm conclusions can be drawn. Yet even here Brunschwig's care and skill are exemplary, and his argument that we should look to Timon rather than Pyrrho as the creator of Pyrrhonism is as convincing as anything could be in this area. This is a collection which specialists must read and even nonspecialists will value for its elegant combination of rigor, intellectual honesty, and philosophical insight. BRAD INWOOD University of Toronto Michael J. B. Allen. Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic. Berkeley: University of California Press, 1994. PP. x + 291. Cloth, $5o.oo. Marsilio Ficino was born in 1433 and died in 1499 at the age of 66. He would have been pleased if he could have known that. For three years before in 1496 (or slightly earlier) he declared in his Commentary on the Fatal Number that 6 was the perfect number and BOOK R~VIEWS 685 that contemplations of the sextile relations of the planets might lead to the return of the golden age of Saturn "some day," This is the fifth volume of Michael Allen's seminal studies of Ficino's Platonic commentaries; if his notable additional articles on further Ficino commentaries were assembled, as they sometime must be, it would be his sixth--not that he takes the same pleasure in numbers as his subject Ficino did. But 6 is the key to Ficino's unraveling of Plato's "fatal number" in Republic 546. To end the suspense, Ficino's solution, aided by Aristotle, Politics V. 1316, is (4 + 3 + 5)3or (6 x 2)3 or 1728. But 1728 what? There is no clue. The book is itself a valuable contribution to the history of philosophy. Allen reviews the history of this topos up to Brumbaugh and Rees. Although Ficino's entry was known and discussed in the sixteenth century, it has been lost from sight since, and Alien restores it importantly to... (shrink)

A number of philosophers from Hobbes to Mill to Parfit have held some combination of the following views about the Golden Rule: (a) It is the cornerstone of morality across many if not all cultures. (b) It affirms the value of moral impartiality, and potentially the core idea of utilitarianism. (c) It is immune from evolutionary debunking, that is, there is no good naturalistic explanation for widespread acceptance of the Golden Rule, ergo the best explanation for its (...) appearance in different traditions is that people have perceived the same non-natural moral truth. De Lazari-Radek and Singer employ all three of these claims in an argument meant to vindicate Sidgwick's ‘principle of universal benevolence’. I argue that the Golden Rule is the cornerstone of morality only in Christianity, it does not advocate moral impartiality, and there is a naturalistic explanation for why versions of the Golden Rule appear in different traditions. (shrink)

Wonder Woman wields a number of magical Amazonian devices: her bulletproof bracelets, her invisible plane, and most importantly for this chapter, her golden lasso of truth. The first thing to notice about the golden lasso is that evildoers bound by it are not only compelled to tell the truth if and when they answer questions, but also compelled to answer Wonder Woman's questions in the first place. The second thing to notice is that answering truthfully does not, (...) in this context, necessarily mean uttering a true sentence. Rather, if a person is tied up with the golden lasso, then they are compelled to answer questions with what they believe is the truth. The chapter shows the examples that contemplating Wonder Woman's golden lasso, and Bizarra's golden lasso, can provide us with a wealth of interesting and entertaining paradoxes and puzzles. (shrink)

Chronostratigraphy is the subfield of geology that studies the relative age of rock strata and that aims at producing a hierarchical classification of (global) divisions of the historical time-rock record. The ‘golden spike’ or ‘GSSP’ approach is the cornerstone of contemporary chronostratigraphic methodology. It is also perplexing. Chronostratigraphers define each global time-rock boundary extremely locally, often by driving a gold-colored pin into an exposed rock section at a particular level. Moreover, they usually avoid rock sections that show any meaningful (...) sign of paleontological disruption or geological discontinuity: the less obvious the boundary, the better. It has been argued that we can make sense of this practice of marking boundaries by comparing the status and function of golden spikes to that of other concrete, particular reference standards from other sciences: holotypes from biological taxonomy and measurement prototypes from the metrology of weight and measures. Alisa Bokulich (2020b) has argued that these ‘scientific types’ are in an important sense one of a kind: they have a common status and function. I will argue that this picture of high-level conceptual unity is mistaken and fails to consider the diversity of aims and purposes of standardization and classification across the sciences. I develop an alternative, disunified account of scientific types that shows how differences in ontological attitudes and epistemic aims inform scientists’ choices between different kinds of scientific types. This perspective on scientific types helps to make sense of an intriguing mid-twentieth-century debate among chronostratigraphers about the very nature of their enterprise. Should chronostratigraphers conventionally make boundaries by designating golden spikes, or should they attempt to mark pre-existing ‘natural’ boundaries with the help of a different kind of scientific type? (shrink)

The Golden Rule is endorsed in oneform or another by most cultures and majorreligions and is still espoused byphilosophers, business ethicists, and popularbusiness authors. Because it also resonateswith undergraduate business majors, it can bean effective teaching tool. This paperdescribes a way of teaching the Golden Rulethrough a series of business-oriented examplesintended to bring out its strengths andweaknesses. The method described alsointroduces students to some basic moralreasoning skills and acquaints them with a widerange of moral issues that arise in (...) business. Kant's Formula of Humanity is discussed in thefinal section as a principle that overcomes atleast some of the Golden Rule's defects. (shrink)

Variations in human skin pigmentation are obvious, but how have skin colour differences evolved? Although clearly a polymorphic trait, the number and identity of key variants has remained unclear. Investigation of pigmentation phenotypes in model organisms provides a route to identify these genes and showed MC1R to be one key locus. Now, cloning of a classic zebrafish mutant, golden, identifies slc24a5 as a gene involved in fish skin pigmentation.1 Strikingly this study identifies the human orthologue, SLC24A5, as likely (...) to make a major contribution to the pale skin colouration of Western Europeans. BioEssays 28: 578–582, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

In this paper, I try to outline what I take to be Naming and Necessity’s fundamental legacy to my generation and those that follow, and the new perspectives it has opened up for twenty-first century philosophy. The discussion is subdivided into three sections, concerning respectively philosophy of language, metaphysics, and metaphilosophy. The general unifying theme is that Naming and Necessity is helping philosophy to recover a Golden Age, by freeing it from the strictures coming from the empiricist and Kantian (...) traditions and reconnecting it to the world and the objects that populate it. Because of this, in the concluding paragraph I tentatively suggest that Kripke’s philosophy may be seen as a sui generis form of naturalism. (shrink)

The book reconstructs the history of Western ethics. The approach chosen focuses the endless dialectic of moral codes, or different kinds of ethos, moral doctrines that are preached in order to bring about a reform of existing ethos, and ethical theories that have taken shape in the context of controversies about the ethos and moral doctrines as means of justifying or reforming moral doctrines. Such dialectic is what is meant here by the phrase ‘moral traditions’, taken as a name for (...) threads of moral discourse, made in turn of other interwoven threads, including transmission of shared codes, appeals to reform of prevailing custom, rational argument about the justification of some precept on the basis of some shared general teaching or principle, and rational argument about the ultimate basis for principles and justification of authoritative teaching. That is, the approach adopted to the reading of ethical texts depends on a firm belief in the fact that philosophers hardly created any ethical doctrine out of nothing. The main point this book tries to highlight is how different philosophical theories emerged and followed each other as a result of attempts at accounting for what was going on in the world of moral traditions. Changes were propelled by controversies between different schools, and highly abstract arguments were the unintended effects of moves made by controversialists forced to transform (and occasionally to turn upside down) their own doctrines in order to face the challenge posed by other arguments. This is the reason why the book examines not only texts that already enjoy pride of place in the history of philosophy (Aristotle, Kant, Hegel), but also other texts usually treated in the histories of religions (the Bible, the Talmud, the Quran), and others considered to be much less philosophical (Plutarchus, Pufendorf). -/- 1. Plato and a response to ethical scepticism. Two different traditions of morality in VI-V century Greece are described. The birth of philosophical questioning of traditional morality and temporal and spatial variation of custom is described within the context of the v century crisis, the demise of traditional aristocratic and tyrannical rule and the birth of democracy. Two conflicting answers to the challenge are reconstructed, namely conventionalist or immoralist theories formulated by the Sophists and the eudemonist and intellectualist Socratic theory. Plato’s own reformulation of Socrates answer to the Sophists is reconstructed. His psychological views, his classification of the four cardinal virtues and his political theory are described as parts of a unitary system, culminating in an extremely realist moral ontology identifying the idea of the good with the essence of the (moral and extra-moral) world itself. -/- 2. Aristotle and the invention of practical philosophy. Aristotle’s invention of practical philosophy as a field separated from first philosophy is shown to be an implication of his break with Plato moral ultra-realism. Aristotle’s agenda in his moral works is arguably dependent on a polemical intention, namely dismantling Socratic intellectualism. The semi-inductive or virtuously circular method of practical philosophy is illustrated, starting with the received opinions of the better and wiser individuals and trying dialectically to sift what is left of mistake and inconsistence in such opinions, finally trying to correct mistakes and make the overall practical science more consistent. The chapter illustrates then the relationship of individual ethics, or ‘monastics’, with the art and the science of the pater familias, or ‘economics’, and the science of the ruler and citizen, or politics. The nature of virtues, or better, excellences of character, is discussed, highlighting the basic role of hexis, or ‘disposition’. Prudence, or better practical wisdom, is the focus of the chapter. Its relationship with bouleusis or deliberation is examined, and its autonomous status vis-à-vis theoretical knowledge is stressed. -/- 3. Diogenes and philosophy as a way of life. The chapter provides an overview of Hellenistic ethics, which almost amounts to Hellenistic schools of philosophy, in so far as ‘philosophy’ became in these centuries primarily the name for a way of life. The typical character of the Cynical movement is highlighted, that of a school of life, not a school aimed at providing any kind of intellectual training was to be provided. -/- 4. Epicurus and ethics as self-care. The peculiar character of the Epicurean school is described, a combination of a science of well-being aiming, more than at pleasure as in the popular view, at reduction of useless suffering, of unnecessary needs, and at a balanced selection of pleasures of the best and most durable kind. -/- 5. Epictetus and ethics as therapy of the passions. The various phases of Stoicism are described, and the shifting place given to ethics in the Stoic system of idea, culminating in the paradoxical view of ethics, its impossibility in principle notwithstanding, as the only truly significant and necessary part of philosophy. Cicero is treated, showing how his own synthesis of various Hellenistic trends is as a truly philosophical enterprise, deserving serious consideration after one or two centuries when he was confined to the role of literate. Epictetus is chosen as the best example of what the Stoic tradition could yield, an art of living based on sophisticated introspection, in turn aimed at making a kind of cognitive therapy possible, dismantling obnoxious passions at their root by systematically correcting false representations. -/- 6. Philo and the reconciliation of Torah and Platonism. A reconstruction of basic ideas from a few books of the Hebrew Bible is provided, starting with the Prophetic tradition and the focus on God’s mercy as the source of motivation and standard for human behaviour. Then a comparative analysis is undertaken of a parallel tradition, namely the three codifications of the Torā (Law or, better, Instruction), highlighting how a core of moral ideas may be recognized as a basis and preamble of codification of civil law, cultural practice, and regulation of ritual purity. The importance of Leviticus is stressed as the turning point when emphasis mercy, typical of the Prophetic tradition, is combined with the legal tradition, yielding the change in sensibility of the Second Temple time. Philo of Alexandria is described as one of the three leading figures – together with Rabbi Hillel and Rabbi Yeshua – at the apex the emergence of the mentioned new sensibility, gradually including mercy as an essential part of justice and establishing the starting point of both the Rabbinic and the Christian tradition. This consists precisely in the precept of one’s neighbour’s love or of the golden rule, two eventually identical precepts whose meaning is arguably more sober and sensible than the long-lasting Christian tradition deriving from John and Augustine has made us believe and no novelty vis-à-vis so-called Ancient-Testament teachings. -/- 7. Augustine and Christianity as Neo-Platonism. The first section examines the moral doctrines of so-called 'ethical Treaties' from the Talmud, a group of treaties, among which the best known is Pirqé Avot, that were left out of the six "orders" of the canon as they did not fit in any of the six groups of issues ritual or legal on which the division was based. According to Maimonides, their peculiar theme is provided by the Deòt, 'opinions', i.e., mental dispositions, that is, the translation of the Greek term hexeis and Arab akhlak (in turn providing in this language the name for ethics as such). The three topics I reconstruct are: i) the notion of Torah: The Torah is understood as the world order itself, or as the ‘Wisdom’ that existed even before creation and was ‘the tool by which the world was built’; however, the Torah is an earthly and human entity, as it was "received" by humans, and from that very moment belongs to them; ii) the relationship between love of God and love of neighbour; the treaties require us to study and practice the Torah ‘for its own sake’, that is, require us to act out of love, not out of fear or hope of reward; iii) the idea of sanctification of daily life: having disappeared with the destruction of the Temple the possibility of any conflict between liturgical service and everyday life, the latter is assumed to be in itself divine service: to give food to the poor has the same value as sacrifices in the Temple, and as an implication, the insistence become recurrent on the goodness of created things in themselves along with a polemic against ascetic currents. The conclusions drawn are: i) the moral teachings of the Talmud and those of Yeshua are, rather than similar, virtually identical; one may safely say that the precept of love and the golden rule are central ones for all Talmudic rabbis, that mercy plays an indispensable role alongside with justice, and the latter is not a different thing from one’s neighbour’s love; ii) a peculiarity of Talmud rabbis facing Yeshua is the idea of study as worship, and knowledge as a source of justice; but this is an idea of Judaism after the Temple's destruction that cannot be attributed to the Pharisees of Yeshua’s time; iii) the relation of study and practice in the Talmud parallels that between faith and deeds in Paul's epistles, that is, respectively faith or learning are a necessary and sufficient condition to be recognized as righteous , but deeds are the inevitable effect of either faith or learning. The sayings ascribed to Yeshua are examined first, yielding the conclusion that a close equivalent may be found for every saying in Talmudic literature and yet the whole is ascribed to one rabbi, with rather consistent stress on God’s mercy and unconditional forgiving as the mark of true imitation of God. Thus, Yeshua’s teaching is pure Judaism. The third section describes briefly the galaxy of Gnostic currents and Manichaeism, trying to sketch the profile of moral teachings resulting from an encounter of Asian spiritual traditions, Hellenistic lore and sparks of teachings from apocalyptic Jewish currents. The last section summarizes the turbulent history of several encounters between Christian currents and Hellenistic philosophical schools. The first one was with late Cynicism. Recent, rather controversial, literature discovered the jargon and a few topics from the Stoic-Cynical popular philosophy in a few books from the New Testament itself. This, far from proving that Rabbi Yeshua had been influenced by cynic preachers, is a proof of the necessity felt by Christian preachers to translate the original ‘Christian’ teaching into a Greek lexicon deeply impregnated with cynic terminology. The second was with Platonism, yielding the mild and temperate moral teaching of Clemens of Alexandria, teaching the sanctity of nature and the human body, the joy of moderate fruition of ‘natural’ kinds of pleasures, and the beauty of the marital life – in short, the opposite of the standard picture of Medieval Christianity. Ambrose of Milan brings about a different kind of synthesis, namely with Middle Platonism, where Stoic themes prevail. The most shocking case is Augustine, where an early Manichean education is overcome in a former phase by a synthesis of Plotinian Neo-Platonism and Christian preaching, yielding a sustained polemic with the Manicheans and rather optimistic views on life and Creation, the body and sexuality, and Hebrew-Judaic tradition not far from Clemens of Alexandria. In a later phase, occasioned by controversy on the opposite front, with such Christian currents as the Pelagians and Donatists, Augustine comes back to heavily anti-Judaic and world-denying ascetic attitudes where is earlier Manichean upbringing seems to emerge again. The tragedy of medieval Christianity will be the later Augustine’s overwhelming influence. A final section is dedicated to the monastic tradition where a curious mixture of world-denying asceticism with an astonishingly penetrating ‘science’ of introspection emerges. -/- 8. Al Farabi and the reconciliation of Islam and Platonism. The Qurān and the qadit, that is, collections of sayings ascribed to the prophet Muhammad contain a wealth of precepts and catalogues of virtues mirroring moral contents from the Jewish and the Christian traditions, among them the basic notion of imitation of the Deity, where mercy is assumed to be its basic trait. An important tradition within Islam, namely Sufism, stressed to the utmost degree the role of mercy, turning Islam into a mystic doctrine centred on retreat from the world, abandonment to God’s will, and a peaceful and fraternal attitude to our fellow-beings. A secular literary tradition originating in the Sassanid Empire, the literature of advice to the Prince had for a time a widespread influence in the newly constituted Arabic-Islamic commonwealth. In a later phase, the legacy of Hellenic philosophy made its way into the intellectual elite of the Islamic world. The first important legacy was Platonic, and the Republic became the main text for Islamic Platonism. Al-Farabi wrote an enjoyable remake of the Platonic Republic, arguing that the citizen’s virtues were the basis on which the political building needs to rest. The secular lawgiver is enlightened by the light of reason in his everyday practice of governance, but room is made for the Prophet as the voice of revealed truth that confirms and completes the rational truth that philosophy may afford. In a second phase also Aristotelian and Stoic influence were assimilated. Miskawayh’s treatise was the masterwork at the time Arabic philosophy reached its Zenith. It is a treatment of the soul’s diseases and their remedies, combining the Aristotelian doctrine of the golden mean with the Stoic doctrine of the passions and elements of Galenic medicine. Towards the eleventh-twelve centuries a war raged among theologians and philosophers, finally won by the former with disappearance of philosophy as such. The newly established mainstream, yet, was no kind of intolerant fanaticism. It drew from the work of mystic theologian Al-Ghazālī, the best heir of Sufism, teaching a tolerant and peaceful attitude to our fellow-beings and a passive attitude to destiny as an expression of the Divine will. -/- 9. Moshe ben Maimon and the reconciliation of Torah and Aristotelian ethics. The encounter between the Talmudic tradition and Hellenic philosophy had taken place a first time in Alexandria at the time of Philo but the two traditions had parted way again. In fact, the kind of Platonic Judaism founded by Philo survived only within Christianity, in the fourth Gospel and then in writings by Clemens of Alexandria. The Talmudic literature had absorbed just less striking traits from the Hellenic Philosophy, namely an idea of ethics as care of the self and a role for the education of character as propaedeutic to theoretical knowledge. In the Arabic-Islamic world, a second round started when Jewish authors writing in Arabic undertook the task to prove the full compatibility of the tradition deriving from Torah and Platonic philosophy. The culmination of this attempt is provided by Moshe ben Maimon who tried to use Aristotelian ethics as a language into which the teaching from the Pirké Avot could be translated. -/- 10. Thomas Aquinas and the reconciliation of Christian morality and Aristotelian ethics. In the first section the fresh start is described of philosophical ethics in Latin Europe at the turn of the Millennium. In a first phase, Anselm and Peter Abelard built on a Platonic and Augustinian legacy. In this phase. remarkable innovations are introduced, including Abelard’s claim of the obliging character of erring consciousness. In a second phase, the rediscovery of Nicomachean Ethics thanks to Latin translation of Arabic versions gives birth to a new wave of ethical studies, recovering the very idea of Aristotelian practical philosophy, with the potential implication of full legitimization of natural morality, i.e. ethics without Revelation. Aquinas’s ethics is a theological ethics out of which it would be vain to try to extract a self-contained philosophical ethics. His treatment of topics in philosophical ethics, yet, does not boil down to repetition of Aristotelian arguments but is rather a creative reshaping of such arguments. For example, he introduces also in the practical philosophy a first principle parallel to the principle of non-contradiction; and he also carries out a synthesis of Aristotelianism, Stoicism, and neo-Platonism. Even though it is essentially moral theology, Aquinas’s doctrine - unlike Augustine – grants full citizenship to "natural" morality, firstly by rejecting the claim that the corruption of human nature due to the original sin is so radical as to leave "pure nature" incapable of moral goodness. The doctrine is presented in a more sophisticated formulation in a few of the Quaestiones, such as De Malo and De Veritate, in the Summa contra Gentes and in the commentaries to Aristotle than in the famous Summa Theologica, but the latter work includes the only or the largest exposition of some decisive part of the theory. Thus, the Summa Theologica should be read for what it is more than criticized for not being what it was not meant to be. It was not meant to be the brilliant synthesis of all that Reason he had been able to produce with what Revelation had added about which the Neo-Thomists used to dream, but rather a manual for the training of preachers and confessors, where theoretical claims are not too demanding and a few serious tensions are left. Besides a jump between the Prima Secundae and the Secunda Secundae, being the former an essay in virtue theory and the latter a handbook for confessors, the most serious tension is perhaps the one between the ethics of right reason presented in most of Ia-IIae and the eudemonistic ethics developed in quaestiones 1-5 of the same part; the alternative ethical theory which also may be found in Augustine, the Stoic view of a cosmic reason eventually coincident with the moral law, was believed by Anselm (followed by John Duns Scotus and William of Ockham) to be incompatible with eudemonism. It is questionable whether Thomas could reduce the tension proving that it is just an apparent tension, in so far as the right reason and bliss derived from knowledge of God tend to coincide, but this is just a conjecture. Thomas’s ethics is a virtue ethic, not a law-based one, and moral judgment focuses on the virtues, particularly charity, not on the commandments and even less on absolute prohibitions; Thomas, however, would not have considered a drastic alternative between law and the virtues such as the one which has been advanced in late twentieth-century philosophy to be justified. Nonetheless, when it discusses ‘special’ virtues, it ceases to be an ethics of virtue and becomes a disappointing and often contradictory discussion of legal and illegal acts. Such a discussion takes most of the time ‘reasonable’ middle positions on controversial issues but not the alternative approach that Aristotelianism would have made possible; even when some occasional Aristotelian claim shows up, such as money’s barrenness as a reason against usury, this seems to be made by an author who apparently ignores the Aristotelian Thomas of the Prima Secundae. It is an ethic of human autonomy which recognizes the binding character of the individual conscience and, potentially, even a duty to disobey unjust laws. It is true that what Thomas writes in his discussion of death penalty and persecution of heretics is simply disgusting, and yet we should blame Thomas the man, not Thomist ethical theory. Finally, Thomas’s ethics is not ethical ‘absolutism’, as both traditionalist Catholic theologians and secularist enemies of dogmatic morality tend to believe. It is instead an ethic of prudential judgment. Exceptions to this approach – or better results of logical fallacies – are such claims as the absolute character of negative precepts and of the existence of "intrinsically evil acts", claims that simply cease to make sense in the light of Thomas’s own distinction between human act and natural act, carrying consequences Thomas did not live long enough to draw or was not consistent enough to dare to draw. -/- 11. Francisco de Vitoria and casuistry. The first topic illustrated is the discussion about the notion of pura natura, namely the human condition after the original sin and before divine revelation. The core notion was already there in Aquinas but was later developed by Caietanus (Thomas de Vio) with a number of interesting implications: firstly a view of human nature as such much more positive than Augustine’s and his followers’ view, including both Calvinists and Jansenists; secondly, the implication that the philosopher’s morality, as opposed to the Christian’s morality, is a quite respectable kind of morality; thirdly, that theocracy and prosecution of the unfaithful lacked justification, with more far-fetching consequences than Aquinas himself had dared to draw. The second topic is casuistry, a new name for a comparatively older way of thinking, which was already there in late Stoicism and Cicero as well as in the Talmudic literature. This is an approach aimed at yielding probable enough solutions for doubtful cases even in absence of completely safe staring points. The genre developed from medieval reference books for confessors and became by the sixteenth-century a sophisticated tool-box for dealing with various fields of applied ethics. Francisco Vitoria, the main authority of Baroque Scholasticism, was a controversial figure, among the proponents of the new discipline of casuistry and a consistent proponent of more separation between the religious and the civil authority, stricter limits to the legitimacy of war, innate rights of non-Christian nations in the New World based on the notion of pura natura, providing a standard of ‘natural’ goodness, previous to revelation, on which the Indian nations were judged to live in a naturally good condition, provided with the institutions of family, justice, and religion had accordingly a right to full respect by Christian sovereigns. Bartolomé de Las Casas, arguing along similar lines, was the leader of a historical battle in defence of the rights of the Indios. -/- 12. Michel de Montaigne and the art of living. A short description of one of the Renaissance Phyrronism, one of the classical philosophies revived in the fifteenth and sixteenth century. Montaigne combines the sceptical epistemology with an understanding of ethics – indeed of philosophy as a whole – in terms of an art of living inspired by two basic ideas, sagesse, that is, practical wisdom as the only kind of rationality available after theology, science, and tradition have declared bankrupt, and an aesthetic ideal of self-transformation through the art of writing and introspection. -/- 13. Pierre Nicole and neo-Augustinianism. The chapter illustrates first the vicissitudes of Augustinianism newly born after the late medieval triumph of Thomist Aristotelianism in the alternative Protestant and Catholic versions processed by the Calvinists and the Jansenists. Then it illustrates the doctrines of Pierre Nicole, Blaise Pascal’s best disciple, on the impossibility of introspection, on the ubiquity of self-deception, on the incurably evil character of the passion of love, and on the two moralities, the one of the man of the world, the morality of honesty which is indispensable for granting peace and order but devoid of any true value for eternal salvation, since the same external behaviour may be prompted by opposite motivations, and the morality of charity, the only true one but also useless to society. The third topic is Pierre Malebranche’s view of self-deception as a ubiquitous phenomenon accounting for human action and responsibility and his reformulated theory of self-love, no less ubiquitous than for Nicole and yet not as incurably evil, given the distinction between morally indifferent and even necessary amour de soi and vicious amour proper, a distinction on which the whole of Rousseau’s moral and political theory rests. -/- 14. Samuel von Pufendorf and the new science of morality. The chapter is dedicated to the discovery of the idea of a ‘new moral science’. Hugo Grotius is discussed first highlighting the real character of his project, much closer to the Thomist idea of a natural law accessible to non-corrupted human reason when human beings are living in a state of pura natura. Then Hobbes’s combination of scepticism, voluntarism, and conventionalism is described and both the continuity with Grotius’s new science, in the search for non-revealed rational morality, and the break with him, in the adoption of voluntarism and refusal of an intellectualist view of natural law, are illustrated. Pufendorf’s work is illustrated as a synthesis of the two previous attempts and the – up to Schneewind underestimated – paradigmatic example of the new science of morality. -/- 15. Richard Cumberland and consequentialist voluntarism. The chapter gives an overview of eighteenth-century Anglican ethics, noticing how the Cambridge tradition gave special weight to natural theology as opposed to positive or revealed theology – and how two Cambridge fellows, John Gay and Thomas Brown, elaborated on Cumberland’s (and Malebranche’s, as well as Leibniz’s) strategy for finding a third way between intellectualist view and voluntarist view of the laws of nature. The result of their elaboration was a kind of a rational-choice account of the origins of natural laws, where a law-giver God chooses among a number possible sets of laws on a maximizing criterion, and God’s maximandum is happiness for his creatures. The chapter notices also how such a solution aimed at solving at once the problem of evil and that of the foundation of moral obligation by proving how God’s choice was justified as far as it was the one minimising the amount of suffering in the world. 16. Richard Price and intuitionism. The chapter describes first the doctrines of the Cambridge Platonists, an example of hyper-rationalist reaction to Calvinism. Secondly it describes the sophisticated and universally ignored – from Sidgwick to Anscombe –version of what was later labelled ‘ethical intuitionism’ – showing how it escapes familiar objections and misrepresentations of intuitionism – from Mill to Rawls – in grounding its argument on transcendental arguments while carefully avoiding recourse to introspection and psychological evidence, which has been taken as a too easy target by critics of intuitionism. Thirdly, the chapter discusses Whewell’s ‘philosophy of morality’, as opposed to ‘systematic morality’, not unlike Kant’s distinction between a pure and an empirical moral philosophy. Whewell worked out a systematization of traditional normative ethics as a first step before its rational justification; he believed that the point in the philosophy of morality is justifying a few rational truths about the structure of morality such as to rule hedonism, eudemonism, and consequentialism; yet a system of positive morality cannot be derived solely from such rational truths but requires consideration of the ongoing dialectics between idea and fact in historically given moralities. Whewell’s intuitionism turns out closer to Kantian ethics than commentators have made us believe until now, and quite different from what Sidgwick meant by intuitionism. -/- 17. Adam Smith and the morality of role-switch. The chapter describes first, Hutcheson’s attempt at basing the ‘new science’ of natural law on different bedrock than Pufendorf and the English Platonists, namely a moral sense, a faculty whose existence is assumed to be proved on an empirical basis. The second step is a reconstruction of Hume’s rejoinder in terms of a new science of man including morality on an ‘experimental’ basis, that is, a ‘Newtonian’ hypothetical-deductive approach, distinguished from Hutcheson’s allegedly uncritical descriptive approach to human nature. The third step is a reconstruction of Adam Smith theory of morality understood as emerging from a spontaneous interplay of exchanges of situations (the most basic meaning of the word ‘sympathy’ as construed by this author). -/- 18. Jeremy Bentham and utilitarianism. The bulk of the chapter is dedicated to the doctrines of Jeremy Bentham. The Enlightenment spirit that suggested the idea of a new morality, free from religion, is illustrated. The notion of utility is illustrated as well as the subsequent formulations of the principle of utility. The idea of felicific calculus is discussed, showing how its inner difficulties prompted several reformulations of the principle of utility in order to avoid undesirable implications of proposed formulations. The role of the thesis of spontaneous convergence between interest and duty is discussed, showing how it left numberless questions open, and the distinction between the virtues of prudence, justice and beneficence is described as a way out of the deadlocks of classical utilitarianism. After Bentham, Mill’s reformed utilitarianism is reconstructed, showing how it is a kind of mixed system – as closer to common sense as it gives up Bentham’s claims to consistency and simplicity – resulting as unintended consequences from the controversies in which Mill was too keen to engage. The hidden agenda of the controversy between Utilitarianism and Intuitionism, going beyond the image of the battle between Prejudice and Reason, is described, showing how both competing philosophical outlooks turn out to be more research programs than self-contained doctrinal bodies, and such programs appear to be implemented, and indeed radically transformed while in progress thanks to their enemies no less than to their supporters. -/- 19. Immanuel Kant, practical reason and judgment. The chapter argues that Kant took from Moses Mendelssohn the idea of a distinction between geometry of morals and a practical ethic. He was drastically misunderstood by his followers precisely on this point. He had learned from the sceptics and the Jansenists the lesson that men are prompted to act by deceptive ends, and he was aware that human actions are also empirical phenomena, where laws like the laws of Nature may be detected. His practical ethics made room for judgment as a holistic procedure for assessing the saliency of relevant moral qualities in one given situation; this procedure yields the same results as the geometry of morals does for abstract cases but does so immediately and without balancing conflicting duties with each other, since what makes for the salient quality of a situation is perceived from the very beginning. Kant's practical philosophy is richer than the received image, making room for an ‘empirical moral philosophy’ or moral anthropology including treatment of commerce, needs, value and price, happiness and well-being; the overall social theory and philosophy of history is less different from Adam Smith's than the received image makes believe; the paradox of happiness is central to Kant's philosophy; a distinction between happiness and well-being is clearly drawn; the distinction plays a basic role in establishing a link between the economic and the moral life. -/- 20. Georg Wilhelm Friedrich Hegel and the critique of abstract universalism. The chapter describes first the Romantic movement and the implications some of its concerns, rescuing passions, community, tradition, the individual as the bearer of a unique destiny, and the longing for organic unity between the individual, mankind and nature. Hegel’s contribution is discussed then, highlighting how, on the one hand, he shared a number of these concerns and on the other he had more rationalist leanings. The notion of morality is the pivotal point of the reconstruction, highlighting how Hegel construes this notion as a key to his own diagnosis of the malaise of modernity – the separation of individual and Gemeinschaft – and how his attack on Kant turns around this very idea. -/- 21. Friedrich Nietzsche against Christianity and the Enlightenment. The chapter illustrates first the idea of deconstruction of the back-world of values. Nietzsche claims to be legitimate heir of the French moralists, Leibniz, Kant and Hegel, in so far as he allegedly carries out to its deepest implications their discovery of what lies behind traditional naïve belief in the existence of an objective realm of values just waiting for description by the philosopher. The two exemplars form which genealogy draws inspiration are the classical philologist’s historical reconstructions of lost meanings and the chemist’s decomposition of elements. Then the genealogy of the notions of good and evil carried out in the first dissertation of Genealogy of morals is illustrated with its paradoxical conclusion that will to power is in fact the only ‘genuine’ kind of goodness. The third point illustrated is the dialectic of ascetism and self-realization with its ambiguous outcome. The suggested interpretation of such outcome is that Nietzsche’s normative ethics is a kind of virtue ethics taking an aesthetic ideal as a normative standard -/- 22. George Edward Moore and ideal utilitarianism. The chapter discusses the ideas of common sense and common-sense morality in Sidgwick. I argue that, far from aiming at overcoming common-sense morality, Sidgwick aimed purposely at grounding a consist code of morality by methods allegedly taken from the natural sciences to reach, also in ethics, the same kind of “mature” knowledge as in the natural sciences. His whole polemics with intuitionism was vitiated by the a priori assumption that the widespread ethos of the educated part of humankind, not the theories of the intuitionist philosophers, was what was worth considering as the expression of intuitionist ethics. In spite of a naïve positivist starting-point, Sidgwick was encouraged by his own approach in exploring the fruitfulness of coherentist methods for normative ethics. Thus, Sidgwick left an ambivalent legacy to twentieth-century ethics: the dogmatic idea of a “new” morality of a consequentialist kind, and the fruitful idea that we can argue rationally in normative ethics albeit without shared foundations. Then it reconstructs the background of ideas, concerns and intentions out of which Moore’s early essays, the preliminary version, and then the final version of Principia Ethica originated. I stress the role of religious concerns, as well as that of the Idealist legacy. I argue that PE is more a patchwork of rather diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. I add a comparison with Rashdall’s almost contemporary ethical work, suggesting that the latter defends the same general claims in a different way, one that manages to pave decisive objections in a more plausible way. I end by suggesting that the emergence of Analytic Ethics was a more ambiguous phenomenon than the received view would make us believe, and that the wheat (or some other gluten-free grain) of this tradition, that is, what logic can do for philosophy, should be separated from the chaff, that is, the confused and mutually incompatible legacies of Utilitarianism and Idealism. -/- 23. Edmund Husserl and the a-priori of action. The chapter illustrates first the idea of phenomenology and the Husserl’s project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the a priori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy carried out in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach’s theory of social acts as a key the grounding of norms, a view that basically sketches the very ideas ‘discovered’ later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section is dedicated to Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of ‘values’ – with surprising affinities with George E. Moore - than philosophers such as Max Scheler who claimed to Husserl’s legitimate heirs. -/- 24. Bertrand Russell and non-cognitivism. The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of ‘good’, its non-cognitive meaning, in a first phase identified with ‘emotive’ meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell’s ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of a rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson’s theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. Last of all, the discussion from the Forties about Hume’s law is described, mentioning Karl Popper’s argument and Richard Hare’s early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- 25. Elizabeth Anscombe and the revival of virtue ethics. The chapter discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. I argue that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. A short look at further developments in the neo-naturalist current is given trough a reconstruction of Philippa Foot’s and Peter Geach’s critiques to the naturalist-fallacy argument and Alasdair MacIntyre’s grand reconstruction of the origins and allegedly unavoidable failure of the Enlightenment project of an autonomous ethic. -/- 26. Richard Hare and neo-Utilitarianism. The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick’s and Moore’s fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine definitely refuted. A glimpse at this uproarious process is given through two examples. The first is Roy Harrod Wittgensteinian transformation of Utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This results in preference utilitarianism combined with a ‘Kantian’ version of rule utilitarianism. The second is Richard Hare’s two-level preference utilitarianism where act utilitarianism plays the function of eventual rational justification of moral judgments and rule-utilitarianism that of action-guiding practical device. -/- 27. Hans-Georg Gadamer and rehabilitation of practical philosophy. The post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named ‘Rehabilitation of practical philosophy’ is described. Among the actors of such rehabilitation there were a few of Heidegger’s most brilliant disciples, and Hans-Georg Gadamer is chosen as a paradigmatic example. His reading of Aristotle’s lesson I reconstructed, starting with Heidegger’s lesson but then subtly subverting its outcome thanks to the recovery of the central role of the notion of phronesis. -/- 28. Karl-Otto Apel and the revival of Kantian ethics. Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This started, instead than the rehabilitation of prudence, with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. An examination of his argument is some detail is offered, followed by a more cursory reconstruction of Jürgen Habermas’s elaboration on Apel’s theory. -/- 29. John Rawls and public ethics as applied ethics. Rawls’s distinction between a “political” and a “metaphysical” approach to one central part of ethical theory, namely the theory of justice, is interpreted as a formulation of the same basic idea at the root of both the principles approach and neo-casuistry, both discussed in the following chapter, namely that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls’ view never will be close – on the basic criteria for judgment. -/- 30. Beauchamp and Childress and bioethics as applied ethics. The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin’s new casuistry. -/- . (shrink)

When literary texts are included in a course on moral philosophy they tend to be classical tragedies or existentialist novels: texts filled with major moral transgressions and agonized debates over rights, wrongs, and relativism. Recently, however, the focus of much discussion on literature and moral philosophy has been Henry James’s last novel, The Golden Bowl. This ought to seem surprising. For The Golden Bowl is a quintessential Jamesian novel. Almost nothing happens. In the course of more than five (...) hundred pages there are two marriages, one affair, and a single act of violence, the smashing of the golden bowl. The rest is reflection, nuance, detail: the creation and preservation of a “‘brilliant, perfect surface,’” one “scarcely more meant to be breathed upon, it would seem, than the cheek of royalty.”1 There are no extreme actions or high-flown speculations. The moral issues among the four central characters either go unspoken or are raised expressly to be suppressed, banished from articulation. And what counts as the expression of the moral maturity and insight of the heroine, Maggie Verver, is her extraordinary ability to keep the truth silen00to put it precisely, to lie. If even there was a novel in which the protagonists shied away from moral debate, it is The Golden Bowl.The challenge for the philosophical critic, it seems to me, is to argue that it is just this stress on surface and silence that makes this novel of interest to moral philosophers, that makes it exemplary for how literature can do something philosophically important that philosophy cannot. 1. Henry James, The Golden Bowl , pp. 445, 172; hereafter cited by page number. Daniel Brudney is an assistant professor of philosophy at the University of Chicago. (shrink)

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal (...) axiom that (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

Our world can be a bewildering place. The sense of awe and wonder at the states of affairs in which we find ourselves immersed give rise to philosophical questions. Philosophical reflection is a critical attempt to come to grips with our place in the world and the various problems we encounter in respect to the complexities encountered in everyday life. In the most basic terms, phenomenology is the study of the structures and relations of phenomena. Phenomenology begins from a descriptive (...) analysis of our experiences of the world. It grants precedent to the first person perspective-how phenomena appear to consciousness. There are any number of problems related to the plenitude of kinds of experiences which confront us through the course of our lives, in addition to the structure of consciousness itself. This volume presents a variety of views on a number of the phenomena of our everyday lives, offering positions on such things from the nature of consciousness to the structures of religious or political experiences. Its appeal, however, should not be limited to philosophers alone-given that all persons can relate to the subject matter of the essays. For instance, one author asks, "what is friendship?" The present work may also be understood as a gesture toward bridging the division between the valuable insights of continental and analytic philosophical traditions. The authors include a combination of established academics, such as Jeffrey Wattles-the best-selling author of The Golden Rule-and young scholars from varied philosophical backgrounds. This collection is divided into four sections: (I) Foundational Elements of Experience; (II) The Experiencing Subject: What is it to be a Subject?; (III) Amongst Others: The Social World; and (IV) Social Objects and Institutions. Each section represents a level of experience, from the most basic structures of experience, to the subject's experience of the world and objects in it, to experiences and interactions with others, ending at the results of the codifications of certain social practices and beliefs. The sections treat their respective topics principally, even if they share material with other essays. Our experiences of the life-world, the world of human praxis, contain a multiplicity of elements; the divisions of this work are meant to demarcate various types of phenomena, not to offer any definitive thesis regarding a hierarchy or structure of relations. (shrink)

Aristotle stated one of the most influential postulates in the history of ethics: virtue is the middle point between two vicious extremes: "…excess and defect are characteristic of vice, and the mean of virtue. For men are good in but one way, but bad in many." The paper argues that between two vices there are two virtues that comprise two different moral perspectives as perceived by stereoethics. For example, two virtues can be found between the vices of miserliness and wastefulness: (...) generosity, which is further from miserliness, and thrift, which is further from wastefulness. Just as there are stereo music and stereo cinema, which convey the full volume of sounds and objects, there is stereo ethics, based on the duality of virtues. From the point of view of stereo ethics we can rethink the "golden rule": "Whatever you wish that men would do to you, do so to them." At the basis of both the golden rule and, later, the Kantian categorical imperative, lies the reversibility of moral subjects: you should put yourself in somebody else's place and treat you neighbor as you wish him or her to treat you. Today, however, ithas become obvious that only the ethics of differentiation can save us from relativism, which is a negative reaction against traditional morals with their universal norms. It is precisely this irreducibility of the individual to the general that may become a source of new moral energy. Two questions form a moral criterion: Would you wish to become an object of your own actions? Could anyone but you be the subject of your actions? The best action is that which corresponds to the needs of the largest number and the capacities of the smallest number of people. Act in such a way that you yourself would like to become an object of your actions, but no one else could be their subject. It is moral to do for others that which no one else can do except myself : to be for-others, but not like-others. (shrink)

The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview of Kummer’s contributions (...) and its immediate influence, I present work that favored intensive computations of particular cases of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active, but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory at large. (shrink)

Plato believed that behind everything in the universe lie mathematical principles. Plato was inspired by Pythagoras (571 BCE), who developed a school of mathematics at Crotona that studied sacred geometry as a form of religion. The school’s motto was “God is number,” or “All is Number”. Pythagoras believed that numbers represented God in pattern, symmetry, and infinity. When one of its students, Hippasus told the world the secret of the existence of irrational numbers, Greek geometry was born and (...) Pythagoras’ idea of divinity in numbers died because how could God not be perfect and symmetrical? In Plato’s Republic he discusses something called The Divided Line, which is a map, of sorts, for reaching what he calls the highest Good, which is the ultimate truth where one realizes the true state of the universe and can see the world for what it really is. Many mathematicians have attempted to plot Plato’s Divided Line only to come across a litany of problems and conundrums. Some have said that it the Divided Line cannot be plotted and is merely an allegory not meant to be plotted. This paper discusses some of the conundrums preventing the plotting of Plato’s Divided Line (not an exhaustive list), including Whole ‘vs’ Separate, Equality ‘vs’ Ontological Dissimilarity, Linear ‘vs’ Non-linear, and Infinity ‘vs’ Finite. This paper also explores a new understanding of the Allegory of the Cave in light of ‘the problem of the irrational.’ In exploring the link between the Divided Line and the ‘the problem of the irrational,’ I was able to plot it. It was found that the Divided Line is not a line in the linear sense, but a spiral, the Golden Ratio! This paper is an example of a new category of scholarly inquiry I call “Math Theory” based on scholarly mathematical axioms in theory, rather than including actual maths. In my papers I use existing mathematical equations and place them in an encompassing theory, rather than finding new formulae to fit an existing theory. Keywords: Pythagoras, divided line, math theory, highest good, all is number. (shrink)

Wittgenstein’s remarks on Frazer’s The Golden Bough were first edited and published in 1967 by Rush Rhees as Wittgenstein’s Bemerkungen über Frazers ‘The Golden Bough’. However, there is another edition, called Ludwig Wittgenstein: Remarks on Frazer’s Anthropology, edited and translated by Kenneth Laine Ketner and James Leroy Eigsti. In this paper I outline at least part of the history of this edition. At the same time, I shall describe some of the characteristic features of the Ketner and Eigsti (...) edition. This presentation takes as its point of departure the correspondence contained in the box “Wittgenstein 143” at the von Wright and Wittgenstein Archives, consisting of twelve letters that passed between Ketner and Eigsti, G.E.M. Anscombe, Rhees, and G.H. von Wright in 1972 and 1973. The presentation will also indirectly throw light on a number of issues concerning the editorial principles applied in publishing Wittgenstein’s remarks. (shrink)

This chapter contains sections titled: The School in the Garden Prehistory and the Rise of Cities The Locus Amoenus and the Origins of Agriculture Diogenes of Oinoanda and the Future Epicurean Golden Age Notes.

EDITOR’S ABSTRACTThis article argues that the early Laozi text underwent three stages: The first had section divisions on the basis of the meaning. The second stage was the formative period of the Laozi text influenced by cosmological numerology; the Silk Manuscript version A is its testimony. The third stage finalized the text through the canonization of the Classic by Emperor Jing; it is represented by the Peking University Han Bamboo Slips, Yan Zun, and Liu Xiang versions and became the received (...) edition. From the Han Bamboo Slips to the Liu Xiang version, the Laozi’s two parts and section numbering became increasingly balanced and symmetric. Ding urges scholars to pay attention to all these developments when studying the Laozi text. (shrink)

For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or reconstructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the "Frege-Russell conception of the natural numbers" or, more briefly, the Frege-Russell numbers. My main (...) concern will be to determine the precise sense in which this conception was, or could be, meant to constitute an analysis.1 I will be mostly concerned with Frege’s views on the matter; but Russell will come up along the way, for illustration and comparison, as will some recent neo-Fregean proposals and results. The structure of the paper is as follows: In the first section, I sketch Frege's general approach. Next, I differentiate several kinds, or modes, of analysis, as further background. In the third section, I zero in on the equivalence class construction, raising the question of why it might, from a Fregean point of view, be seen as 'the right' construction, thus as an analysis in a strong sense. In the fourth section, I provide a contrasting, more conventionalist view of the matter, often associated with the Carnapian notion of explication, and expressed in some remarks by Russell. I then discuss the motivation for the Frege-Russell numbers in more depth. In the sixth section, I introduce a neo-Fregean alternative, to be examined along similar lines. Finally, I reflect further on the significance of the kinds of arguments available in this connection. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Some Sources for Hume's Opening Remarks to Treatise LIVJII Graham Solomon Hume opens Book I, Part IV, Section III of the Treatise with these remarks: Several moralists have recommended it as an excellent method ofbecoming acquainted with our own hearts, and knowing our progress in virtue, to recollect our dreams in a morning, and examine them with the same rigour, that we wou'd our most serious and deliberate actions. (...) Our character is the same throughout, say they, and appears best where artifice, fear, and policy have no place, and men can neither be hypocrites with themselves nor others. The generosity, or baseness of our temper, our meekness or cruelty, our courage or pusilanimity, influence the fictions of the imagination with the most unbounded liberty, and discover themselves in the mostglaring colours. Who were these moralists? One looks in vain in the work of Malebranche, Locke, Shaftesbury and Hutcheson for such a recommendation. Did anyone make that recommendation? One moralist who did was "John Shadow," in a letter to Joseph Addison published in The Spectator, no. 586, 27 August 1714. Addison introduces Shadow's letter with the remark that it "is built upon a thought that is new, and very well carried on; for which Reasons I shall give it to the Publick without Alteration, Addition, or Amendment." I quote at length, for easy comparison with Hume: Sir, It was a good Piece of Advice which Pythagoras gave to his Scholars. That every Night before they slept they should examine what theyhad been a doing that Day, and so discover what Actions were worthy of Pursuit to Morrow, and what little Vices were to be prevented from slipping unawares into a Habit. If I might second the Philosopher's Advice, it should be mine, That in a morning before my Scholar rose, he should consider what he had been about that Night, and with the Volume XVI Number 1 57 GRAHAM SOLOMON same Strictness, as if the Condition, he has believed himself to be in, was real. Such a Scrutiny into the Actions ofhis Fancy must be of considerable Advantage, for this Reason, Because the Circumstances which a Man imagines himself in during Sleep, are generally such as entirely favour his Inclinations good or bad, and give him imaginary Opportunities of pursuingthem to the utmost; so thathis Temper will lye fairly open to his View, while he considers howitis moved when free from those Constraints which the Accidents ofreal Life put it under. Dreams are certainly the Result of our waking Thoughts, and our daily Hopes and Fears are what give the mind such nimble Relishes of Pleasure, and such severe Touches ofPain, in its Midnight Rambles. AMan that murders his Enemy, or deserts his Friend in a Dream, had need to guard his Temper against Revenge and Ingratitude, and take heed that he be not tempted to do a vile thing in Pursuit of false, or the Neglect of true Honour... I think it has been observed in the Course of your Papers, how much one's Happiness or Misery may depend upon the Imagination: ofwhich Truth those strange Workings ofFancy in Sleep are no inconsiderable Instances; so that not only the Advantage a Man has ofmaking Discoveries ofhimself, but a Regard to his own Ease or Disquiet, may induce him to accept ofmy Advice... Shadow has been identified as the poet John Byrom by various of the later editors of The Spectator? Of these, D. F. Bond footnotes Byrom's reference to Pythagoras, noting the publication in English of André Dacier's The Life ofPythagoras, with his Symbolism and Golden Verses; together with the Life ofHierocles, and his Commentaries upon the Verses. Bond notes Hierodes' comments on the following Verses: Never suffer Sleep to close thy Eye-lids, after thy going to Bed, Till thou hast examin'd by thy Reason all thy Actions of the Day Wherein have I done amiss? What have I done? What have I omitted that I ought to have done? If in this Examination, thou find that thou hast done amiss, reprimand thy self severely for it: And if thou has done any Good, rejoice. Dacier cites Porphyry and Marcus Aurelius... (shrink)

The vast majority of biological taxonomists use the Linnaean system when constructing classifications. Taxa are assigned Linnaean ranks and taxon names are devised according to the Linnaean rules of nomenclature. Unfortunately, the Linnaean system has become theoretically outdated. Moreover, its continued use causes a number of practical problems. This paper begins by sketching the ontological and practical problems facing the Linnaean system. Those problems are sufficiently pressing that alternative systems of classification should be investigated. A number of proposals (...) for an alternative system are introduced and evaluated. The best aspects of those proposals are brought together to form a post-Linnaean system, and a comparison of the Linnaean and post-Linnaean systems is conducted. The final section of this paper considers not only the theoretical reasons for replacing the Linnaean system, but also the practical feasibility of adopting an alternative system. (shrink)

Clarke and Beck discuss in their sections on congruency and confounds literature that has challenged the claim that the approximate number system represents numerical content. We argue that the propositions put forward by these studies aren't that far from the indirect model of number perception suggested by C&B.

Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed (...) some light on relevant passages of the Grundlagen. I will argue that Yourgrau does not make his case.The arguments with which we are concerned are found in the last three sections of Yourgrau's paper. A pervasive difficulty in these sections is that it is not clear exactly what Yourgrau is arguing against. The stated object of his attack is the Fregean thesis, a thesis about what numbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is that numbers number, where, roughly speaking, a number n numbers an object x just in case n can be legitimately assigned to x. The reason for this shift in emphasis appears to be rooted in a misconception. As we’ll see in more detail shortly, Yourgrau's argument against the Fregean thesis is based on an extension of a well known argument of Frege's found in §§22-3 of the Grundlagen, which Glenn Kessler has tagged the ‘relativity argument,’. According to Yourgrau, this is an argument ‘to the effect that what is literally numbered cannot simply be concrete objects’. This is incorrect. Frege himself clarifies the point of the argument in §21 with the following preface:In language, numbers (i.e., numerals] most commonly appear in adjectival form and attributive construction in the same sort of way as the words "hard" or "heavy" or "red," which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color. (shrink)

Encrypted in Derrida’s contribution to the Capri Seminar on Religion in 1994 are three retrievals: of his discussions of speech and of systems of inscription; of a concealment of splittings in the supposed continuities of traditions; and of a complicity between the operations of religion and those of a dissipation of the unities of science, Enlightenment, and knowledge, into proliferating autotelic tele-technologies. These retrievals take place between the lines of this discussion of faith, knowledge and religion, which arrives in two (...) halves, each in twenty-six sections. The first half arrives in italics, as spoken on the day, and ends by invoking Voltaire on toleration and a contrast between Christianity as Institution and Christianity as the legacy of Jesus and the Apostles. The second half, appended as a written supplement, with footnotes, is signed and dated April 26, 1995. Husserl’s epoche arrives as recurrent performance, challenging the unity of Heidegger’s Ereignis; contrasting modes for the arrival of futurity are invoked in a juxtaposition of the names: Kant, Hegel, Husserl, Heidegger, and Bergson, thus providing more than two sources for Derrida’s meditations on religion. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative (...) cosmologies, such as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

The Danish Golden Age of the first half of the nineteenth century endured in the midst of a number of different kinds of crisis -- political, economic, and cultural. The many changes of the period made it a dynamic time, one in which artists, poets, philosophers, and religious thinkers were constantly reassessing their place in society. This book traces the different aspects of the cultural crisis of the period through a series of case studies of key figures, including (...) Johan Ludvig Heiberg, Hans Lassen Martensen, and Søren Kierkegaard. Far from just a historical analysis, however, the book shows that many of the key questions that Danish society wrestled with during the Golden Age remain strikingly familiar today."--Publisher's website. (shrink)

This paper's aim is threefold. First, I wish to show that there is an analogy in section nine that arises out of the interaction of the interlocutors; this analogy is, or has, a certain comic adequatic to the traditional (e.g. Aquinas's) arguments about proofs for the existence of God. Second, Philo's seemingly inconsequential example of the strange necessity of products of 9 in section nine is a perfected analogy of the broken arguments actually given in that section, destroying Philo's earlier (...) arguments. Finally, I raise the question of the designer's intent in creating such a humourous piece. (shrink)

This paper's aim is threefold. First, I wish to show that there is an analogy in section nine that arises out of the interaction of the interlocutors; this analogy is, or has, a certain comic adequatic to the traditional arguments about proofs for the existence of God. Second, Philo's seemingly inconsequential example of the strange necessity of products of 9 in section nine is a perfected analogy of the broken arguments actually given in that section, destroying Philo's earlier arguments. Finally, (...) I raise the question of the designer's intent in creating such a humourous piece. (shrink)

"Annual dinner and act golden gavel competition." Ethos: Official Publication of the Law Society of the Australian Capital Territory, (194), pp. 18.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:An American Scholar Recalls Karl Barth’s Golden Years as a Teacher (1958–1964) by Raymond Kemp Anderson, and: The Westminster Handbook to Karl Barth ed. by Richard E. BurnettMatthew R. JantzenAn American Scholar Recalls Karl Barth’s Golden Years as a Teacher (1958–1964) Raymond Kemp Anderson lewiston, ny: edwin mellen press, 2013. 438 pp. $159.95The Westminster Handbook to Karl Barth Edited by Richard E. Burnett louisville, ky: westminster (...) john knox press, 2013. 242 pp. $35.00On April 2, 1966, Karl Barth received a letter from Peter Vogelsanger, informing him that Emil Brunner—the recipient of Barth’s thunderous “Nein!” on the subject of natural theology in 1934—was on his deathbed. Two days later, Barth responded and asked Vogelsanger to tell Brunner that “the time when I thought I should say No to him is long since past, and we all live only by the fact that a great and merciful God speaks his gracious Yes to all of us.” The irenic, compassionate, and affirming tone of this letter is typical of the “mature” Barth, whom Raymond Anderson studied under from 1958 to 1964 as a ThD student at the University of Basel. This period of doctoral study is the subject of Anderson’s interesting and eminently readable new book. Anderson enjoyably weaves together several different genres in his reflections on his experience with Barth, smoothly transitioning back and forth between personal memoir, constructive theological argument, and thoughtful interpretation of Barth’s life and writings.Structurally, the book offers a series of recollections and reflections gathered loosely around common themes rather than a tightly knit argument pursued rigorously from beginning to end. In other words, the work is a series of sketches from the artist’s notebook, as opposed to one intricate and detailed portrait focusing on a single subject. [End Page 207]In the first five chapters of the book, Anderson sketches a picture of the elderly Karl Barth who served as his “doktorvater,” drawing material from his student notes and personal memories of the years he spent with Barth in Basel. While Anderson finds continuity between the earlier and later writings of Barth, he suggests that the older Barth began to increasingly unfold the “fuller, grace-centered and human-shaped positive implications” of the earlier writings (viii). In Anderson’s experience, Barth’s early appeal to “Let God be God!” had in those later years “mellowed to an even deeper appeal to let God be himself, human as well, in the most unexpected ways” (11). This mellowing extended beyond Barth’s writing to his personality and demeanor as a teacher and theologian. The Barth whom Anderson knew was humble, understated, and compassionate, a sympathetic listener and a generous interpreter—in short, an “un-dogmatic” dogmatician (139).In the sixth chapter, Anderson shifts gears and reproduces extensive transcriptions of his own notes from several of Barth’s biweekly English-language colloquia on the topics of natural theology, the Old Testament promise, Paul Tillich, and existentialism. Anderson suggests that these notes are particularly valuable because in them one witnesses Barth explaining the bare essentials of his thinking in clear and simple English terms. This is true for large portions of the transcriptions. However, it must be said that there are also portions of these transcriptions that suffer from the lack of clarity that one might expect to find in student notes of discussions conducted in a language with which Barth was not completely comfortable. Nevertheless, these transcriptions provide previously unpublished primary source material from Barth that is worth examining.From chapter 7 until the end of the book, Anderson takes up the task of “sketching key insights and special teachings from the mature Barth that in the years since Barth’s death have shown themselves to carry special significance for our American college classroom, church school, and pulpit” (205). These include, but are not limited to, Barth’s attitude toward America, his emphasis on the priority of grace, his theology of nature (not his natural theology), and his positions on theories of religion, satisfaction theories of the atonement, election, universalism, and even the possibility of extraterrestrial life. This section also includes... (shrink)

Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...) argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers. (shrink)

In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider the (...) shortest length of a proof of A , the minimal depth of a proof of A and the minimal number of steps in a proof of A . The main results are the following: a bound on the depth in terms of the number of steps: Theorem 2.2, a bound on the depth in terms of the length: Theorem 2.3, a bound on the length in terms of the number of steps for restricted systems: Theorem 3.1. These results are applied to obtain several corollaries. In particular we show: a bound on the number of steps in a cut-free proof, some speed-up results, bounds on the number of steps in proofs of Paris-Harrington sentences. Some papers related to our research are listed in the references. We were especially influenced by Parikh's paper [17] on the famous conjecture of Kreisel . Many important problems in this field remain open. We hope that our paper will contribute to progress in this area. It should be noted that some results of this paper can be equally well obtained using unification theory , by translating a complexity-of-proof problem into a unification problem. A unification algorithm solving the unification problem can then be constructed and the complexity of the unification algorithm analyzed. As pointed out by the referee this method can be used to solve the problem stated in Section 3 for some non-simple schematic systems. (shrink)

In an attempt to increase the number of organs available for transplantation, section 43 of the Human Tissue Act 2004 provides, for the first time, a statutory basis for the non-consensual preservation of organs. However, several issues arise out of the terminology of the section relating to where the preservation steps can be carried out and, indeed, what preservation steps can be performed which may affect the success of this attempt to increase the organ donor pool.

In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider the (...) shortest length of a proof of A , the minimal depth of a proof of A and the minimal number of steps in a proof of A . The main results are the following: a bound on the depth in terms of the number of steps: Theorem 2.2, a bound on the depth in terms of the length: Theorem 2.3, a bound on the length in terms of the number of steps for restricted systems: Theorem 3.1. These results are applied to obtain several corollaries. In particular we show: a bound on the number of steps in a cut-free proof, some speed-up results, bounds on the number of steps in proofs of Paris-Harrington sentences. Some papers related to our research are listed in the references. We were especially influenced by Parikh's paper [17] on the famous conjecture of Kreisel . Many important problems in this field remain open. We hope that our paper will contribute to progress in this area. It should be noted that some results of this paper can be equally well obtained using unification theory , by translating a complexity-of-proof problem into a unification problem. A unification algorithm solving the unification problem can then be constructed and the complexity of the unification algorithm analyzed. As pointed out by the referee this method can be used to solve the problem stated in Section 3 for some non-simple schematic systems. (shrink)

Early sections of the paper develop a view of the natural numbers and a view of counting which are suggested by the remarks of several modern philosophers. Further investigation of these views leads to one of the main theses of the paper: a special kind of quantifier, the "numerical quantifier" is essential to counting. The remainder of the paper suggests the rudiments of a new view of the natural numbers, a view which maintains that numerical quantifiers are one kind of (...) natural number. (shrink)

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity (...) -- Axiomatic set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

Background: The rapid spread of COVID-19 infection has led countries across the globe to take various measures to contain the outbreak, including the closure of Universities. Forcing University students to stay at home has created enormous stress and uncertainty in their daily life.Objective: This study aimed to assess the perceived stress and coping strategies among undergraduate health science students of Jimma University amid the COVID-19 outbreak.Materials and methods: An online cross-sectional survey was conducted involving 337 undergraduate health science students from (...) August to September 5, 2020. The perceived stress scale -10 and Brief-COPE scale were used to assess the level of stress and coping strategies, respectively. Statistical Package for Social Science Version 22 was employed for data analysis. Logistic regression was conducted to identify predictors of high perceived stress.Results: The overall mean [±standard deviation ] age of the participants was 22.88 years. The mean PSS score was 22.16, and high perceived stress was reported in 121 participants. The overall mean coping score was 72.34, and approach coping was the predominantly used strategy for coping with stress. Personal perception of being stressed by the daily number of COVID-19 cases/deaths in Ethiopia, rare online talk/chat with friends, presence of confusion due to the inconsistent strategies developed by the health/government authorities in view of the scientific recommendations, perception of self/family members being at risk of getting sick, decreased household income following the COVID-19 pandemic, practicing denial, self-blame, planning, and religion as means of coping with stress were associated with high perceived stress.Conclusion: Over one-third of the participants had a high level of perceived stress, and the majority of them were practicing effective means of coping with stress. The authors recommend that the hosting University in collaboration with the concerned bodies develop innovative strategies to improve the psychological well-being of the students. (shrink)