Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the sum (...) of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

Aristotle created logic and developed it to a level of great sophistication. There was nothing there before; and it took more than two millennia for something better to come around. The astonishment experienced by readers of the Prior Analytics, the most important of Aristotle's works that present the discipline, is comparable to that of an explorer discovering a cathedral in a desert. This article explains and evaluates some of Aristotle's views about propositions and syllogisms. The most important omission is the (...) difficult subject of syllogisms involving modalities. Aristotle distinguishes two relations of opposition that can obtain between propositions with the same subject- and predicate-expressions: contrariety and contradiction. In every canonical syllogism, one term is common to the two premises: it is called “middle term,” or simply “middle.” The remaining two terms of the premises are the only ones occurring in the conclusion: they are called “extreme terms,” or simply “extremes.”. (shrink)

The aim of this article is to understand an important passage in the history of the sciences of the psyche: starting from the psychiatric problematization — and the consequent emergence — of the concept and the object called ‘sexuality’ in the second half of the 19th century, it attempts to show a series of continuities and discontinuities between this kind of reasoning and the birth of psychoanalysis in the first years of the 20th century. The particular focus is therefore directed (...) on two texts: Krafft-Ebing’s Psychopathia Sexualis and Freud’s Three Essays on the Theory of Sexuality. The argument runs along three intertwined axes: (1) an historico-epistemological analysis of the concepts and their transformations in the field of the science of sexuality; (2) an analysis of the power relationships between patients and physicians; and (3) an account of the psychiatric technologies of the self that have as an effect the emergence of new forms of ‘objective’ knowledge of the subject. The broader goal is to trace a map of the simultaneous and correlate coming into being and transformations both of new forms of objects and of new forms of subjects through the mediation of scientific concepts and techniques. (shrink)

In this paper I rely on recent literature that emphasises the importance of recognition in Hegel's philosophy in order to apply the recognition-theoretic approach to the notion of sacrifice in the Phenomenology of Spirit. Firstly, I conduct a preliminary analysis by examining the general meaning of sacrifice as a form of determinate negation. Secondly, I focus on two phenomenological moments (the struggle between ?faith? and ?pure insight?, and the cult) in order to answer the question, ?Is a real (effective and (...) unselfish) sacrifice possible?? Finally, I argue that sacrifice should be considered as a Darstellung, and I explain the twofold connection between sacrifice and recognition. I conclude that there is no sacrifice without recognition, and the process of recognition is intrinsically sacrificial. (shrink)

The purpose of this paper is to contribute to shed some light on the early Stoics' practice of managing platonic suggestions to construct their epistemology. Instances of such a practice, which scholars have recently focussed on, are the Stoic reassessment of the account of phantasia Plato offers in the Sophist and the image of the wax block as discussed in the Theaetetus. In this work I put forward a comparison between the simile of the soul-book, as presented by Socrates in (...) the Philebus (39a1-c2), and the Stoic image of the soul as a sheet in which conceptions are inscribed. I try to show that a far-reaching investigation of the relationship between Plato and early Stoic epistemology should take such a comparison into due account. In section one, I go into the details of the comparison and argue that Plato's perceptual judgment (this is how I translate the term doxa as it is used in the relevant section of the Philebus) is compatible with Stoic phantasia. In section two, I try to show that the theorisation of assent enable the Stoics to reply to an objection Aristotle made to Plato's definition of phantasia as a mixture of perception and judgment. (shrink)

The aim of this chapter is to reconstruct a hypothetical genealogy of the U.S. national motto “in God we Trust” by comparing the juridical and theological concept of “depositum”. According to Philo of Alexandria, the deposit was the most sacred institutional act of ancient social life, because it had both a religious and a sociological function. According to the Epistulae to Timothy the term ‘deposit’ defined the legacy of the Christian faith of which the disciple of St. Paul was entrusted. (...) His task was to manage this legacy and to spread it among the others. Hence the deposit defined at the same time a contract based upon good faith and a symbolic space of “security”, namely a container that protected an unchangeable content: the oral knowledge transmitted by Christ to the Apostoles and, indirectly, to St. Paul. The depositum was also the procedure through which the word of Christ would acquire all its potential. On the other hand, the contract defined as “depositum” by Roman law was characterized by a centrality of the so-called bona fides and by the distinction between regular and irregular deposit. This means that the principle of good faith should lead the conducts of the manager whose task is exactly to look after an object called Christian faith. How can we interpret the word ‘trust’ according to the juridico-political remarks? The purpose of this chapter is to explain all these related issues. (shrink)

The article aims at describing an alternative way to the Foucaldian escape of sovereignty. According to Foucault the only chance to reach this goal is to “go beyond” this concept as well as of linked concepts such as “law” and “institution”. On the one hand this vision is affected by the erroneous identification of law with the order of the sovereign, while the original private dimension of law is totally neglected. On the other hand, Foucault cannot assume that it is (...) also possible to delegitimize sovereignty with the very tools of law, namely in a trial. The article deals with the case of the «mutilated sovereignty» of the Italian State which has been acknowledged by a court in 2006. The government has been compensated for the damages suffered by the State because of the illegal activity in a region. The sovereignty has been “estimated”. But estimating something unquantifiable like sovereignty is destroying its symbolic force. (shrink)

Biopolitics, as interaction of power and subjectivity, creates new ways of making law. It is no longer the definition of borders. It gives legitimacy to emerging practices.

The institution is always a heteronomous construction which supposes the intervention of a “fiat” establishing a break in the continuum of the natural succession of events. This beginning is a sequence of acts leading to a practical judgment on a reality that exists only because of this qualification. This is the sense of the legal verb instituere. The paper tests this vision of the institution on the case of a widespread practice in the managerial world: the 360-degree feedback. A Jesuit (...) genealogy of this practice illustrates new cultures within the firm and the consequences on the subjectivity level. (shrink)

Christ as symbol in Kant¿s religion -- Hegel's conception of God -- The reality of religion in Hegel's idealist metaphysics -- Hegel's version of the ontological argument for the existence of God -- The trinity and the I -- The death of God and recognition of the self -- Beyond subjectivism -- The relevance of Hegel's philosophy of religion today.

The version of the paradox of false judgement examined at Tht. 188c10–189b9 relies on the assumption that to judge falsehoods is to judge the things which are not. The presentation of the argument displays several syntactic ambiguities: at several points it allows the reader to adopt different syntactic connections between the components of sentences. For instance, when Socrates says that in a false judgement the cognizer is “he who judges the things which are not about anything whatsoever” (188d3–4), how should (...) the clause “about anything whatsoever” be construed? In common with “he who judges” and “the things which are not” (in which case the cognizer would be “he who judges about anything whatsoever the things which are not about it”), or exclusively with “he who judges” (in which case the cognizer would be “he who judges about anything whatsoever the things which are not”)? The most plausible answer is that both construals are envisaged. Accordingly, the argument has two branches corresponding to these two alternative construals. In particular, it attempts to show that in both cases the cognizer will address what does not exist – an impossibility. The idea that a false judgement is concerned with what is not about its reference has a clear echo in the Sophist. The way in which the problem is handled in the Theaetetus provides a hint that can help to find a solution for the hotly debated issue of the interpretation of the Sophist’s account of false statement. (shrink)

This paper deals with a case of Virgilian ambiguity, namely the famous hemistich at Aen. 4.298 omnia tuta timens. By highlighting a plausible reading with a causal force (‘fearing everything too calm’, ‘because of the excessive calmness’), it seeks to demonstrate that this hemistich is an ambiguous passage. This view is confirmed through the imitation by Valerius Flaccus, who, in alluding to the Virgilian passage (Argonautica 8.408–12), highlights its ambiguity by including both of the most plausible readings.

The study of the neuroscience and genomics of mental illness are increasingly intertwined. This is mostly due to the translation of medical technologies into psychiatry and to technological convergence. This article focuses on psychosis. I argue that the convergence of neuroscience and genomics in the context of psychosis is morally problematic, and that ethics scholarship should go beyond the identification of a number of ethical, legal, and social issues. My argument is composed of two strands. First, I argue that we (...) should respond to technological convergence by developing an integrated, patient-centred approach focused on the assessment of individual vulnerabilities. Responding to technological convergence requires that we integrate insights from several areas of ethics, translate bioethical principles into the mental health context, and proactively try to anticipate future ethical concerns. Second, I argue that a nuanced understanding of the concept of vulnerability might help us to accomplish this task. I borrow Florencia Luna’s notion of ‘layers of vulnerability’ to show how potential harms or wrongs to individuals who experience psychosis can be conceptualised as stemming from different sources, or layers, of vulnerability. I argue that a layered notion of vulnerability might serve as a common ground to achieve the ethical integration needed to ensure that biomedical innovation can truly benefit, and not harm, individuals who suffer from psychosis. (shrink)

Since the microbiological revolution, most infectious diseases have been defined and classified according to an etiologic criterion, i.e. the identification of single, external necessary causes (for example, Mycobacterium for tuberculosis). This is not the case with cancer. Not only external necessary causes of cancer have not been identified, but also the morphological classification cannot be based on univocal criteria. Although neoplasia and anaplasia appear to be universal attributes of cancer, these events are only quantitative. Neoplastic growth can be fast or (...) slow (development may take weeks or years), and tissue pathologies are difficult to detect from normal tissue in some cancers but are obvious in others. Common special properties of anaplasia appear to be concealed in the wide range of morphologies. In the absence of a coherent morphological definition, and of external necessary causes (such as bacteria for infectious diseases), a mechanistic definition could be adopted. However, unless molecular biology discovers specific mechanistic steps in carcinogenesis, which indicate the existence of necessary events in carcinogenesis, we cannot adopt a univocal (monothetic) definition of cancer. The alternative is to use a polythetic definition, according to Wittgenstein's model of a long rope twisted together out of many shorter fibres. (shrink)

In 1959, the Charles Darwin Station and the Galápagos National Park were established, formally inaugurating conservation on the archipelago. In the same year, a utopian colony from the United States arrived. Whereas scholars have dismissed the latter and focused on the former, this essay unveils the science-inspired utopianism common to both enterprises. Investing science with the exclusive role of producing all knowledge and steering politics, leaders of the two initiatives aspired not only to protect nature but also to forge a (...) new humanity. Describing how such ambitions burst along lines of race, class, and nationality, I argue that these enterprises consolidated the current understanding of the Galápagos as “pristine”: a site fit for research and tourism but unhospitable to people. Drawing on archival and historical documents, this essay aims to reinvigorate two conversations: one between science and technology studies and conservation, and the other between STS and utopian studies. If recent attempts at bridging the divide between science and imagination have emphasized how powerful actors shape human society, this essay considers the long-lasting effects of scientific imaginaries on a politics of nature. (shrink)

The paper deals with the art of cross-examination or probe (peirastiké) wich is, according to Aristotle, a part of dialectic and aims at revealing falle pretensions to knowledge. A detailed discussion of the relevant passages from the Sophistical Refutations shows that "peirastic" argumenta were not easily distinguishablc forro the arguments used by the sophists against the scientists in order to undermine their reputation. It is also shows that the difficulty of telling dialectic from sophistry is a theme Aristotle inherits frorn (...) Plato's Sophist. (shrink)

The author argues that one of the “circles” that constitute Hegel’s philosophical system, as it is displayed in the Encyclopedia, is the circle between the I and the spirit. Specifically, the author focuses on the emergence of spirit as a self and an I, and on the encounter of the I with nature. The author also argues that absolute spirit maintains fundamental intersubjective and perspectival features that are proper to the I, and that grasping the circular movement between the I (...) and the spirit in the context of Hegel’s discussion of absolute Geist is also relevant to appreciating how normative categories of social thought can be challenged and altered through Geist’s ability to achieve critical distance by overcoming subject/object distinctions. (shrink)

Using the example of air pollution, I criticize a restricted utilitarian view of environmental risks. It is likely that damage to health due to environmental pollution in Western countries is relatively modest in quantitative terms (especially when considering cancer and comparing such damage to the effects of some life-style exposures). However, a strictly quantitative approach, which ranks priorities according to the burden of disease attributable to single causes, is questionable because it does not consider such aspects as inequalities in the (...) distribution of risks. Secondly, the ability of epidemiological research to identify some health effects is limited. Third, the environment has symbolic and aesthetic components that overcome a strict evaluation of damage based on the impairment of human health. It is not acceptable that priorities be set just balancing the burden of disease caused by pollution in the environment against economic constraints. As an example of a computation that inherently includes economic analysis, I refer to the proposal of an estimator of mortality in coal mining, i.e., a rate which puts deaths in the numerator and tons of coal extracted in the denominator. According to this estimator, mortality due to accidents decreased from 1.15 to 0.42 in the period 1950–1970 in the United States, for each million tons of coal extracted. However, considering the steep decline in the workforce in the same period, the traditional mortality rate (deaths over persons-time) actually increased. The proposal of a measure of mortality based on the amount of coal extracted is just one example of the attempts to influence decisions by including an economic element (productivity) in risk assessment. This paper has three purposes: One, to describe empirical research concerning the health effects of environmental pollutants; two, to discuss the scientific principles and methods used in the identification of environmental hazards; and three, to critically discuss some of the ethical principles which are applied in medicine and in the assessment and management of risk. (shrink)