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)

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 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)

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.

This paper aims to discuss the coherence and consistency of the Stoic and the Nietzschean “art of dying at the right time”. Throughout this paper, we will use this expression to refer to the Stoics’ and Nietzsche’s treatment both of involuntary and voluntary death, inasmuch as both seem to be strongly connected to and grounded on the notion of timeliness. Taking this notion as a guiding thread, we will emphasize the several similarities that link their approach to suicide. Indeed, as (...) will be shown, it is plausible to assume that Nietzsche’s understanding of voluntary death is particularly influenced by the Stoic tradition. At the same time, we will point out the relevant differences that make these two approaches differ. In dealing with the Stoic and the Nietzschean attitude towards suicide, the underlying question will be whether the legitimization and defense of voluntary death is compatible—and if so, to which extent—with their teachings, in particular, with their notions of happiness and affirmation of life, on the one hand, and their ideals of living in accordance with nature and amor fati, on the other. (shrink)

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)

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)

Chapter Θ10 of Aristotle's Metaphysics is traditionally taken to be about the truth of intuitions, namely episodes of an immediate and sub-propositional grasp of entities. This exegesis however saddles Aristotle with a broken-backed theory of truth because in other passages of his works he claims that truth and falsehood apply only to items of a propositional nature and denies that sub-propositional items can be true or false. An alternative exegesis is preferable which takes Θ10 to be about the truth of (...) existential statements and judgements concerning simple items. (shrink)

This article explores Hegel's conception of experience, positing it as the entry point for grasping the implications of the philosophy of nature. The article briefly examines Hegel's view of nature, focusing on its transformative journey from externality to integration with the conscious I. Subsequently, the purpose of Hegel's philosophy of nature is discussed, and recent interpretations are compared. The article unfolds the notion of experience as a bridge between the subjective dimension explored in the Phenomenology of Spirit and the understanding (...) of reality presented in the Encyclopedia. Experience, considered in its threefold meaning of unveiling, actively interpreting, and generating rationality within nature, dynamically shapes both the self‐conscious subject and the natural world across logic, nature, and spirit. Finally, the article highlights experience as mediating both the epistemological and the metaphysical relationship between nature and spirit. The article concludes by arguing that the transformative power of experience plays a central role in overcoming the separation between spirit and nature, fostering a mediated unity between the human subject and the natural world. (shrink)

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if λ > ωα then the logic with the quantifier “there existα many” is (λ,λ)-compact if and only if either λ is weakly compact or λ is singular of cofinality<ωα. As a corollary, for every infinite cardinals λ and μ, there exists a (λ,λ)-compact (...) non-(μ,μ)-compact logic if and only if either λ<μ orcfλshrink)

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction and the (...) third excluded principles in the context of his research on foundation of geometry; (4) Parmenides’s metaphysical and physical conceptions have their bases in his speculation on geometry; (5) Parmenides used the principle of sufficient reason. Enriques’s reading is worth being expounded and discussed within the historical, philosophical and scientific context in which it is inserted. Since Enriques’s ideas are not widely known and discussed, my research has the purpose to fill this gap. The article also aims to provide elements to illustrate the discussion on Parmenides in the first half of the last century. (shrink)

One of the complications of a clear evaluation of different positions called “realism” in metaphysics and ontology is discrepancy in terminology and variance of basic intuitions inherent this notion. I recommend a taxonomy that distinguishes three kinds of variance: variance in the sets of conditions for a philosophical position to be acknowledged as actual realism, variance in strength and variance in conceptual frameworks. Within this last case, I propose to differentiate realism in epistemology, in ontology, and in metaphysics, intersecting these (...) three variants with the local/global realism dichotomy. The taxonomy here provided aims at being meta-philosophical; expressive enough for a fine-grained articulation of different philosophical positions in the recent debate, including the question of metaphysical grounding; and impartial, with no need to be connected to the defense of one form or another of the philosophical positions called “realism.”. (shrink)

Scholars of aristotelian political philosophy generally agree that the project of the ideal polis of Politics VII – VIII is strictly linked to Ethics. They disagree however on the nature of the constitution outlined. It is broadly accepted that it is a "polity". In this paper I deal with the topic of aristocracy in aristotelian political thought and I show that, throughout Politics, Aristotle never swerved from the idea of aristocracy as the optimal constitution, where the truly virtuous rule. Finally (...) I argue that the ideal polis of Politics VII – VIII, though it is never explicitly thus termed, is an aristocracy. (shrink)

SummaryIn the 1780s the anatomist Vincenzo Malacarne discussed the possibility of testing experimentally whether experience can induce significant changes in the brain. Malacarne imagined taking two littermate animals and giving intensive training to one while the other received none, then dissecting their brains to see whether the trained animal had more folds in the cerebellum than the untrained one. This experimental design somewhat anticipated one used 180 years later by Mark R. Rosenzweig at the University of California, Berkeley. This paper (...) explores some methodological aspects of the case study just outlined by pointing out that our grounds for being interested in it are neither merely neuroscientific (for, strictly speaking, Malacarne's proposal was false) nor narrowly historical (for there is no causal chain linking Malacarne's ideas to Rosenzweig's experiment). Rather, the really interesting point here is to what extent Malacarne's ideas are similar to Rosenzweig's, a point that we can better investigate by employing certain conceptual tools borrowed typically (but not exclusively) from (a certain kind of) philosophy. If we do not handle the analogy with care, we run the risk of ‘discovering’ nothing but void platitudes or anachronistically misleading common features. (shrink)

The study of evil and the different forms in which it manifests itself has long been the interest of a significant number of scholars, mainly philosophers and theologians. Yet, following the libera...