The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

Aristotle's theory of truth, which has been the most influential account of the concept of truth from Antiquity onwards, spans several areas of philosophy: philosophy of language, logic, ontology and epistemology. In this 2004 book, Paolo Crivelli discusses all the main aspects of Aristotle's views on truth and falsehood. He analyses in detail the main relevant passages, addresses some well-known problems of Aristotelian semantics, and assesses Aristotle's theory from the point of view of modern analytic philosophy. In the process (...) he discusses most of the literature on Aristotle's semantic theory to have appeared in the last two centuries. His book vindicates and clarifies the often repeated claim that Aristotle's is a correspondence theory of truth. It will be of interest to a wide range of readers working in both ancient philosophy and modern philosophy of language. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. (...) The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)

Some philosophers argue that false speech and false belief are impossible. In the Sophist, Plato addresses this 'falsehood paradox', which purports to prove that one can neither say nor believe falsehoods. In this book Paolo Crivelli closely examines the whole dialogue and shows how Plato's brilliant solution to the paradox is radically different from those put forward by modern philosophers. He surveys and critically discusses the vast range of literature which has developed around the Sophist over the past fifty (...) years, and provides original solutions to several problems that are so far unsolved. His book will be important for all who are interested in the Sophist and in ancient ontology and philosophy of language more generally. (shrink)

Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.

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)

At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of .

Resumen:La filosofía ofrece múltiples ópticas para considerar el curso de la historia de la humanidad, perspectivas que van desde lo epistemológico hasta lo metafísico. Entre aquellas posibilidades interpretativas se encuentra el juego, específicamente la concepción antropológica del ser humano en tanto homo ludens –tema ya trabajado por Holzapfel en una obra previa–. A partir de dicha concepción lúdica del ser humano es posible analizar la dialéctica de los diversos tipos de juegos en el desarrollo histórico. La presente obra constituye una (...) invitación a recorrer el despliegue del homo ludens hasta las repercusiones de su desregulación agonal (juego de competencia) en nuestros días, proponiendo una solución lúdica a la crisis actual. (shrink)

The main goal of this paper is to argue the relevance of Hegel’s notion of the Trinity with respect to two aspects of Hegel’s idealism: the overcoming of subjectivism and his conception of the ‘I’. I contend that these two aspects are interconnected and that the Trinity is important to Hegel’s strategy for addressing these questions. I first address the problem of subjectivism by considering Hegel’s thought against the background of modern philosophy. I argue that the recognitive structure of Hegel’s (...) idealism led him to give the Trinity a decisive role in his philosophical account. Next, I discuss the Trinity by analysing the three divine persons. This analysis paves the way for the conclusion, where I argue that the Trinity represents a model for re-thinking the ‘I’ in a way that overcomes a ‘naïve realist’ and a ‘subjective’ account of the self. I suggest that Hegel’s absolute idealism can be conceived as an approach to the ‘I’ that considers the role of acts of mutual recognition for the genesis of self-conscious thought, and that the Trinity is the Darstellung of the relational and recognitive structure of the ‘I’. (shrink)

_An examination of the philosophical notion of sacrifice from Kant to Nietzsche._.

This paper studies the relationship between Argumentation Logic, a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic. In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of sentences in AL and Natural Deduction proofs of the complement of these sentences. The proof of this equivalence uses a restricted form (...) of ND proofs, where hypotheses in the application of the Reductio of Absurdum inference rule are required to be “relevant” to the absurdity derived in the rule. The paper also discusses how the argumentative re-interpretation of PL could help control the application of ex-falso quodlibet in the presence of inconsistencies. (shrink)

It is usually maintained that a subject with manifestly contradictory beliefs is irrational. How can we account, then, for the intuitive rationality of dialetheists, who believe that some manifest contradictions are true? My paper aims to answer this question. Its ultimate goal is to determine a characterization of (or rather a constraint for) rational belief approvable by both the theorists of Dialetheism and its opponents. In order to achieve this goal, a two-step strategy will be adopted. First, a characterization of (...) rational belief applicable to non-dialetheist believers will be determined; this characterization will involve the semantic apparatus of Nathan Salmon’s Millian Russellianism but will get rid of the problematic and obscure notion of mode of presentation (guise in his own terminology), replacing it with a couple of novel devices, belief subsystems and cognitive coordination. Second, using ideas from Graham Priest, the leading proponent of Dialetheism, such a characterization will be modified, so as to devise a new one able to account for the intuitive rationality of both dialetheist and non-dialetheist believers. (shrink)

Este ensayo, dedicado a las doctrinas psicológicas de Alejandro, se divide en tres partes: la primera ilustra, a través de ejemplos tratados por el De anima, la concepción que tenía Alejandro de su actividad filosófica. Dado que Aristóteles ha transmitido las doctrinas más verdaderas, cree Alejandro, lo que hay que hacer es simplemente exponerlas de nuevo del modo más claro y completo, valiéndose de todo lo que dice Aristóteles respecto de las funciones psíquicas, incluso en obras diferentes del tratado principal. (...) La segunda parte del ensayo se centra en la sección inicial (1-26 Bruns) del tratado alejandrino, donde principalmente se prueba que el alma, como cualquier otra forma, es sólo la conjunción de las capacidades del cuerpo, cuya forma es el alma. Más aún, argumenta Accattino, tales capacidades anímicas nunca pueden expresarse independientemente del cuerpo, y menos aún con la desaparición del cuerpo. Por lo tanto, como forma del cuerpo, el alma es completamente mortal. La otra tesis célebre de Alejandro (la identificación del intelecto activo con el dios aristotélico de Metafísica Lambda) es tratada por Accattino en la tercera parte de su ensayo. Allí examina la noética del De intellectu de Alejandro y la sección dedicada a la noética en su De anima (80, 16-91, 6). En esta parte de su artículo el autor aclara, primero, los términos usados en la noética alejandrina (intelecto en potencia o intelecto “material”, intelecto entendido como “hábito”, intelecto “que viene de afuera”, el intelecto “agente”); luego ilustra el modo en que Alejandro da cuenta de la actividad intelectiva del intelecto humano y, finalmente, se concentra en el papel diferente que atribuye al intelecto agente (o el intelecto “que viene de afuera”, identificado por Alejandro con el intelecto divino) en el De intellectu y en la sección del De anima, respectivamente, de modo de mostrar que la posición más madura de Alejandro es la indicada en el De anima. (shrink)

Medical humanities and ethics are getting more and more important in Europe as essential disciplines of the core curriculum for health-care professionals. The idea of the physician as a technician shows itself to be unbearable because of the global historical changes we daily face in caring settings. We deal with chronic diseases, which require a sensitive physician/patient covenant and a good performance in communication skills1 because a whole life-style transformation is often necessary. Moreover, citizens are more informed about both the (...) technological progress and their civil rights, so that a shared decision has to be prepared and implemented by exploring the emotional reactions to illness, by explaining the .. (shrink)

This paper covers the theme of the death of God considered from a Hegelian standpoint. For Aristotle, the image of God as ‘thought thinking itself’ was an image of the knowledge aspired to in philosophy. With the notion of God becoming man and his insistence on the icon of the Cross, Hegel challenged the Aristotelian goal of philosophy as immutable knowledge of an ‘ultimate’ reality. Hegel viewed the crisis of normativity as strictly linked to the conception of the self. It (...) is Nietzsche who is best known for alluding to the full significance of this image for modern life, but Hegel’s thought on the complex relations of philosophy and religion in the modern world can be regarded as an attempt to think through this same historical phenomenon. In this paper, I focus on the philosophical relevance of Hegel’s notion of the death of God. I argue that unpacking the significance of the ‘truths’ presented symbolically in modern Christianity is crucial in unders.. (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)

The aim of the paper is to clarify the theoretical core of Solger's thought, the foundation for his aesthetics. I first analyze Solger's dialectic of double negation. Secondly I focus on Solger's gnoseology, which is orientated toward grasping the equilibrium between the Infinite (God) and the finite (world) consisting in this double negation. Lastly I investigate the notion of sacrifice, connecting it with Solger's ironic dialectic and showing its relevance to a complete understanding of his thought.

Este ensayo, dedicado a las doctrinas psicológicas de Alejandro, se divide en tres partes: la primera ilustra, a través de ejemplos tratados por el De anima, la concepción que tenía Alejandro de su actividad filosófica. Dado que Aristóteles ha transmitido las doctrinas más verdaderas, cree Alejandro, lo que hay que hacer es simplemente exponerlas de nuevo del modo más claro y completo, valiéndose de todo lo que dice Aristóteles respecto de las funciones psíquicas, incluso en obras diferentes del tratado principal. (...) La segunda parte del ensayo se centra en la sección inicial (1-26 Bruns) del tratado alejandrino, donde principalmente se prueba que el alma, como cualquier otra forma, es sólo la conjunción de las capacidades del cuerpo, cuya forma es el alma. Más aún, argumenta Accattino, tales capacidades anímicas nunca pueden expresarse independientemente del cuerpo, y menos aún con la desaparición del cuerpo. Por lo tanto, como forma del cuerpo, el alma es completamente mortal. La otra tesis célebre de Alejandro (la identificación del intelecto activo con el dios aristotélico de Metafísica Lambda) es tratada por Accattino en la tercera parte de su ensayo. Allí examina la noética del De intellectu de Alejandro y la sección dedicada a la noética en su De anima (80, 16-91, 6). En esta parte de su artículo el autor aclara, primero, los términos usados en la noética alejandrina (intelecto en potencia o intelecto “material”, intelecto entendido como “hábito”, intelecto “que viene de afuera”, el intelecto “agente”); luego ilustra el modo en que Alejandro da cuenta de la actividad intelectiva del intelecto humano y, finalmente, se concentra en el papel diferente que atribuye al intelecto agente (o el intelecto “que viene de afuera”, identificado por Alejandro con el intelecto divino) en el De intellectu y en la sección del De anima, respectivamente, de modo de mostrar que la posición más madura de Alejandro es la indicada en el De anima. (shrink)

Name der Zeitschrift: Klio Jahrgang: 96 Heft: 1 Seiten: 324-333.

Between the 1970s and the 1980s social practices were the object of theoretical research in some areas of sociology and cultural anthropology, to meet the need to integrate structuralist, functionalist or Marxist objectivist theories of society by using more sensitive types of approach to social actors, who were viewed as subjects capable of individual decisions, actions and interpretations. In particular, the role of reflexion on social practices became more relevant in the critique of society as an organic, unified whole, also (...) stressing an alternative to liberal outlooks and describing society in the basic terms of relationships between individuals. Social practices are constituted by an organic set of base elements usually applicable also outside structured practices but assuming a peculiar network of relationships within them. This studies is an attempt to show the distinct traits that rationality criteria take while operating inside social, cooperative practices, also pointing to the consequences that this configuration has in the relationship between practictioners and institutions. (shrink)

_ Source: _Volume 48, Issue 2, pp 175 - 196 This article provides an analysis of the development of the notions of “self” and “nature” through three stages of Heidegger’s thought. The main contention is that Heidegger’s conceptions of the self and nature are indissolubly connected to each other, and that such connection appears through three concerns that represent important elements of continuity: 1) the “irreducibility of the self,” conceived in a non-subjectivist way; 2) the recovery of a non-objectivist “originary” (...) account of nature; 3) the overall commitment to the overcoming of the polarization between subject and object. I argue that there is a parallelism in the way self and nature are addressed in each of the three phases; and that the transformations of the notions are functional to the project of addressing the concerns mentioned earlier. I conclude by addressing the “violence of nature,” which remains a “blind spot” in the philosophy of the later Heidegger. (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)