There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a subset (...) of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

Knowing is an activity through which agents and world produce themselves. This is often expressed by the enactive claim that agents bring forth a world. I analyse this idea for different modes of agent–environment engagement: interactional, transactional, and constitutional. Something is produced in each case. Bringing forth a world is not only an epistemic but an ontological claim. Acts in their fine structure result from a process of fact production, or f/acts. F/acts co-emerge with their 'preconditions', e.g.intentions, affordances, across the (...) subject/object divide. F/acts define their inner temporality and affectivity, comprising both event and experience. A plurality of worlds is admitted in this enactive view, without entailing antirealism. We cannot bring forth just any world. World resistance organizes action and experience. I touch on the implications for objectivity and free will and discuss the primordiality of activity, community, and relationality. From a notion of groundlessness in early enactive work, I suggest that a participatory universe is better conceived as a meshwork of groundless grounds. (shrink)

Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...) in the foundational controversy of the 1920s. In addition, they reveal Weyl's hitherto unknown objections to Becker's detailed attempt (Mathematische Existenz, 1927) to ground the transfinite phenomenologically. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( \sqsubseteq (...) \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

This paper explores the epistemology of extrapolation from model organisms to humans in molecular medicine. We take into account two common views on the issue, the homology view and the disanalogy view. In response to both interpretations, we argue that the foundational basis of extrapolations cannot simply be provided by homology and that relevant disanalogies can, thanks to the techniques of molecular biology, be experimentally controlled and exploited to allow useful and reliable extrapolations. The case of "humanised mice" in the (...) context of cancer stem cell research provides evidence of how animal models can be construed to approximate bona fide causal analogue models of human diseases. To supplement this view we show how the epistemology of model organisms needs to take into account the engineering side of molecular medicine. Model organisms are often manipulated to create analogies or remove disanalogies with the target system. We maintain that highlighting this feature is fundamental to explain what warrants extrapolation in the search for the molecular causes of disease. (shrink)

I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools . In addition, I put Frege's considerations in the context of a widespread debate in Germany (...) on ‘directions’ as a central notion in the theory of parallels. (shrink)

Still today it remains unclear whether Galileo ever climbed the leaning tower of Pisa in order to drop bodies from its top. Some believe that he established the principle of equal speeds for falling bodies by means of an ingenious thought experiment. However, the reconstruction of that thought experiment circulating in the philosophical literature is no more than a cartoon. In this paper I will tell the story of the thought processes behind the cartoon.Keywords: Galileo Galilei; Thought experiment; Falling bodies.

In this article, I argue that the interpretation of Kant's a priori in Marburg neo-Kantianism involved a historiographical problem concerning the Platonic interpretation of the history of exact sci...

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 show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations (...) are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism. (shrink)

Bringing together contributors from philosophy, international relations, security studies, and strategic studies, New Wars and New Soldiers offers a truly interdisciplinary analysis reflective of the nature of modern warfare. This comprehensive approach allows the reader to see the broad scope of modern military ethics, and to understand the numerous questions about modern conflict that require critical scrutiny. Aimed at both military and academic audiences, this paperback will be of significant interest to researchers and students in philosophy, sociology, military and strategic (...) studies, international relations, politics, and security studies, acting as an ideal course text or as supplementary reading. (shrink)

During the 1930s the fascist government launched a programme for the reclamation of the Pontine Marshes, one of the largest forested wetlands in Italy. In less than a few years the muddy and uneven ground of the forest was transformed into flat land to be cultivated and into solid surface where three new towns were built. Hegemonic narratives describe the fascist reclamation as a process that imposed a solid form upon the raw materials of nature, thereby establishing an unbridgeable divide (...) between nature and culture, natural and built environment. The article challenges this dualism, drawing on ethnographic and historical materials to explore spatial and temporal zones in-between fluidity and solidity. It suggests an approach in which fluidity and solidity are understood as patterns of social and ecological relations rather than mutually exclusive properties of matter, thus exposing the continuity between them. (shrink)

Martin Heidegger and Emanuele Severino reflected on the meaning of technology more than anyone else in the twentieth century. Their philosophies are irreconcilable. They converge on this simple recognition and its implications: techno‐science dominates our time. But they disagree even on the interpretation of this domination. Exploring this disagreement will help us understand the leading dynamics of our civilization. Therefore, the intention in this paper is to unveil, for English speakers, the value of Severino’s philosophy in relation to Heidegger and (...) the meaning technology. We will see that, ultimately, their disagreement concerns the originary truth of Being and has repercussions on how they conceptualize technology and the possibility of redemption from it. Heidegger indicated the letting‐be of beings in their freedom as the possible path beyond technology. Severino saw Heidegger’s indication as destined to remain trapped in technology itself. If we understand why this was so – from Severino’s point of view – this may open a new path for us: the path of day, the path that may truly lead beyond technology. The aim of this paper is, finally, to indicate one reason why delving into Severino’s works is truly worthwhile: if it is possible for the truth to unveil itself beyond willing – where Heidegger couldn’t see – then Severino’s works may the place where this possibility appears in coherent conceptual form. (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 chapter contains sections titled: Signification Truth Note Further Reading.

The intent we propose will be to retrace a few fundamental passages of the philosophical and metaphysical though of the Spanish philosopher, considering two conceptual pairs that refer to the quest...

In the Dreams of a Spirit-Seer, Elucidated by Dreams of Metaphysics (1766), Kant remarks that Stahl, with his admission of immaterial forces for the explanation of organisms, was “closer to the truth than Hoffmann and Boerhaave, to name but a few,” although the latter adopted a “more philosophical method.” This puzzling statement is very significant for the understanding of Kant’s reception of animism, as it documents Kant’s reaction to the issues raised by the Leibniz-Stahl controversy and his striking preference for (...) Stahl’s nonmechanistic account of organisms. Kant agrees with Stahl that organisms suggest the existence of immaterial thinking beings, but at the same time, the example of this speculative hypothesis leads him to question the explanatory power of metaphysical hypotheses in natural philosophy in general, as well as the possibility of empirically distinguishing among different hypotheses, such as monadology, materialism, and hylozoism. After the analysis of Kant’s skeptical conclusions in the Dreams of a Spirit-Seer, I discuss how this earlier connection of medicine, life sciences, and metaphysics leaves traces in Kant’s later work, by analyzing Kant’s discussion of Samuel Sömmering’s claim that matter “can be animated” in On the Organ of the Soul (1796) and the preliminary drafts for this essay. (shrink)

Can taxation and the redistribution of wealth through the welfare state be conceived as a modern system of circulation of the gift? But once such a gift is institutionalized, regulated and sanctioned through legal mechanisms, does it not risk being perverted or corrupted, and/or not leaving room for genuinely altruistic motives? What is more: if the market’s utilitarian logic can corrupt or ‘crowd out’ altruistic feelings or motivations, what makes us think that the welfare state cannot also be a source (...) of corruption? To explain the standard answers to the abovementioned questions as well as their implications I will first re-examine two opposing positions assumed here as paradigmatic examples of other similar positions: on the one hand, Titmuss’s work and the never-ending debate about it; on the other, Godbout’s position, in-so-far as it shows how Titmuss’s arguments can easily be turned upside down. I will then introduce and reinterpret Einaudi’s “critical point” theory as a more complex and richer anthropological explanation of the problems and answers considered herein. Through the analysis of these paradigmatic positions I will develop two interrelated arguments. 1) The way these problems are posed as well as the standard answers to them are: a) subject to fallacies: the dichotomy fallacy and the fallacy of composition; b) too reductive and simplistic: we should at least try to clarify what kind of ‘gift’ or ‘corruption’ we are thinking about, and who or what the ‘giver’, the ‘corrupter’, the ‘receiver’ and/or the ‘corrupted’ party are. 2) The answers to these problems cannot be found by merely following a theoretical approach, nor can they be merely based on empirical evidence; instead, they need to take into account the forever troublesome, ambiguous and unpredictable matter of human freedom. (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)

This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in [9]. Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic (...) countermodel of S with respect to Gand is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

Standard applications of evolutionary game theory look at a single game and focus on the evolution of behavior for that game alone. Instead, this article uses tools from evolutionary game theory to study the competition between choice mechanisms in a rich and variable multigame environment. A choice mechanism is a way of subjectively representing a decision situation, paired with a method for choosing an act based on this subjective representation. We demonstrate the usefulness of this approach by a case study (...) that shows how subjective representations in terms of regret that differ from the actual fitness can be evolutionarily advantageous. (shrink)

In this afterword I will try to re-launch the inquiry into the causes of good-bad polity and good-bad relationships between man and society, individual and institutions. Through an analogy between Einaudi’s search for good government and Calvino’s “Invisible cities”, I will sketch an account of the human and invisible foundations – first of all: trust/distrust – of any good-bad polity.

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)

When a quantified premise such as: Everyone loves anyone who loves someone, occurs with a premise such as: Anne loves Beth, it follows immediately that everyone loves Anne. It also follows that Carol loves Diane, where these two individuals are in the domain of discourse. According to the theory of mental models, this inference requires the quantified premise to be used again to update a model of specific individuals. The paper reports four experiments examining such iterative inferences. Experiment 1 confirmed (...) that they are harder than immediate inferences. Experiment 2 extended the finding to negative inferences, i.e., granted that Anne does not love Beth, it follows from the quantified premise that Carol does not love Diane. Experiment 3 established that intermediate steps referring to specific individuals are accepted more readily than intermediate steps referring to quantified variables. Experiment 4 showed that the participants' written justifications corroborated the model theory. (shrink)

In many countries, life expectancy has increased considerably in past years, and the importance of finding ways to ensure good levels of wellbeing through aging has become more important than ever. Arts based interventions are promising in this respect, and the literature suggests that musical activities can reduce isolation and anxiety and foster feelings of achievement and self-confidence. The present study examined the effects of group music making programs on the health and wellbeing of nursing home residents in Southern Switzerland. (...) A team of professional and student musicians delivered 10 weekly music sessions in four nursing homes, focusing on singing, rhythm-based activities with percussion instruments, and listening to short, live performances. 22 participants (16 women and 6 men, aged 72-95 years, mean 83.6, SD ± 6.9) were recruited to take part in the study and were interviewed after the last music session. The data were analyzed with thematic analysis to investigate how residents experienced group music making and its effects. The findings show that the music programs were beneficial for residents’ wellbeing. Music plays an important role in their lives, both in their pasts and presently, and being involved in musical activities offers engagement and novelty in daily life, providing learning opportunities and facilitating interpersonal relationships. Moreover, these results were due to interactions with the musicians involved. Residents particularly appreciated the opportunity to listen to live performances as part of the sessions. This study suggests that nursing home residents value music and that music based interventions play an important and direct role in enhancing their wellbeing. (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 Soul Chariot Allegory in Plato and the Kaṭha Upaniṣad].

The book presents an interdisciplinary exploration aimed at renewing interest in Luigi Einaudi’s search for “good government”, broadly understood as “good society”. Prompted by the Einaudian quest, the essays - exploring philosophy of law, economics, politics and epistemology - develop the issue of good government in several forms, including the relationship between public and private, public governance, the question of freedom and the complexity of the human in contemporary societies.

The article examines the meaning of spiritual essence within absolute knowing. The analysis presented will shed light on the logical and phenomenological difference between the object of experience and the object of consciousness. The form of spiritual essence is introduced through a syllogistic structure and seems to determinate the scientific character of absolute knowing. Hegel's conception of syllogism in the Phenomenology is not the one of his mature works, but proves to be more articulate than the syllogism as it was (...) conceived in the Jena period. The syllogistic structure of spiritual essence discloses the logical dimension beneath the phenomenological path. (shrink)

In his third essay on earthquakes, Kant refers to “Pater Bina’s” electric interpretation of seismic phenomena. Although not a distinguished scholar, and maybe for that reason frequently confused with a certain “Father Isidore Binet”, Bina was nevertheless a noteworthy author. A Cassinese benedictine, Andrea Bina was a philosopher interested in sciences just like Kant; he studied Newton, translated Wolff, invented a seismoscope and was appreciated by his contemporaries at home and beyond the Alps. Kant’s laconic quotation, followed by a value (...) judgement regarding only Bina’s “audacity”, raises some questions, including, in primis those about the meaning of his hasty judgment. A plausible well-grounded answer should be looked for in the bio-bibliographical outline of the neglected author and in the perusal of his writings. The analysis of Bina’s Ragionamento sopra le cagioni de’ terremoti (1751) contributes to our knowledge of the eighteenth-century cultural background and helps us understand the degree of knowledge of the seismic phenomena acquired by men who – amidst many difficulties and hindered by the limits of their science – could only rely on secondhand data often imbued with misconceptions. Comparing Bina’s work – although indirectly – with Kant’s Fortgesetzte Betrachtung der seit einiger Zeit wahrgenommenen Erderschütterungen (1756) may help bring to light some convergences, as well as differences, which might be of use in clarifying some peculiarities of the Prussian Naturforscher. (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)

In the literature on the Moral Limits of the Markets, Kant’s moral philosophy is often employed to assess the amoral or immoral nature of the commercial sphere. Markets and morality are antipodes since the instrumentality of market transactions excludes or undermines moral values. The kingdom of ends, where everything has either a price or a dignity, closes the door to market logic. The present paper challenges this view, which is also endorsed by business ethics authors advocating for Moral Purism. I (...) will show that Kant imagined a market within the Kingdom of Ends where everyone pursues their own aims while assisting others in pursuing theirs. This model, built on the universalization of the maxim of mutual assistance and the duty of honoring the spirit of mutually beneficial contracts, can be employed to judge the morality of real (empirical) market transactions. (shrink)

The aim of my paper will be to provide a commentary on the introduction to the French edition of Ethics and the Limits of Philosophy (1985) by Bernard Williams (1929–2003) and to show the Nietzschean legacy that is made explicit there. In this introduction, called “L'éthique, question de style?” and published in 1990, Williams reflects on some of the problems of style that his book poses to French readers, to whom he feels his work is less familiar. Furthermore, Williams recalls (...) some moments of the Royaumont colloquium (which he attended in 1958) and dwells on some peculiarities that distinguish him from analytic philosophy, “French” philosophy, Wittgenstein and Heidegger. Finally, the text closes with a description of the image of the philosopher to whom Williams feels closest—that of Nietzsche—and illustrates the reasons that distance him from other models of philosophical writing. (shrink)

[Does the gymnosophist’s reply to Alexander’s question on the origin of time indeed reflect an Indian doctrine?] The episode of Alexander’s interview with the gymnosophists has come down to us in several versions, among which the one in Plutarch’s Vita Alexandri is the most renowned. In this connection, the question arises whether the solutions given by the naked philosophers to the puzzles propounded by Alexander can be shown to reflect genuine Indian doctrines. Challenging Dumézil’s reply in the affirmative, the author (...) contends that they cannot. While most questions and answers are scarcely relevant to the investigation, as being of little (if any) philosophical import, the analysis concentrates on the more significant ones, and especially on the solution offered to the question as to which of the two — day or night — came first. According to Dumézil, the gymnosophist’s answer reported by Plutarch, i. e. that the day came first, by one day, reflects the vedic doctrine of the primeval cosmogonic role of Dawn and Light. Against this may be argued in the first place that such doctrine does not enjoy any prominent status in the Vedas themselves — quite to the contrary, it stands up disadvantegeously to many all-important texts, such as the Nāsadīyasūkta, which assign the primeval status to Darkness — and cannot therefore be regarded as being specifically Indian any more than its opposite. Secondly, it is shown that the Greek tradition is at great variance on this very point, to the extent that all logically conceivable solutions (i. e., precedence of day by one day / day by one night / night by one day / night by one night) are represented in some version or other. This inconsistency appears to stem from the fact that no particular doctrine (Indian or whatever) was envisaged; according to the present author, we have reason to believe that the gymnosophist’s reply was rather meant to set off by means of a paradox the sheer impossibility of a solution (all four alternatives being equivalent to that effect). This interpretation is reinforced by the gymnosophist’s own remark confessing the aporetical nature of his reply, and finally by a further recourse to paradox — this time a variant of the well-known “paradox of the liar” — which the author lays bare in the otherwise inexplicable dénouement of the anecdote. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze and (...) the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

This introduction provides a re-reading of Luigi Einaudi’s "On Abstract and Historical Hypotheses and on Value Judgments in Economic Sciences", focusing on how Einaudi conceived the relationship among economics, the humanities and values. In particular, its aim is: (§ 1) to explain the reasons why this essay can be considered a confession of a humanist-economist who constantly stepped “beyond the hedge of the garden reserved to the economist”; (§ 2) to clarify the nature of one of the main doubts that (...) Einaudi had concerning the issue of value judgments, with specific reference to the problem of entanglement of fact and value; (§ 3) to cast further light on why, at the end of his life, Einaudi claimed: “I proudly place economic disciplines within the humanities”. (shrink)