Femtosecond laser microfabrication has emerged in the last decade as a powerful technique for direct inscription of low loss optical waveguides in practically any transparent dielectric substrate, showing outstanding versatility. Prototyping of new devices is made rapid, cheap and easy: optical circuits are written directly buried in the substrate, using the laser beam as an optical pen, without any need of costly masks as required by conventional photolithography. Many proof-of-principle demonstrations of integrated optics can be obtained, including splitters, directional couplers, (...) and Mach–Zehnder interferometers. Actually, the road towards applications has just been opened, and the unique capabilities of femtosecond laser micromachining will enable achievements inconceivable with other technologies. In this work, the femtosecond laser fabrication technique is discussed, together with its application to the realization of integrated photonic quantum circuits. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

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.

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)

Neuroeconomics, neuromarketing, neuroaesthetics, and neurotheology are just a few of the novel disciplines that have been inspired by a combination of ancient knowledge along with recent discoveries about how the human brain works.This fascinating and thought provoking new book critically questions our love affair with brain imaging.

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)

Social factors have so far been neglected in embodied theories of perception despite the wealth of phenomenological insights and empirical evidence indicating their importance. I examine evidence from developmental psychology and neuroscience and attempt an initial classification according to whether social factors play a contextual, enabling, or constitutive role in the ability to perceive objects in a detached manner, i.e. beyond their immediate instrumental use. While evidence of cross-cultural variations in perceptual styles and the influence of social cues on visual (...) attention could not be said to play more than a contextual role, other factors such as the intricate developmental links between dyadic and triadic interactions in infancy, as well as episodes of peer-learning in children, play enabling roles. A common element in these factors is the presence and resolution of interpersonal conflict. Detached object perception could not develop without these social factors. I argue, in addition, that social skills such as managing partial social acts which are addressed to and completed by others, linguistic mediation, makebelieve play, and the ability to control perspectival switches are constitutive -- i.e. are of the essence -- of the ability to see objects as present with a detached attitude. I discuss the prospects of incorporating such social elements into dynamical interpretations of the sensorimotor approach through the enactive notion of participatory sense-making. (shrink)

Quine is one of the most influential of contemporary philosophers, whose work has ranged broadly across a great number of topics and issues in a career spanning some fifty years. In this collection a group of distinguished philosophers offer a sustained critical evaluation of the full range of Quine's writings. Amongst the topics addressed are interpretation, epistemology, ontology, modality, and mathematical truth. This collection will certainly influence all future discussion of Quine. The contributors include: George Boolos, H-N. Castaneda, Donald Davidson, (...) Umberto Eco, Dagfinn Follesdal, James Higginbotham, Charles Parsons, Hilary Putnam, Barry Stroud, and Bas van Fraassen. However, Quine is given the last word, responding to the essays in the final contribution. (shrink)

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)

It is reported that in reply to John Wisdom’s request in 1944 to provide a dictionary entry describing his philosophy, Wittgenstein wrote only one sentence: “He has concerned himself principally with questions about the foundations of mathematics”. However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called transitional phase. Marion’s book represents a giant leap forward in this direction. In the (...) preface, Marion provides a diagnosis for why it has taken such a long time to obtain an accurate picture of Wittgenstein’s ideas in the foundations of mathematics. When the Remarks on the Foundations of Mathematics came out in 1956 the reception by specialists, such as Kreisel, was negative. This led many Wittgenstein scholars to set aside the issues in the foundations of mathematics and go on with the business of the day, focusing on Wittgenstein’s philosophy of language and psychology. However, these early negative appraisals were severely limited by two facts. First of all, the nature of the Remarks was a hindrance to an understanding of what Wittgenstein was up to. The book was edited by Wittgenstein’s literary executors by collating together passages from several manuscripts dating from 1937 to 1944, cutting, however, many passages in between remarks. Second, many of the original manuscripts and typescripts of the transitional phase were not available and thus it was virtually impossible to obtain a balanced picture of Wittgenstein’s development. Finally, a stark contraposition between the early and late Wittgenstein did not encourage people to work seriously on the development of Wittgenstein’s position from the Tractatus through the transitional period to the later writings. (shrink)

After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition of the solution to (...) the antinomies as found in Principia Mathematica. In the process of explaining the theory of Principia, Behmann also presented an original approach to the foundations of mathematics which saw in sense perception of concrete individuals the Archimedean point for a secure foundation of mathematical knowledge. The last part of the paper points out an important numbers of connections between Behmann's work and Hilbert's foundational thought. (shrink)

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

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

Large Language Models (LLMs) are generative AI systems capable of producing original texts based on inputs about topic and style provided in the form of prompts or questions. The introduction of the outputs of these systems into human discursive practices poses unprecedented moral and political questions. The article articulates an analysis of the moral status of these systems and their interactions with human interlocutors based on the Habermasian theory of communicative action. The analysis explores, among other things, Habermas's inquiries into (...) the analogy between human minds and computers, and into the status of atypical participants in the linguistic community such as genetically modified subjects and animals. Major conclusions are the LLMs seem to qualify as authors that originally participate in discursive practices but do display only a structurally derivative form of communicative competence and fail to meet the status of communicative agents. In this sense, while the contribution of AI writing systems in public discourse and deliberation can support the process of mutual understanding within the community of speakers, the human actors involved in the development, use, and diffusion of these systems share a collective responsibility for the disclosure of AI authorship and verification and adjudication of validity claims. (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.

This article explores the concept of landscape through the lens of performativity, challenging the traditional visual-centric understanding rooted in Western art and culture but without denying the visual and representational character of landscape. It examines the evolution of landscape representation, from its origins in linear perspective and Cartesian dualism to contemporary approaches that integrate performative practices. The analysis highlights the dialectical tension between visual representation and immersive, multisensory experiences, arguing for a more integrated view that acknowledges the performative aspects of (...) the visual. By re-evaluating the role of distance, vision, and representation, the article advocates for a nuanced understanding of landscape that balances the visual with embodied practices, ultimately proposing that landscape should be seen as a dynamic interplay between seeing and performing. (shrink)

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and (...) sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space. (shrink)

The aim of the paper is to discuss the influence exercised by Russell's thought inGöttingen in the period leading to the formulation of Hilbert's program in theearly twenties. I show that after a period of intense foundational work, culminatingwith the departure from Göttingen of Zermelo and Grelling in 1910 we witnessa reemergence of interest in foundations of mathematics towards the end of 1914. Itis this second period of foundational work that is my specific interest. Through theuse of unpublished archival sources (...) I will describe how Hilbert, Behmann, and Bernays,among others, were influenced by and reacted to the technical and philosophical thesespresented in Principia Mathematica. I also argue that there are some elements of continuity between Russell's approach and Hilbert's program as it was presented inthe early twenties. (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)

A recent article of Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay, and Ramsey finds the first examples of simple structures with formulas which do not fork over the empty set but are universally measure zero. In this article we give the first known simple $\omega $ -categorical counterexamples. These happen to be various $\omega $ -categorical Hrushovski constructions. Using a probabilistic independence theorem from Jahel and Tsankov, we show how simple $\omega $ -categorical structures where a formula forks over $\emptyset $ (...) if and only if it is universally measure zero must satisfy a stronger version of the independence theorem. (shrink)

It has often been claimed that (i) Aristotle's expression 'protasis' means 'premiss' in syllogistic contexts and (ii) cannot refer to the conclusion of a syllogism in the Prior Analytics. In this essay we produce and defend a counter-example to these two claims. We argue that (i) the basic meaning of the expression is 'proposition' and (ii) while it is often used to refer to the premisses of a syllogism, in Prior Analytics 1.29, 45b4-8 it is used to refer to the (...) conclusion of a syllogism. In our view, the best explanation of Aristotle's use of the expression 'protasis' is that it means proposition throughout but is frequently used without change of meaning (in certain specific contexts) to refer to the premisses from which a conclusion follows. In Prior Analytics 1.29, 45b4-8 he uses 'protasis' to refer to the conclusion when he needs a single expression to refer to both the conclusion and one of the premisses of the syllogism that constitutes the core of a syllogism through the impossible. If we are correct, we have shown that the view that the expression 'the final protasis' in EN 7.3, 1147b9ff must mean 'the final premiss' and so cannot refer to the conclusion of the relevant syllogism is mistaken. (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)

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)

In the sentence “Tom sits,” the name distinguishes Tom from anyone else, whereas the predicate assimilates Tom, Theaetetus, and anyone else to whom the predicate applies. The name marks out its bearer and the predicate groups together what it applies to. On that ground, his name is used to trace back Tom, and the predi- cate is used to describe and classify what it applies to. In both cases, the semantic link is a direct link between expressions and particulars. Here, (...) I will explore the workings of predicative names along the direction just hinted at. The analysis of predication has been less central to philosophical investigation than that of referen- tial expressions. Some problems have concerned the unity of the sentence—what makes us understand “The baby cries” as a sentence rather than a list of words? Other problems have been what a predicate was taken to stand for, properties and relations, and the understanding of either at the ontological level. If a predicate refers to a property or a relation, yet predication, which is central to our understand- ing of predicates, applies it to one or more particulars. On the background hinted at, these problems might be differently viewed. (shrink)

We will discuss a mathematical proof found in Wittgenstein’s Nachlass, a constructive version of Euler’s proof of the infinity of prime numbers. Although it does not amount to much, this proof allows us to see that Wittgenstein had at least some mathematical skills. At the very last, the proof shows that Wittgenstein was concerned with mathematical practice and it also gives further evidence in support of the claim that, after all, he held a constructivist stance, at least during the transitional (...) period of his thought (1929-33). (shrink)

In Umberto Eco's semiotics, the encyclopedia is a multidimensional space of semiosis. It is a complex system of shared knowledge that governs the production and interpretation of signs inside communicative contexts. Every semiotic act involves the elements that form the encyclopedia. By means of several examples and comparisons with different semiotic theories, my paper aims to show how semiosis is governed by semantic categorizations, pragmatic rules, and narrative frames that the encyclopedia articulates and makes operative for interpreters and producers of (...) signs. (shrink)

In Sophistical Refutations 8 Aristotle claims that every sophistical refutation depends on a false belief which is implicitly held by the victim of the fallacy and can normally be elicited from him as an explicit additional premiss. In this case the fallacious argument will be turned into a valid one, albeit with a false premiss. The paper discusses the nature of the FVP and tries to discover how it works when it tacitly causes the false appearance of a fallacious argument.

Nietzsche’s view of suicide is a topic which in the last years has been the focus of works such as Julian Young’s and Paul S. Loeb’s. Within this context, this paper seeks to add new elements to the discussion. To this purpose, Nietzsche’s attitude to suicide will be explored from two different points of view. The first part of the paper focuses on the distinction between voluntary (free) and involuntary (natural) death. Nietzsche’s appraisal of both will be scrutinized. In particular, (...) through the comparison with the Classical and, especially, Stoic philosophy and through the critique of the religious (particularly Christian) conception of death, it will be shown, among other things, that Nietzsche defends the rationality of suicide, presents a view of voluntary death as emptied of morality and fights against the Christian denaturalization of suicide. In the second part of the paper, suicide will be considered from a philosophical-existentialist viewpoint, that is, as a possible consequence of the meaninglessness of human existence. The problem is to judge whether life is or is not worth living in a world devoid of meaning and purpose. Nietzsche’s attitude to suicide will be analyzed in a chronological way (early, middle and late Nietzsche). Special attention will be given to the role played by art. The relevant conclusion is that, although in different ways, Nietzsche gives an affirmative answer to the question whether life is worth living in a world devoid of meaning and purpose. (shrink)

We recorded Event-Related Potentials to investigate differences in the use of gender information during the processing of reflexive pronouns. Pronouns either matched the gender provided by role nouns (such as “king” or “engineer”) or did not. We compared two types of gender information, definitional information, which is semantic in nature (a mother is female), or stereotypical (a nurse is likely to be female). When they followed definitional role-nouns, gender-mismatching pronouns elicited a P600 effect reflecting a failure in the agreement process. (...) When instead the gender violation occurred after stereotypical role-nouns the Event Related Potential response was biphasic, being positive in parietal electrodes and negative in anterior left electrodes. The use of a correlational approach showed that those participants with more “feminine” or “expressive” self sex-role descriptions showed a P600 response for stereotype violations, suggesting that they experienced the mismatch as an agreement violation; whereas less “expressive” participants showed an Nref effect, indicating more effort spent in linking the pronouns with the possible, although less likely, counter-stereotypical referent. (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)

This paper aims to foster an interdisciplinary dialogue between Ricoeur’s phenomenological- hermeneutical thought and human geography, in particular with respect to the issue of landscape interpretation. The connection draws on the idea that landscapes and lived spaces can be read as texts, not unfamiliar to human geography and semiotics from 1980s onward. In the first part of the paper I will briefly expound some theories of landscape which make use of the metaphors “landscape as cultural image” and “landscape as text” (...) in human and cultural geography. Then, I will discuss the main contribution of Ricoeur to the issue of space. The philosopher already envisioned a possible application of his “threefold mimesis” of Time and Narrative to architectural spaces. In the conclusion, I will propose to rejuvenate the geographical metaphor of “landscape as text” by introducing a possible application of the Ricoeurian notion of “meaningful action as text” to landscape. (shrink)

Using web standards, such as uniform resource identifiers (URIs), XML and HTTP, for naming and describing resources which are not information objects is the key difference between the Web as we know it today and the Semantic Web. Naming and interlinking this type of resources by HTTP URIs (instead of individual constants in a formal language) is the key feature which distinguishes traditional knowledge representation from web-scale knowledge representation. However, this use of URIs brought back attention to the old philosophical (...) problem of identity and reference in a new form. In this paper, we analyze the new version of the problem, provide a formal model for dealing with it when interlinking knowledge on the Web, and argue for the need of a distinction between the use of URIs for describing and accessing resources, and the use of URIs for fixing the reference . We show that in the current practice of linking data these roles are not clearly distinguished, and that this fact may cause unwanted effects and prevent some basic forms of data integration. We also discuss the role of an entity name system as a potential piece of infrastructure for fixing the reference in the Semantic Web. (shrink)

Forms of contemporary life attest to the dissolution of the concept of the ‘people’ and the renewed importance of the idea of the ‘multitude’. Though they took center stage in the seventeenth century debate that spawned much of our ethico-political lexicon, these two notions are polar opposites. The ‘people’ is by its very nature centripetal. Converging towards a general will, it acts as an interface between citizens and the State. The ‘multitude’ is plural. Fleeing all political unity, it shuns negotiations (...) with the sovereign and refuses to delegate its rights to that power; it is a recalcitrant and disobedient entity with a taste for certain forms of non-representative democracy. For example, Hobbes claims that citizens in rebellion against the State represent “the multitude against the people.” But while Hobbes spotted the greatest hindrance to the workings of the State within this multitude, Spinoza found in it the roots of liberty. The political existence of ‘multiples’ as such has been stricken from the horizon of modernity: not only by Absolute State theorists, but also by Rousseau, the liberal tradition, and the socialist movement itself. (shrink)

This article introduces a novel theoretical framework for addressing epistemic injustice—a phenomenon where certain groups or individuals are systematically excluded from knowledge creation and dissemination processes—by employing ontological relativity and conceptual analysis. “Ontological relativity” refers to a philosophical perspective that posits our understanding of reality as being shaped by our toolbox of concepts, categories, language, and social practices; “conceptual analysis” is a method of inquiry that involves the rigorous examination and deconstruction of a particular concept or set of concepts in (...) order to uncover their constituent elements, relationships, and underlying assumptions. To exemplify the effectiveness of the ontology‐based approach, two paradigmatic applications are explored: (a) educational practices and (b) clinical practice and access to health care. Through the presentation of these applications and the step‐by‐step illustration of the applied methodology, the aim of the article is to showcase the efficacy of ontology in tackling epistemic injustices, suggesting innovative paths for future research in this domain. (shrink)