Quine e Tarski sul nominalismo - Quine and Tarski were kindred philosophical spirits. They rejected the analytic/synthetic distinction and shared a strong distaste for modal notions. Moreover, they both had nominalistic leanings. In this article I trace the nominalistic engagement of these two giants of contemporary analytic philosophy. Using recently discovered material from the Quine archive at Harvard, I begin by describing Quine’s engagement with nominalism up to 1940. I then summarize the impact of the 1940-1941 discussions on nominalism between (...) Carnap, Quine and Tarski and mention their influence on Goodman. The third part of the article deals with Quine’s allegiance to nominalism and his subsequent reluctant acceptance of Platonism. The fourth part focuses on Tarski’s defence of nominalism in Amersfoort in 1953. In the conclusion, Quine’s and Tarski’s approaches to nominalism are compared with some contemporary nominalistic programs. (shrink)

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)

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)

In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...) η-conversions) that the authors have investigated in recent work. (shrink)

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic, natural deduction and the normalization theorems, the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these (...) results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics. (shrink)

In the last decades, Systems Biology (including cancer research) has been driven by technology, statistical modelling and bioinformatics. In this paper we try to bring biological and philosophical thinking back. We thus aim at making diferent traditions of thought compatible: (a) causality in epidemiology and in philosophical theorizing—notably, the “sufcient-component-cause framework” and the “mark transmission” approach; (b) new acquisitions about disease pathogenesis, e.g. the “branched model” in cancer, and the role of biomarkers in this process; (c) the burgeoning of omics (...) research, with a large number of “signals” and of associations that need to be interpreted. In the paper we summarize frst the current views on carcinogenesis, and then explore the relevance of current philosophical interpretations of “cancer causes”. We try to ofer a unifying framework to incorporate biomarkers and omic data into causal models, referring to a position called “evidential pluralism”. According to this view, causal reasoning is based on both “evidence of diference-making” (e.g. associations) and on “evidence of underlying biological mechanisms”. We conceptualize the way scientists detect and trace signals in terms of information transmission, which is a generalization of the mark transmission theory developed by philosopher Wesley Salmon. Our approach is capable of helping us conceptualize how heterogeneous factors such as micro and macro-biological and psycho-social—are causally linked. This is important not only to understand cancer etiology, but also to design public health policies that target the right causal factors at the macro-level. (shrink)

On a popular view dating back to Russell, descriptions, both definite and indefinite alike, work syntactically and semantically like quantifiers. I have an argument against Russell's view. The argument supports a different picture: descriptions can behave syntactically and semantically like variables. This basic idea can be implemented in very different systematic analyses, but, whichever way one goes, there will be a significant departure from Russell. The claim that descriptions are variables is not new: what I offer is a new way (...) of defending it. The argument centers on attitude reports. I argue that we should recognize a new reading of descriptions under attitude reports, which I call ‘singular opaque’. The existence of this reading cannot be explained on the traditional Russellian view, and demands a switch to the variable view. Along the way, some interesting new facts about attitude reports come to light. (shrink)

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.

According to Ernst Cassirer, the transition from the concept of substance to that of mathematical function as a guide of knowledge coincided with the end of ancient and the beginning of modern theoretical thought. In the first part of this article we argue that a similar transition has also taken place in the practical sphere, where mathematical function occurs in one of its specific forms, which is that of the algorithm concept. In the second part we argue that with the (...) rise of modernity the idea of substance and the related concepts of category and classification, which are deeply embedded in western culture, have not been totally supplanted by that of function. The intertwining of the concepts of substance and function has generated contradictory hybrids. These hybrids are used as a key for the understanding of the different repercussions of algorithmic logic on society in terms of social integration. (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)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

In the lively discussions on Galileo's laws of motion after the Pisan's death, we observe what might be called a new “Galilean affair.” That is, a trial brought against his new science of motion mainly by French and Italian Jesuits with the substantial adherence of M. Mersenne. This new trail was originated by Gassendi's presentation of Galileo's de motu not simply as a perfectly coherent doctrine, but also as a convincing argument in favor of the truth of Copernicanism.

Ever since the early decades of this century, there have emerged a number of competing schools of ecology that have attempted to weave the concepts underlying natural resource management and natural-historical traditions into a formal theoretical framework. It was widely believed that the discovery of the fundamental mechanisms underlying ecological phenomena would allow ecologists to articulate mathematically rigorous statements whose validity was not predicated on contingent factors. The formulation of such statements would elevate ecology to the standing of a rigorous (...) scientific discipline on a par with physics. However, there was no agreement as to the fundamental units of ecology. Systems ecologists sought to identify the fundamental organization that tied the physical and biological components of ecosystems into an irreducible unit: the ecosystem was their fundamental unit. Population ecologists sought, instead, to identify the biological mechanisms regulating the abundance and distribution of plant and animal species: to these ecologists, the individual organism was the fundamental unit of ecology, and the physical environment was nothing more than a stage upon which the play of individuals in perennial competition took place. As Joel Hagen has pointed out, the two schools were thus dividied by fundamentally different and irreconcilable assumptions about the nature of ecosystems.Notwithstanding these divisive efforts to elevate the image of ecology, the discipline remained in the shadows of American academia until the mid-1960s, when systems ecologists succeeded in projecting ecology onto the national scene. They did so by seeking closer involvement with practical problems: they argued before Congress that their approach to the theoretical problems of ecology was uniquely suited to the solution of the impending “environmental crisis.” With the establishment of the International Biological Program, they succeeded in attracting unprecedented levels of funding for systems ecology research. Theoretical population ecologists, on the other hand, found themselves consigned to the outer regions of this new institutional landscape. The systems ecologists' successful capture of the limelight and the purse brought the divisions between them and population ecologists into sharper relief — hence the hardening of the division of ecology observed by Hagen.45I have argued that the population biologist Richard Levins, prompted by these institutional developments, sought to challenge the social position of systems ecology, and to assert the intellectual priority of theoretical population ecology. He attempted to do so by articulating a nontrivial and rather carefully thought out classification of ecological models that led to the disqualification of systems analysis as a legitimate approach to the study of ecological phenomena. I have suggested that — ultimately —Levins's case against systems analysis in ecology rested on the view that an aspiration to realism and prediction was incompatible with an interest in theoretical issues, a concern that he equated with the search for generality. He sought to reinforce this argument by exploiting the fact that systems ecologists had staked their future on the provision of technical solutions to the problems of the “environmental crisis”: he associated systems ecologists' aspiration to realism and precision with a concern for practical issues, trading on the widely accepted view that practical imperatives are incompatible with the aims of scientific inquiry.46 These are plausible, but nonetheless questionable, claims which have now become an integral part of ecological knowledge. And finally, I hope to have shown how even the most abstract levels of scientific argument are shaped by political considerations, and how discussions of the conceptual development of modern ecology might benefit from a greater consideration of its historical and social dimensions.47. (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)

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)

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.

This paper explores the death of God narrative through the lens of kenosis, drawing insights from thinkers such as Marcel, Heidegger, Vattimo, and Girard. It investigates the implications of kenotic thought for contemporary religious and philosophical discourse, exploring various interpretations of kenosis, ranging from Altizer and Žižek’s apocalyptic views to Vattimo’s more hopeful perspective. Through critical engagement with these viewpoints, this paper advocates for a nuanced understanding of kenosis inspired by Hegel, one that bypasses both radical theology and excessive optimism. (...) Methodologically, this study adopts a hermeneutic approach, analyzing key texts and engaging in philosophical dialogue. This paper concludes that rethinking kenotic thought could provide a robust framework for grappling with the death of God in the contemporary context, offering avenues for ethical reflection, social critique, and speculative renewal. (shrink)

Nous faisons usage de machines, de chaussures, de cartes, en vue de notre vie, de sa conservation et de son développement. Mais c’est la vie elle-même qui est avant tout « usable », et pour laquelle machines, chaussures, cartes sont utilisées. L’ usage de soi, de son existence, est le présupposé et la poutre maîtresse de tous les autres usages. Or l’usage de soi se fonde sur le détachement de soi. Est utilisée une existence à laquelle on ne peut pas (...) toujours s’identifier, qui ne se possède pas entièrement et qui, sans être vraiment étrangère, n’est pas non plus complètement familière. Autrement dit, l’usage de la vie concerne l’espèce qui, en plus de vivre, doit rendre sa vie possible. Le jeu de scène théâtral récapitule et amplifie les procédés par lesquels l’être humain se sert de son existence. L’activité de l’acteur est un modèle incomparable de l’usage de la vie et du souci de soi. Pour reconstituer avec précision les « technologies du soi », il convient de regarder de près les écrits de Stanislavski, Mejerchol’d, Brecht et Grotowski. (shrink)

The purpose of this paper is 1) to focus on the last section of the In Parmenidem, analyzing Proclus’ reflection on the relationship between the First God and what he calls the “axioms of contradiction”, accompanied by an attempt to harmonize in a subordinate sense the Aristotelian perspective with the Platonic one; 2) to analyze the reception of this idea in Nicholas of Cusa, the first Latin author to be systematically influenced by the In Parmenidem. It will be possible to (...) show how Cusanus develops a perspective that, on the one hand, finds its explicit antecedent in Proclus and, on the other, how he radicalizes Proclus’ perspective, developing theoretical tensions that we can find unsystematically in Proclus’ own thought. Proclus is aware that the Principle of all reality—and of science itself—must be conceived as in itself unknowable. At the same time, he seeks to save the ability of human knowledge to describe reality. Starting from an idea of the relationship between God and the laws of contradiction close to that of Proclus, Cusanus develops an epistemology that, on the one hand, recognizes the principle of contradiction as the ultimate principle of reason and, on the other hand, comes to the conclusion of a separation between thought and reality outside thought. (shrink)

More than any other philosopher, Duns Scotus and Simondon both gave extensive consideration to the relation between what is primarily common and what is primarily singular. Pointing to certain resonances between their ideas can help us to develop a theoretical model to decipher the mode of being of the contemporary multitude. This article deals with: 1. The critique that Duns Scotus and Simondon address to everyone who believes that the matter form pair can account for the process of individuation; 2. (...) The gap separating the notion of the « universal » from that of the « common », and therefore, the need to precisely define the ontological and logical status of the « common » without any surreptitious use of categories linked to the « universal 1); 3. The paradoxical relation involving both addition and subtraction - between the individuated individual and « common nature »; and 4. The question of angels , a source of enduring fame in school textbooks for Duns Scotus, re-examined here in the light of Simondon ’s concepts of « transindividuality » and of « collective individuation ». (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)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

The main aim of this paper is to put Peano’s opinion about the unacceptability of the actual infinitesimal notion into evidence. First we briefly focus on the cultural environment where Peano’s considerations originated and developed. Then we examine Peano’s article of 1892, “Dimostrazione dell’impossibilità di segmenti infinitesimi costanti” [Peano 1892].

Ce texte examine l’affirmation d’Aristote qui se trouve dans les Seconds Analytiques II 19, que la perception porte sur l’universel. L’examen s’effectuera par le biais du De Anima II 6 et III 6-8 où Aristote décrit les objets de la perception et de l’intellect. L’auteur soutient que selon Aristote, la perception humaine porte toujours sur l’universel contenu dans le particulier parce que l’unité de la substance individuelle est garante de l’unité de l’acte de perception. Par conséquent, l’analyse en termes de (...) trois objets de perception n’est que le résultat de la méthode analytique qu’Aristote emploie afin d’étudier l’acte de perception. (shrink)

The question of how, according to Aristotle, the principles of science are acquired remains contested among scholars. An aspect of this broader topic concerns the role of induction, and whether it is able to provide us with knowledge of natural necessity without the assistance of intuition. In a recent publication in this journal, David Botting argues in favour of the enumerative/empiricist interpretation of induction and criticizes the intuitive/rationalist interpretation of it, a version of which was defended in one of my (...) publications. He thinks that Aristotle is like Hume: both understand the cognitive process of induction similarly; and, both are equally skeptical about acquiring knowledge of natural necessity through induction. My reply argues that reading Aristotle’s induction in Humean terms is problematic in several respects. I argue, in addition, that natural necessity can be known through induction if nous is involved. My explanation of how this is possible relies on thinking of the act of noēsis in terms of an act of recognition. Botting claims, furthermore, that Aristotle only differs from Hume in that the former does have a non-inductive and non-intuitive method by which natural necessity may become known, and which Botting calls “the constructive proof of necessity”. My reply examines this method, showing how certain steps in it rely on cognitive acts that are really acts of intuition merely expressed in Humean terms. Despite the criticisms, I end with suggestions for how Botting’s account might offer original paths of research to Aristotle scholars seeking to answer the question of the acquisition of principles of science, particularly in the early stages of this process. (shrink)

The aim of the paper is to investigate the role played by causality, and more specifically the no-signaling condition, in the assessment of the quantum theory. To this end, we discuss why it is important that even a non-relativistic theory such as Quantum Mechanics doesn’t imply a violation of this condition. Then, we use this argument to prove an original result stating that the destructive behaviour of the measurement process on the entanglement properties of quantum systems is a necessary and (...) unavoidable feature of the quantum theory. Finally, we critically review the no-cloning theorem. The original formulation of the theorem states that a linear quantum cloning machine, designed in order to successfully clone states that coincide with appropriate basis vectors, fails to copy states that are a non-trivial superposition of those basis vectors; we will furthermore prove that such a linear cloning device, even with the hypothesis that it can only clone basis vectors successfully, may provide a violation of the no-signaling condition and therefore cannot exist. (shrink)

In the lecture Nietzsche: l’homme devant la mort de dieu, Gabriel Marcel highlights the extraordinary topicality of Nietzsche’s thought and figure. The French philosopher seems to say to his hearers: Nietzsche is here, among us, he does not belong to the past, but, on the contrary, he is the most contemporary of contemporaries. Nietzsche’s philosophy of the death of God is a mine of ideas and insights that need to be enhanced. There is still much about him to be discovered. (...) Nietzsche, then – and nihilism as such – is by no means outdated, precisely because, Marcel exclaims, before claiming to have left him behind, it is better to make sure we have reached him. (shrink)

The aim of this paper is to say something significant about Stanley Cavell's style. To accomplish this task, we adopt a distant reading approach, quantifying what seems to be an idiosyncratic use of parentheses. After outlining our methodological approach and the choices of texts from Cavell's corpus, we will present the results of our quantitative analysis. Two kinds of results will be presented and interpreted: the result of a comparison between Cavell and other authors (i.e. why Cavell's use of parentheses (...) is exceptional) and the result of a quantitative analysis of Cavell's texts (i.e. how Cavell uses parentheses throughout his books). For both results, we will provide our own interpretation. In the conclusion, we will draw the moral of this parenthetical story, hoping to open future parentheses. (shrink)

The specific complexity of the question of genres depends on the plurality of the problems to which genre is pertinent and relevant. When Croce proclaimed, at the beginning of the century, the non-existence of the genre, he reduced the entire range of problems to the sole question relative to a work's belonging to a genre. In more recent times, there has been an attempt to reduce genre to the property of the linguistic act, in a methodological framework that understands poetics (...) exclusively as the science of literature. Against such reductionism, it is important to keep in mind a wider, more articulated idea of poetics as a pragmatic meditation, to investigate genres according to the multiple lines of systematization that are pertinent to them. (shrink)

Towards the end of The Coming Community (1993) [La comunità che viene, 1990], Giorgio Agamben writes something that may be interpreted as a paraphrase of Franz Kafka's famous statement that while t...