Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the (...) core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism. (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)

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)

In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of (...) interpolation for the implication-free fragment. (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 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)

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.

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.

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)

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)

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)

In "The Measure of the Mental" (Davidson 1990), replying to a series of criticisms, that grow out of inadvertence or misunderstanding, Davidson has revisited his thesis concerning the physical and the mental, which he called "anomalous monism" (henceforth, AM). The thesis is subtle and elusive, as it is most often the case with Davidson: there is only one kind of event and state, which has a physical description (i.e., a description in physical terms) and may have a mental description too (...) (i.e., a description in mental terms) -- that shows the monism. But there is no strict law to go from a mental to a physical description of events and states or vice versa -- that shows the anomalousness.This sophisticated third way captures the intuition, generally shared today, that we are physical machines, whereas it acknowledges the mind a peculiarity: the mental is identical with a part of the physical, but no part of the mind is specifically identifiable with any part of the physical; or, more weakly, each mental event or state is identical with a physical one, though there is no systematic way to connect the mental and the physical. (shrink)

In his book Semantic Relationism, Kit Fine propounds an original and sophisticated semantic theory called ‘semantic relationism’ or ‘relational semantics’, whose peculiarity is the enrichment of Kaplan’s, Salmon’s and Soames’ Russellian semantics (more specifically, the semantic content of simple sentences and the truth-conditions of belief reports) with coordination, “the very strongest relation of synonymy or being semantically the same”. In this paper, my goal is to shed light on an undesirable result of semantic relationism: a report like “Tom believes that (...) Cicero is bald and Tom does not believe that Tully is bald” is correct according to Fine’s provided truth-conditions of belief reports, but its semantic content is (very likely) a contradiction. As I will argue in the paper, even the resort to the notion of token proposition, introduced in Fine’s recent article “Comments on Scott Soames’ ‘Coordination Problems’”, does not suffice to convincingly eliminate the contradiction; moreover, it raises new difficulties. (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...

"The fact is, man is an etymologizing animal."Etymologizing—the practice of connecting one word with one or more other similar-sounding words that are believed to elucidate its meaning1—is a complex and putatively universal phenomenon.2 Thus, to take two representative examples far apart in time and space, etymologizing practices figure prominently in some episodes of the Hebrew Bible,3 but also provide some modern influential thinkers with an important mode of argument.4 Perhaps etymologizing is so pervasive because it offers a pliable and powerful (...) tool for addressing a key question, namely, why is something called what it is?While this question has universal appeal, only a few cultures seem to have addressed it... (shrink)

The homeopathic principle of similitude is not based on the principle of vaccination but on the more general principle of inversion of effects, a widespread medical phenomenon. Based on the systemic networks which play an important role in response to stress, this principle concerns the reorganization of regulation systems, through a coherent response to the medicine. This model is backed by a large number of published studies from our laboratory and others, by toxicological evidence such as the emerging fields of (...) ‘hormesis’, of neuropharmacology, and of systems biology. The immune system is just one example of the possible application of this law of similitude, which constitutes the true ‘heart’ of the homeopathic idea, and again ethically justifies the attempt to apply it to experimental pharmacology. (shrink)

A default theory can be seen as a way for representing a set of formulae, i.e., its extensions. In this paper, we characterize the sets of formulae that can be expressed by a default theory according to various semantics: justified, constrained, rational, cumulative, QDL, CADL, and two semantics with priorities. These characterizations imply some non-translatability results between semantics.

[ES] El artículo es una introducción a un nuevo enfoque para la filosofía de las matemáticas, conocido con el nombre de «la filosofía de la práctica matemática». El nuevo enfoque encontró su expresión en la colección La Filosofía de la Práctica Matemática editada por el autor. El artículo sitúa la «filosofía de la práctica matemática» dentro del contexto de otras tradiciones en la filosofía de las matemáticas y traza las similitudes y diferencias con estas tradiciones. [EN] The article is an (...) introduction to a new approach to the philosophy of mathematics that goes under the name of «the philosophy of mathematical practice». The new approach found its expression in the collection The Philosophy of Mathematical Practice edited by the author. The article situates the «philosophy of mathematical practice» within the context of other traditions in the philosophy of mathematics and outlines the similarities and differences with those traditions. (shrink)

This issue of Itinera aims to address the connections between architecture and the performing arts in its various aspects and from multiple points of view. The growing emphasis on the performative character of artistic practices, namely, their ability to involve spectators directly and pervasively (Dixon 2007), imbues the relationship between architecture, the performing arts, and the spectator’s experience. The sharing of the scenic space by spectators and performers is essential for the co-production of a common energy which operates as a (...) “transforming force” and thereby opens up the shared experience of discovering oneself and the other as a union of the body and the mind (Fischer-Lichte 2004). (shrink)