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.

According to the orthodox account developed by Kaplan, indexicals like I, you, and now invariably refer to elements of the context of speech. This essay argues that the orthodoxy is wrong. I, you, and the like are shifted by certain modal operators and hence can fail to refer to elements of the context, for example, I can fail to refer to the speaker. More precisely, indexicals are syntactically akin to logical variables. They can be free, in which case they work, (...) roughly, on the Kaplan model. But they can also be bound: this happens, in a systematic fashion, when they are in the scope of epistemic modals or attitude verbs. The new view has two interesting philosophical consequences. First, it vindicates a broadly Fregean perspective on referential expressions, essentially refuting the idea that indexicals are rigid designators. Second, it suggests a new picture of the interaction between context and linguistic meaning: compositional semantics does not need to look at the context and hence has no need for a context parameter. (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)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (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)

In a recent paper, Christian List (2014) has argued for the compatibilism of free will and determinism. Drawing on a distinction between physical possibility (used in defining determinism) and agential possibility (used in defining free will), List constructs a formal two-level model in which the two concepts are consistent. This paper's first contribution is to show that though List's model is formally consistent, philosophically it falls short of establishing a satisfactory compatibilist position. Ensuingly, an analysis of the shortcomings of the (...) model leads to the identification of a controversial epistemological assumption implicit in the statements of both compatibilist and incompatibilist positions. Arguing that this assumption is not currently satisfied, the paper's second contribution is to show that neither the compatibilist nor the incompatibilist position is presently well-founded. (shrink)

The present article aims at providing some clarification on the Horkheimer-Neurath 1937 debate, so as to make three main claims: (a) around 1937 (even though perhaps neither in the early 1930s, at the time of his review of Mannheim’s Ideology and Utopia, nor after the Second World War, at the time of Adorno’s disenchanted statement, “the whole is the false”), Horkheimer belonged to the Hegelian-Marxist tradition stemming from Lukács’s History and Class Conscioussness (1923); (b) notwithstanding Neurath’s semantic and epistemological holism, (...) his fallibilism, his rejection of Wertfreiheit in the social sciences, his commitment to socialism, there is still a gulf between his position and Horkheimer’s, for Neurath did not accept the main methodological claim made by the latter, namely, the Lukács-inspired view that what “constitutes the decisive difference between Marxism and bourgeois thought” is the Hegelian “point of view of totality”; (c) highlighting the main differences between Neurath’s and Lukács’s versions of Marxism – one concerning the very idea of dialectic, and the other concerning the epistemic privilege of the proletariat – can throw some light on and help understand better the distinctive features of Lukács’s Hegelianization of Marxism. (shrink)

Part one: the act of speaking -- The speaker as performing artist -- The absolute performative -- The repetition of anthropogenesis -- Part two: toward a critic of interiority -- Second-degree sensualism: a physiognomic project -- In praise of reification -- Part three: from the beginning and right now -- Natural history -- The multitude and the principle of individuation -- Appendix: Wittgenstein and the question of atheism.

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)

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)

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)

In this article, I draw upon the ‘post-Kantian’ reading of Hegel to examine the consequences Hegel’s idea of God has on his metaphysics. In particular, I apply Hegel’s ‘recognition-theoretic’ approach to his theology. Within the context of this analysis, I focus especially on the incarnation and sacrifice of Christ. First, I argue that Hegel’s philosophy of religion employs a distinctive notion of sacrifice (kenotic sacrifice). Here, sacrifice is conceived as a giving up something of oneself to ‘make room’ for the (...) other. Second, I argue that the idea of kenotic sacrifice plays a fundamental role in Hegel’s account of Christ. Third, I conclude by sketching some of the consequences of Hegel’s idea of a God who renounces his own divinity for an idealistically conceived metaphysics. My main thesis is that the notion of incarnation is conceived by Hegel as the expression of a spirit that advances only insofar as it is willing to withdraw and make room for the other. A kenotic reading of the Hegelian notion of the incarnation is also useful in terms of a clarification of the dispute between ‘left Hegelians’ and ‘right Hegelians’ concerning the status of the idea of God in Hegel’s philosophy. (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)

We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.

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)

In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the (...) form p i,m i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic. (shrink)

In this paper, I propose the idea that the French mathematician Michel Chasles developed a foundational programme for geometry in the period 1827–1837. The basic concept behind the programme was to show that projective geometry is the foundation of the whole of geometry. In particular, the metric properties can be reduced to specific graphic properties. In the attempt to prove the validity of his conception, Chasles made fundamental contributions to the theory of polarity and also understood that a satisfactory development (...) of projective geometry has to overcome the specificity of that theory itself. In this perspective, he developed his ideas on duality and homography, showing their dependence on the concept that he was going to pose at the basis of geometry: the anharmonic ratio, today called cross-ratio. The conceptual itinerary that starts from Chasles’ studies on polarity and ends with his results based on the cross-ratio represents the itinerary of his foundational programme. I will follow this complex and interesting line of thought, place it in the context of what was then called descriptive geometry, and outline a connection with the later great results of Von Staudt, Cayley, and Klein. (shrink)

La struttura a livelli modella il tutto e le sue parti con grande generalità. Lo dimostrano le argomentazioni teoriche (4.3), (4.4) e (4.5), e lo comprova la casistica che è stata aggiunta. Una tale struttura non presenta affatto i problemi a), b) e c) che sono tipici della struttura ad albero. Essa corregge inoltre deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza visiva, infine, ne facilita la diffusione sul piano professionale (...) e tecnico.Per concludere, ritengo che la struttura a livelli possa fornire un contributo anche alle ricerche di ontologia e in particolare possa favorire i tentativi di unificazione condotti sia sul piano teorico, sia su quello applicativo [Uschold 1996]. Le difficoltà ed i limiti che la teoria degli insiemi oppone ad un formalismo generale (ad esempio quando riduce la casistica della relazione concetto di livello possiede una valenza estremamente ampia e ciò lo predispone per gli auspicati sviluppi ontologici. (shrink)

In this study some typical aspects of human behavior are reconsidered in a new evolutionary perspective. Firstly, a theoretical paradigm is introduced, according to which animals show a natural propensity to maintain behavior far beyond the time when the triggering motivation has been removed;, these drifting conducts are defined as Vestigial Drifting Drives or. Such a paradigm is then applied to those human attitudes that once conferred an adaptive advantage on our species but have now become dysfunctional within the framework (...) of the current ecological crisis. In this context, human beings are considered the repository of VDDs that may play out as evolutionary threats. This thesis is supported by many examples and references that, hopefully, could stimulate scientific debate and further research in evolutionary anthropology, psychology, and related disciplines. (shrink)

The two theories of pancreatic enzyme secretion, those of exocytosis and transmembrane flow, are described. Data thought to support the theory of transmembrane flow of single molecules from pancreatic acinar cells are first reviewed, and the conditions which could allow these data to be explained by the theory of exocytosis of enzyme quanta, i.e. secretory granules, are then discussed.The evidence suggesting short‐term modulation of the composition of pancreatic juice is also considered, and its possible explanations at the organ and cellular (...) level are discussed, in the light of suggested theories on enzyme secretion pathways. (shrink)

ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

L’articolo si pone il problema del perché Vico avesse pensato alla sua impresa come ad una scienza e si fosse occupato di confrontarla con la scienza della natura. Si passano in rassegna l’uso di concetti come degnità, assiomi, postulati, tenendo fermo che Vico non fu né un cartesiano, né un galileiano, e come non si lasci racchiudere nelle gabbie dell’apriorismo e del platonismo: egli ha solo fatto sue alcune idee o tesi presenti entro quelle tradizioni. Vico si guarda bene dall’effettuare (...) una scelta precisa e definitiva tra quelle realtà alle quali attribuiamo oggi il nome di razionalismo e empirismo. Si richiama contemporaneamente e negli stessi testi sia alla tradizione del geometrismo cartesiano sia a quella di Bacone e delpensiero dei baconiani del tardo Seicento, facendone un uso alquanto libero. L’articolo contiene inoltre osservazioni su Vico lettore di Cogitata et visa e di De dignitate et augmentis scientarum di Bacone. (shrink)

[Patañjali, Yogasūtras with Bhoja’s Rājamārtaṇḍa Commentary. With an Introduction, Translation, Subcommentary and Notes by Paolo Magnone].

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 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)

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)