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 philosophical analysis of mathematical explanations concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences. The second deals with the problem of whether mathematical explanations occur within mathematics itself. Accordingly, this entry surveys the contributions to both areas, it shows their relevance to the history of philosophy and science, it articulates their connection, and points to the philosophical pay-offs to (...) be expected by deepening our understanding of the topic. (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.

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)

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)

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)

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.

Scientific literature on particular themes in ontology is extremely abundant, but it is often very hard for freshmen or sophomores to find a red thread between the various proposals. This text is an opinionated introduction, a preliminary text to research in ontology from the so called standard approach to ontological commitment, that is from the particular point of view that connects ontological questions to quantificational questions. It offers a survey of this viewpoint in ontology together with their possible applications through (...) a broad array of examples and open problems and, at the same time, essential references to the classics of philosophy, so as to allow non-specialists to understand the terms and analysis procedures characterizing the discipline. Its result is a wide-ranging overview of the issued tackled by ontology, with a particular focus on the most relevant problems of contemporary debate. (shrink)

As part of the Historical Materialism research stream on immaterial labour, cognitive capitalism and the general intellect, begun in issue 15.1, this articles explores the importance of the expression 'general intellect', proposed by Marx in the Grundrisse, for an analysis of linguistic and intellectual work in contemporary capitalism. It links the notion of general intellect to the crisis of the law of value, the political significance of mass intellectuality, and the definition of democracy in a world where knowledge is a (...) productive force in its own right. (shrink)

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

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)

Constrained coherence is compared to coherence and its role in the behavioural interpretation of coherence is discussed. The equivalence of these two notions is proven for coherent conditional previsions, showing that the same course of reasoning applies to several similar concepts developed in the realm of imprecise probability theory.

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)

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic has promoted (...) modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation. (shrink)

Since the microbiological revolution, most infectious diseases have been defined and classified according to an etiologic criterion, i.e. the identification of single, external necessary causes (for example, Mycobacterium for tuberculosis). This is not the case with cancer. Not only external necessary causes of cancer have not been identified, but also the morphological classification cannot be based on univocal criteria. Although neoplasia and anaplasia appear to be universal attributes of cancer, these events are only quantitative. Neoplastic growth can be fast or (...) slow (development may take weeks or years), and tissue pathologies are difficult to detect from normal tissue in some cancers but are obvious in others. Common special properties of anaplasia appear to be concealed in the wide range of morphologies. In the absence of a coherent morphological definition, and of external necessary causes (such as bacteria for infectious diseases), a mechanistic definition could be adopted. However, unless molecular biology discovers specific mechanistic steps in carcinogenesis, which indicate the existence of necessary events in carcinogenesis, we cannot adopt a univocal (monothetic) definition of cancer. The alternative is to use a polythetic definition, according to Wittgenstein's model of a long rope twisted together out of many shorter fibres. (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)

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)

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)

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)

Speaker’s meaning is the act at the core of meaning shift, where meaning can be the very act or its output. What are its conditions, which intentions direct it? What’s its mechanics? I will give a first answer to the first question. Then, I will discuss the mechanics of speaker’s meaning, as well as meaningful links different from speaker’s meaning. This will bring me to surmise a second answer to the first question. Along the way, I will compare the act (...) of meaning with other acts. In closing, I will try a limited elucidation of the notion of intention, which I use throughout. On these issues there is the conspicuous tradition of studies, originating from the late Paul Grice, to confront us with. Rather naturally, I will move from it. But I am interested in the notion of speaker’s meaning and its place in an analysis of meaning, and not in that tradition as such. The notion of speaker’s meaning, I think, is relevant even for those who do not subscribe to a Gricean approach to meaning, as I don’t. (shrink)

In this article I present the extracts and summary of heuristic and speculative observations on various aspects I feel are problematic in the practice of modern physics, the definitions and methods of which are the premise for the whole of Science. The illustrations will be fully developed in a later, more extensive and in-depth work in which some theoretical solutions will also be put forward; therefore in the interests of brevity all assertions will not be demonstrated fully in this article. (...) I will initially discuss the problem with thinking of Reality as basically being made up of ontologically autonomous “parts”; I will recall how the existence of the vacuum is demonstrated through the thermodynamic experiments about heat capacities run by W. Nernst and the experiments of W. Lamb and H. Casimir ; the vacuum will be defined as an object that precedes matter and space, and actually illustrated as an evolving singularity, which all existence draws from; the non-isolability... (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)