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)

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.

This paper has two related goals. Firstly, after briefly clarifying the theoretical core of Solger's thought, it will analyse his metaphysics from Hegel's point of view, emphasizing that sacrifice is, for Solger, the fundamental structure of the relationship between the finite and the Infinite. Secondly, it will investigate the main reasons behind Hegel's criticism of Solger, showing that they have different conceptions of privation and negation and concluding that Solger and Hegel have different aims. Hegel's aim consists in recomposing the (...) unity of finite and infinite, whereas Solger's thought is structured on the rupture between these two. (shrink)

Présentation En novembre 1958, le poète surréaliste égyptien Georges Henein publiait dans la revue de Boris Souvarine, Le Contrat social, une étude intitulée, « Bruno R. et la “nouvelle classe” ». Ainsi, presque vingt ans après la publication à compte d’auteur de La Bureaucratisation du monde, un périodique aussi bien informé que celui-là continuait à ignorer le nom de l’auteur de cette étude. Elle avait pourtant résolu, dès 1939, un des principaux problèmes que ce siècle a rencontré : « la (...) nature de la nouvelle société russe », selon les mots de Guy Debord. Mais elle avait aussi posé des jalons essentiels pour comprendre la place de la bureaucratie dans ce pays ainsi que dans les autres grandes formations sociales capitalistes sous le nom de « collectivisme bureaucratique », bien que son auteur demeurât dans une obscurité propice à toutes les récupérations et sans qu’aucune revue française prît le soin de le traduire. Po... (shrink)

Italian Abstract: Per giustificare l’autorità e la validità della scienza economica, gli economisti sono spesso ricorsi all’argomento che le leggi e i postulati di questo sapere sono verità scientifiche, nel senso di verità empiriche, logiche o autoevidenti. Tuttavia, questo discorso, in quanto discorso legittimante o discorso sull 'importanza' della scienza economica, sembra contraddire una siffatta argomentazione giacché non statuisce né verità empiriche né verità logiche, e tanto meno verità autoevidenti. A quale tipo di verità, allora, fa riferimento la predica della (...) scienza economica? Perché la scienza economica, in quanto sapere, viene predicata come una ‘legge’ a cui bisognerebbe obbedire? Esiste un legame storico e teoretico tra la struttura giuridico-politica della legittimità e la predica, la retorica e/o il discorso della scienza economia nella sfera pubblica? In che senso un sapere è un 'istituzione'? -/- In questo articolo esamino il ‘caso Einaudi’ come exemplum dei discorsi sulla scienza economica fatti dagli economisti nella sfera pubblica. Analizzando la predicazione e la riflessione epistemologica di Einaudi e confrontandola con quella di Pareto, Robbins, Weber e Schumpeter, vedremo come sullo sfondo di note dicotomie quali positivo/normativo, fatti/valori, essere/dover essere, analisi/visione, si stagli la contrapposizione epistemologico-antropologica tra Ragione e passioni, spesso assimilata a un’altra perdurante antitesi: Ragione e fede. Muovendo dalla prospettiva dell’«antropologia dogmatica» di Pierre Legendre, e attraverso un rovesciamento solo apparentemente paradossale delle categorie giuridiche e teologiche presenti nel discorso einaudiano, cercherò di formulare una nozione di normatività della scienza economica, estendibile anche ad altri saperi, in vista di un superamento della (falsa) contrapposizione tra Ragione e passioni. -/- English Abstract: To legitimate the authority and the validity of the economic science, economists have often claimed that the laws and the postulates of this savoir are scientific truths, in the sense of empirical, logical or self-evident truths. However, this discourse, as a legitimating discourse, or as a discourse on the ‘significance’ of the economic science, seems to contradict such a claim since it does not assert either empirical, logical or self-evident truths. To what type of truth, then, does the preaching of the economic science refer? Why is the economic science, as a savoir, preached as a ‘law’ to which one should obey? Is there an historical and theoretical nexus between the legal-political structure of the legitimacy and the preaching, rhetoric or discourse of the economic science? What does it mean that a savoir is an ‘institution’? -/- In this article I examine the ‘Einaudi case’ as an exemplum of the discourses on the economic science done by economists in the public sphere. Analysing Einaudi’s preaching and epistemological speculation and comparing it with that of Pareto, Robbins, Weber and Schumpeter, I will show how from the background of well known dichotomies – such as positive/normative, fact/values, to be/ought to be, analysis/vision – the epistemological-anthropological opposition between Reason and passions emerges. This opposition is often assimilated to another long-lasting antithesis: that between Reason and faith. Moving from the perspective of Pierre Legendre’s «dogmatic anthropology», and by an apparently paradoxical reversal of the juridical and theological concepts of Einaudi’s discourse, I will try to formulate a notion of normativity of economic science, which is also applicable to other sciences, in view of an overcoming of the (false) opposition between Reason and passions. (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)

Why do humans imagine alternatives to reality? The experiments conducted by Byrne explain the mental mechanisms we use when we do just this – that is, imagine one, or more, alternative reality. But why do we do this? The general reason is to give ourselves an explanation of the world, to tell stories; at times to console ourselves, and at times to despair. A good story is not only based on a description of what happened, but also hints at, or (...) explains, what might have happened. Depending on our aim, we construct different kinds of counterfactuals. In all cases, however, we are faced with constraints. These constraints are specific to a given domain of beliefs and use of counterfactuals. (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)

Most of the work in default logic is about default theories that are completely specified. In this category are the proposals of appropriate semantics for default logic, the characterizations of the complexity of reasoning with a default theory, the algorithms for finding consequences of default theories, etc. Relatively little attention has been paid to the process of building a default theory, and most of the work on this topic is about translating knowledge bases from other formalisms (such as circumscription, autoepistemic (...) logic, and action description languages) into default logic. This paper is about expressing knowledge in default logic. In particular, we assume that defaults are initially formulated as normal, and are then corrected using specific inference examples. (shrink)

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as (...) early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics. (shrink)

Here, I defend the view that fictional narratives are illusionary and that fictional names are to be accounted metalinguistically, a blend of Walton’s and Donnellan’s theories. Besides, I offer a remedial semantic for sentences external to the story which connects those uses back to the text of the story and to the neighborhood of its retellings.

An Authoritarian Scenario. The long-term war against « terrorism » embarked upon by the Bush administration in the aftermath of September 11th 2001 goes far beyond its strictly military dimension. It also involves a fundamental onslaught on democratic and social rights, both in the USA and in European countries. The result of this combination between the military and a political dimension is the establishment of an architecture of control operating in the service of the most brutal sectors of the imperialist (...) bourgeoisie and of the accumulation of capital. (shrink)