For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...) should we be realist regarding these theories? Two diff erent proposals have been made: on the one hand, there are those who insist on a direct ontological interpretation of the wave function as representing physical bodies, and on the other hand there are those who claim that quantum mechanics is not really about the wave function. In this paper we will present and discuss one proposal of the latter kind that focuses on the notion of primitive ontology. (shrink)
What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in (...) time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wave function, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wave function is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. That is, we need more structure than the one provided by the wave function. As a response, quantum theories about the wave function can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wave function ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wave function; 2- Even if the wave function is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time. (shrink)
Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully, this theory is seen to be an empirically adequate many-worlds theory and not an empirically (...) inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett’s. (shrink)
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...) space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)
Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about matter moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...) space-time points. The role of the wave function then is to govern the motion of the matter. Introduction Bohmian Mechanics Ghirardi, Rimini, and Weber 3.1 GRWm 3.2 GRWf 3.3 Empirical equivalence between GRWm and GRWf Primitive Ontology 4.1 Primitive ontology and physical equivalence 4.2 Primitive ontology and symmetry 4.3 Without primitive ontology 4.4 Primitive ontology and quantum state Differences between BM and GRW 5.1 Primitive ontology and quadratic functionals 5.2 Primitive ontology and equivariance A Plethora of Theories 6.1 Particles, fields, and flashes 6.2 Schrödinger wave functions and many-worlds The Flexible Wave Function 7.1 GRWf without collapse 7.2 Bohmian mechanics with collapse 7.3 Empirical equivalence and equivariance What is a Quantum Theory without Observers? CiteULike Connotea Del.icio.us What's this? (shrink)
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...) real objects in an observer-independent way. (shrink)
Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of of the quantum formalism.
A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a “primitive ontology” (PO), i.e., variables describing the distribution of matter in 4-dimensional space-time. In this paper, we illustrate the value of having a PO. We do so by focusing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To (...) this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory. (shrink)
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical (...) limit becomes very simple: when do the Bohmian trajectories look Newtonian? (shrink)
The volume presents a set of invited papers based on analyses of legal discourse drawn from a number of international contexts where often the English language ...
How much do animals matter--morally? Can we keep considering them as second class beings, to be used merely for our benefit? Or, should we offer them some form of moral egalitarianism? Inserting itself into the passionate debate over animal rights, this fascinating, provocative work by renowned scholar Paola Cavalieri advances a radical proposal: that we extend basic human rights to the nonhuman animals we currently treat as "things." Cavalieri first goes back in time, tracing the roots of the debate (...) from the 1970s, then explores not only the ethical but also the scientific viewpoints, examining the debate's precedents in mainstream Western philosophy. She considers the main proposals of reform that recently have been advanced within the framework of today's prevailing ethical perspectives. Are these proposals satisfying? Cavalieri says no, claiming that it is necessary to go beyond the traditional opposition between utilitarianism and Kantianism and focus on the question of fundamental moral protection. In the case of human beings, such protection is granted within the widely shared moral doctrine of universal human rights' theory. Cavalieri argues that if we examine closely this theory, we will discover that its very logic extends to nonhuman animals as beings who are owed basic moral and legal rights and that, as a result, human rights are not human after all. (shrink)
Rules and Exemptions: The Politics of Difference Within Liberalism Content Type Journal Article Pages 213-217 DOI 10.1007/s11158-009-9098-y Authors Maria Paola Ferretti, University of Bremen Centre for European Law and Politics (ZERP) Universitätsallee GW1 28358 Bremen Germany Lenka Strnadová, University of West Bohemia in Pilsen Department of Politics and International Studies Sedláčkova 15 30100 Plzeň Czech Republic Journal Res Publica Online ISSN 1572-8692 Print ISSN 1356-4765 Journal Volume Volume 15 Journal Issue Volume 15, Number 3.
In this study, Paola Marrati approaches—in an extremely insightful, rigorous, and well-argued way—the question of the philosophical sources of Derrida's thought through a consideration of his reading of both Husserl and Heidegger. A central focus of the book is the analysis of the concepts of genesis and trace as they define Derrida's thinking of historicity, time, and subjectivity. Notions such as the contamination of the empirical and the transcendental, dissemination and writing, are explained as key categories establishing a guiding (...) thread that runs through Derrida's early and later works. Whereas in his discussion of Husserl Derrida problematizes the relationship between the ideality of meaning and the singularity of its historical production, in his interpretation of Heidegger he challenges the very idea of the originary finitude of temporality. This book is essential reading not only for those interested in the philosophical roots of deconstruction, but for all those interested in the central questions of history and temporality, subjectivity and language, that pervade contemporary debates in cultural, literary, and visual theory alike. (shrink)
Introduction Without a leg to stand on Sandra Kemp and Paola Bono The project that became The Lonely Mirror had been to edit an international collection of ...
There are now several, realist versions of quantum mechanics on offer. On their most straightforward, ontological interpretation, these theories require the existence of an object, the wavefunction, which inhabits an extremely high-dimensional space known as configuration space. This raises the question of how the ordinary three-dimensional space of our acquaintance fits into the ontology of quantum mechanics. Recently, two strategies to address this question have emerged. First, Tim Maudlin, Valia Allori, and her collaborators argue that what I have just (...) called the ‘most straightforward’ interpretation of quantum mechanics is not the correct one. Rather, the correct interpretation of realist quantum mechanics has it describing the world as containing objects that inhabit the ordinary three-dimensional space of our manifest image. By contrast, David Albert and Barry Loewer maintain the straightforward, wavefunction ontology of quantum mechanics, but attempt to show how ordinary, three-dimensional space may in a sense be contained within the high-dimensional configuration space the wavefunction inhabits. This paper critically examines these attempts to locate the ordinary, three-dimensional space of our manifest image “within” the ontology of quantum mechanics. I argue that we can recover most of our manifest image, even if we cannot recover our familiar three-dimensional space. (shrink)
The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...) by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)
The 16th and 17th centuries marked a period of transition from the vitalistic ontology that had dominated Renaissance natural philosophy to the Early Modern mechanistic paradigm endorsed by, among others, the Cartesians and Newtonians. This paper focuses on how the tensions between vitalism and mechanism played themselves out in the context of 16th and 17th century chemistry and chemical philosophy. The paper argues that, within the fields of chemistry and chemical philosophy, the significant transition that culminated in the 18th century (...) Chemical Revolution was not a transition from vitalism to full-blown mechanism. Rather, chemical philosophy shifted from a vitalistic theory of matter and spirits to a naturalistic, physicalistic, and corpuscularian conception of chemical properties and reactions. Despite being naturalistic, physicalistic, and corpuscularian, however, this theory was not fully mechanistic. Special attention is paid to the contributions made by Paracelsus, Sebastien Basso, Jan Baptista van Helmont, and Robert Boyle to this ontological transition. (shrink)
The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...) terminology, and of the radicalization of Bolzano's anti‐Kantianism. Bolzano's evolution is understood as a coherent move, once the criticism expressed in the Beyträge on the notion of quantity is compared with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is enriched by the discovery that two unknown texts mentioned by Bolzano in the Beyträge can be identified with works by von Spaun and Vieth respectively. Bolzano's evolution is interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano's unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, the author claims that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and suggests that the question of ideal elements in mathematics, apart from being a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. (shrink)
: The concepts of intention and intentionality were particularly significant notions within the Christian, Jewish, and Islamic medieval philosophical traditions, and they regained philosophical importance in the twentieth century. The theories of intention and intentionality of the medieval Islamic philosopher and physician Ibn Sina and the phenomenological philosopher and mathematician Edmund Husserl are examined, compared, and contrasted here, showing that Ibn Sina's conception of intention is naturalistic and, in its naturalism, is influenced by the medical professional culture to which Ibn (...) Sina belonged. As well, Husserl's anti-naturalistic conception of intentionality is influenced by his background as a mathematician and by his desire to ground mathematics and the empirical sciences in a truly scientific philosophy. In conclusion, an argument is presented for the superiority of the Husserlian transcendentalist account of intentionality over the Avicennian naturalistic account, on the grounds that the latter falls prey to psychologism and reductionism, the two specters that according to Husserl must haunt all naturalistic accounts of consciousness. (shrink)
The sixteenth and seventeenth centuries marks a period of transition between the vitalistic ontology that had dominated Renaissance natural philosophy and the Early Modern mechanistic paradigm endorsed by, among others, the Cartesians and Newtonians. This paper will focus on how the tensions between vitalism and mechanism played themselves out in the context of sixteenth and seventeenth century chemistry and chemical philosophy, particularly in the works of Paracelsus, Jan Baptista Van Helmont, Robert Fludd, and Robert Boyle. Rather than argue that these (...) natural philosophers each embraced either fully vitalistic or fully mechanistic ontologies, I hope to demonstrate that these thinkers adhered to complicated and nuanced ontologies that cannot be described in either purely vitalistic or purely mechanistic terms. A central feature of my argument is the claim that a corpuscularian theory of matter does not entail a strictly mechanistic and reductionistic account of chemical properties. I also argue that what marks the shift from pre-modern vitalistic chemical philosophy to the modern chemical philosophy that marked the Chemical Revolution is not the victory of mechanism and reductionism in chemistry but, rather, the shift to a physicalistic and naturalistic account of chemical properties and vital spirits. (shrink)
There are certain kinds of risk for which governments, rather than individual actors, are increasingly held responsible. This article discusses how regulatory institutions can ensure an equitable distribution of risk between various groups such as rich and poor, and present and future generations. It focuses on cases of risk associated with technological and biotechnological innovation. After discussing various possibilities and difficulties of distribution, this article proposes a non-welfarist understanding of risk as a burden of cooperation.
The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...) analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers. (shrink)
This paper defends an interpretation of Husserl''s theory of language, specifically as it appears in the Logical Investigations, as an example of a larger body of theories dubbed ''language as calculus''. Although this particular interpretation has been previously defended by other authors, such as Hintikka and Kusch, this paper proposes to contribute to the discussion by arguing that what makes this interpretation plausible are Husserl''s distinction between the notions of meaning-intention and meaning-fulfillment, his view that meaning is instantiated through meaning-intending (...) acts of transcendental consciousness, and his view that the content of meaning-intending acts is ideal meaning simpliciter. As well, the paper argues that the phenomenological method of reduction itself presupposes the notion that reality as such can be reached by subtracting the influence of the language of the natural attitude and its ontological commitments and it, thus, presupposes the conception of language as a reinterpretable calculus. (shrink)
The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a form of pragmatism is not a faithful interpretation of Peano’s (...) conception, but it is essential to understand the relations of Peano’s logic with other philosophical traditions and some epistemological aspects of Peano’s perspective, such as the search for a universal language. (shrink)
: In his book Monad and Thou: Phenomenological Ontology of the Human Being, Japanese philosopher Hiroshi Kojima proposes to redefine the I-Thou relation, first extensively investigated by Martin Buber, and to reconcile the notions of ‘individuality’ and ‘community’ in terms of his new phenomenological ontology of the human being as monad. In this essay, Kojima’s ideas are examined concerning the monad and intersubjectivity, and it is shown how these ideas can be extended and brought to bear on issues concerning human (...) encounters with the environment and, in particular, to nonhuman animals. (shrink)
The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...) might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)
Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic as a move against a premise of an (...) argument for the AI-thesis, and suggests making a distinction between a broad and a narrow notion of algorithm that might be used to reformulate the question as a foundational problem for argumentation theory. (shrink)
Granting differential treatment is often considered a way of placing some groups in a better position in order to maintain or improve their cultural, economic, health-related or other conditions, and to address persistent inequalities. Critics of multiculturalism have pointed out the tension between protection for groups and protection for group members. The ‘rule-and-exemption’ approach has generally been conceived as more resistant to such criticism insofar as exemptions are not conceded to minorities or ethical and religious groups as such, but to (...) individuals who are part of those groups. However, I show that when a government grants an exemption, it inevitably provides a definition of the relevant group in question, and the tendency is to take cultural membership as ‘given’ or as defined by group spokespersons. I discuss some problems related to these definitions and defend instead a definition based on shared group interests. (shrink)
This essay offers a novel approach for understanding the poetry of negritude and its role in the struggle for black liberation by appealing to Giambattista Vico’s insights on the historical, cultural, and myth-making function of poetry and of the mythopoetic imagination. The essay begins with a discussion of Vico’s aesthetic historicism and of his ideas regarding the role of imagination, poetry, and myth-making and then brings these ideas to bear on the discussion of the function of negritude poetry, focusing primarily (...) on the writings of Aimé Césaire and on Jean-Paul Sartre’s essay, Black Orpheus. (shrink)
The paper analyses the role played by the concept of ‘common ground’ in argumentation theories. If a common agreement on all the rules of a discursive exchange is required, either at the beginning or at the end of an argumentative practice, then no violation of the rules is possible. The paper suggests an alternative understanding of ‘common ground’ as something that can change during the development of the argumentative practice, and in particular something that can change without the practice being (...) stopped, just as one sometimes violates the rule of a game without stopping playing. The analysis of some historical examples shows that the violation of rules sometimes leads to a consensual change of a set of beliefs and values. The argumentative rationality thus needs to be reconsidered in the light of the analysis of the conditions under which it would be legitimate to change the rules of an argumentative practice: ‘common ground’ and the right to disagreement, even radical or violent, could then be defended as essential components of argumentative rationality. (shrink)
At the beginning of the xxth century the high rate of analphabetism and the recent unification of the country, achieved only in 1870, had required a vast program of school and university reforms which were accompanied by a debate on two fundamental questions: whether the university should depend on public funds or become autonomous, and whether the curriculum should be specialized or remain general as in the modern era. The 1859 Casati reform had separated the faculty for literature and philosophy (...) from the faculty for mathematical, physical and natural sciences, thus introducing for the first time specialized curricula. (shrink)
Subject of my paper is the connection between Hegel’s philosophy of nature and the new conception of subjectivity developed in his works. At the centre of my reflection is the origin of desire from biological needs of the animal world, as affirmed by Hegel in the Encyclopaedia of philosophical sciences and inPhenomenology of Spirit. The animal nutrition is periodical: hunger and thirst are forms of lack, from which, in Hegel’s eyes, arises the first form of self‐consciousness: they produce a first, (...) obscure and indefinite sense of self. The correspondent concept in Phenomenology of Spirit is desire, as awareness of limits, and also as necessity to overcome them: as impulse to action. The fight and recognition which follow imply this natural source. The formation (Bildung) of subjectivity itself presupposes in Hegel this fundamental role of desire: What I want to analyse is the measure in which philosophy of nature influenced Hegel’s theory of subjectivity. Researches of the last decades give a new evaluation of the importance of this part of his philosophy and show the evident links to romantic philosophy of nature. My paper intends to demonstrate that desire in Hegel’s philosophy shows an evident cognitive value and can be considered a key-instrument for a new conception of reason, not opposed to passions. This approach can be interesting within the present international debate about the strategic role of passions in our post-modern world. (shrink)
In [4] it is shown that only using exponentiation can one prove the existence of non trivial solutions of Pell equations in IΔ 0 . However, in this paper we will prove that any Pell equation has a non trivial solution modulo m for every m in IΔ 0.
Grouping severe mental disorders into a global category is likely to lead to a “theory of everything” which forcefully explains everything and nothing. Speculation even at the phenotypic level of the single disorder cannot be fruitful, unless specific and testable models are proposed. Inclusive fitness must be incorporated in such models. (Published Online November 9 2006).
We study the measure independent character of Godel speed-up theorems. In particular, we strengthen Arbib's necessary condition for the occurrence of a Godel speed-up [2, p. 13] to an equivalence result and generalize Di Paola's speed-up theorem [4]. We also characterize undecidable theories as precisely those theories which possess consistent measure independent Godel speed-ups and show that a theory τ 2 is a measure independent Godel speed-up of a theory τ 1 if and only if the set of undecidable (...) sentences of τ 1 which are provable in τ 2 is not recursively enumerable. (shrink)
The assumption that origins can be defined as a hermeneutic paradigm in the humanities and in the sciences is explored in relation to specific theoretical ...
In 1964, Jacques Derrida’s long essay “Violence and Metaphysics” opened a dialogue with Emmanuel Levinas that would not be interrupted until Derrida’srecent death. Published only three years after the appearance of Totality and Infinity and at a moment when Derrida’s own early texts were still in the course of elaboration, this text right away recognizes the legitimacy and the import of Levinas’s philosophical project. Derrida pays homage to the Levinasian attempt to interrogate the whole of the western philosophical tradition beginning (...) from its Greek origin — which should not be understood as an empirical place but as a system of categories and fundamental concepts, elaborated for the first time in Greece and structuring the entire philosophical discourse. According to Levinas, these concepts are dominated by “the supremacy of the One and the Same” (cf. TO 35) making the long history of philosophy a history that takes place in the shadow of Parmenides, who would still command — all the more surely from afar — the phenomenology of Husserl and the ontology of Heidegger. The reservations that Derrida expresses in “Violence and Metaphysics” concern more Levinas’s discursive strategy than his intentions. He does not contest the desire to open philosophy to another origin than the Greek origin, no more than the necessity of making resonate in philosophical discourse the call of an alterity capable of contesting the supremacy of the One and the Same. His reservations are situated, rather, at the level of the strategy to follow in order to render this opening finally effective. (shrink)
The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.
It has been tempting for many historians of fourth century North Africa to view the Donatist Church as a patriarchal movement. However Donatism exhibited varied contours during its period of ascendancy in north Africa, and the female presence often led to tension, even schism, within itself. The purpose of this article is to discuss the Donatist movement through a gender perspective and to explain the role of the women who lived between the Great Persecution and the Conference of Carthage (411). (...) In particular, the article examines Lucilla and other women of the Donatist movement. (shrink)
The possibility to interpret expected and nonexpected utility theories in purely probabilistic terms has been recently investigated. Such interpretation proposes as guideline for the Decision Maker the comparison of random variables through their probability to outperform a stochastic benchmark. We apply this type of analysis to the model of Becker and Sarin, showing that their utility functional may be seen as the probability that an opportune random variable, depending on the one to be evaluated, does not outperform a non-random benchmark. (...) Further, the consequent choice criterion is equivalent to a sort of probability of ruin. Possible interpretations and financial examples are discussed. (shrink)
In discussing rational choice theory (RCT) as an explanation of demand behavior, Becker (1962, Journal of Political Economy, 70, 1?13) proposed a model of random choice in which consumers pick a bundle on their budget line according to a uniform distribution. This model has then been used in various ways to assess the validity of RCT and to support as-if arguments in defense of it. This paper makes both historical and methodological contributions. Historically, it investigates how the interpretation of Becker (...) random behavior evolved between the original 1962 article and the modern experimental literature on individual demand, and surveys six experiments in which it has been used as an alternative hypothesis to RCT. Methodologically, this paper conducts an assessment of the as-if defense of RCT from the standpoint of Becker's model. It argues that this defense is ?weak? in a number of senses, and that it has negatively influenced the design of experiments about RCT. (shrink)
