We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept of total (...) Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete. (shrink)

Nelson’s programme for a stochastic mechanics aims to derive the wave function and the Schroedinger equation from natural conditions on a diffusion process in configuration space. If successful, this pro- gramme might have some advantages over the better-known determin- istic pilot-wave theory of de Broglie and Bohm. The essential points of Nelson’s strategy are reviewed, with particular emphasis on concep- tual issues relating to the role of time symmetry. The main problem in Nelson’s approach is the lack of strict equivalence (...) between the cou- pled Madelung equations and the Schroedinger equation. After a brief discussion, the paper concludes with a possible suggestion for trying to overcome this problem. (shrink)

This article examines the philosophical implications underlying Bacon's views on historical knowledge, paying special attention to that variety of historical knowledge described by Bacon as “natural.” More specifically, this article explores the interplay of history and fable. In the sphere of thought, fabula is the equivalent to materia in nature. Both are described by Bacon as being “versatile” and “pliant.” In Bacon's system of knowledge, philosophy, as the domain of reason, starts from historiae and fabulae, once memory and the imagination (...) have fulfilled their cognitive tasks. This means that, for Bacon, there is no such thing as a pure use of reason. He advocates a kind of reason that, precisely because it is involved with matter's inner motions, is constitutively 'impure'. The article shows how the terms historia and fabula cover key semantic areas in defining Bacon's philosophy: historia may mean “history” as well as “story,” fabula “myth” as well “story.” In both cases, we can see significant oscillations from a stronger meaning to a weaker one, as if the power of nature decreases moving from histories and myths to stories. On the other hand, there are cases in which Bacon seems to stick to a diachronic view of the meaning of fables and histories, such that the transition from myths to history, especially natural history, is described as a collective effort towards reality and enlightenment. (shrink)

We prove that the Weihrauch lattice can be transformed into a Brouwer algebra by the consecutive application of two closure operators in the appropriate order: first completion and then parallelization. The closure operator of completion is a new closure operator that we introduce. It transforms any problem into a total problem on the completion of the respective types, where we allow any value outside of the original domain of the problem. This closure operator is of interest by itself, as it (...) generates a total version of Weihrauch reducibility that is defined like the usual version of Weihrauch reducibility, but in terms of total realizers. From a logical perspective completion can be seen as a way to make problems independent of their premises. Alongside with the completion operator and total Weihrauch reducibility we need to study precomplete representations that are required to describe these concepts. In order to show that the parallelized total Weihrauch lattice forms a Brouwer algebra, we introduce a new multiplicative version of an implication. While the parallelized total Weihrauch lattice forms a Brouwer algebra with this implication, the total Weihrauch lattice fails to be a model of intuitionistic linear logic in two different ways. In order to pinpoint the algebraic reasons for this failure, we introduce the concept of a Weihrauch algebra that allows us to formulate the failure in precise and neat terms. Finally, we show that the Medvedev Brouwer algebra can be embedded into our Brouwer algebra, which also implies that the theory of our Brouwer algebra is Jankov logic. (shrink)

In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then go on (...) to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov, Contextuality from Quantum Physics to Psychology.]. (shrink)

Since Kraeplin and Kretschmer, the clarification of the limits between ordinary sadness and clinical depression has been a major concern. Much of the controversy has focused on whether and on which bases can be fixed a boundary in the continuum from the experience of sadness to major depressive episode. The new emphasis on the role of clinical judgment introduced by DSM-5 can be regarded as a way to address these issues, though leaving several questions open. After examining the implications of (...) the main topics raised by this still ongoing discussion, we will argue that in a clinical reality both mobility and intensity of emotional states may account for the discontinuity between ordinary sadness and clinical depression. (shrink)

IL MOSTRO E L'EROE. Quando Pomponio Algieri da Nola, all’età di soli 24 anni, viene bruciato vivo a Roma in piazza Navona, Giordano Bruno di anni ne ha appena otto. Oltre che per la giovane età del condannato, l’esecuzione è insolita anche per il luogo e il metodo scelto dall’Inquisizione: anziché le solite fascine, per alimentare il fuoco viene approntato un pentolone di pece, olio e trementina, nel quale viene immersa la povera vittima.

Charles Taylor’s monumental book A Secular Age has been extensively discussed, criticized, and worked on. This volume, by contrast, explores ways of working with Taylor’s book, especially its potentials and limits for individual research projects. Due to its wide reception, it has initiated a truly interdisciplinary object of study; with essays drawn from various research fields, this volume fosters substantial conversation across disciplines.

The essays collected in this volume explore the fundamental issues of philosophical realism, including metaphysical realism. Do things exist and have properties independently of being objects of thought or perception? epistemological realism: Is it possible to know any part of reality in and of itself? and ontological realism: Are there universals?

This essay questions the self-sufficiency of abstract, non-consequentialist, principles as a defence of a libertarian regime. The argument focuses on the difficulties involved in attempts to defend the priority of negative rights if an attractive conception of freedom and an agent-relative view about our reasons to respect rights are to be upheld. The paper closes by suggesting how libertarianism could gain support from various, and perhaps mutually irreducible and even conflicting, considerations in a wide consequentialist system.

A number of articles have highlighted the resemblances between Collingwood’s and Wittgenstein’s positions in the domains of philosophy of language, anthropology, and logic. The introduction of this essay recalls some aspects of these resem­blan­ces. However, the main difference between the two philosophers con­sists in their attitudes toward metap­hysics. Whereas Wittgenstein’s thesis in On Certainty is that “I know” does not tolerate metaphysical emphasis, Collingwood claims in An Essay on Metaphysics that it is the specific task of metaphysics to articulate our (...) basic presuppositions in their historical transformations. That difference has been noted, but never really examined. Moreover, the majority of Collingwood scholars see no reason why his historical study of basic presuppositions should usurp the name of metaphysics and, therefore, reject the term as an unfortunately chosen one. The main purpose of this essay is to explain why Collingwood’s term “metaphysics” is not so idiosyncratic as it is supposed to be and in what sense his metaphysics differs from Wittgenstein’s approach. (shrink)

The latest book by Louis Dupré, The Quest of the Absolute, is the third and final volume of a trilogy on the intellectual history of modernity. It follows Passage to Modernity (1993) and The Enlightenment and the Intellectual Foundations of Modern Culture (2004). Elegant writing and remarkable erudition go hand in hand with a deep insight into the objectives, achievements and deadlocks of the Romantic movement. It is not possible to look into the overwhelming variety of issues and figures that (...) come to the fore in this book and the trilogy as a whole; instead, this article focuses on Dupré’s central claim as to the development and significance of modern Western culture, starting from a specific question that time and again recurs as a key motive throughout the three volumes of his trilogy: are we postmodern or late modern? Dupré’s answer that we are dwellers of a late modern era rather than inhabitants of a postmodern age is dependent on his definition of modernity as a still ongoing ‘event that has transformed the relation between the cosmos, its transcendent source, and its human interpreter’. Since we are still standing in the midst of the event of modernity, shaped by the evolutionary process of and the strains and tensions within and between its three waves (humanism, Enlightenment, romanticism), Dupré underlines the necessity to move from hermeneutic to ontological questions. He even explicitly pleads for the rediscovery of a symbolic religious language in a tentative search for its ontological dimension and for a source of significance beyond the realm of human mind. The main question, however, is whether contemporary Western man is still capable of such a rediscovery. (shrink)

In a recently published study combining transcranial magnetic stimulation and electroencephalography (TMS-EEG), an early component of TMS-evoked potentials (TEPs), i.e., M1-P15, was proposed as a measure of transcallosal inhibition between motor cortices. Given that early TEPs are known to be highly variable, further evidence is needed before M1-P15 can be considered a reliable index of effective connectivity. Here, we conceived a new preregistered TMS-EEG study with two aims. The first aim was validating the M1-P15 as a cortical index of transcallosal (...) inhibition by replicating previous findings on its relationship with the ipsilateral silent period (iSP) and with performance in bimanual coordination. The second aim was inducing a task-dependent modulation of transcallosal inhibition. A new sample of 32 healthy right-handed participants underwent behavioral motor tasks and TMS-EEG recording, in which left and right M1 were stimulated both during bimanual tasks and during an iSP paradigm. Hypotheses and methods were preregistered before data collection. Results show a replication of our previous findings on the positive relationship between M1-P15 amplitude and the iSP normalized area. Differently, the relationship between M1-P15 latency and bimanual coordination was not confirmed. Finally, M1-P15 amplitude was modulated by the characteristics of the bimanual task the participants were performing, and not by the contralateral hand activity during the iSP paradigm. In sum, the present results corroborate our previous findings in validating the M1-P15 as a cortical marker of transcallosal inhibition and provide novel evidence of its task-dependent modulation. Importantly, we demonstrate the feasibility of preregistration in the TMS-EEG field to increase methodological rigor and transparency. (shrink)

Name der Zeitschrift: Frühmittelalterliche Studien Jahrgang: 47 Heft: 1 Seiten: 7-52.

_Brill's Companion to Medieval and Early Platonism_ explores the impact exercised by Platonism on philosophy and many other fields of European culture, and the links it established with Christian, Jewish, Byzantine and Arabic traditions of thought during the Middle Ages and the early modern period.

Gottesbeweise gehören zu den großen Themen der abendländischen Philosophie. Im 20. Jahrhundert sind sie mit Hilfe der modernen Logik neu formuliert worden und auch in der analytischen Philosophie werden Gottesbeweise seit Jahrzehnten kontrovers diskutiert. Offenkundig ist die Frage nach der Existenz Gottes im nachmetaphysischen Zeitalter aktueller denn je. Der Band versammelt die großen Gottesbeweise des Mittelalters und der Neuzeit ebenso wie die klassischen Einwände von Hume und Kant. Die sprachanalytische Debatte wird ausführlich dokumentiert und ein eigener Teil ist Kurt Gödel (...) gewidmet, dessen ontologischer Beweis bis heute nicht stichhaltig widerlegt worden ist. Umfassende einleitende Essays führen in die Problematik der Gottesbeweise ein und bieten gut verständliche Rekonstruktionen der jeweiligen Beweisversuche. (shrink)