t. 1. Parte general. Confesión y interrogatorio -- t. 2. Juramento y prueba escrita.

The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, (...) notations may play a crucial role in mathematical discovery in different ways. Some examples are given to illustrate these ways. (shrink)

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last (...) century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality. (shrink)

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (shrink)

This article argues that political realists have at least two strategies to provide distinctively political normative judgements that have nothing to do with morality. The first ground is instrumental normativity, which states that if we believe that something is a necessary means to a goal we have, we have a reason to do it. In politics, certain means are required by any ends we may intend to pursue. The second ground is epistemic normativity, stating that if something is true, this (...) gives us a reason to believe it. In politics, there are certain empirical regularities that ought to be acknowledged for what they are. Both sources are flawed. Instrumental normativity only requires coherence between attitudes and beliefs, and one can hang on to false beliefs to preserve attitudes incompatible with reality. I may desire to eschew power relations, and accordingly I may imagine politics to be like a camping trip. Epistemic normativity, on the other hand, operates critically, striking down existing normative claims. It shows us that politics is nothing like a camping trip, but it doesn’t tell us what we should do about it. We conclude by showing that if the two are taken together, they remedy each other’s flaws. (shrink)

Marcus William Hunt argues that when co-parents disagree over whether to raise their child (or children) as a vegan, they should reach a compromise as a gift given by one parent to the other out of respect for his or her authority. Josh Millburn contends that Hunt’s proposal of parental compromise over veganism is unacceptable on the ground that it overlooks respect for animal rights, which bars compromising. However, he contemplates the possibility of parental compromise over ‘unusual eating,’ of animal-based (...) foods obtained without the violation of animal rights. I argue for zero parental compromise, rejecting a rights-oriented approach, and propose a policy that an ethical vegan parent and a non-vegan co-parent should follow to determine how to raise their children. (shrink)

Why do we remember the past and not the future? What does it mean for time to "flow"? Do we exist in time or does time exist in us? In lyric, accessible prose, Carlo Rovelli invites us to consider questions about the nature of time that continue to puzzle physicists and philosophers alike. For most readers this is unfamiliar terrain. We all experience time, but the more scientists learn about it, the more mysterious it remains. We think of it (...) as uniform and universal, moving steadily from past to future, measured by clocks. Rovelli tears down these assumptions one by one, revealing a strange universe where at the most fundamental level time disappears. He explains how the theory of quantum gravity attempts to understand and give meaning to the resulting extreme landscape of this timeless world. Weaving together ideas from philosophy, science and literature, he suggests that our perception of the flow of time depends on our perspective, better understood starting from the structure of our brain and emotions than from the physical universe. (shrink)

Cet article comporte, outre l'élaboration d'un système de notation des gestes, un inventaire descriptif des gestes et des mimiques utilisés par les artistes lyriques, une définition des différents paramètres gestuels ainsi qu'une étude des rapports geste/parole et geste/mimique. Les gestes et les mimiques sont classés selon leurs fonctions. On distingue deux catégories de gestes : les gestes à valeur de signal, autrement dit les gestes faits avec intention de communiquer et qui ne sont pas spécifiques aux chanteurs d'opéra puisqu'on les (...) retrouve dans le théâtre parlé, et les gestes à valeur d'indice, c.à.d. des gestes faits sans intention de communiquer : ce sont les gestes idiolectaux, (c.à.d. des gestes spécifiques au chanteur et qui sont conditionnés par de multiples facteurs : origine sociale ou géographique, sexe, morphologie, psychologie, etc...), les gestes esthétiques qui sont des accompagnements purement plastiques du texte chanté, les gestes imposés par les contraintes théâtrales (costumes, accessoires) et les gestes inhérents à la technique vocale. En ce qui concerne les mimiques, on peut les classer également en deux catégories : les mimiques à valeur expressive, qui ne présentent pas d'intérêt particulier et les mimiques sans valeur expressive regroupant les mimiques d'accompagnement (crispations musculaires, grimaces ou rides qui correspondent à un effort vocal et n'ont aucune raison d'être particulière) et les mimiques fonctionnelles, c.à.d. les mimiques liées à la technique vocale. L'application des méthodes linguistiques et notamment de la commutation, permet de dégager des traits pertinents aussi bien au niveau des gestes qu'à celui des mimiques. (shrink)

One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, Rovelli examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the 21-year-old Werner Heisenberg first developed quantum theory, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to (...) be magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercly debate the theory's meaning, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships, not substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for understanding the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better understand our place in it. (shrink)

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

At least since Kuhn’s Structure, philosophers have studied the influence of social factors in science’s pursuit of truth and knowledge. More recently, formal models and computer simulations have allowed philosophers of science and social epistemologists to dig deeper into the detailed dynamics of scientific research and experimentation, and to develop very seemingly realistic models of the social organization of science. These models purport to be predictive of the optimal allocations of factors, such as diversity of methods used in science, size (...) of groups, and communication channels among researchers. In this paper we argue that the current research faces an empirical challenge. The challenge is to connect simulation models with data. We present possible scenarios about how the challenge may unfold. (shrink)

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...) effectiveness of mathematics in natural science. (shrink)

In this paper, I discuss some of Maximilian de Gaynesford’s arguments regarding indexicals. Although I agree with his treatment of the first singular personal pronoun as a prototype of demonstrative expressions, I challenge his refusal to treat indexicals as complex demonstratives. To offer an alternative to this refusal I try to develop a common ground from different theories that consider indexicals as linguistic constructions that embed a nonlinguistic element, following an original idea in Frege’s latest writings. These views form the (...) backdrop on which we can put forward the claim of treating all indexicals as complex demonstratives. In the central part of the paper, I criticize each of de Gaynesford’s arguments against the reduction of indexicals to complex demonstratives. Besides, I propose a new definition of the concept of “demonstration” as a nonlinguistic feature of all indexicals in their referential uses, to contrast de Gaynesford’s rejection of the idea that demonstrations are an essential feature of indexicals. Eventually, I strengthen my claim by distinguishing indexicals from proper names and definite descriptions on the ground that only perceptual indexicals necessarily require an accompanying demonstration. However, the main point of the paper is a negative one, that is the rejection of de Gaynesford’s arguments against the reduction of indexicals to complex demonstratives. More work is needed to reach a positive conclusion on this topic. (shrink)

Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.

Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.

Christopher Meckstroth’s book The Struggle for Democracy poses and attempts to solve a central problem of democratic theory: what he calls the ‘paradox of authorization’, whereby the very activity of spelling out the political content of democracy is said to potentially contradict its object, since the democratic theorist may end up substituting himself or herself for ‘the people’ in deciding what this form government amounts to in practice. In order to avoid this problem, Meckstroth suggests that the political content of (...) democracy ought to be extrapolated out of concrete political struggles, by submitting competing claims to represent the people’s will to a rational scrutiny that tests them for internal coherence. While pointing out the intrinsic interest and originality of this approach, the review also advances some reservations concerning the posited criterion’s capacity to perform all the work Meckstroth assigns it. In the end, the proposed solution to the ‘paradox of authorization’ may fall prey to... (shrink)

Background: For many years the body of literature known as ‘care ethics’ or ‘ethics of care’ has been discussed as regards its status and nature. There is much confusion and little structured discussion. The paper of Klaver et al. (2014) was written as a discussion article to which we respond. Objectives: We aim to contribute to the ongoing discussion about the status and nature of care ethics. Research design: Responding to ‘Demarcation of the ethics of care as a discipline’ by (...) Klaver et al. (2014) and ‘Three versions of an ethics of care’ by Edwards (2009), we identified shared concerns and formulated criticisms of both texts in order to develop an alternative view. Participants and research context: This paper has been written from the academic context of a master in care ethics an policy. Ethical considerations: We have tried to be fair and respectful to the authors discussed. Findings: Both Klaver et al. (2014) and Edwards (2009) raise important concerns about the question if care ethics can be considered an academic discipline, and to what extend it can be seen as a moral theory. Despite shared concerns, their arguments fail to convince us in all respects. Discussion and conclusion: We propose to conceive care ethics as an interdisciplinary field of inquiry, incorporating a dialectical relation between empirical research and theoretical reflection. Departing from the notion of caring as a practice of contributing to a life-sustaining web, we argue that care ethics can only profit from a loosely organized academic profile that allows for flexibility and critical attitude that brings us close to the good emerging in specific practices. This asks for ways of searching for a common focus and interest that is inherently democratic and dialogical and thus beyond demarcation. (shrink)

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...) in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories. (shrink)

A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of (...) the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered. (shrink)

Nel febbraio 1912 Wittgenstein venne ammesso al Trinity College con Russell come supervisor, e iniziò a seguire le lezioni di Moore. E’ probabile che leggesse il libretto di Moore, Ethics, pubblicato al suo arrivo a Cambridge, o che ritrovasse nelle lezioni di Moore alcune delle suggestioni presenti nel libro. Ma dopo il Tractatus Wittgenstein dedicò poco spazio alle riflessioni sull’etica e quel poco in un periodo ristretto di tempo, agli inizi degli anni ‘30, dalla Conferenza sull’etica2 alle lezioni del ’32-33. (...) Alle lezioni del 32-33 assistettero sia Alice Ambrose che George E. Moore, che ci lascianpo diversi tipi di appunti:3 Ambrose riporta frasi di Wittgenstein, Moore presenta e rielabora le sue idee. Una lettura comparata di questi appunti dà un’idea abbastanza chiara di quanto Wittgenstein in quegli anni riuscisse a fondere le sue idee sui giudizi morali con le sue idee sulla grammatica filosofica che veniva elaborando nel Big Typescript. (shrink)

In quanto segue si d× in poche pagine un'idea del paradigma classico della logica assiomatica; Ë un richiamo alla terminologia e ai simboli che si useranno in seguito. I due successivi capitoli presentano i problemi ce hanno segnato la nascita del paradigma classico e un confronto con il paradigma tradizionale della logica aristotelica.

According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.