Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)
Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must “forget time”, and how this can be done in the classical and in the quantum theory. The idea is to (...) develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time. (shrink)
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe “handles” though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it (...) is a consequence of a relational structure of physical quantities. (shrink)
Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had damaging effects on the fertility of science. I also suggest that recent important empirical results, such as the detection of the Higgs particle and gravitational waves, and the failure to detect supersymmetry where many expected to find it, question the validity of certain philosophical (...) assumptions common among theoretical physicists, inviting us to engage in a clearer philosophical reflection on scientific method. (shrink)
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.
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.
Is reality three-dimensional and becoming real, or is reality four-dimensional and becoming illusory? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations.
This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in (...) philosophy of science which are are raised by, or a relevant for, the research on quantum gravity. (shrink)
The concept of dignity is notoriously vague. In this paper it is argued that the reason for this is that there are three versions of dignity that are often confused. First we will take a short look at the history of the concept of dignity in order to demonstrate how already from Roman Antiquity two versions of dignity can be distinguished. Subsequently, the third version will be introduced and it will be argued that although the three versions of dignity hang (...) together, they should also be clearly distinguished in order to avoid confusion. The reason for distinguishing the three versions is because all three of them are only partially effective. This will be demonstrated by taking the discussion about voluntary ‘dying with dignity’ as an example. Inspired by both Paul Ricoeur’s concept of ethics and the ethics of care a proposition will be done as to how the three versions of dignity may sustain each other and help achieve what neither one of the versions can do on its own. (shrink)
This article discusses the relation between empirical and normative approaches in bioethics. The issue of dwarf tossing, while admittedly unusual, is chosen as a point of departure because it challenges the reader to look with fresh eyes upon several central bioethical themes, including human dignity, autonomy, and the protection of vulnerable people. After an overview of current approaches to the integration of empirical and normative ethics, we consider five ways that the empirical and normative can be brought together to speak (...) to the problem of dwarf tossing: prescriptive applied ethics, theoretical ethics, critical applied ethics, particularist ethics and integrated empirical ethics. We defend a position of critical applied ethics that allows for a two-way relation between empirical and normative theories. Against efforts fully to integrate the normative and the empirical into one synthesis, we propose that the two should stand in tension and relation to one another. The approach we endorse acknowledges that a social practice can and should be judged both by the gathering of empirical data and by normative ethics. Critical applied ethics uses a five stage process that includes: (a) determination of the problem, (b) description of the problem, (c) empirical study of effects and alternatives, (d) normative weighing and (e) evaluation of the effects of a decision. In each stage, we explore the perspective from both the empirical (sociological) and the normative ethical point of view. We conclude by applying our five-stage critical applied ethics to the example of dwarf tossing. (shrink)
Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue against mereology. We show some time travel scenarios are structurally equivalent to more standard ones not involving time travel; and that the three main theories about persistence through time can each solve both the time travel scenario as well as the structurally similar classical scenario. Time travel scenarios that are not similar to more standard arguments (...) are instead problematic because they are open to different, incompatible interpretations. We conclude that compared to the classical arguments against mereological principles, time travel scenarios do not add anything new. (shrink)
The view that the subject matter of epistemology is the concept of knowledge is faced with the problem that all attempts so far to define that concept are subject to counterexamples. As an alternative, this article argues that the subject matter of epistemology is knowledge itself rather than the concept of knowledge. Moreover, knowledge is not merely a state of mind but rather a certain kind of response to the environment that is essential for survival. In this perspective, the article (...) outlines an answer to four basic questions about knowledge: What is the role of knowledge in human life? What is the relation between knowledge and reality? How is knowledge acquired? Is there any a priori knowledge? (shrink)
Following the invitation of the editors of Foundations of Physics, I give here a personal assessment of string theory, from the point of view of an outsider, and I compare it with the theory, methods, and expectations of my own field.
We asked some of the best philosophers of pragmatics to offer their original perspectives on the following question: to what extent do the novelties developed in these last years shed new light on defining the content of what is said? They answered with passion and without avoiding strong criticism of central ideas on opposite sides. The primary purpose of this collection is to provide a survey of what may be considered the main contemporary debate in the philosophy of language. Scholars (...) and people already involved in the debate will find in the papers new challenges. As Aristotle would say “what is said is said in many ways”. TOC 1 CARLO PENCO, FILIPPO DOMANESCHI What is said: a Short History in Quotes 2 UNA STOJNIC AND ERNEST LEPORE What’s What’s said? 3 JASON STANLEY Context and Logical Form 4 MASSIMILIANO VIGNOLO Surprise Indexicalism 5 KENT BACH The Lure of Linguistification 6 MANUEL GARCIA CARPINTERO Explicit Performatives 7 CLAUDIA BIANCHI Illocutions in Context 8 CATHERINE WEARING Metaphor and the Scope Argument 9 FRANCOIS RECANATI Reference through Mental Files 10 ROBYN CARSTON Word Meaning, What is Said and Explicature 11 KEPA KORTA Grice’s Requirements on What is Said 12JOANA GARMENDIA Ironically Saying and Implicating 13 JOHN MACFARLANE Non Indexical Contextualism 14 EROS CORAZZA AND JEROM DOKIC On Situationalism: Situations with an Attitude 15 MICHAEL DEVITT Three Methodological Flaws of Linguistic Pragmatism 16 JOHN PERRY Direct Discourse, Indirect Discourse and Belief. (shrink)
In the 1960s molecular population geneticists used Monte Carlo experiments to evaluate particular diffusion equation models. In this paper I examine the nature of this comparative evaluation and argue for three claims: first, Monte Carlo experiments are genuine experiments: second, Monte Carlo experiments can provide an important meansfor evaluating the adequacy of highly idealized theoretical models; and, third, the evaluation of the computational adequacy of a diffusion model with Monte Carlo experiments is significantlydifferent from the evaluation (...) of the emperical adequacy of the same diffusion model. (shrink)
Ethical veganism is the view that raising animals for food is an immoral practice that must be stopped because of the harm it causes to the animals, the environment, and our health. Carlo Alvaro argues the only way to stop that harm is to acquire the virtues that enable us to act justly and benevolently toward animals.
The sixth century -- Anaximander's contributions -- Atmospheric phenomena -- Earth floats in space, suspended in the void -- Invisible entities and natural laws -- Rebellion becomes virtue -- Writing, democracy, and cultural crossbreeding -- What is science? -- Between cultural relativism and absolute thought -- Can we understand the world without Gods? -- Prescientific thought.
The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.
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)
This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.
In the paper we investigate typed axiomatizations of the truth predicate in which the axioms of truth come with a built-in, minimal and self-sufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The (...) framework considered will give rise to some methodological remarks on the construction of truth theories and provide us with a privileged point of view to analyze the notion of truth arising from compositional principles in a typed setting. (shrink)
The article examines the development of Husserl’s early philosophy from his Habilitationsschrift to the Philosophie der Arithmetik . An attempt will be made at reconstructing the lost Habilitationsschrift . The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. The article contains an extensive and detailed comparison of these texts to illustrate the changes in Husserl’s position before and after February 1890. This date is (...) taken as a turning point in his development, because of Husserl’s announcement in a letter to Carl Stumpf that he was mistaken in his basic assumption, i.e. that the analysis of the concept of Anzahl would yield a foundation for arithmetic. Some interesting conclusions in this respect can also be drawn from an unpublished lecture that Husserl held in the WS 1889/90, in which he anticipates aspects of his position hitherto deemed to belong to the last phases of the PA. (shrink)
From antiquity several philosophers have claimed that the goal of natural science is truth. In particular, this is a basic tenet of contemporary scientific realism. However, all concepts of truth that have been put forward are inadequate to modern science because they do not provide a criterion of truth. This means that we will generally be unable to recognize a scientific truth when we reach it. As an alternative, this paper argues that the goal of natural science is plausibility and (...) considers some characters of plausibility. (shrink)
In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...) role diagrams play as means of discovery and understanding. Alternatively, this paper purports to show that the view that the method of mathematics is the analytic method is capable of dealing with diagrams qua diagrams, and of accounting for such role. (shrink)
The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...) our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)
In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...) consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)
Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major (...) disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure. (shrink)
The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)
This is a profound study of Aristotle's concept of phronesis, or practical wisdom. Carlo Natali critically reconsiders Aristotle's famous doctrine of contemplations, relating it to contemporary theories of the good life.
The question that is the subject of this article is not intended to be a sociological or statistical question about the practice of today’s mathematicians, but a philosophical question about the nature of mathematics, and specifically the method of mathematics. Since antiquity, saying that mathematics is problem solving has been an expression of the view that the method of mathematics is the analytic method, while saying that mathematics is theorem proving has been an expression of the view that the method (...) of mathematics is the axiomatic method. In this article it is argued that these two views of the mathematical method are really opposed. In order to answer the question whether mathematics is problem solving or theorem proving, the article retraces the Greek origins of the question and Hilbert’s answer. Then it argues that, by Gödel’s incompleteness results and other reasons, only the view that mathematics is problem solving is tenable. (shrink)
Notions like meaning, signal, intentionality, are difficult to relate to a physical word. I study a purely physical definition of "meaningful information", from which these notions can be derived. It is inspired by a model recently illustrated by Kolchinsky and Wolpert, and improves on Dretske classic work on the relation between knowledge and information. I discuss what makes a physical process into a signal.