There is a tension between Dispositionalism––the view that all metaphysical modality is grounded in actual irreducible dispositional properties––and the possibility of time travel. This is due to the fact that Dispositionalism makes it much harder to solve a potentiality-based version of the grandfather paradox. We first present a potentiality-based version of the grandfather paradox, stating that the following theses are inconsistent: 1) time travel is possible, 2) powers fully ground modality, 3) self-defeating actions are impossible, 4) time-travellers retain their intrinsic (...) powers upon time-travelling, and 5) time-travellers are ordinary agents with basic intrinsic potentialities. We then consider a number of potential solutions, and find them wanting. We argue that the metaphysical impossibility of performing a self-defeating action acts as a necessary perfect mask––while time-travel lets us “slip” the potentiality under the mask, thus generating the contradiction. We conclude considering what are the options for the dispositionalist. (shrink)

Dispositionalism is the theory of modality according to which all (metaphysical and natural) modal truths are made true by some actual irreducibly dispositional property. The relationship between Dispositionalism and time is yet to be satisfactorily explored. In this paper we contribute to this task by examining how Dispositionalism deals with ‘dated truths’: propositions involving a specific time, e.g. “It might rain at 12.30”. We examine two possible accounts: the first, 'Dated Manifestations Strategy', is the idea that powers are very fine-grained, (...) and tend towards temporally very specific manifestations. We argue that such strategy should not be adopted, for it leads to unnecessary violations of ontological parsimony; it is unable to accommodate an ontology of platonic universals; and it is incapable of offering a principled explanation of the forward-looking nature of powers. We offer an alternative account, the "Duration Strategy", which relies on an independently determined arrow of time and the existence of some “duration facts” that specify how long a power takes to bring about its manifestation. We argue that the Duration Strategy is to be preferred. We then flesh out the account by exploring the connection between powers, duration facts, and processes. (shrink)

Vetter (2015) develops a localised theory of modality, based on potentialities of actual objects. Two factors play a key role in its appeal: its commitment to Hardcore Actualism, and to Naturalism. Vetter’s commitment to Naturalism is in part manifested in her adoption of Aristotelian universals. In this paper, we argue that a puzzle concerning the identity of unmanifested potentialities cannot be solved with an Aristotelian conception of properties. After introducing the puzzle, we examine Vetter’s attempt at amending the Aristotelian conception (...) in a way that avoids the puzzle, and conclude that this amended version is no longer to be considered naturalistic. Potentiality theory cannot be both actualist and naturalist. We then argue that, if naturalism is to be abandoned by the actualist, there are good reasons to adopt a Platonist conception of universals, for they offer a number of theoretical advantages and allow us to avoid some of the problems facing Vetter’s theory. (shrink)

In this paper I argue that even the most radical metaphysics of powers (such as that adopted by Mumford & Anjum, Cartwright, or Groff) are compatible with eternalism. I first offer a taxonomy of powers ontologies, and attempt to characterise the difference between moderate and radical powers ontologies – the latter are characterised by an emphasis on production and dynamicity. I consider an argument by C. Friebe to the effect that the productive character of powers is inconsistent with Eternalism and (...) find it wanting. I then elucidate the notion of dynamicity that radical powers theorists employ by making apparent their link with an ontology of irreducible processes. Finally, I respond to an argument by Donatella Donati to the effect that eternalism entails a reductive account of change which is inconsistent with process ontologies, and show that the the two are compatible. I conclude that we have no reason to think that radical powers metaphysics (and, a fortiori, every powers ontology) are not compatible with eternalism. (shrink)

Establishing Dispositionalism as a viable theory of modality requires the successful fulfilment of two tasks: showing that all modal truths can be derived from truths about actual powers, and offering a suitable metaphysics of powers. These two tasks are intertwined: difficulties in one can affect the chances of success in the other. In this paper, I generalise an objection to Dispositionalism by Jessica Leech and argue that the theory in its present form is ill-suited to account for de re truths (...) about merely possible entities. I argue that such difficulty is rooted in a problem in the metaphysics of powers. In particular, I contend that the well-known tension between two key principle of powers ontology, namely Directedness and Independence has received an unsatisfactory solution so far, and that it is this unsatisfactory solution concerning the status of “unmanifested manifestations” that makes it hard for Dispositionalism to account for mere possibilia. I develop a novel account of the status of unmanifested manifestations and an overall metaphysics of powers which allows to better respond to Leech's objection and handle mere possibilia. The central idea of the proposal is that unmanifested manifestations are akin to mere logical existents, and are best characterised as non-essentially non-located entities. (shrink)

Establishing Dispositionalism as a viable theory of modality requires the successful fulfilment of two tasks: (i) showing that all modal truths can be derived from truths about actual powers, and (ii) offering a suitable metaphysics of powers. These two tasks are intertwined: difficulties in one can affect the chances of success in the other. In this paper, I generalise an objection to Dispositionalism by Jessica Leech and argue that the theory in its present form is ill-suited to account for de (...) re truths about merely possible entities. I argue that such difficulty is rooted in a problem in the metaphysics of powers. In particular, I contend that the well-known tension between two key principle of powers ontology, namely Directedness (all powers are “for” their manifestation) and Independence (some powers might fail to bring about their manifestation) has received an unsatisfactory solution so far, and that it is this unsatisfactory solution concerning the status of “unmanifested manifestations” that makes it hard for Dispositionalism to account for mere possibilia. I develop a novel account of the status of unmanifested manifestations and an overall metaphysics of powers which allows to better respond to Leech's objection and handle mere possibilia. The central idea of the proposal is that unmanifested manifestations are akin to mere logical existents, and are best characterised as non-essentially non-located entities. (shrink)

In this paper I argue that even the most radical metaphysics of powers (such as that adopted by Mumford and Anjum, Cartwright, or Groff) are compatible with eternalism. I first offer a taxonomy of powers ontologies, and attempt to characterise the difference between moderate and radical powers ontologies—the latter are characterised by an emphasis on _production_ and _dynamicity_. I consider an argument by C. Friebe to the effect that the productive character of powers is inconsistent with Eternalism and find it (...) wanting. I then elucidate the notion of _dynamicity_ that radical powers theorists employ by making apparent their link with an ontology of irreducible processes. Finally, I respond to an argument by Donatella Donati to the effect that eternalism entails a reductive account of change which is inconsistent with process ontologies, and show that the the two are compatible. I conclude that we have no reason to think that radical powers metaphysics (and, a fortiori, every powers ontology) are not compatible with eternalism. (shrink)

In this paper we examine whether and how powers ontologies can back formal causation. We attempt to answer three questions: i) what is formal causation; ii) whether we need formal causation, and iii) whether formal causation need powers and whether it can be grounded in powers. We take formal causal explanations to be explanations in which something's essence features prominently in the explanans. Three kinds of essential explanations are distinguished: constitutive, consequential, and those singling out something's propria. This last kind (...) of explanation has been somewhat overlooked in the literature, but we argue that it features in much of the most relevant uses of formal explanations in philosophy and science. These are the explanations for why an object has certain propertis that are not, properly speaking, parts of its essence, but that belong to it more intimately than just being part of its consequential essence: they are the properties that ‘flow’ from something's essence. It is argued that a powers metaphysics is uniquely placed to make sense of this last phenomenon. We then distinguish three grades of involvement in which powers might be salient for formal causal explanations: i) powers might be the subject matter of the essence operator, ii) the essence of something might include (or be exhausted) by powers, or iii) powers can explain how propria can flow from something's constitutive existence. (shrink)

Dispositionalism is the theory of modality that grounds all modal truths in powers: all metaphysically possible and necessary truths are to be explained by pointing to some actual power, or absence thereof. One of the main reasons to endorse dispositionalism is that it promises to deliver an especially desirable epistemology of modality. However, so far this issue has not be fully investigated with the care it is due. The aim of this paper is to fill this gap. We will cast (...) some doubts on whether the dispositionalist really is in a better position to explain our modal knowledge. In fact, we argue that there is a tension between some core tenets of a powers metaphysics and the very features that make dispositionalism the ideal backdrop for a desirable epistemology of modality. We conclude that this leaves dispositionalists who want to deliver the promised epistemology with a hard, currently unfulfilled, task. (shrink)

In this dissertation, I develop a metaphysics of powers to ground Dispositionalism, the theory of the source of modality according to which all alethic modal truths are grounded in dispositional properties instantiated in the actual world. I consider a number of key theses that powers metaphysics display, and investigate which can be incorporated in the metaphysical base of Dispositionalism, and how. In the first part I examine the interaction of two core principles of powers ontologies: Directedness, the thesis that powers (...) ‘point at’ their manifestations, and Independence, the thesis that powers can fail to manifest. These two principles are in tension: there is an argument, known as Too Much Possibility, to the effect that they are inconsistent. I examine various strategies to resist the argument. These involve Physical Intentionality, numerical identity between power and manifestation, process ontologies, and platonic universals. I conclude that they are all unsatisfactory. In the second part, I develop a ‘minimal metaphysics of powers’ that is immune from the threat of Too Much Possibility. This involves considering unmanifested manifestations to be akin to Mere Logical Existents. I argue that the best way to avoid the tension at the heart of powers ontologies is to conceive of unmanifested manifestations as non-essentially non-spatiotemporally located entities. I then consider some consequences of minimal metaphysics: I examine which ontological category the manifestations of power can belong to, and what are the prospects of grounding metaphysical, as opposed to natural, modality. Finally, in the third part, I investigate whether further key theses of powers ontologies can be incorporated into the minimal metaphysics. This leads to discuss the relationship of the minimal metaphysics with grounding and dependency relations, the metaphysics of time, the truthmaking principle, and tendential theories of powers. (shrink)

This chapter introduces readers to the empirical questions at issue in debates over gendered pronouns and assesses the plausibility of various possible answers to these questions. It has two parts. The first is a general introduction to the linguistics and psychology of grammatical gender. The second focuses on the meanings of gendered pronouns in English. It begins with a discussion of some methodological limitations of empirical approaches to the topic and the normative implications of those limitations. It then argues against (...) three simple theories of the semantics of gendered pronouns in English and proposes an alternative that fares better: the Gender-First View. Finally, it discusses the singular use of 'they' and its connection to nonbinary gender identities. (shrink)

The term 'covert mixed quotation' describes cases in which linguistic material is interpreted in the manner of mixed quotation — that is, used in addition to being mentioned — despite the superficial absence of any commonly recognized conventional devices indicating quotation. After developing a novel theory of mixed quotation, I show that positing covert mixed quotation allows us to give simple and unified treatments of a number of puzzling semantic phenomena, including the projective behavior of conventional implicature items embedded in (...) indirect speech reports and propositional attitude ascriptions, so-called 'c-monsters,' metalinguistic negation, metalinguistic negotiation, and 'in a sense' constructions. (shrink)

In this paper I address issues related to the problem of future contingents and the metaphysical doctrine of fatalism. Two classical responses to the problem of future contingents are the third truth value view and the all-false view. According to the former, future contingents take a third truth value which goes beyond truth and falsity. According to the latter, they are all false. I here illustrate and discuss two ways to respectively argue for those two views. Both ways are similar (...) in spirit and intimately connected with fatalism, in the sense that they engage with the doctrine of fatalism and accept a large part of a standard fatalistic machinery. (shrink)

Existing work on gaslighting ties it constitutively to facts about the intentions or prejudices of the gaslighter and/or his victim’s prior experience of epistemic injustice. I argue that the concept of gaslighting is more broadly applicable than has been appreciated: what is distinctive about gaslighting, on my account, is simply that a gaslighter confronts his victim with a certain kind of choice between rejecting his testimony and doubting her own basic epistemic competence in some domain. I thus hold that gaslighting (...) is a purely epistemic phenomenon—not requiring any particular set of intentions or prejudices on the part of the gaslighter—and also that it can occur even in the absence of any prior experience of epistemic injustice. Appreciating the dilemmatic character of gaslighting allows us to understand its connection with a characteristic sort of epistemic harm, makes it easier to apply the concept of gaslighting in practice, and raises the possibility that we might discover its structure and the associated harm in surprising places. (shrink)

The inclusion problem for theories of gender arises when those theories inappropriately fail to include certain individuals in the gender categories to which they ought to belong. The inclusion problem affects both of the most influential traditions in feminist theorizing about gender: social-position accounts and identity accounts. I argue that the inclusion problem can be solved by adopting a structured theory of gender which incorporates aspects of both social-position accounts and identity accounts. According to the theory I favor, an individual’s (...) gender is determined by their gender identity if they have one; otherwise, it is determined by their social position. My structured approach to gender offers a more direct solution to the gender inclusion problem than alternatives recently advocated by Barnes (2020), Jenkins (2023), and others. It also points the way to a simple solution to inclusion problems that arise at the level of gendered language. (shrink)

Branching time is a popular theory of time that is intended to account for the openness of the future. Generally, branching-time models the openness of the future by positing a multiplicity of concrete alternative futures mirroring all the possible ways the future could unfold. A distinction is drawn in the literature among branching-time theories: those that make use of moment-based structures and those that employ history-based ones. In this paper, I introduce and discuss a particular kind of openness relative to (...) the possibility that time ends (doomsday). I then show that whereas moment-based branching structures cannot represent this kind of openness, history-based structures can account for it. The conclusion is that history-based structures have an advantage over moment-based ones. (shrink)

Recent work on the semantics and pragmatics of slurs has explored a variety of ways of explaining their potential to derogate, with the most popular family of approaches appealing to either: (i), the doxastic or evaluative attitudes or commitments expressed by — or (ii), the propositions concerning such attitudes or commitments semantically or pragmatically communicated by — the speakers who use them. I begin by arguing that no such speaker-oriented approach can be correct. I then propose an alternative treatment of (...) slurs, according to which they are semantically associated with both descriptive and directive content. On the view I defend, when speakers use slurs, they simultaneously propose to add an at-issue proposition to the conversational common ground and issue a not-at-issue directive to their interlocutors to adopt a derogatory perspective toward members of the targeted group. This proposal both avoids the problems faced by other accounts and opens up a novel way of thinking about the phenomenon of appropriation. (shrink)

A lot of attention has recently been devoted to the notion of Trustworthy AI (TAI). However, the very applicability of the notions of trust and trustworthiness to AI systems has been called into question. A purely epistemic account of trust can hardly ground the distinction between trustworthy and merely reliable AI, while it has been argued that insisting on the importance of the trustee’s motivations and goodwill makes the notion of TAI a categorical error. After providing an overview of the (...) debate, we contend that the prevailing views on trust and AI fail to account for the ethically relevant and value-laden aspects of the design and use of AI systems, and we propose an understanding of the notion of TAI that explicitly aims at capturing these aspects. The problems involved in applying trust and trustworthiness to AI systems are overcome by keeping apart trust in AI systems and interpersonal trust. These notions share a conceptual core but should be treated as distinct ones. (shrink)

Quotation marks in natural language that do not function straightforwardly as devices for securing reference to linguistic objects have generally been categorized as instances of either mixed quotation or scare quotation. I argue that certain uses of quotation marks in natural language resist assimilation to either of these two theoretical categories, as well as to the more familiar categories of pure and direct quotation. It follows that we must recognize a novel type of quotation in natural language, which I call (...) dummy quotation because it involves the contribution of semantically minimal `dummy meanings' to composition. I develop a semantic theory of dummy quotation and show that it is better able than rival proposals to account for the troublesome examples in question. (shrink)

While growing empirical evidence suggests a continuity between human and non-human psychology, many philosophers still think that only humans can act and form beliefs rationally. In this paper, we challenge this claim. We first clarify the notion of rationality. We then focus on the rationality of beliefs and argue that, in the relevant sense, humans are not the only rational animals. We do so by first distinguishing between unreflective and reflective responsiveness to epistemic reasons in belief formation and revision. We (...) argue that unreflective responsiveness is clearly within the reach of many animals. We then defend that a key demonstration of reflective responsiveness would be the ability to respond to undermining defeaters. We end by presenting some empirical evidence that suggests that some animal species are capable of processing these defeaters, which would entail that even by the strictest standards, humans are not the only rational animals. (shrink)

When we witness a great actor, musician, or sportsperson performing, we share something of their experience. Only recently has it become clear just how this sharing of experience is realised within the human brain. 'Mirrors in the brain' provides an accessible overview of mirror neurons, written by the man who first discovered them.

Can rational communication proceed when interlocutors are uncertain which contents utterances contribute to discourse? An influential negative answer to this question is embodied in the Stalnakerian principle of uniformity, which requires speakers to produce only utterances that express the same content in every possibility treated as live for the purposes of the conversation. The principle of uniformity enjoys considerable intuitive plausibility and, moreover, seems to follow from platitudes about assertion; nevertheless, it has recently proven controversial. In what follows, I defend (...) the principle by developing two arguments for it based on premises reflecting the central aims and assumptions of possibility-carving frameworks for modeling inquiry—that is, frameworks which describe the evolution of individuals’ attitudinal states in terms of set-theoretic operations defined over a domain of objects representing possibilities. (shrink)

Speakers assert in order to communicate information. It is natural, therefore, to hold that the content of an assertion is whatever information it communicates to its audience. In cases involving uncertainty about the semantic values of context-sensitive lexical items, moreover, it is natural to hold that the information an assertion communicates to its audience is whatever information audience members are in a position to recover from it by assuming that the proposition it semantically determines is true. This sort of picture (...) corresponds to an influential and widely endorsed theory of assertoric content: diagonalism. I begin by arguing that, despite its intuitive appeal, diagonalism should be rejected because it conflicts with our intuitive judgments about the circumstances in which the contents of speakers’ assertions would be true or false. I then show that the failure of diagonalism requires us to either abandon a familiar way of thinking about information and rational assertion or hold that the content of an assertion is not always the information it communicates. I suggest that we choose the latter horn of this dilemma — assertoric content is better characterized in terms of the commitments speakers undertake than in terms of the information they communicate. (shrink)

Horizontalism is the thesis that what a speaker asserts in literally and sincerely uttering an indicative sentence is some horizontal proposition of her utterance; diagonalism is the thesis that what a speaker asserts in literally and sincerely uttering an indicative sentence is some diagonal proposition of her utterance. Recent work on assertion has reached no clear consensus favoring either horizontalism or diagonalism. I explore a novel strategy for adjudicating between the two views by considering the advantages and disadvantages which would (...) accrue to a linguistic community as a result of adopting different committal practices—that is, practices of associating utterances with the propositions to which speakers undertake assertoric commitments in uttering them—ultimately concluding that a horizontalist practice has important advantages over its competitors. (shrink)

_Demonstrates how the ethical underpinning of Hegel’s political and social philosophy has relevance for contemporary democratic life._.

Famously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rule-following behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea that a rule (...) is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates essential aspects of the communitarian understanding of rule-following. Make the following experiment: say “It’s cold here” and mean “It’s warm here”. Can you do it?Ludwig Wittgenstein, Philosophical Investigations, 1953, §510.I can’t say “it’s cold here” and mean “it’s warm here”—at least, not without a little help from my friends.David Lewis, Convention. (shrink)

Let the label binary category terms refer to natural language expressions like ‘woman’, ‘man’, ‘female’, and ‘male’. Focusing on ‘woman’ and ‘female’, I develop a novel, empirically supported theory of the meanings of English binary category terms. Given plausible assumptions about the metaphysics of sex and gender, this gender-first theory predicts that the sentence ‘Trans women are women’ expresses a truth in all contexts and the sentence ‘Women are adult human females’ expresses a truth in most ordinary contexts — thus (...) that these two sentences can and usually do express logically consistent contents. The key feature of the proposed theory is that it treats both ‘woman’ and ‘female’ as sensitive to an individual’s gender when that individual belongs to a gendered category and to an individual’s sex otherwise. The existence and plausibility of a gender-first theory of this kind opens up conceptual room for trans-inclusive positions in the philosophy of sex and gender which endorse the claim that women are adult human females, thereby both accounting for trans women’s experiences of their bodies as female and helping to disarm the sentence ‘Women are adult human females’ as a trans-exclusionary slogan. (shrink)

Greg Ray (2014) believes he has discovered a crucial oversight in Donald Davidson’s semantic programme, recognition of which paves the way for a novel approach to Davidsonian semantics. We disagree: Ray’s novel approach involves a tacit appeal to pre-existing semantic knowledge which vitiates its interest as a development of the Davidsonian programme.

One important distinction in the debate over the nature of epistemic justification is the one between propositional and doxastic justification. Roughly, while doxastic justification is a property of beliefs, propositional justification is a property of propositions. On a rather common view, which accounts for doxastic justification in terms of propositional justification plus the so-called ‘basing relation’, propositional justification is seen as the prior notion, and doxastic justification is explained in terms of it. According to the opposing view, the direction of (...) explanation needs to be reversed, and doxastic justification should be seen as primary. I distinguish between two notions of priority, and I argue that they give different verdicts with respect to the issue of which notion of justification comes first. The lesson may be taken to be that propositional and doxastic justification are in a relation of intertwinement. (shrink)

The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branching-tree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show that there is an (...) incompatibility between the way branching-tree models account for the open future and the possibility of time travel. That is, I argue that once time travel enters the picture, branching time fails to model the openness of the future by means of alternative future branches. I show how this holds independently of whether branching-time models are cashed out in A-theoretic or B-theoretic terms. (shrink)

This paper introduces a new kind of explanation that we describe as ‘purely theoretical’. We first present an example, E, of what we take to be a case of purely theoretical explanation. We then show that the explanation we have in mind does not fit neatly into any of the existing categories of explanation. We take this to give us prima facie motivation for thinking that purely theoretical explanation is a distinctive kind of explanation. We then argue that it can (...) earn its keep via application to two existing literatures: the literature on how we explain the truth of true negative existential propositions and the literature on how we explain the truth of true propositions about the past. We reply to some possible concerns regarding the introduction of purely theoretical explanations. We conclude that there is nothing obviously wrong with them and explore the ramifications for particular debates in metaphysics. (shrink)

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction) stresses the importance of including it in the definition of convention. I discuss arguments pro et contra to (...) argue that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. (shrink)

Taking the inspiration from some points made by Scott Sturgeon and Albert Casullo, I articulate a view according to which an important difference between undermining and overriding defeaters is that the former require the subject to engage in some higher-order epistemic thinking, while the latter don’t. With the help of some examples, I argue that underminers push the cognizer to reflect on the way she formed a belief by challenging the epistemic worthiness of either the source of justification or the (...) specific justificatory process. By contrast, overriders needn’t pose any such challenge. I also consider some problems for the proposed view, and I put forward some possible solutions. Finally, I provide some details on how undermining defeat works in different cases. (shrink)

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} on an additional time variable, named intrinsic time at variance (...) with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g˙μν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{g}}_{\mu \nu }$$\end{document} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[gμν,πμν]=K[gμν,πμν]-S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }] = {\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }] - S[g_{\mu \nu }]$$\end{document}, playing formally the role of a Hamilton function, where S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} is the standard Einstein–Hilbert action while K[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} and not of energy. Since the Einstein–Hilbert action S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document} gives rise to a cosmological constant term in the path-integral approach. (shrink)

Cet article soutient que Plotin a écrit l’ Ennéade VI 8 (39) pour mener ses élèves à voir que notre liberté est fondée sur l’Un, un but poursuivi par le biais d’une polémique avec le De fato et le De anima d’Alexandre d’Aphrodise. La première partie cherche à établir que le « discours téméraire » introduit au chapitre 7 est une interprétation de la position du De fato sur la liberté des dieux. Plotin lit la thèse de son adversaire en (...) transférant au niveau de l’Un une structure tripartite constituée par la nature, la raison et le hasard, une structure qu’Alexandre utilisait pour expliquer les événements des réalités en devenir. La seconde partie propose de voir le traité comme un procédé dialectique. Plotin commence son enquête par le niveau de l’âme et celui de l’Intellect. Il arrive ensuite au discours sur l’Un, où il essaie de franchir progressivement les limites du langage en analysant les positions alternatives du point de vue du discours, des mots et enfin de la pensée. Ce faisant, il insiste sur le renversement des thèses d’Alexandre : l’Un est simple et donc il n’est pas contraint par sa nature, il est libre grâce à une volonté incapable de choisir parmi les contraires et tournée métaphoriquement vers elle-même. (shrink)