We introduce a quite natural Frege-style set theory, which we call Strong-Frege-2 equation image, a sort of simplification of the theory considered in 13 and 1 . We give a model of a weaker variant of equation image, called equation image, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π11 sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of (...) 5 and 15. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} and a sublanguage L of the language of the formula, we can decide whether \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} has a uniform interpolant with respect to L in K4. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free case is proved using a reduction to the Gödel Löb Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the μ-calculus. (shrink)

We consider the relation between the uniform interpolation property and the elimination of non-standard quantifiers (the bisimulation quantifiers) in the context of the ?-calculus. In particular, we isolate classes of frames where the correspondence between these two properties is nicely smooth.

We show that the complete first order theory of an MV algebra has equation image countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are equation image and that all ω-categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators (...) of any locally finite variety of MV algebras is ω-categorical. (shrink)

We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...) way, thus providing a sort of “canonical” set of values for the functional representation. (shrink)

In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.

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)

We focus on Timothy Williamson’s recent attack on the epistemological significance of the a priori–a posteriori distinction, and offer an explanation of why, fundamentally, it does not succeed. We begin by setting out Williamson’s core argument, and some of the background to it and move to consider two lines of conciliatory response to it—conciliatory in that neither questions the central analogy on which Williamson's argument depends. We claim, setting aside a methodological challenge to which Williamson owes an answer, that no (...) satisfactory such reconciliation is in prospect. Rather, as we then argue, —and it is on this that we base our overall negative assessment of his argument—Williamson’s core analogy is flawed by an oversight. We conclude with some brief reflections on Williamson’s ideas about the imagination as a source of knowledge. Our principal conclusion is only that Williamson’s argument fails to perform as advertised. A constructive case for confidence, to the contrary, that the intuitive contrast between a priori and a posteriori reflects something of fundamental epistemological significance is prefigured in our final section, but will not be elaborated here. (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)

Limiting dangerous climate change is now widely believed to require negative emissions, a prospect some believe to be unjust and unacceptably risky. While NETs are not risk-free, I argue tha...

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)

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)

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)

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)

This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death of the (...) scientific methodology. In this paper, we offer a defense to these and other objections. To counter the conspiracy objection, we draw upon the philosophical literature on time travel, and conclude that the picture of the world offered by the superdeterminist does not need to be particularly surprising or conspiratorial. We then move on to other recent objections, in particular those that focus on the methodology of science and the nature of the physical laws compatible with superdeterminism. A key ingredient of our arguments is that the principle of statistical independence may be violated in theory, but valid for practical purposes. Our overarching goal is to offer a defense of superdeterminism with respect to its main objections, so that it can earn its keep as a legitimate contender among the possible interpretations of quantum mechanics. (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)

The goal of this paper is to defend the general tenet that time travelers cannot change the past within B-theoretical models of time, independently of how many temporal dimensions there are. Baron Pacific Philosophical Quarterly, 98, 129–147 offered a strong argument intended to reach this general conclusion. However, his argument does not cover a peculiar case, i.e. a B-theoretical one-dimensional model of time that allows for the presence of internal times. Loss Pacific Philosophical Quarterly, 96, 1–11 used the latter model (...) to argue that time travelers can change the past within such model. We show a way to debunk Loss’s argument, so that the general tenet about the impossibility of changing the past within B-theoretical models is maintained. (shrink)

Proponents of deliberative democracy believe deliberation provides the best chance of finding effective and legitimate climate policies. However, in many societies there is substantial evidence of biased cognition and polarisation about climate change. Further, many appear unable to distinguish reliable scientific information from false claims or misinformation. While deliberation significantly reduces polarisation about climate change, and can even increase the provision of reliable beliefs, these benefits are difficult to scale up, and are slow to affect whole societies. In response, I (...) propose a combined strategy of ‘thinking and nudging’. While deliberative theorists tend to view nudging askance, combining deliberation with nudges promises to be a timelier and more effective response to climate change than deliberation alone. I outline several proposals to improve societal deliberative capacity while reducing climate risks, including media reform, strategic communication and framing of debates, incentivising pro-climate behaviour change, and better education about science. (shrink)

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)

This paper explores mutable futurism, the view according to which the future can literally change—that is, it can happen that a future time t changes from containing an event E to lacking it. Mutable futurism has received little attention so far, and the details and implications of the view are underexplored in the literature. For instance, it currently lacks a precise metaphysical model and a formal semantics. Although we do not endorse mutable futurism, our goal here is to strengthen the (...) case for mutable futurism and help establish it as a worthy contender in the debate on the philosophy of time. To attain this goal, we try to make mutable futurism, along with its metaphysical and inferential commitments, as clear as possible, by providing it with a coherent metaphysical model and a plausible semantics, and we show that it can be backed by theoretical reasons. (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.

Hybrid organisations combine different elements from the for-profit and non-profit domains, and they usually operate in a resource-scarce environment. For these reasons, they continuously face various resources constraints, yet their hybrid nature could be translated into an opportunity. The purpose of our study was to investigate how a hybrid organisation can overcome resource constraints in developing countries by exploiting their own hybrid nature. In the unique research setting offered by Kenyan social enterprises, we identified five creative approaches implemented by social (...) enterprises. Finally, we present a grounded model that clearly explains which hybrid harvesting strategies can be implemented to overcome resource constraints, exploiting their hybrid potential. Our work contributes to knowledge about resource constraints in the social entrepreneurship literature and extends social bricolage theory. Limitations and future research approaches are also presented. (shrink)

The urgency of climate change has never been greater, nor the moral case for responding to it more compelling. This review essay critically compares Darrel Moellendorf's Mobilizing Hope and Catriona McKinnon's Climate Change and Political Theory. Moellendorf's book defends the moral importance of poverty alleviation through sustainable economic growth and argues for a mass climate movement based on the promise of a more prosperous future. By contrast, McKinnon provides a political vocabulary to articulate the many faces of climate injustice, and (...) to critically examine proposed policy solutions—notably including the indefinite pursuit of economic growth. While both find reasons to be hopeful, their wide-ranging accounts reflect different visions of what a just and sustainable future might look like. They reflect different understandings of sustainable development and the significance of environmental values; the scope of permissible climate activism; and the ethics of geoengineering. Building upon them, I argue in favor of a more pluralistic vision of a just climate future, one that is capable of speaking to the range of moral interests bearing upon the climate and biodiversity crises, and that supports sustainable development that is inclusive of diverse human-nature relationships. (shrink)

I extend the Higher-Order View of Undermining Defeat (HOVUD) defended in Melis (2014) to account for the defeat of propositional justification. In doing so, I clarify the important notion of higher-order commitment, and I make some considerations concerning the defeat of externalist epistemic warrants.

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)

One emerging issue in contemporary epistemology concerns the relation between animal knowledge, which can be had by agents unable to take a view on the epistemic status of their attitudes, and reflective knowledge, which is only available to agents capable of taking such a view. Philosophers who are open to animal knowledge often presume that while many of the beliefs of human adults are formed unreflectively and thus constitute mere animal knowledge, some of them—those which become subject of explicit scrutiny (...) or are the result of a deliberative effort—may attain the status of reflective knowledge. According to Sanford Goldberg and Jonathan Matheson (2020), however, it is impossible for reflective subjects to have mere animal knowledge. If correct, their view would have a number of repercussions, perhaps most notably the vindication of a dualism about knowledge, which would frustrate attempts to provide a unified account of knowledge-attributions to human adults, very young children, and non-human animals. I discuss Goldberg and Matheson’s proposal, outline some of the ways in which it is insightful, and argue that it is ultimately unsuccessful because it neglects the inherent temporal dimension of knowledge acquisition. While the article is pitched as a reply to Goldberg and Matheson, its primary aim is to highlight significant connections between the debates on the relation between animal and reflective knowledge, propositional and doxastic justification, and the theory of epistemic defeat. (shrink)