Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations for (...) an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem, and explore some versions of anti-exceptionalism about abstraction. I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V. I finally consider how the abstractionist can compare between competing criteria, and argue that anti-exceptionalists should be pluralists about abstraction. (shrink)

Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is (...) central to the neo-logicist program in the philosophy of mathematics ; in this paper we submit that, even if the neo-logicists wish to venture into the metaphysics of grounding, they can avoid the SR Principle. In Section 1 we introduce neo-logicism. In Sections 2 and 3 we examine the SR Principle. We then formulate an account of arithmetical facts which does not rest on the SR Principle; we finally argue that the neo-logicists should avoid the SR Principle in favour of this alternative proposal. (shrink)

The goal of this paper is to review and critically discuss the philosophical aspects of probabilistic seismic hazard analysis (PSHA). Given that estimates of seismic hazard are typically riddled with uncertainty, diferent epistemic values (related to the pursuit of scientifc knowledge) compete in the selection of seismic hazard models, in a context infuenced by non-epistemic values (related to practical goals and aims) as well. We frst distinguish between the diferent types of uncertainty in PSHA. We claim that epistemic and nonepistemic (...) considerations are closely related in the selection of the appropriate estimate of seismic hazard by the experts. Finally, we argue that the division of scientifc responsibility among the experts can lead to responsibility gaps. This raises a problem for the ownership of the results (“no one’s model” problem) similar to the “problem of many hands” in the ethics of technology. We conclude with a plea for a close collaboration between philosophy and engineering. (shrink)

The aim of this paper is to clarify under what conditions a philosophical problem arises. I will describe two ways in which we might perceive a question as a problem. First, when we fnd ourselves inclined to believe in propositions that appear incompatible with each other. Second, when we fnd ourselves inclined to believe in propositions that seem incompatible with our desires. I will discuss both of these cases and articulate a didactic strategy – the Clash Strategy – which can (...) be used in order to plan and facilitate dialogic inquiry in the classroom. This strategy suggests introducing stimuli that will help students appreciate the clash that drives the philosophical question to be explored during the dialogue. In summary, this paper aims to ofer insights to all teachers interested in promoting dialogic inquiry, whether philosophical or otherwise, in education. (shrink)

Richard Kimberly Heck and Paolo Mancosu have claimed that the possibility of non-Cantorian assignments of cardinalities to infinite concepts shows that Hume's Principle (HP) is not implicit in the concept of cardinal number. Neologicism would therefore be threatened by the ‘good company' HP is kept by such alternative assignments. In his review of Mancosu's book, Bob Hale argues, however, that ‘getting different numerosities for different countable infinite collections depends on taking the groups in a certain order – but it is (...) of the essence of cardinal numbers that the cardinal size of a collection does not depend upon how its members are ordered'. This paper's goal is to implement Hale's response to the Good Company problem by producing a Cantorian argument for HP. In Section 2, we present the Heck-Mancosu argument against neologicism. In Section 3, we discuss Hale's defence of Hume's Principle. In Section 4, we discuss Cantor's abstractionist definitions of number. In Section 5, we argue that good abstraction must comply with what we call ‘Gödel’s Minimal Account of Abstraction’ (GMAA). We finally show (Sections 5 and 6) that non-Cantorian theories of cardinality fail to satisfy GMAA. (shrink)

Minimalism and Trivialism are two recent forms of lightweight Platonism in the philosophy of mathematics: Minimalism is the view that mathematical objects arethinin the sense that “very little is required for their existence”, whereas Trivialism is the view that mathematical statements have trivial truth‐conditions, that is, that “nothing is required of the world in order for those conditions to be satisfied”. In order to clarify the relation between the mathematical and the non‐mathematical domain that these views envisage, it has recently (...) been proposed that both Linnebo's notion of sufficiency and Rayo's “just is”‐operator can, or even should, be interpreted in terms of metaphysicalgrounding. This interpretation makes Minimalism and Trivialism akin to Aristotelianism in the philosophy of mathematics, according to which mathematical entities depend for their existence and their properties on non‐mathematical ones. In this paper we raise a general objection to this interpretation. We highlight a tension – a “Big Picture” Problem – between the metaphysical picture underlying both Minimalism and Trivialism, on the one side, and the metaphysics of Platonism and Aristotelianism on the other. We then consider various ways in which Linnebo and Rayo could respond. We finally argue that Minimalism and Trivialism are closer to Aristotelianism than to Platonism; however, even though these positions are not forms of traditional Platonism, they are not standard forms of Aristotelianism either. (shrink)

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in (...) Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic. (shrink)

Theodor Adorno's famous aesthetic theory was not merely a theory of the aesthetic; it also made a wider claim about the aesthetic implications of all theory. At the same time we have to deal with aesthetic objects and events in which an aesthetic theory is inherent, which show themselves as art. From both sides--theory and aesthetics--a link can be made to the etymological meaning of theōria, which understands the theoretical as a seeing or perspective. Featuring lucid essays by major thinkers, (...) the book examines this link, focusing equally on the aesthetic implications of theory and the theoretical implications of aesthetic events. (shrink)

Wir reden gelegentlich von Kompromissen, die wir mit uns selbst schließen. Aber ist diese Rede angemessen oder gar berechtigt? Schließlich lassen sich wesentliche Merkmale von Kompromissen mit anderen nicht auf das Selbstverhältnis einer Person übertragen. Dennoch kann sich die Rede unter gewissen Umständen als sinnvoll erweisen. Der Artikel gibt Kriterien dafür an und stellt sich vor allem die Frage, ob und in welcher Hinsicht solche selbstbezüglichen Kompromisse eine Gefahr für die Integrität der Person darstellen.

Technological innovation is almost always investigated from an economic perspective; with few exceptions, the specific technological and social nature of innovation is often ignored. We argue that a novel way to characterise and make sense of different types of technological innovation is to start considering uncertainty. This seems plausible since technological development and innovation almost always occur under conditions of uncertainty. We rely on the distinction between, on the one hand, uncertainty that can be quantified (e.g. probabilistic risk) and, on (...) the other, deep forms of uncertainty that may resist the possibility of being quantified (e.g. severe or fundamental uncertainties). On the basis of these different ingredients of uncertainty in technological innovation, we propose a new taxonomy that reveals the technological nature of innovation. Unlike previous taxonomies employed to handle different types of technological innovations, our taxonomy does not consider the economic value of innovation alone; it is much more oriented towards societal preferences and forms of technological uncertainty. Finally, we investigate the coherence of our proposal with the dual nature of technological artefacts, showing that innovation can be grounded on structural and functional factors and not just on economic ones. (shrink)

In Thin objects: an abstractionist account (Oxford University Press, 2018), Øystein Linnebo claims that ‘mathematical objects are thin in the sense that very little is required for their existence’. Linnebo articulates his view in an abstractionist manner: according to Linnebo, the truth of the right‐hand side of a Fregean abstraction principle, which states that two items stand in a given equivalence relation, is sufficient for the truth of its left‐hand side, which states that the same abstract object is associated to (...) both items. This special issue contains nine articles discussing different aspects of Linnebo's book. In this introduction, we provide an opinionated introduction to the Special Issue and an overview of the contributions. (shrink)

According to constitutivism, we can justify the authority of aims and norms on the ground that they are inescapable. Constitutivist views divide between ambitious and modest ones. According to ambitious constitutivism, the inescapability of aims grounds their unconditional authority, whereas according to modest constitutivism, the inescapability of aims only grounds their conditional authority. Either way, both forms of constitutivism share the assumption that inescapability grounds authority, which in turn presupposes that at the foundation of normativity we find aims and norms (...) that can be evaluated as having or lacking authority. In this paper I shall defend a form of constitutivism that rejects this assumption. According to this view, which I shall call Hinge Constitutivism, at the foundation of epistemic normativity we find an aim, the truth-aim, that is altogether beyond the evaluation in terms of the ordinary notion of authority. Moreover, I shall argue that to aim at truth is a condition of possibility for justifying the authority of any other aims or norms. In this sense, to aim at truth is a hinge of deliberation. (shrink)

Epistemische Tugenden sind Eigenschaften des forschenden Subjekts, die in wissenschaftlichen Kulturen als Bedingung fur die Produktion, Vermittlung oder den Erwerb von Wissen angesehen werden. Sie lassen sich nicht auf ein abstraktes Sollen reduzieren, wie es oft von Ethikkommissionen oder politischen Bewegungen an die Wissenschaft herangetragen wird. Die methodische Erzeugung von Wissen ware kaum moglich, wenn es nicht erkenntnisfordernde Tugenden wie Geduld, Aufmerksamkeit, Genauigkeit, Intuition, Wahrhaftigkeit, Neugierde, Strenge oder Zuverlassigkeit gabe, die den an sich prekaren Erkenntnisprozess stabilisieren und in eine bestimmte (...) Richtung lenken. Die Beitrage dieses Sammelbandes befassen sich mit epistemischen Tugenden aus (wissenschafts-)historischer, philosophischer, medien- und literaturwissenschaftlicher Perspektive. Ein Schwerpunkt liegt dabei auf dem Verhaltnis von wissenschaftlichen und soziokulturellen beziehungsweise moralischen Normen. Mit Beitragen von: Lorraine Daston, Martin Doll, Andreas Gelhard, Raymond Geuss, Ruben Hackler, Michael Hagner, Jens Kertscher, Markus Krajewski, Marcel Lepper, Martin Mulsow, Oliver Nievergelt, Tanja Paulitz, Robert Proctor, Katja Sabisch, Sandro Zanetti, Cornelia Zumbusch. (shrink)

Contemporary views of truth-directedness endorse what I shall call the Common-Element Argument. According to this argument, there is something in common between judgment and other attitudes like assumption and imagination: they all regard their contents as true. Since this regarding-as-true feature is not distinctive of judgment - the argument goes - it can’t explain its truth-directedness. On this ground, theorists have been motivated to endorse an inflationary view that tries to capture truth-directedness by appealing to some further feature: intentions, second-order (...) representations, sub-personal mechanisms, or subjugation to norms are the most discussed candidates for fulfilling this role. In this paper I will argue that the Common-Element Argument is unsound. It rests on a false premise, namely that there is some common element such as a regarding-as-true component between judgment and other cognitive attitudes. I shall reject Velleman’s and Railton’s defenses of the Common-Element-Argument. Then I will discuss three influential inflationary accounts of truth-directedness: Railton’s account, Velleman’s teleological account, and Shah and Velleman’s conceptualist account. I shall argue that they all face a phenomenological and an explanatory challenge. Finally, I shall sketch a deflationary view of truth-directedness that evades these challenges. (shrink)

In this paper I discuss a new kind of hinge epistemology which is called transcendental hinge epistemology. According to this view, hinges are immune from doubt because it is impossible to doubt them coherently, and this impossibility arises because any attempt to doubt them will presuppose their truth. Such an immunity is possessed only by inescapable hinges, that is, hinges that must be presupposed in every inquiry. I will argue that current hinge epistemologies fail to provide a satisfactory anti-sceptical strategy (...) because they focus on escapable hinges, that is, hinges with respect to which one can entertain coherent doubts. (shrink)

The aim of this paper is to vindicate the Cartesian quest for certainty by arguing that to aim at certainty is a constitutive feature of cognition. My argument hinges on three observations concerning the nature of doubt and judgment: first, it is always possible to have a doubt as to whether p in so far as one takes the truth of p to be uncertain; second, in so far as one takes the truth of p to be certain, one is (...) no longer able to genuinely wonder whether p is true; third, to ask the question whether p is to desire to receive a true answer. On this ground I clarify in what sense certainty is the aim of cognition. I then argue that in judging that p we commit ourselves to p’s being certain and that certainty is the constitutive norm of judgment. The paper as a whole provides a picture of the interplay between doubt and judgment that aims at vindicating the traditional insight that our ability to doubt testifies our aspiration to know with absolute certainty. (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

In this paper, I present an interpretation of Wittgenstein's remarks on the experience of wonder at the existence of the world. According to this interpretation, Wittgenstein's feeling of wonder stems from perceiving the existence of the world as an absolute miracle, that is, as a fact that is in principle beyond explanation. Based on this analysis, I will suggest that Wittgenstein's experience is akin to what has been described by other authors such as Coleridge, Pessoa, Heidegger, Scheler, Sartre, and Hadot, (...) among many others. Through a comparison between Wittgenstein and Coleridge on the experience of existence, I shall highlight some core features of this experience, chief among them the use of the notion of nothingness in clarifying what is understood in the experience, the role of intuition, and the presence of a specific pathos. As a whole, this paper aims to provide a contribution to the project of a phenomenology of the experience of existence and intends to create a bridge for a dialogue between Wittgenstein and the phenomenological tradition on the enigma of existence. (shrink)

Abstraction principles and grounding can be combined in a natural way Modality: metaphysics, logic, and epistemology, Oxford University Press, Oxford, pp 109–136, 2010; Schwartzkopff in Grazer philosophische studien 82:353–373, 2011). However, some ground-theoretic abstraction principles entail that there are circles of partial ground :775–801, 2017). I call this problem auto-abstraction. In this paper I sketch a solution. Sections 1 and 2 are introductory. In Sect. 3 I start comparing different solutions to the problem. In Sect. 4 I contend that the (...) thesis that the right-hand side of an abstraction principle is prior to its left-hand side motivates an independence constraint, and that this constraint leads to predicative restrictions on the acceptable instances of ground-theoretic abstraction principles. In Sect. 5 I argue that auto-abstraction is acceptable unless the left-hand side is essentially grounded by the right-hand side. In Sect. 6 I highlight several parallelisms between auto-abstraction and the puzzles of ground. I finally compare my solution with the strategies listed in Sect. 3. (shrink)

Compromises are arrived at when, in spite of the efforts of those participating to mediate and defend their position in a rationally acceptable manner, each remains with his judgment while, at the same time, a decision must be made without further delay. What this means is that the parties agree to an option about which they are not, in their heart of hearts, entirely convinced. This article examines the notion of moral compromise, concentrating thereby on the case of political praxis. (...) It asks whether, in view of the complexity and multiplicity of morally relevant decisions encountered in a pluralist society, it is at all realistic to expect much else from political institutions than what Rawls dismissively refers to as a modus vivendi and whether a conception of justice that is true or reasonable only given the reasonable pluralism of comprehensive doctrines is still a conception of justice, and not simply a compromise between the contending doctrines. (shrink)

According to some Philosophy for Children theorists, the pedagogy of the Community of Inquiry hinges upon the acceptance of a pragmatist epistemology. The underlying idea is that it is possible to participate, and to justify participation, in a community of inquiry only if some pragmatist view of truth and knowledge is true and accepted by the participants engaged in dialogue. In this article we argue that this claim is false. In this way, we want to free the pedagogy of the (...) Community of Inquiry from some epistemological assumptions that we regard as unwarranted. To support our contention, we shall highlight two distinctions that are important in order to appreciate the connection between epistemology and education: first, the distinction between the disposition of intellectual humility and the belief in fallibilism; second, the belief in the existence of Cartesian certainties and the attitude of psychological certainty. Finally, we also argue that to vindicate dialogic inquiry it is neither necessary to adopt a pragmatist theory of truth, nor is it necessary to regard warranted judgement as the primary aim of inquiry. In contrast, we argue that truth is the aim of inquiry, and so is the aim of children when they participate in a dialogic inquiry. In this way we also suggest a justification of philosophy with children that does not instrumentalize it. (shrink)