In a recent paper, Jeanne Peijnenburg and David Atkinson [ Studia Logica, 89:333-341 ] have challenged the foundationalist rejection of infinitism by giving an example of an infinite, yet explicitly solvable regress of probabilistic justification. So far, however, there has been no criterion for the consistency of infinite probabilistic regresses, and in particular, foundationalists might still question the consistency of the solvable regress proposed by Peijnenburg and Atkinson.

The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in mind is (...) not as hopeless as it appears to be in his article. In fact, for many practically important examples, through the use of likelihoods one can succeed in circumventing the zero-fit problem. 1 The Zero-fit Problem on Infinite State Spaces 2 Elga's Critique of the Infinitesimal Approach to the Zero-fit Problem 3 Two Examples for Infinitesimal Solutions to the Zero-fit Problem 4 Mathematical Modelling in Nonstandard Universes? 5 Are Nonstandard Models Unnatural? 6 Likelihoods and Densities A Internal Probability Measures and the Loeb Measure Construction B The (Countable) Coin Tossing Sequence Revisited C Solution to the Zero-fit Problem for a Finite-state Model without Memory D An Additional Note on ‘Integrating over Densities’ E Well-defined Continuous Versions of Density Functions. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...) aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.

This article establishes the existence of a definable , countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers . The underlying ultrafilter is the one constructed by Kanovei and Shelah [10].

This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification (...) has rather unwelcome consequences—formally resembling the Sorites paradox—as soon as it is iterated and combined with a natural Bayesian perspective on probabilistic inferences. We conclude that strong versions of foundationalism and infinitism should be abandoned. Positively, we provide a rough sketch for a graded formal coherence notion, according to which infinite regresses of epistemic justification will often have more than a minimal degree of coherence. (shrink)

The defence of The No Alternatives Argument in a recent paper by R. Dawid, S. Hartmann and J. Sprenger rests on the assumption that the number of acceptable alternatives to a scientific hypothesis is independent of the complexity of the scientific problem. This note proves a generalisation of the main theorem by Dawid, Hartmann and Sprenger, where this independence assumption is no longer necessary. Some of the other assumptions are also discussed, and the limitations of the no-alternatives argument are explored.

Łoś's theorem for bounded D -ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [4], is established.

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Cerreia-Vioglio et al. :341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory, is employed.

Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, (...) formal epistemology has so far only been concerned with one particular—arguably not even very natural—way of formalising coherence of belief systems; it has by no means refuted the viability of coherentism. In contrast to the existing literature, we formalise belief systems as families of assignments of (conditional) degrees of belief (which may be compatible with several subjective probability measures). Within this framework, we propose a Bayesian formalisation of the thrust of BonJour’s coherence concept in The structure of empirical knowledge (Harvard University Press, Cambridge, 1985), using a combination of Bayesian confirmation theory and basic graph theory. In excursions, we introduce graded notions for both logical and probabilistic consistency of belief systems—the latter being based on certain geometrical structures induced by probabilistic belief systems. For illustration, we reconsider BonJour’s “ravens” challenge (op. cit., p. 95f.). Finally, potential objections to our proposed formal coherence notion are explored. (shrink)

This note employs the recently established consistency theorem for infinite regresses of probabilistic justification (Herzberg in Stud Log 94(3):331–345, 2010) to address some of the better-known objections to epistemological infinitism. In addition, another proof for that consistency theorem is given; the new derivation no longer employs nonstandard analysis, but utilises the Daniell–Kolmogorov theorem.

We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we investigate what (...) Herzberg means by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non , and we ventilate our misgivings about Herzberg’s suggestion that the notion of solvability might help the foundationalist. (shrink)

Recent studies on mind‐wandering reveal its potential role in goal exploration and planning future actions. How to understand these explorative functions and their impact on planning remains unclear. Given certain conceptions of intentions and beliefs, the explorative functions of mind‐wandering could lead to regular reconsideration of one's intentions. However, this would be in tension with the stability of intentions central to rational planning agency. We analyze the potential issue of excessive reconsideration caused by mind‐wandering. Our response resolves this tension, presenting (...) a model that aligns the roles of mind‐wandering in planning with empirical evidence and the sustained stability of intentions. (shrink)

Aristoteles' Ethik gipfelt bekanntlich in der Lehre, dass das vollkommene Glück in der betrachtenden oder kontemplativen Lebensform (bios theoretikos) besteht. In diesem kognitiven Vollzug zeigt sich der Mensch als mit der an Seligkeit herausragenden Tätigkeit Gottes am nächsten verwandt. Auch wenn der Begriff der Kontemplation (theoria) sowohl für Aristoteles' Glückskonzeption als auch für seine Gotteslehre eine zentrale Rolle spielt, so ist es alles andere als klar, was genau mit diesem Begriff gemeint ist: Worin genau besteht dieser kognitive Vollzug und was (...) ist sein Gegenstand? Steht diese Tätigkeit überhaupt noch in einem Zusammenhang mit der Natur des Menschen? Vollziehen Gott und Mensch dieselbe Art von theoria nur in einem unterschiedlichen zeitlichen Ausmass oder ist der Unterschied tiefgreifender? Die vorliegende Abhandlung unterzieht diesen für Aristoteles' Ethik und philosophische Theologie zentralen Begriff einer grundlegenden Analyse."--Publisher's website. (shrink)

Frederik L. Schodt explores his lifelong fascination with the Heart Sutra: its mesmerizing mantra, its ancient history, the 'emptiness' theory, and the way it is used around the world as a metaphysical tool to overcome chaos and confusion and reach a new understanding of reality--a perfection of wisdom."--Back cover.

Abstract:T.L. Short’s Charles Peirce and Modern Science, in which he discusses Peirce’s intimate relation to modern science, simultaneously functions as Short’s own philosophical testament. Short’s overall argument is that Peirce takes inquiry to be the main definition of science, implying that all other definition attempts or central issues of science are but products of inquiry: methods, experiments, observations, conclusions, results, syntheses, theory buildings, system constructions, laws, predictions, metaphysical assumptions, scientific values, etc. On this basis, Short develops central Peircean ideas such (...) as inquiry into inquiry, phenomenology, and his “normative sciences” as elements of a reinvigorated and metaphysically ambitious version of empiricism. In this process, however, certain problems appear, such as Short’s tendency to refute any relevance in scientific investigations of systematicity, the a priori, the strive for conclusions and results. (shrink)

Current European innovation and security policies are increasingly channeled into efforts to address the assumed challenges that threaten European societies. A field in which this has become particularly salient is digitized EU border management. Here, the framework of responsible research and innovation (RRI) has recently been used to point to the alleged sensitivity of political actors towards the contingent dimensions of emerging security technologies. RRI, in general, is concerned with societal needs and the engagement and inclusion of various stakeholder groups (...) in the research and innovation processes, aiming to anticipate undesired consequences of and identifying socially acceptable alternatives for emerging technologies. However, RRI has also been criticized as an industry-driven attempt to gain societal legitimacy for new technologies. In this article, we argue that while RRI evokes a space where different actors enter co-creative dialogues, it lays bare the specific challenges of governing security innovation in socially responsible ways. Empirically, we draw on the case study of BODEGA, the first EU funded research project to apply the RRI framework to the field of border security. We show how stakeholders involved in the project represent their work in relation to RRI and the resulting benefits and challenges they face. The paper argues that applying the framework to the field of (border) security lays bare its limitations, namely that RRI itself embodies a political agenda, conceals alternative experiences by those on whom security is enacted upon and that its key propositions of openness and transparency are hardly met in practice due to confidentiality agreements. Our hope is to contribute to work on RRI and emerging debates about how the concept can (or cannot) be contextualized for the field of security—a field that might be more in need than any other to consider the ethical dimension of its activities. (shrink)

This book investigates a number of central problems in the philosophy of Charles Peirce grouped around the realism of his semiotics: the issue of how sign systems are developed and used in the investigation of reality. Thus, it deals with the precise character of Peirce's realism; with Peirce's special notion of propositions as signs which, at the same time, denote and describe the same object. It deals with diagrams as signs which depict more or less abstract states-of-affairs, facilitating reasoning about (...) them; with assertions as public claims about the truth of propositions. It deals with iconicity in logic, the issue of self-control in reasoning, dependences between phenomena in their realist descriptions. A number of chapters deal with applied semiotics: with biosemiotic sign use among pre-human organisms: the multimedia combination of pictorial and linguistic information in human semiotic genres like cartoons, posters, poetry, monuments. All in all, the book makes a strong case for the actual relevance of Peirce's realist semiotics. (shrink)

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. 11 EUCh. (...) These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)

We characterise the intermediate logics which admit a cut-free hypersequent calculus of the form \, where \ is the hypersequent counterpart of the sequent calculus \ for propositional intuitionistic logic, and \ is a set of so-called structural hypersequent rules, i.e., rules not involving any logical connectives. The characterisation of this class of intermediate logics is presented both in terms of the algebraic and the relational semantics for intermediate logics. We discuss various—positive as well as negative—consequences of this characterisation.

This paper discusses the uniqueness thesis, a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement. Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

Indledning -- Nihilisme. Kunst ; Uddannelse ; Ontologi -- Ontologi. Musik ; Musikdidaktik ; Pædagogik -- Konklusion.

Artifacts are probably our most obvious everyday encounter with technology. Therefore, a good understanding of the nature of technical artifacts is a relevant part of technological literacy. In this article we draw from the philosophy of technology to develop a conceptualization of technical artifacts that can be used for educational purposes. Furthermore we report a small exploratory empirical study to see to what extent teachers’ intuitive ideas about artifacts match with the way philosophers write about the nature of artifacts. Finally, (...) we suggest a teaching and learning strategy for improving teachers’ concepts of technical artifacts through practical activities. (shrink)

This article sets out to research and resolve the conceptual lag between the family as defined and recognised in law and the multiplicity of queer constellations of ‘intimate citizenship’ in which families are actually done. The focus is on adult unions outside of conjugal coupledom. The family law practices, and awareness and expectations of adults in such unions were analysed through 21 interviews and the content analysis of 40 documents and were projected against the applicable legal mould. The article then (...) proposes to resolve the existing conceptual lag by advancing a conception of the family as a malleable, open-ended assemblage, in lieu of the current rigid status approach in family law, which is both under- and overinclusive. The proposed conception does justice to the increasing fluidity of family formations, which are not always already domestic, dyadic and sexual. (shrink)

SUMMARYThe history of the law of nations is generally seen as a synonym for the history of the laws of war. Yet, a strictly bilateral perspective can distort our interpretation of early modern diplomacy. The Peace of Utrecht inaugurated an era of relative stability in the European state system, based on balance-of-power politics and anti-hegemonic legal argumentation. Incidental conflicts ought to be interpreted against this background. Declarations of war issued in 1718, 1719 and 1733 during the War of the Quadruple (...) Alliance and the Polish Succession should not be read as doctrinal surrogates for trials between two parties, but as manifestos in a European arena. (shrink)