A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition (...) of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle. (shrink)

The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the common cause principle, by proving results (...) that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field. (shrink)

A partition $\{C_i\}_{i\in I}$ of a Boolean algebra $\cS$ in a probability measure space $(\cS,p)$ is called a Reichenbachian common cause system for the correlated pair $A,B$ of events in $\cS$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set $I$ is called the size of the common cause system. It is shown that given any correlation in $(\cS,p)$, and given any finite size $n>2$, the probability space (...) $(\cS,p)$ can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size $n$ for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of \cS$ contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated. (shrink)

A partition $\{C_i\}_{i\in I}$ of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite (...) natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. (shrink)

We show that various fragments of the intuitionistic/constructive theory of the reals are decidable.

Let $L = \langle, +, h_q, 1\rangle_{q \in \mathbb{Q}}$ where $\mathbb{Q}$ is the set of rational numbers and $h_q$ is a one-place function symbol corresponding to multiplication by $q$. Then the $L$-theory of Scott's model for intuitionistic analysis is decidable.

Based on the paper [4] we show that true second‐order arithmetic is interpretable over the real‐algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras.

We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.

We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows.

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities (...) on probability zero events in the Borel–Kolmogorov Paradox also can be calculated using conditional expectations. The alleged clash arising from the fact that one obtains different values for the conditional probabilities on probability zero events depending on what conditional expectation one uses to calculate them is resolved by showing that the different conditional probabilities obtained using different conditional expectations cannot be interpreted as calculating in different parametrizations of the conditional probabilities of the same event with respect to the same conditioning conditions. We conclude that there is no clash between the correct intuition about what the conditional probabilities with respect to probability zero events are and the technically proper concept of conditionalization via conditional expectations—the Borel–Kolmogorov Paradox is just a pseudo-paradox. (shrink)

Review by: Maté Szabó The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 110-112, March 2013.

Anything other than paraphrasing the well-known Heraclitean aphorism would not be more appropriate to portray the crux of the contribution of the three philosophers of the Budapest School, Gábor Hofer-Szabó, Miklós Rédei and Lázló E. Szabó, in the ongoing discussion of the principle of the common cause . Indeed, ‘common causes love to hide’ and for that reason critics and aspirant falsifiers of PCC find correlations which, at a first level of analysis, might lack a common cause (...) explanation. But as the authors argue such correlations do not amount to disconfirming evidence for the principle, since PCC does not specify where to search for a common cause of a correlation; it just states that there is one. PCC is neither falsifiable, nor verifiable; it is a metaphysical doctrine that can only be assessed for its plausibility in the light of theories of empirical science. This idea fosters the investigation of the existence of common causes of correlations in two fundamental physical t .. (shrink)

…entities? 2. How to be a nominalist 2.1. “Speak with the vulgar …” 2.2. “…think with the learned” 3. Arguments for nominalism 3.1. Intelligibility, physicalism, and economy 3.2. Causal..

This chapter describes how philosophical theorizing about justice can be connected with empirical research in the social sciences. We begin by drawing on some received distinctions between ideal and non-ideal approaches to theorizing justice along several different dimensions, showing how non-ideal approaches are needed to address normative aspects of real-world problems and to provide practical guidance. We argue that there are advantages to a transitional approach to justice focusing on manifest injustices, including the fact that it enables us to set (...) aside some reasonable disagreements about justice. The ‘bottom-up’ approach we advocate, for which we borrow Wolff’s term ‘real-world political philosophy’, is an empirically-informed normative analysis that attends to specific, identifiable injustices, and thus is partial, though not isolationist. We illustrate our approach by considering how different models of the nature of disability suggest different kinds of remedy for injustices faced by persons living with disabilities. We reflect on the nature and significance of vulnerabilities, and we assess the role of public opinion in normative theorizing, suggesting a particular significance for the opinions and experiences of marginalized groups. We finally reflect on the relevance of European legal and institutional frameworks for theorizing justice in Europe. (shrink)

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document} be a finite collection of finite algebras of finite signature such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}) has meet semi-distributive congruence lattices. We prove that there exists a finite collection \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1 of finite algebras of the same signature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}_1 \supseteq (...) \mathcal{K}$$ \end{document}, such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable.We show also that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$HS(\mathcal{K}) \subseteq SP(\mathcal{K})$$ \end{document}, then SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates. (shrink)

Most philosophers believe that a person can have an obligation only insofar as she is able to fulfil it, a principle generally referred to as “Ought Implies Can”. Arguably, this principle reflects something basic about the ordinary concept of obligation. However, in a paper published recently in this journal, Wesley Buckwalter and John Turri presented evidence for the conclusion that ordinary people in fact reject that principle. With a series of studies, they claimed to have demonstrated that, in people’s judgements, (...) obligations persist irrespective of whether those who hold them have the ability to fulfil them. We argue in this paper that due to some problems in their design, Buckwalter & Turri’s conclusions may not be war- ranted. We present the results of a series of studies demonstrating the problems with their design and showing that, with an improved design, people judge that obligation depends on ability after all. (shrink)

Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic second-order sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain "built-in" relations, such as the successor relation). The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence.

Knowledge ascriptions seem context sensitive. Yet it is widely thought that epistemic contextualism does not have a plausible semantic implementation. We aim to overcome this concern by articulating and defending an explicit contextualist semantics for ‘know,’ which integrates a fairly orthodox contextualist conception of knowledge as the elimination of the relevant alternatives, with a fairly orthodox “Amherst” semantics for A-quantification over a contextually variable domain of situations. Whatever problems epistemic contextualism might face, lack of an orthodox semantic implementation is not (...) among them. (shrink)

This paper argues for a reappraisal of extant scholarship on delegation in the domain of financial regulation. Through an examination of Japan's experience with financial regulation between 1992 and 2003, it is demonstrated that crisis-induced institutional development entails a shift toward a more flexible, trustee-type bureaucratic structure. While the logic presented in this paper is far from a universally applicable theory of institutional change, it calls into question the relevance of more conventional approaches to the origins of delegation of authority, (...) notably the approach that uses unified and divided government as a key variable. A renewed emphasis on the role of extra-political sources of transfers of authority inside the executive, and also between the legislature and the executive, therefore, is in order. (shrink)

Contemporary Complex Cinema. Complex conditions: the resurgence of narrative complexity ; Complex cinema as brain-candy for the empowered viewer ; Narrative taxonomies: simple, complex, puzzle plots -- Cognitive Approach to Contemporary Complex Cinema. Why an (embodied-)cognitive approach? ; Various forms of complexity and their effects on sense making ; Problematizing narrative linearity ; Complicating narrative structures and ontologies ; Under-stimulation and cognitive overload ; Contradictions and unreliabilities ; A cognitive approach to classifying complexity ; Deceptive unreliability and the twist film (...) ; Disorienting but solvable puzzle films ; Impossible puzzle films -- Narrative Complexity and Dissonant Cognitions. The concept of cognitive dissonance ; Cognitions in dissonance: from social psychology to narrative engagement ; Types of dissonance in narrative comprehension ; Narrative incongruities ; Narrative impossibilities ; Cognitive access to impossible storyworlds: immersed and reflected operations ; 'Impossibilities' and embodied cognition ; Disrupting viewers' reliance on image schemas by perceptual impossibility ; Disrupting viewers' reliance on image schemas by formal impossibility -- Taming Dissonance: Cognitive Operations and Interpretive Strategies. Cognitive dissonance versus narrative coherence ; Reducing dissonance: interpretation and naturalization ; Foregrounding ; Narrating agency and authorship ; Artefact emotions and metareflexive appreciation ; Interpretation as dissonance reduction ; Coping with dissonance: frame-switches and poetic and aesthetic readings ; Frame-switching as hermeneutic play in impossible puzzle films ; Switching between narrative and symbolical readings: Enemy and Mulholland Drive ; Cognitive hesitation and the fantastic -- Impossible Puzzle Films: Between Art-Cinema and (Post-) Classical Narration. From art-cinema to puzzle films ; Art-cinema as a narrative mode ; Dissonance in modernist art-cinema ; Art-cinema as a cognitive reception frame ; Narrative complexity and meaning-making in art-cinema ; Impossible puzzle films and (post-)classical narration ; High degree of tellability ; Identification with goal-oriented characters ; Strong reliance on classical genre elements ; Adherence to classical narrative cohesion devices ; Inclusion of quasi-rational frames of naturalization -- Wallowing in Dissonance: The Attractiveness of Impossible Puzzles. Hermeneutic play and interpretive multiplicity ; Orientation, navigation, mapping ; Game logic and the fascination in failure ; Effort justification ; Diegetization of decoupling ; Fascination in infinity ; Destabilized ontological certainty ; Eudaimonic motivations and intrinsic needs. (shrink)

In this paper, I critically analyze Andrea Sangiovanni’s approach to international justice in the EU that he labels Reciprocity-based Internationalism (RBI). I aim to show that the type of reciprocity RBI operates with is not a morally attractive ground for distributive justice because it cannot cope with the case of member states’ inability to reciprocate the production of collective goods at the EU level. I illustrate this with the case of disability. I contrast RBI’s understanding of reciprocity with Christie Hartley’s (...) ‘relationship model’. I argue that the relationship model of reciprocity should characterize the EU, whose two core normative features are fraternity and equal status. The advantage of the relationship model is that it calls for a stronger type of solidarity than RBI does. That not only entails the willingness to support those worse-off members that cannot productively reciprocate other member states’ efforts at the EU level but also calls for a higher redistribution rate within the EU. In the paper, I make three comparisons between RBI’s ‘productive reciprocity’ and the relationship model. The first concerns non-EU-integration-related disadvantages; the second concerns membership cases, such as accession to federations and supranational unions, while the third comparison examines EU-integration-related disadvantages. I argue that the relationship model is a better alternative to RBI in both integration-related and non-integration-related disadvantages. Also, the relationship model can justify accession cases where previous historical ties are relevant, which are outside of the purview of RBI. (shrink)

Moti Mizrahi provides experimental evidence according to which subjects judge that a person ought to ? even when she cannot ?. He takes his results to constitute a falsification of the alleged intuitiveness of the ‘Ought Implies Can’ principle. We point out that in the light of the fact that (a) ‘ought’ is multiply ambiguous, that (b) only a restricted set of readings of ‘ought’ will be relevant to the principle, and that (c) he did not instruct his subjects appropriately (...) – or otherwise ensure that in their ‘ought’ judgements they applied the relevant concept(s) – Mizrahi’s conclusions appear premature. We suggest two ways in which the experimental design could be adjusted or supplemented. First, Mizrahi could instruct (or prime) subjects to read the ‘ought’ question in a particular way. Second, he could complement his experiment by asking follow-up questions aimed at uncovering the implications for blame of subjects’ judgements. Once these adjustments are applied, an experiment with a similar outcome would be more significant. (shrink)

It is known that every α-dimensional quasi polyadic equality algebra (QPEA α ) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties . The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally equivalent to QPEA. It is shown, among others, that from every (...) algebra in a β-dimensional algebra can be obtained in QPEA β where , moreover the algebra obtained is representable in a sense. (shrink)

I will argue that Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality since, for the argument to be effective, operators must be uniquely associated with measur...

Mutually beneficial exchanges in markets can be exploitative because one party takes advantage of an underlying injustice. For instance, employers of sweatshop workers are often accused of exploiting the desperate conditions of their employees, although the latter accept the terms of their employment voluntarily. A weakness of this account of exploitation is its tendency for over-inclusiveness. Certainly, given the prevalence of global and domestic socioeconomic inequalities, not all exchanges that take place against background injustices should be considered exploitative. This paper (...) offers a framework to identify exploitation in mutually beneficial exchange, focusing on the case of sweatshop labor. It argues that an employer can be viewed as taking unfair advantage of an underlying injustice if and only if the employer’s surplus from the exchange in the unjust state of affairs exceeds the surplus it could maximally obtain in a just state of affairs. The paper illustrates the applicability of this framework using three different conceptions of justice and argues that it is superior to microlevel accounts of exploitation that regard background justice as irrelevant. The paper concludes by describing some normative implications that follow from judging an exchange exploitative. (shrink)

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism model (...) for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments. (shrink)

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a ‘common causal justification’ of these non-classical Bell inequalities is possible. We will show that although (...) the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities. (shrink)

Our paper consists of three parts. In the first part we explain the concept of mental fictionalism. In the second part, we present the various versions of fictionalism and their main sources of motivation.We do this because in the third part we argue that mental fictionalism, as opposed to other versions of fictionalism, is a highly undermotivated theory.

Leading scholars in the philosophy of language and theoretical linguistics present brand-new papers on a major topic at the intersection of the two fields, the distinction between semantics and pragmatics. Anyone engaged with this issue in either discipline will find much to reward their attention here. Contributors: Kent Bach, Herman Cappelen, Michael Glanzberg, Jeffrey C. King, Ernie Lepore, Stephen Neale, F. Recanati, Nathan Salmon, Mandy Simons, Scott Soames, Robert J. Stainton, Jason Stanley, Zoltan Gendler Szabo.

In this paper, we provide a comprehensive survey of the space of possible analyses of the phenomenon of quantifier domain restriction, together with a set of considerations which militate against all but our own proposal. Among the many accounts we consider and reject are the ‘explicit’ approach to quantifier domain restric‐tion discussed, for example, by Stephen Neale, and the pragmatic approach to quantifier domain restriction proposed by Kent Bach. Our hope is that the exhaustive discussion of this special case of (...) context‐dependence will provide guidelines for how to decide, for an arbitrary case of context‐dependent discourse, whether it should be treated syntactically, semantically, or pragmatically. (shrink)

This paper develops an account of how economic and political institutions can limit the applicability of principles of justice even in non-relational cosmopolitan conceptions. It shows that fundamental principles of justice underdetermine fair distributive shares as well as justice -based requirements. It argues that institutions partially constitute the content of justice by determining distributive shares and by resolving indeterminacies about justice -based requirements resulting from strategic interaction and disagreement. In the absence of existing institutions principles of justice might not be (...) applicable for assessing distributions or guiding individual action and institutional design. Hence, accepting a specific cosmopolitan conception of justice is insufficient to settle global distributive questions. (shrink)

Rorty on Politics, Culture, and Philosophy: A Defence of his Romanticism Rorty's historicist romanticism is a peculiar and oft criticized feature of his neopragmatism. I attempt to show that it should be regarded not so much as a more or less exceptionable philosophical approach, but rather, as a practice in ‘cultural politics’—which is his ultimate definition for philosophy—prompted by his acute political concerns and his views on the nature of moral progress.

Cognitive control is a set of mechanisms that help us process conflicting stimuli and maintain goal-relevant behaviour. According to the Affective Signalling Hypothesis, conflicting stimuli are aversive and thus elicit (negative) affect, moreover – to avoid aversive signals – affective and cognitive systems work together by increasing control and thus, drive conflict adaptation. Several studies have found that affective stimuli can indeed modulate conflict adaptation, however, there is currently no evidence that phasic affective states not triggered by conflict also trigger (...) improved cognitive control. To investigate this possibility, we intermixed trials of a conflict task and trials involving the passive viewing of emotional words. We tested whether affective states induced by affective words in a given trial trigger improved cognitive control in a subsequent conflict trial. Applying Bayesian analysis, the results of four experiments supported the lack of adaptation to aversive signals, both in terms of valence and arousal. These results suggest that phasic affective states by themselves are not sufficient to elicit an increase in control. (shrink)

The problem of imaginative resistance holds interest for aestheticians, literary theorists, ethicists, philosophers of mind, and epistemologists. We present a somewhat opinionated overview of the philosophical discussion to date. We begin by introducing the phenomenon of imaginative resistance. We then review existing responses to the problem, giving special attention to recent research directions. Finally, we consider the philosophical significance that imaginative resistance has—or, at least, is alleged to have—for issues in moral psychology, theories of cognitive architecture, and modal epistemology.