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

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)

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.

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 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)

Unconscious processes, by whatever name they may be known , are invariably operationalized by the dissociation paradigm, any situation involving the dissociation between two indicators , one of availability and the other, of accessibility , such that, ε>α. Subliminal perception has been traditionally defined by a special case of the dissociation paradigm in which availability exceeds accessibility when accessibility is null . Construct validity issues bedevil all dissociation paradigms since it is not clear what might constitute appropriate indicators that, moreover, (...) are pure and exhaustive. Semantic and theoretic drifts in the recent literature—e.g., the confusion of different versions of the dissociation paradigm, the equation of conscious–unconscious with direct–indirect tests, and the foisting of the criterion of qualitative differences—have tended to undermine emerging theoretic parsimony. On the other hand, a crucial factor has been left out of theory development: time. Both ε and α can rise and fall over time, often asynchronously, and so dissociations may wax and wane and, even, reverse over time. Some laboratory evidence suggests that accessibility measures , as they approach chance, may actually dip below chance . If so, d′=0 , could be an averaging artifact of positive and negative d′s. Conscious accessibility is not either–or but more or less, and variable over time. (shrink)

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)

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)

Repression has become an empirical fact that is at once obvious and problematic. Fragmented clinical and laboratory traditions and disputed terminology have resulted in a Babel of misunderstandings in which false distinctions are imposed (e.g., between repression and suppression) and necessary distinctions not drawn (e.g., between the mechanism and the use to which it is put, defense being just one). “Repression” was introduced by Herbart to designate the (nondefensive) inhibition of ideas by other ideas in their struggle for consciousness. Freud (...) adapted repression to the defensive inhibition of “unbearable” mental contents. Substantial experimental literatures on attentional biases, thought avoidance, interference, and intentional forgetting exist, the oldest prototype being the work of Ebbinghaus, who showed that intentional avoidance of memories results in their progressive forgetting over time. It has now become clear, as clinicians had claimed, that the inaccessible materials are often available and emerge indirectly (e.g., procedurally, implicitly). It is also now established that the Ebbinghaus retention function can be partly reversed, with resulting increases of conscious memory over time (hypermnesia). Freud's clinical experience revealed early on that exclusion from consciousness was effected not just by simple repression (inhibition) but also by a variety of distorting techniques, some deployed to degrade latent contents (denial), all eventually subsumed under the rubric of defense mechanisms (“repression in the widest sense”). Freudian and Bartlettian distortions are essentially the same, even in name, except for motive (cognitive vs. emotional), and experimentally induced false memories and other “memory illusions” are laboratory analogs of self-induced distortions. Key Words: avoidance; Bartlett; defense; denial; distortion; Ebbinghaus; false-memories; Freud; inhibition; repression; suppression. (shrink)

Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *-independence is equivalent to (...) operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised. (shrink)

In diesem Aufsatz erläutere ich Leibniz' Versuche, seinen Infinitesimalkalkül zu rechtfertigen. Die Untersuchung zielt ab auf ein klareres Verständnis, wie tief Leibniz die Begriffe, Ziele und Methoden im Hinblick auf das fragliche Problem faßte. Mein Überblick ist in zwei Teile gegliedert. Der erste stellt die Definition und den Gebrauch einiger Leibnizscher Begriffe dar, die bei der Rechtfertigung des Calculus eine wichtige Rolle spielen. Im zweiten skizziere ich, auf welche Weise Leibniz die Infinitesimalrechnung zu rechtfertigen versuchte.

Relativistic locality is interpreted in this paper as a web of conditions expressing the compatibility of a physical theory with the underlying causal structure of spacetime. Four components of this web are distinguished: spatiotemporal locality, along with three distinct notions of causal locality, dubbed CL-Independence, CL-Dependence, and CL-Dynamic. These four conditions can be regimented using concepts from the categorical approach to quantum field theory initiated by Brunetti, Fredenhagen, and Verch (2003). A covariant functor representing a general quantum field theory is (...) defined to be causally local if it satisfies the three CL conditions. Any such theory is viewed as fully compliant with relativistic locality. We survey current results indicating the extent to which an algebraic quantum field theory satisfying the Haag–Kastler axioms is causally local. (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)

We prove that it is decidable of a finite algebra whether it has a near-unanimity term operation, which settles a ten-year-old problem. As a consequence, it is decidable of a finite algebra in a congruence distributive variety whether it admits a natural duality.

Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection 1 of finite algebras of the same signature, , such that SP( 1) is finitely axiomatizable.We show also that if , then SP( 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)

Reichenbach’s Common Cause Principle is the claim that if two events are correlated, then either there is a causal connection between the correlated events that is responsible for the correlation or there is a third event, a so called (Reichenbachian) common cause, which brings about the correlation. The paper reviews some results concerning Reichenbach’s notion of common cause, results that are directly relevant to the problem of how one can falsify Reichenbach’s Common Cause Principle. Special emphasis will be put on (...) the question of whether EPR-type correlations can have an explanation in terms of Reichenbachian common causes. Most of the results to be recalled indicate that falsifying Reichenbach’s Common Cause Principle is much more tricky than one may have thought and that, contrary to some claims in the literature, there is no conclusive proof yet that the EPR correlations predicted by ordinary, non-relativistic quantum mechanics cannot have a common cause; furthermore, recent results about possible Reichenbachian common causes of correlations predicted by quantum field states between spacelike separated local observable algebras in algebraic quantum field theory strongly indicate that there may very well exist Reichenbachian common causes of superluminal correlations predicted by quantum field theory. (shrink)

If $\mathcal{A}$ (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $\mathcal{A}$ (V 1 ), B∈ $\mathcal{A}$ (V 2 ) correlated in the normal state φ there exists a projection C (...) belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2 , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle. (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.

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V1) andA(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the (...) vacuum state between events inA(V1) andA(V2) have a genuinely probabilistic common cause, then the local algebrasA(V1) andA(V2) must be statistically independent in the sense of C*-independence. (shrink)

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)

We investigate the general properties of general Bayesian learning, where ``general Bayesian learning'' means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...) a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes' rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

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)

John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections (...) focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history. (shrink)

The purpose of this study is to demonstrate that the teaching of Clement of Alexandria on marriage is closely related to the author’s soteriology and cosmology. The study focuses on the Third Book of Stromateis, which provides insight into the different Christian views on marriage at the end of the second century. Study of the Third Book of Stromateis also reveals Clement’s unique method of argument, by means of which he corrects the theological positions of his opponents. Last but not (...) least, Clement’s discussions of family life provide a window onto the social life of the Late Empire from the point of view of a second-century Christian philosopher. (shrink)