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.

In this paper, I am going to offer a reconstruction of a challenge to intuition-based armchair philosophy that has been put forward by experimental philosophers of a restrictionist stripe, which I will call the 'master argument'. I will then discuss a number of popular objections to this argument and explain why they either fail to cast doubt on its first, empirical premise or do not go deep enough to make for a lasting rebuttal. Next, I will consider two more promising (...) objections, the grounding objection and the expertise objection, which aim at the second, epistemic premise of the argument. Against this background, I will then suggest what I call 'conservative restrictionism' as the most reasonable default reaction to the experimentalist challenge, which is a combination of the two views of local restrictionism and methodological conservativism. (shrink)

Philosophical analysis was the central preoccupation of 20th-century analytic philosophy. In the contemporary methodological debate, however, it faces a number of pressing external and internal challenges. While external challenges, like those from experimental philosophy or semantic externalism, have been extensively discussed, internal challenges to philosophical analysis have received much less attention. One especially vexing internal challenge is that the success conditions of philosophical analysis are deeply unclear. According to the standard textbook view, a philosophical analysis aims at a strict biconditional (...) that captures the necessary and sufficient conditions for membership in the relevant category. The textbook view arguably identifies a necessary condition on successful philosophical analyses, but understood as a sufficient condition it is untenable, as I will argue in this paper. To this end, I first uncover eight conditions of adequacy on successful philosophical analyses, some of which have rarely been spelled out in detail. As we shall see, even sophisticated alternatives to the textbook view fail to accommodate some of these conditions. I then propose the concept grounding view as a more promising account of philosophical analysis. According to this view, successful philosophical analyses require necessary biconditionals that are constrained by grounding relations among the concepts involved. Apart from providing a satisfactory account of philosophical analysis in its own right, the concept grounding view is also able to meet the challenge that the success conditions of philosophical analysis are problematically unclear. (shrink)

This chapter proceeds from the standard picture of the relation between intuitions and experimental philosophy: the alleged evidential role of intuitions about hypothetical cases, and experimental philosophy’s challenge to these judgments, based on their variation with philosophically irrelevant factors. I will survey some of the main defenses of this standard picture against the x-phi challenge, most of which fail. Concerning the most popular defense, the expertise defense, I will draw the bleak conclusion that intuitive expertise of the envisaged kind is (...) largely a myth. Next, I will consider the mischaracterization objection, which has mainly been developed by Deutsch and Cappelen on the basis of textual evidence: that philosophers do not appeal to intuitions as evidence for their case judgments, but instead argue for them. This would render the x-phi challenge mostly irrelevant, due to its focus on intuitions about hypothetical cases. I will then consider a few instructive replies to the mischaracterization objection, which are all unconvincing on further inspection. Finally, I will discuss some potential normative consequences of the mischaracterization objection, and I will argue that it recommends a shift away from the excessive focus on intuitions about cases in metaphilosophy and experimental philosophy, towards more work on the role of argumentation in the method of cases. More speculatively, I claim that philosophers should always argue for their case judgments, even if they have strong intuitions about them, because an argument-based methodology would be more transparent and philosophically fruitful than one that mainly relies on intuition. (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)

By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff–von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in their 1936 paper that (...) the quantum propositional system should be isomorphic to an abstract projective geometry. Looking at the paper now I see, that I forgot to say this, which should be said somewhere in the first §: That while common logics did apply to quantum mechanics, if the notion of simultaneous measurability is introduced as an auxiliary notion, we wished to construct a logical system, which applies directly to quantum mechanics – without any extraneous secondary notions like simultaneous measurability. And in order to have such a consequent, one-piece system of logics, we must change the classical class calculus of logics. (J. von Neumann to G. Birkhoff, November 21, 1935). (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 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)

The traditional epistemological approach towards judgments like BACHELORS ARE UNMARRIED or ALL KNOWLEDGE IS TRUE is that they are justified or known on the basis of understanding alone. In this paper, I develop an understanding-based account which takes understanding to be a sufficient source of epistemic justification for the relevant judgments. Understanding-based accounts face the problem of the rational revisability of almost all human judgments. Williamson has recently developed a reinforced version of this problem: the challenge from expert revisability. This (...) is the problem that even the best candidate judgments for understanding-based justification can be rationally rejected by the relevant experts, who may not even have any disposition or inclination to accept these judgments. However, I argue that expert revisability is fully compatible with the proposed understanding-based epistemology, because expert revisability is true of sufficient sources of epistemic justification in general. A remaining metaphysical worry is that understanding might end up being ‘too thin’ to play the envisaged epistemological role. This worry can be countered with a novel metaphysics of understanding involving second-order dispositions. (shrink)

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)

Abstract:Alasdair Maclntyre (1984) asserts that the ethical systems of the Enlightenment (formalism and utilitarianism) have failed to provide a meaningful definition of “good.” Lacking such a definition, business managers have no internal standards by which they can morally evaluate their roles or acts. Maclntyre goes on to claim that managers have substituted external measures of “winning” or “effectiveness” for any internal concept of good. He supports a return to the Aristotelian notion of virtue or “excellence.” Such a system of virtue (...) ethics depends on an interrelationship of the community, one’s roles in that community, and the virtues one needs to perform that role well. This article develops Maclntyre’s concept of virtue ethics and shows how this paradigm fits well with existing theories about organizational behavior. (shrink)

According to the ‘expertise defence’, experimental findings suggesting that intuitive judgments about hypothetical cases are influenced by philosophically irrelevant factors do not undermine their evidential use in (moral) philosophy. This defence assumes that philosophical experts are unlikely to be influenced by irrelevant factors. We discuss relevant findings from experimental metaphilosophy that largely tell against this assumption. To advance the debate, we present the most comprehensive experimental study of intuitive expertise in ethics to date, which tests five well- known biases of (...) judgment and decision-making among expert ethicists and laypeople. We found that even expert ethicists are affected by some of these biases, but also that they enjoy a slight advantage over laypeople in some cases. We discuss the implications of these results for the expertise defence, and conclude that they still do not support the defence as it is typically presented in (moral) philosophy. (shrink)

Experimental philosophy is one of the most recent and controversial developments in philosophy. Its basic idea is rather simple: to test philosophical thought experiments and philosophers’ intuitions about them with scientific methods, mostly taken from psychology and the social sciences. The ensuing experimental results, such as the cultural relativity of certain philosophical intuitions, has engaged – and at times infuriated – many more traditionally minded "armchair" philosophers since then. In this volume, the metaphilosophical reflection on experimental philosophy is brought yet (...) another step forward by engaging some of its most renowned proponents and critics in a lively and controversial debate. In addition to that, the volume also contains original experimental research on personal identity and philosophical temperament, as well as state-of-the-art essays on central metaphilosophical issues, like thought experiments, the nature of intuitions, or the status of philosophical expertise. -/- This book was originally published as a special issue of Philosophical Psychology. (shrink)

Miklos Vetö | Résumé : La philosophie occidentale, depuis ses origines helléniques jusqu’aux grands systèmes postcartésiens, n’a jamais su donner sa place au particulier, au singulier. L’intelligibilité du singulier ne pouvait être exposée en concept qu’à partir de la réhabilitation du temps et de l’image par la philosophie critique. Kant présente le singulier à travers le grand philosophème esthétique du Génie. Chez Hegel le singulier se trouve « déduit » dans la Philosophie du droit à travers la figure du (...) Prince. Et le second Schelling rapatrie quasiment la notion en philosophie théologique avec la monstration de Dieu qui affirme sa personnalité dans l’abandon kénotique de son propre être en faveur de l’être du Monde. |: Western metaphysics, from its Greek origins till the great post-Cartesian systems, has never been able to do justice to the particular, the singular. The intelligibility of the singular could be conceptualized only through the rehabilitation of time and image in the Critical philosophy. It is in the great esthetical philosopheme of Genius that the singular appears in Kant. Hegel “deduces” it in his Philosophy of Law in the guise of the Prince. And the second Schelling brings the notion back into philosophical theology via the manifestation of God affirming his personality by renouncing his own being in favour of the being of the world. (shrink)

Most philosophers believe that testimony is not a fundamental source of knowledge, but merely a way to transmit already existing knowledge. However, Jennifer Lackey has presented some counterexamples which show that one can actually come to know something through testimony that no one ever knew before. Yet, the intuitive idea can be preserved by the weaker claim that someone in a knowledge-constituting testimonial chain has to have access to some non-testimonial source of knowledge with regard to what is testified. But (...) even this weaker claim has a counterexample which I develop in close connection with a safety-account of knowledge. Thus, testimonial statements can sometimes enable us to know something for which none of our informants has any source of knowledge available. I conclude that my counterexample nevertheless does not affect the core of our intuitions about testimony, although it establishes that testimony can indeed be a fundamental source of knowledge. (shrink)

We show that the usual axiom system of quasi polyadic equality algebras is strongly redundant. Then, so called non‐commutative quasi‐polyadic equality algebras are introduced (), in which, among others, the commutativity of cylindrifications is dropped. As is known, quasi‐polyadic equality algebras are not representable in the classical sense, but we prove that algebras in are representable by quasi‐polyadic relativized set algebras, or more exactly by algebras in.

Experimental restrictionists have challenged philosophers’ reliance on intuitions about thought experiment cases based on experimental findings. According to the expertise defense, only the intuitions of philosophical experts count—yet the bulk of experimental philosophy consists in studies with lay people. In this paper, we argue that direct strategies for assessing the expertise defense are preferable to indirect strategies. A direct argument in support of the expertise defense would have to show: first, that there is a significant difference between expert and lay (...) intuitions; second, that expert intuitions are superior to lay intuitions; and third, that expert intuitions accord with the relevant philosophical consensus. At present, there is only little experimental evidence that bears on these issues. To advance the debate, we conducted two new experiments on intuitions about knowledge with experts and lay people. Our results suggest that the intuitions of epistemological experts are superior in some respects, but they also pose an unexpected challenge to the expertise defense. Most strikingly, we found that even epistemological experts tend to ascribe knowledge in fake-barn-style cases. This suggests that philosophy, as a discipline, might fail to adequately map the intuitions of its expert practitioners onto a disciplinary consensus. (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)

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)

Three classes are introduced which are closely related to the class included in the title. It is proven that the class obtained from by replacing axiom C4 by the commutativity of single substitutions can be considered as the abstract class in the Resek–Thompson theorem, thus it is representable by set algebras. Then the class is defined and it is shown that the necessary and sufficient condition for neat embeddability of an algebra in CAα into is the validity of the merry-go-round (...) properties. Finally, the class is introduced which class is a counterpart of among the polyadic like algebras. (shrink)

There is an extensive literature related to the algebraization of first‐order logic. But the algebraization of full second‐order logic, or Henkin‐type second‐order logic, has hardly been researched. The question arises: what kind of set algebra is the algebraic version of a Henkin‐type model of second‐order logic? The question is investigated within the framework of the theory of cylindric algebras. The answer is: a kind of cylindric‐relativized diagonal restricted set algebra. And the class of the subdirect products of these set algebras (...) is the algebraization of Henkin‐type second‐order logic. It is proved that the algebraization of a complete calculus of the Henkin‐type second‐order logic is a class of a kind of diagonal restricted cylindric algebras. Furthermore, the connection with the non‐standard enlargements of standard complete second‐order structures is investigated. (shrink)

New numerical solutions of 3+1D covariant kinetic theory are reported for nuclear collisions in the energy domain Ecm∼200 AGeV. They were obtained using the MPC 0.1.2 parton transport code employing high parton subdivision to retain Lorentz covariance. The solutions are compared to those of relativistic hydrodynamics employing Cooper–Frye isotherm freeze-out. The transport solutions follow a different dynamical path than hydrodynamics due to large dissipative effects when pQCD scattering rates and HIJING initial conditions are assumed. The transport freeze-out four-volume is sensitive (...) to the reaction rates. The final transverse momentum distributions are found to deviate by up to an order of magnitude from those of Cooper–Frye frozen hydrodynamics. (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)

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.

La question de la fondation n’a cessé de hanter la métaphysique. Elle a reçu trois formulations majeures dans l’Idéalisme Allemand. Chez Kant la subjectivité a priori est montrée comme la base de la validité de la connaissance humaine. Dans la spéculation hégélienne, les notions mêmes de substrat ou fondement cèdent le pas à l’unité de la forme et de la matière, de l’historique et du conceptuel, c’est-à-dire à la transparence du réel tout entier. Finalement, chez Schelling l’idée de Dieu est (...) repensée pour réunir l’intelligibilité de l’essence et la factualité de l’existence. (shrink)

The purpose of this research was to describe attitudes of nursing students (and paramedic officers) towards marginalized clients. Convenience quota sampling in a major health faculty was employed. Students participated on a voluntary basis. A 58-item Likert scale, developed by the authors, assessed the student nurses’ attitudes. In general, attitudes towards homeless clients were neutral; detailed analyses, however, revealed that student nurses would decline to care for homeless clients in various situations. Personal experience with homeless patients and positive attitudes of (...) nurses significantly contributed to increased quality of care and equality of treatment for homeless clients. Certain student nurse behaviors warrant immediate attention to prevent marginalized patients from being exposed to unfair, inaccessible and biased nursing care. Based on our results, we recommend that further research attention be paid to the role of ethics education and faculty behaviors, as faculty members serve as role models for professionalization. (shrink)

According to the mischaracterization objection developed by Max Deutsch and Herman Cappelen, philosophers do not appeal to intuitions as evidence for their judgments about thought experiment cases, but rather argue for their case judgments. Although Deutsch and Cappelen present numerous case studies in support of this claim, the reception of the mischaracterization objection has been surprisingly negative so far. In this paper, I will first clarify and elaborate the mischaracterization objection, explain its metaphilosophical significance, and then argue that all extant (...) replies to it fail. The mischaracterization objection is therefore much stronger than it is widely assumed to be, with potentially far-reaching metaphilosophical consequences for the restrictionist challenge from experimental philosophy and the philosophical import of intuitions about hypothetical cases. (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.

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)

The Swamping Problem is one of the standard objections to reliabilism. If one assumes, as reliabilism does, that truth is the only non-instrumental epistemic value, then the worry is that the additional value of knowledge over true belief cannot be adequately explained, for reliability only has instrumental value relative to the non-instrumental value of truth. Goldman and Olsson reply to this objection that reliabilist knowledge raises the objective probability of future true beliefs and is thus more valuable than mere true (...) belief. I argue against their proposed solution to the Swamping Problem that the conditional probability of future true beliefs given knowledge is not clearly higher than given mere true belief. (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)

The Bayes Blind Spot of a Bayesian Agent is, by definition, the set of probability measures on a Boolean σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebra that are absolutely continuous with respect to the background probability measure of a Bayesian Agent on the algebra and which the Bayesian Agent cannot learn by a single conditionalization no matter what evidence he has about the elements in the Boolean σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma (...) $$\end{document}-algebra. It is shown that if the Boolean algebra is finite, then the Bayes Blind Spot is a very large set: it has the same cardinality as the set of all probability measures ; it has the same measure as the measure of the set of all probability measures ; and is a “fat” set in topological sense in the set of all probability measures taken with its natural topology. Features of the Bayes Blind Spot are determined from the perspective of repeated Bayesian learning when the Boolean algebra is finite. Open problems about the Bayes Blind Spot are formulated in probability spaces with infinite Boolean σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebras. The results are discussed from the perspective of Bayesianism. (shrink)

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)

Arguments from fairness as described in Aristotle’s _Rhetoric_ are usually taken to aim at mitigating the strictness of the law or, in terms of procedure, to favour the defendant. This paper considers a more inclusive interpretation, that is, that arguments from fairness can work both ways. In the example given in the _Rhetoric,_ arguments from fairness are directed at a restrictive interpretation of the text. That may not be necessary however. Likewise, fairness may speak for the claimant. Two examples may (...) support this conclusion: a judicial speech by Hyperides, and the doctrine of issues appearing in Hellenistic school rhetoric. (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.

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)

Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The paper looks at how the tension has been perceived and articulated by some physicists, mathematicians and mathematical physicists. Some sources of the tension are identified and it is claimed that the tension is both natural and fruitful for both physics and mathematics. An attempt is made to explain why mathematical precision is typically not welcome in physics.

This paper has two parts, a historical and a systematic. In the historical part it is argued that the two major axiomatic approaches to relativistic quantum field theory, the Wightman and Haag-Kastler axiomatizations, are realizations of the program of axiomatization of physical theories announced by Hilbert in his 6th of the 23 problems discussed in his famous 1900 Paris lecture on open problems in mathematics, if axiomatizing physical theories is interpreted in a soft and opportunistic sense suggested in 1927 by (...) Hilbert, Nordheim, and von Neumann. To show this, Section 2 recalls first some of Hilbert's views about the axiomatic approach to physical theories as these were formulated in his 6th problem. It will be .. (shrink)

Treating species as individuals and not classes has been crucial to the integration of evolutionary theory with modern systematics. Despite the theoretically important role the concept of individuality plays in modern phylogenetic systematics and in evolutionary theory more generally, many have been content to rely on common-sense intuitions about what counts as an individual. One of the most often cited intuitions is that individuals should be defined intrinsically. Unfortunately, common-sense intuitions like this one have proven to be inadequate for identifying (...) and characterizing historical individuals (like species). An examination of real-world biological examples shows that our common-sense intuitions are equally inadequate when applied to at least some biological organisms--the paradigm individuals. (shrink)