In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an interpolant formula \(\chi\) formulated in the intersection of the vocabularies of \(\phi\) and \(\psi\), such that \(\mathfrak{M}\models\phi\to\chi\) and \(\mathfrak{M}\models\chi\to\psi\), that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation (...) property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic. (shrink)

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...) companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. (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)

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)

The literature on antecedents of corporate social responsibility strategies of firms has been predominately content driven. Informed by the managerial sense-making process perspective, we develop a contingency theoretical framework explaining how political ideology of managers affects the choice of CSR strategy for their firms through their CSR mindset. We also explain to what extent the outcome of this process is shaped by the firm’s internal institutional arrangements and external factors impacting on the firm. We develop and test several hypotheses using (...) data collected from 129 Chinese managers. The results show that managers with a stronger socialist ideology are likely to develop a mindset favouring CSR, which induces the adoption of a proactive CSR strategy. The CSR mindset mediates the link between socialist ideology and CSR strategy. The strength of the relationship between the CSR mindset and the choice of CSR strategy is moderated by customer response to CSR, industry competition, the role of government, and CSR-related managerial incentives. (shrink)

In the article [2] a hierarchy of modal logics has been defined to capture the logical features of Bayesian belief revision. Elements in that hierarchy were distinguished by the cardinality of the set of elementary propositions. By linking the modal logics in the hierarchy to the modal logics of Medvedev frames it has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. However, the infinite case (...) remained open. In this article we prove that the modal logic of Bayesian belief revision determined by standard Borel spaces is also not finitely axiomatizable. (shrink)

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...) companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. (shrink)

The classical interpretation of probability together with the principle of indifference is formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called labelling invariance is defined in the category of Haar probability spaces; it is shown that labelling invariance is violated, and Bertrand’s paradox is interpreted as the proof of violation of labelling invariance. It is shown that Bangu’s attempt to block the emergence of Bertrand’s paradox by requiring the re-labelling (...) of random events to preserve randomness cannot succeed non-trivially. A non-trivial strategy to preserve labelling invariance is identified, and it is argued that, under the interpretation of Bertrand’s paradox suggested in the paper, the paradox does not undermine either the principle of indifference or the classical interpretation and is in complete harmony with how mathematical probability theory is used in the sciences to model phenomena. It is shown in particular that violation of labelling invariance does not entail that labelling of random events affects the probabilities of random events. It also is argued, however, that the content of the principle of indifference cannot be specified in such a way that it can establish the classical interpretation of probability as descriptively accurate or predictively successful. 1 The Main Claims2 The Elementary Classical Interpretation of Probability3 The General Classical Interpretation of Probability in Terms of Haar Measures4 Labelling Invariance and Labelling Irrelevance5 General Bertrand’s Paradox6 Attempts to Save Labelling Invariance7 Comments on the Classical Interpretation of Probability. (shrink)

George Molnar came to see that the solution to a number of the problems of contemporary philosophy lay in the development of an alternative to Hume's metaphysics. This alternative would have real causal powers at its centre. Molnar set about developing a thorough account of powers that might persuade those who remained, perhaps unknowingly, in the grip of Humean assumptions. He succeeded in producing something both highly focused and at the same time wide-ranging. He showed both that the notion of (...) a power was central and that it could serve to dispel a number of long-standing philosophical problems.Molnar's account of powers is as realist as any that has so far appeared. He shows that dispositions are as real as any other properties. Specifically, they do not depend for their existence on their manifestations. Nevertheless, they are directed towards such manifestations. Molnar thus appropriates the notion of intentionality, from Brentano, and argues that it is the essential characteristic of powers. He offers a persuasive case for there being some basic and ungrounded powers, thus ruling out the reducibility of the dispositional to the non-dispositional. However, he does allow that there are non-power properties as well as power properties. In this respect, his final position is dualistic.This is contemporary metaphysics of the highest quality. It is a work that was almost complete when its author died. It has been edited for publication by another specialist in the subject, Stephen Mumford, who has also provided an introduction that will allow non-specialists to become acquainted with the issues. David Armstrong, one of the greatest living metaphysicians and personal friend of George Molnar, has provided a Foreword. (shrink)

We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among (...) these modal logics are determined and it is shown that the logic of Bayes and Jeffrey updating are very close. It is shown that the modal logic of belief revision determined by probabilities on a finite or countably infinite set of elementary propositions is not finitely axiomatizable. The significance of this result is that it clearly indicates that axiomatic approaches to belief revision might be severely limited. (shrink)

A probability space is common cause closed if it contains a Reichenbachian common cause of every correlation in it and common cause incomplete otherwise. It is shown that a probability space is common cause incomplete if and only if it contains more than one atom and that every space is common cause completable. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the principle is only falsifiable if conditions on the common cause (...) are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause. (shrink)

The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause Principle.

We extend a result by Gallow concerning the impossibility of following two epistemic masters, so that it covers a larger class of pooling methods. We also investigate a few ways of avoiding the issue, such as using non-convex pooling methods, employing the notion of imperfect trust or moving to higher-order probability spaces. Along the way we suggest a conceptual issue with the conditions used by Gallow: whenever two experts are considered, whether we can trust one of them is decided by (...) the features of the other! (shrink)

We report a solution to an open problem regarding the axiomatization of the convex hull of a type of nonclassical evaluations. We then investigate the meaning of this result for the larger context of the relation between rational credence functions and nonclassical probability. We claim that the notions of bets and Dutch Books typically employed in formal epistemology are of doubtful use outside the realm of classical logic, eventually proposing two novel ways of understanding Dutch Books in nonclassical settings.

The classical interpretation of probability together with the principle of indifference is formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called labelling invariance is defined in the category of Haar probability spaces; it is shown that labelling invariance is violated, and Bertrand’s paradox is interpreted as the proof of violation of labelling invariance. It is shown that Bangu’s attempt to block the emergence of Bertrand’s paradox by requiring the re-labelling (...) of random events to preserve randomness cannot succeed non-trivially. A non-trivial strategy to preserve labelling invariance is identified, and it is argued that, under the interpretation of Bertrand’s paradox suggested in the paper, the paradox does not undermine either the principle of indifference or the classical interpretation and is in complete harmony with how mathematical probability theory is used in the sciences to model phenomena. It is shown in particular that violation of labelling invariance does not entail that labelling of random events affects the probabilities of random events. It also is argued, however, that the content of the principle of indifference cannot be specified in such a way that it can establish the classical interpretation of probability as descriptively accurate or predictively successful. (shrink)

In this paper we study the interaction between symmetric logic and probability. In particular, we axiomatize the convex hull of the set of evaluations of symmetric logic, yielding the notion of probability in symmetric logic. This answers an open problem of Williams ( 2016 ) and Paris ( 2001 ).

We show a somewhat surprising result concerning the relationship between the Principal Principle and its allegedly generalized form. Then, we formulate a few desiderata concerning chance-credence norms and argue that none of the norms widely discussed in the literature satisfies all of them. We suggest that the New Principle comes out as the best contender.

We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of the (...) common cause completability result are formulated. (shrink)

The Bayes Blind Spot of a Bayesian Agent is the set of probability measures on a Boolean 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 conditionalizing no matter what evidence he has about the elements in the Boolean 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. (shrink)

U clanku autori se bave militantnim potencijalom koncepta avangarde. Pojavljujuci se u politici i umetnosti u prvoj polovini 19. veka i nastojeci da unisti gotovo celokupnu tradiciju 'burzoaskog' prosvetiteljstva, politicka i umetnicka avangarda nikada nije bila sposobna da se oslobodi svojih korena u vojnickom nacinu razmisljanja. Njena prava sustina je lezala u stvaranju bojnih polja u svakoj oblasti javnog zivota gde je postojala sansa da se unisti gradjansko drustvo - njegova politika, njegova umetnost, njegov nacin razmisljanja, njegova civilizacija. U ime (...) jos necuvene slobode, ona je sirila nasilje i sejala totalitarino seme po sprzenoj zemlji. A na kraju je nisu pobedili njeni mnogobrojni neprijatelji zato jer je postala zrtva vlastite destruktivnosti. (shrink)

U clanku autori se bave militantnim potencijalom koncepta avangarde. Pojavljujuci se u politici i umetnosti u prvoj polovini 19. veka i nastojeci da unisti gotovo celokupnu tradiciju 'burzoaskog' prosvetiteljstva, politicka i umetnicka avangarda nikada nije bila sposobna da se oslobodi svojih korena u vojnickom nacinu razmisljanja. Njena prava sustina je lezala u stvaranju bojnih polja u svakoj oblasti javnog zivota gde je postojala sansa da se unisti gradjansko drustvo - njegova politika, njegova umetnost, njegov nacin razmisljanja, njegova civilizacija. U ime (...) jos necuvene slobode, ona je sirila nasilje i sejala totalitarino seme po sprzenoj zemlji. A na kraju je nisu pobedili njeni mnogobrojni neprijatelji zato jer je postala zrtva vlastite destruktivnosti. (shrink)

U clanku autori ispituju tri pozicije u estetickoj raspravi o uzvisenom koja se vodila u 18. veku - Edmunda Berka, Imanuela Kanta i Fridriha Silera. Oni takodje pokusavaju da rekonstruisu politicku pozadinu svake od ovih teorijskih pozicija: starorezimski konzervativizam, republikanski liberalizam i romanticarsku zudnju za 'trecim putem'. Najsofisticiraniju i najzreliju teoriju uzvisenog pronalaze u Silerovim estetickim delima, pogotovo u onima koja su usledila nakon njegovog razocarenja u Francusku revoluciju i u kojima su najtemeljnije razmatrani odnosi izmedju uzvisenog i paradoksa istorijskog (...) nasilja. (shrink)

In this article the authors are reconstructing the dichotomies which the young Theodor Adorno was trying to detect in the music of the bourgeois epoch and personify in two antipodes - Franz Schubert and Ludwig van Beethoven. Although already a devotee of Arnold Sch?nberg and the 20th century music avantgardism, Adorno was, in his works prior to his exile from Germany, intensively dealing with Schubert and his opposition towards Beethoven. While Beethoven was a bold and progressive revolutionary, fascinated by the?practical (...) reason? and the mission to rise up and reach the stars, Schubert wanted none of it. Instead, he was looking backwards, to primordial nature and the possibility of man to participate in its mythic cycles of death and regeneration. The lack of synthesis between this two opposing tendencies in the music of early bourgeois epoch lead to the?negative dialectics? of Sch?nberg and 20th century music avantgardism and to the final separation of Beethovenian musical progress and Schubertian musical mimesis. (shrink)

Autorka u clanku rekonstruise kompleksnu sliku Franca Suberta koju je stvorio Teodor Adorno u nekoliko osvrta na ovog kompozitora, a najvise u clanku?Subert? iz 1928. Adorno je te, 1928. godine doziveo Suberta kao tragicnog kompozitora cija muzika obitava u oblasti htonskih bogova, a da ipak otkriva radost?putujuceg naroda, opsenara i cudotvoraca?. Ipak, nije objasnio kako ova radost moze da prezivi u paklenim pejsazima Subertove htonske muzike. Tek kasnije Adorno je bio spreman da u Subertu prepozna, zahvaljujuci njegovom?habitusu?, i kafanskog sviraca, (...) ne pominjuci vise?putujuci narod, opsenare i cudotvorce?. Te dve predstave Suberta-Subert kao osluskivac htonskih bogova i Subert kao kafanski svirac-pokazale su se kao zanimljiv par vredan dalje teorijske elaboracije koju Adorno, nazalost, nikada nije sproveo. PR Projekat Ministarstva nauke Republike Srbije, br. 177019: Identiteti srpske muzike u svetskom kulturnom kontekstu. (shrink)

In this article the authors are reconstructing the dichotomies which the young Theodor Adorno was trying to detect in the music of the bourgeois epoch and personify in two antipodes - Franz Schubert and Ludwig van Beethoven. Although already a devotee of Arnold Sch?nberg and the 20th century music avantgardism, Adorno was, in his works prior to his exile from Germany, intensively dealing with Schubert and his opposition towards Beethoven. While Beethoven was a bold and progressive revolutionary, fascinated by the?practical (...) reason? and the mission to rise up and reach the stars, Schubert wanted none of it. Instead, he was looking backwards, to primordial nature and the possibility of man to participate in its mythic cycles of death and regeneration. The lack of synthesis between this two opposing tendencies in the music of early bourgeois epoch lead to the?negative dialectics? of Sch?nberg and 20th century music avantgardism and to the final separation of Beethovenian musical progress and Schubertian musical mimesis. (shrink)

In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12].

By a celebrated theorem of Morley, a theory T is ℵ1‐categorical if and only if it is κ‐categorical for all uncountable κ. In this paper we are taking the first steps towards extending Morley's categoricity theorem “to the finite”. In more detail, we are presenting conditions, implying that certain finite subsets of certain ℵ1‐categorical T have at most one n‐element model for each natural number (counting up to isomorphism, of course).

The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka– Németi and Sain.

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)

There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also shown that given the (...) mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation. (shrink)

In this paper we discuss the ``admissibility troubles'' for Bayesian accounts of direct inference proposed in, which concern the existence of surprising, unintuitive defeaters even for mundane cases of direct inference. We first show that one could reasonably suspect that the source of these troubles was informal talk about higher-order probabilities: for cardinality-related reasons, classical probability spaces abound in defeaters for direct inference. We proceed to discuss the issues in the context of the rigorous framework of Higher Probability Spaces. However, (...) we show that the issues persist; we prove a few facts which pertain both to classical probability spaces and to HOPs, in our opinion capturing the essence of the problem. In effect we strengthen the message from the admissibility troubles: they arise not only for approaches using classical probability spaces---which are thus necessarily informal about metaprobabilistic phenomena like agents having credences in propositions about chances---but also for at least one respectable framework specifically tailored for rigorous discussion of higher-order probabilities. (shrink)

This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a (...) single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C∗ - algebras with respect to operations (completely positive unit preserving linear maps on C∗ - algebras)as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory. (shrink)

In this paper we dispel the supposed ``admissibility troubles'' for Bayesian accounts of direct inference proposed by Wallmann and Hawthorne, which concern the existence of surprising, unintuitive defeaters even for mundane cases of direct inference. We show that if one follows the majority of authors in the field in using classical probability spaces unimbued with any additional structure, one should expect similar phenomena to arise and should consider them unproblematic in themselves: defeaters abound! We then show that the framework of (...) Higher Probability Spaces allows the natural modelling of the discussed cases which produces no troubles of this kind. (shrink)

Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract Principal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an open (...) question. (shrink)