The use of artificial intelligence (AI) to aid legal decision making has become prominent. This paper investigates the use of AI in a critical issue in employment law, the determination of a worker’s status—employee vs. independent contractor—in two common law countries (the U.S. and Canada). This legal question has been a contentious labor issue insofar as independent contractors are not eligible for the same benefits as employees. It has become an important societal issue due to the ubiquity of the gig (...) economy and the recent disruptions in employment arrangements. To address this problem, we collected, annotated, and structured the data for all Canadian and Californian court cases related to this legal question between 2002 and 2021, resulting in 538 Canadian cases and 217 U.S. cases. In contrast to legal literature focusing on complex and correlated characteristics of the employment relationship, our statistical analyses of the data show very strong correlations between the worker’s status and a small subset of quantifiable characteristics of the employment relationship. In fact, despite the variety of situations in the case law, we show that simple, off-the-shelf AI models classify the cases with an out-of-sample accuracy of more than 90%. Interestingly, the analysis of misclassified cases reveals consistent misclassification patterns by most algorithms. Legal analyses of these cases led us to identify how equity is ensured by judges in ambiguous situations. Finally, our findings have practical implications for access to legal advice and justice. We deployed our AI model via the open-access platform, https://MyOpenCourt.org/, to help users answer employment legal questions. This platform has already assisted many Canadian users, and we hope it will help democratize access to legal advice to large crowds. (shrink)

Ignorant speech, which spreads falsehoods about people and policies, is pervasive in public discourse. A popular response to this problem recommends countering ignorant speech with more speech, rather than legal regulations. However, Mary Kate McGowan has influentially argued that this ‘counterspeech’ response is flawed, as it overlooks the asymmetric pliability of conversational norms: the phenomenon whereby some conversational norms are easier to enact than subsequently to reverse. After demonstrating that this conversational ‘stickiness’ is an even broader concern for counterspeech than (...) McGowan suggests—it applies not just to oppressive or hateful speech, but also to ordinary policy-related misinformation—I argue that a more sophisticated account of counterspeech can nevertheless overcome it. First, the stickiness objection overlooks the distinction between ‘negative’ and ‘positive’ counterspeech. Instead of directly negating a distorted proposition, positive counterspeech affirms a correct proposition that is inconsistent with the falsehoods at hand. This, I contend, allows it to counter ignorant speech without triggering the properties that render it sticky. Second, the stickiness objection presupposes an unrefined conception of counterspeech’s temporality. Counterspeech should be understood as a diachronic process, which not only follows, but also pre-empts, ignorant utterances. Drawing on speech-act theories of silencing, I argue that pre-emptive counterspeech can condition the conversational context so as to prevent subsequent ignorant utterances from enacting sticky conversational norms. Thus, this theoretically-refined conception of counterspeech helps appreciate how verbal responses might overcome the stickiness of conversational norms; and, in doing so, it reveals that this stickiness need not provide reasons to prefer legal remedies to counterspeech. (shrink)

Does intellectual property satisfy the requirements of the Lockean proviso, that the appropriator leave “enough and as good” or that he at least not “deprive others”? If an author's appropriation of a work he has just created is analogous to a drinker “taking a good draught” in the flow of an inexhaustible river, or to someone magically “causing springs of water to flow in the desert,” how could it not satisfy the Lockean proviso?

A great deal has been made of the question of whether nano-materials provide a unique set of ethical challenges. Equally important is the question of whether they provide a unique set of regulatory challenges. In the last 18 months, the US Environmental Protection Agency has begun the process of trying to meet the regulatory challenge of nano using the Toxic Substances Control Act (1976)(TSCA). In this central piece of legislation, ‘newness’ is a critical concept. Current EPA policy, we argue, does (...) not adequately (or ethically) deal with the novelty of nano. This paper is an exploration of how to do a better job of accounting for nanomaterials as ‘new.’ We explore three alternative ways that nanomaterials might be made to fall under the TSCA regulatory umbrella. Since nanomaterials are of interest precisely because of the exciting new properties that emerge at the nano-scale, each of these three alternatives must meet what we call the ‘novelty condition’ and avoid what we call the ‘central paradox’ of existing regulatory policy. Failure to meet either of these conditions is a moral failure. We examine both the strengths and weaknesses of each alternative in order to illuminate the conceptual, practical, and moral challenges of novelty. (shrink)

This contribution focuses on legal issues raised by the audiovisual broadcasting of performing arts, which has significantly increased due to the SARS-CoV-2 pandemic. First, we contextualize this practice and briefly present the emergence and evolution of the practice of “filmed theater”, as well as any other form of performances (e.g., concert, ballet, opera) originally conceived for the stage but subsequently diffused through other channels. Secondly, we address the current legal issues that have arisen because of the increase of such practice (...) due to the containment measures taken by government. Two axes are of particular attention: the matter of copyrights and related rights, on the one hand, and the question of public financing, on the other. Concerning intellectual property, audiovisual broadcasting leads to several legal consequences and issues: effectiveness of related rights, emergence of new modes of exploitation and new authors, recognition of the recording as an original work, etc. This new practice is, moreover, likely to disrupt the categories established by public funding legal mechanisms, which are often poorly adapted to hybrid artistic objects. The objective of this part is therefore to analyze the new legal issues raised by the audiovisual distribution of performances. Finally, we go beyond exclusively legal issues to examine the very specificities of performing arts and, more specifically, the possible loss that would result from a fixation of a production on a reproducible medium, making its diffusion possible beyond the stage. (shrink)

A great deal has been made of the question of whether nano-materials provide a unique set of ethical challenges. Equally important is the question of whether they provide a unique set of regulatory challenges. In the last 18 months, the US Environmental Protection Agency has begun the process of trying to meet the regulatory challenge of nano using the Toxic Substances Control Act (1976)(TSCA). In this central piece of legislation, ‘newness’ is a critical concept. Current EPA policy, we argue, does (...) not adequately (or ethically) deal with the novelty of nano. This paper is an exploration of how to do a better job of accounting for nanomaterials as ‘new.’ We explore three alternative ways that nanomaterials might be made to fall under the TSCA regulatory umbrella. Since nanomaterials are of interest precisely because of the exciting new properties that emerge at the nano-scale, each of these three alternatives must meet what we call the ‘novelty condition’ and avoid what we call the ‘central paradox’ of existing regulatory policy. Failure to meet either of these conditions is a moral failure. We examine both the strengths and weaknesses of each alternative in order to illuminate the conceptual, practical, and moral challenges of novelty. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a (...) la luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a (...) la luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

En el presente artículo, se examinan y discuten dos argumentos con consecuencias reduccionistas debidos a Jaegwon Kim y a Theodore Sider respectivamente. De acuerdo con el argumento de Kim, la superveniencia fuerte implicaría la coexistencia necesaria de propiedades (es decir, tal y como normalmente se interpreta, la reducción). De acuerdo con el de Sider, ocurriría lo mismo con la superveniencia global. Uno y otro hacen un uso esencial de sendas nociones de propiedad maximal, las cuales son discutidas aquí a (...) la luz de una interpretación natural e interesante de la teoría de las propiedades implícita en sus argumentos. Bajo esta nueva interpretación, en términos modelo-teóricos (véase apartado 4), obtenemos diversas posibilidades de relaciones formales entre las tesis de superveniencia y la reducción, según la lógica utilizada. Al menos bajo una interpretación interesante, los argumentos de Kim y Sider no son correctos, quedando demos-trado así que dichos argumentos no son válidos en general. We discuss and analyze two reductive arguments due to Jaegwon Kim and Theodore Sider respectively. According to the first one, strong supervenience would imply necessary coextension of properties (i.e., reduction). According to the second, this would be also the case of global supervenience. Kim and Sider make essential use of their respective notions of maximal properties, which we analyze here in the light of a natural and interesting interpretation of the underlying theory of properties. Under this interpretation, in terms of model theory (see § 4), we obtain different possibilities of formal relations between the superveniencie theses and reduction, depending on the logic we use. Under at least one interesting interpretation, the arguments of Kim and Sider are not correct and we become the conclusion that these arguments are not valid in general. (shrink)

A property, F, is maximal iff, roughly, large parts of an F are not themselves Fs.' Maximality makes trouble for a recent analysis of intrinsicality by Rae Langton and David Lewis.

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and (...) M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

We provide results allowing to state, by the simple inspection of suitable classes of posets , that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of (...) choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. (shrink)

Infinitely many intermediate propositional logics with the disjunction property are defined, each logic being characterized both in terms of a finite axiomatization and in terms of a Kripke semantics with the finite model property. The completeness theorems are used to prove that any two logics are constructively incompatible. As a consequence, one deduces that there are infinitely many maximal intermediate propositional logics with the disjunction property.

In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...) of maximality principles. (shrink)

A property, F, is maximal i?, roughly, large parts of an F are not themselves Fs. Maximal properties are typically extrinsic, for their instantiation by x depends on what larger things x is part of. This makes trouble for a recent argument against microphysical superve- nience by Trenton Merricks. The argument assumes that conscious- ness is an intrinsic property, whereas consciousness is in fact maximal and extrinsic.

Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide a fix: we show that $\mathcal {L}_{\omega \omega }^{-} $ is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, (...) we use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity. (shrink)

This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the (...) Kripke semantics of maximal constructive logics extending the logic ST of Scott, for which, in turn, a semantical characterization in terms of Kripke frames has been given. In the present part we complete the illustration of the method of the first part, having in mind some aspects which might be interesting for a classification of the maximal constructive logics, and an application of the heuristic content of the method to detect the nonmaximality of apparently maximal constructive logics. Thus, on the one hand we introduce the logic AST , which is compared with ST and is seen as a logic “alternative” to it, in a sense which will be precisely explained. We provide a Kripke semantics for AST and show that there are maximal constructive logics which neither are extensions of ST nor are extensions of AST. Finally, we give a further application of the results of the first part by exhibiting the Kripke semantics of a maximal constructive logic extending AST. On the other hand, we compare the maximal constructive logics presented in both parts of the paper with a constructive logic introduced by Maksimova , which has been conjectured to be maximal by Chagrov and Zacharyashchev ; from this comparison a disproof of the conjecture arises. (shrink)

This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part (...) illustrates infinitely many maximal logics with the disjunction property extending the well-known logic of Scott, and aims to provide a first picture of the method, sufficient for the reader who wish to achieve an overall understanding of it without entering into the further aspects developed in the second part. From this point of view, the latter will not be self-standing, but will be seen as a prosecution and a complement of the former, with the aim that the material presented in the whole paper can be used as a starting point for a classification of the subject. (shrink)

In this paper we study symmetric inference systems (that is, pairs of inference systems) as refutation systems characterizing maximal logics with certain properties. In particular, the method is applied to paraconsistent logics, which are natural examples of such logics.

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically (...) all three-valued paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa's school. Then we show that in contrast, paraconsistent logics based on three-valued properly nondeterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise way the vast variety of the (deterministic) three-valued maximally paraconsistent matrices. The corresponding weaker notion of maximality, called premaximal paraconsistency, captures the "core" of maximal paraconsistency of all possible paraconsistent determinizations of a non-deterministic matrix, thus representing what is really essential for their maximal paraconsistency. (shrink)

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper (...) is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle of cautious monotony. It is established that, under the maximality rule, F + is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth . From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth . Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. (shrink)

This paper investigates a connection between the semantic notion provided by the ordering * among theories in model theory and the syntactic SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1. It is shown here that SOP3 implies SOP2 implies SOP1. In Shelah's article 229) it was shown that SOP3 implies *-maximality and we prove here that *-maximality in a model of GCH implies a property called SOP2″. It has (...) been subsequently shown by Shelah and Usvyatsov that SOP2″ and SOP2 are equivalent, so obtaining an implication between *-maximality and SOP2. It is not known if SOP2 and SOP3 are equivalent. Together with the known results about the connection between the SOPn hierarchy and the existence of universal models in the absence of GCH, the paper provides a step toward the classification of unstable theories without the strict order property. (shrink)

Maximizers in isolated Prisoner's Dilemmas are doomed to frustration. But in Braybrooke's view maximizers might do better in a series, securing Pareto-optimal arrangements if not from the very beginning, at least eventually. Given certain favourable special conditions, it can be shown according to Braybrooke and shown even without question-begging motivational or value assumptions, that in a series of Dilemmas maximizers could manage to communicate a readiness to reciprocate, generate thereby expectations of reciprocation, and so give rise to optimizing reciprocations which, (...) in due course, would reinforce expectations, the net result of all this being an increasingly stable practice to mutual benefit. In this way neighbours could learn to be good neighbours: they could learn to respect each other's property, to engage in reciprocal assistance, and perhaps even to make and keep promises covering a range of activities. So maximizers are, Braybrooke holds, capable of a society of sorts. Out of the ashes they might build something. But even under favourable conditions they could not build much and most conditions would defeat them almost entirely, for many-person Dilemmas whether isolated or in series would be quite beyond them, question-begging motivational assumptions aside. In settings at all like those in which we live, utility maximization assuming only ‘traditional’ motivation is self-defeating without remedy, and most certainly not an adequate basis for social life.' The probable inference from as a conception of individual rationality: for surely truly rational agents would be if not perfectly well designed at least better designed for communal living than utility maximizers would be assuming only ‘traditional’, non-question-begging values or motivation. Or, if this inference is denied and maximization is not challenged as a conception of rationality, we can conclude instead, Braybrooke has more recently suggested, that the advice, ‘Be rational,’ is incomplete, and when addressed to groups should be supplemented by, ‘And be somewhat ‘untraditional’ in your values; respect at least some rules that would make coordination and cooperation possible even in many-person interaction problems.’. (shrink)

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction (...) with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity. (shrink)

Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure 〈H,∈〉 by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC that provide a strong structure theory for these classes. These axioms (...) are variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins. (shrink)

Possible worlds are maximal possibilities. But what kind of thing is a maximal possibility? Not a maximal individual: there are maximal possibilities that are not maximal individuals, because each maximal individual could have any one of several maximal properties. And not a maximal property: there are maximal possibilities that are not maximal properties, because each maximal property could be had by any one of many possible maximal (...) individuals. So if you like your worlds concrete, you should say that they are maximal facts, and if you like your worlds abstract, you should say that they are maximal propositions. (shrink)

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some (...) transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type. (shrink)

In this paper, I develop an argument for the thesis that ‘maximality is extrinsic’, on which a whole physical object is not a whole of its kind in virtue of its intrinsic properties. Theodore Sider has a number of arguments that depend on his own simple argument that maximality is extrinsic. However, Peter van Inwagen has an argument in defence of his Duplication Principle that, I will argue, can be extended to show that Sider's simple argument fails. However, van (...) Inwagen's argument fails against a more complex, sophisticated argument that maximality is extrinsic. I use van Inwagen's own commitments to various forms of causation and metaphysical possibility to argue that maximality is indeed extrinsic, although not for the mundane reasons that Sider suggests. I then argue that moral properties are extrinsic properties. Two physically identical things can have different moral properties in a physical world. This argument is a counterexample to a classical ethical supervenience idea (often attributed to G.E. Moore) that if there is identity of physical properties in a physical world, then there is identity in moral properties as well. I argue moral value is ‘border sensitive’ and extrinsic for Kantians, utilitarians, and Aristotelians. (shrink)

To hold that only one conscious thing is sitting in your chair, philosophers have appealed to maximality: If a property M is maximal, then anything that has property M does not have large proper parts that have property M. Philosophers have said that ordinary objects are maximal, including houses, cats, rocks, and have argued by analogy that consciousness is maximal. I argue that the maximality principle mistakenly excludes some members of a kind. Thus, it is not the (...) correct principle to explain why, for example, you are conscious but the proper part that is all-of-you-but-your-arm is not conscious. (shrink)

This paper explores a variety of perfect being theism that combines Yujin Nagasawa’s maximal God thesis with the view that God is not atemporal. We argue that the original maximal God thesis still implicitly relies on a “static” view of divine perfections. Instead, following the recent re-evaluation of divine immutability by analytic philosophers, we propose that thinking of divine great-making properties as fluctuating but nevertheless remaining maximal either for every time t or across all times strengthens (...) the original maximal God thesis. Furthermore, we show that “temporalising” Nagasawa’s maximal God and adopting what we call the fluctuating maximal God thesis provides more effective ways of responding to objections to perfect being theism, in particular, the argument from evil and some conceptual problems pertaining to the Incarnation. Finally, we demonstrate that our proposal is compatible with Christian Scriptures and coheres with numerous biblical passages better than Nagasawa’s original proposal does. (shrink)

The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction.

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory - a theory which is conservative over its base, but can't be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that (...) the deflationist still needs some additional principles, which would permit him to construct his preferred theory of truth. (shrink)

We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will (...) be also investigated. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each (...) n. A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

The dominant approach to environmental policy endorsed by conservative and libertarian policy thinkers, so-called “free market environmentalism”, is grounded in the recognition and protection of property rights in environmental resources. Despite this normative commitment to property rights, most self-described FME advocates adopt a utilitarian, welfare-maximization approach to climate change policy, arguing that the costs of mitigation measures could outweigh the costs of climate change itself. Yet even if anthropogenic climate change is decidedly less than catastrophic, human-induced climate change is likely (...) to contribute to environmental changes that violate traditional conceptions of property rights. Viewed globally, the actions of some countries—primarily industrialized nations—are likely to increase environmental harms suffered by other countries—less developed nations that have not made any significant contribution to climate change. It may well be that aggregate human welfare would be maximized in a warmer, wealthier world, or that the gains from climate change will offset environmental losses. Yet such claims, even if demonstrated, would not address the normative concern that the consequences of anthropogenic global warming would infringe upon the rights of people in less-developed nations. As a consequence, this paper calls for a rethinking of FME approaches to climate change policy. (shrink)

The question of how properties are individuated is extremely important. Consider the following proposals. To be in pain is to be in a certain neurological state. To be red is to appear red to normal observers in standard conditions. To be obligatory is to maximize the good. Each makes a claim of property identity. Each is a substantive metaphysical thesis of wide interest. None can be studied with due scrutiny in the absence of a general account of property identity. (...) Here, I will survey existing accounts and suggest a new account in terms of grounding that has some advantages over the other candidates. (shrink)

Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2-indiscernible types are realized.

© The Author 2018. Published by Oxford University Press. All rights reserved. Logical geometry provides a broad framework for systematically studying the logical properties of Aristotelian diagrams. The main aim of this paper is to present and illustrate the foundations of a computational approach to logical geometry. In particular, after briefly discussing some key notions from logical geometry, I describe a logical problem concerning Aristotelian diagrams that is of considerable theoretical importance, viz. the task of finding the maximal (...) Boolean complexity of a given family of Aristotelian diagrams, and I then present and discuss a simple algorithm for automatically solving this task. This algorithm is naturally implemented within the paradigm of logic programming. In order to illustrate the theoretical fruitfulness of this algorithm, I also show how it sheds new light on several well-known families of Aristotelian diagrams. (shrink)

In this paper we shall discuss properties of saturation in monotonic neighbourhood models and study some applications, like a characterization of compact and modally saturated monotonic models and a characterization of the maximal Hennessy-Milner classes. We shall also show that our notion of modal saturation for monotonic models naturally extends the notion of modal saturation for Kripke models.

Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω (...) and produces a maximal almost disjoint family of subsets of ω of size ω1; there is no perfect set of random reals over V in V[ r][ d], where r is random over V and d Hechler over V[r], thus answering a question of the first and second authors. (shrink)

A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise "constructively incompatible constructive logics". We use a notion of "semiconstructive" logic and define wide sets (...) of "constructive" logics by representing the "constructive" logics as "limits" of decreasing sequences of "semiconstructive" logics. Also, we introduce some generalizations of the usual filtration techniques for propositional logics. For instance, "filtrations over rank formulas" are used to show that any two different logics belonging to a suitable uncountable set of "constructive" logics are "constructively incompatible". (shrink)

Post in 1944 began studying properties of a computably enumerable set A such as simple, h-simple, and hh-simple, with the intent of finding a property guaranteeing incompleteness of A . From the observations of Post and Myhill , attention focused by the 1950s on properties definable in the inclusion ordering of c.e. subsets of ω, namely E = . In the 1950s and 1960s Tennenbaum, Martin, Yates, Sacks, Lachlan, Shoenfield and others produced a number of elegant results relating (...) ∄-definable properties of A , like maximal, hh-simple, atomless, to the information content of A . Harrington and Soare gave an answer to Post's program for definable properties by producing an ∄-definable property Q which guarantees that A is incomplete and noncomputable, but developed a new Δ 3 0 -automorphism method to prove certain other properties are not ∄-definable. In this paper we introduce new ∄-definable properties relating the ∄-structure of A to deg, which answer some open questions. In contrast to Q we exhibit here an ∄-definable property T which allows such a rapid flow of elements into A that A must be complete even though A may possess many other properties such as being promptly simple. We also present a related property NL which has a slower flow but fast enough to guarantee that A is not low, even though A may possess virtually all other related lowness properties and A may simultaneously be promptly simple. (shrink)

In [60] N. Belnap presented an 8-element matrix for the relevant logic R with the following property: if in an implication A → B the formulas A and B do not have a common variable then there exists a valuation v such that v(A → B) does not belong to the set of designated elements of this matrix. A 6-element matrix of this kind can be found in: R. Routley, R.K. Meyer, V. Plumwood and R.T. Brady [82]. Below we prove (...) that the logics generated by these two matrices are the only maximal extensions of the relevant logic R which have the relevance property: if A → B is provable in such a logic then A and B have a common propositional variable. (shrink)

ABSTRACT:A key factor in the decision to convert a publicly owned company to private status is the expectation that value will be created, providing the firm with rent. These rents have implications regarding the property rights of the firm’s capital-contributing constituencies. We identify and analyze the types of rent associated with the newly private firm. Compared to public firms, going private allows owners the potential to partition part of the residual risk to bond holders and employees, rendering them to be (...) co-residual risk bearers with owners. We propose that new promotion-based contracts with bond holders and employees, reflecting their particular investments, be negotiated as the firm migrates from public to private status. These contracts should acknowledge the firm’s intent to maximize shareholder value and its need to take the risks necessary to do so, but support that the firm’s survival not be undermined due to its possibly opportunistic owners. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction (...) class='Hi'>properties between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)