Provability, Computability and Reflection.

We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if is a regular ultrafilter on λ such that and M is a model whose theory is countable, then is λ+-saturated iff it realizes all φ-types of size λ.

Let T 1 , T 2 be countable first-order theories, M i ⊨ T i , and ������ any regular ultrafilter on λ ≥ $\aleph_{0}$ . A longstanding open problem of Keisler asks when T 2 is more complex than T 1 , as measured by the fact that for any such λ, ������, if the ultrapower (M 2 ) λ /������ realizes all types over sets of size ≤ λ, then so must the ultrapower (M 1 ) λ /������. (...) In this paper, building on the author's prior work [12] [13] [14], we show that the relative complexity of first-order theories in Keisler's sense is reflected in the relative graph-theoretic complexity of sequences of hypergraphs associated to formulas of the theory. After reviewing prior work on Keisler's order, we present the new construction in the context of ultrapowers, give various applications to the open question of the unstable classification, and investigate the interaction between theories and regularizing sets. We show that there is a minimum unstable theory, a minimum TP 2 theory, and that maximality is implied by the density of certain graph edges (between components arising from Szemerédi-regular decompositions) remaining bounded away from 0, 1. We also introduce and discuss flexible ultrafilters, a relevant class of regular ultrafilters which reflect the sensitivity of certain unstable (non low) theories to the sizes of regularizing sets, and prove that any ultrafilter which saturates the minimal TP 2 theory is flexible. (shrink)

The same research proposal was submitted to 24 district health authority (DHA) research ethics committees in different parts of the country. The objective was to obtain permission for a multi-centre research project. The study of neonatal care in different types of unit (regional, subregional and district), required that four health authorities were approached in each of six widely separated health regions in England. Data were collected and compared concerning aspects of processing, including application forms, information required, timing and decision-making. The (...) key finding was that ethics committees received and processed the applications variably, reflecting individual factors and local problems. To improve consensus and facilitate multicentre studies, standard forms and instructions are suggested and the establishment of a national committee or advisory group advocated. (shrink)

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, (...) syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS''s). This generalization allows us to define BRS''s in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers. (shrink)

Some theorists, worried about liberalism’s potential as a foundation for public health ethics, suggest that republicanism provides a better background of justification for public health policies, interventions, etc. In this article, this suggestion is put to the test, and it is argued that (i) contemporary (civic) republicanism and liberalism are not nearly as opposed as it is sometimes suggested, and that (ii) the kind of republicanism which one leading scholar in the field, Bruce Jennings, as an alternative to liberalism, does (...) not reflect the contemporary understanding of republicanism as held by, e.g. Phillip Pettit et al. (shrink)

In their “social contextual view” of emotional mimicry, authors Hess and Fischer (2022) put forward emotional mimicry as a social regulator, considering it a social act, bound to certain affiliative contexts or goals. In this commentary, we argue that the core function of mimicry is to ease predicting conspecifics’ behaviours and the environment, and that as a consequence, this often smoothens social interactions. Accordingly, we make three main points. First, we argue that there is no good reason to believe that (...) the mimicry of negative expressions is fundamentally different than the mimicry of positive or ambiguous or autonomic expressions. Second, we give examples of empirical evidence that mimicry is not always a social act. Third, we show that mimicry has primary benefits for the mimicker. As such, we will briefly summarise and elaborate on the relevant findings in these respects, and propose a comparative, multi-method and ecologically valid approach which can explain the multifaceted character of the phenomenon. (shrink)

For a first-order formula φ(x; y) we introduce and study the characteristic sequence ⟨P n : n < ω⟩ of hypergraphs defined by P n (y₁…., y n ):= $(\exists x)\bigwedge _{i\leq n}\varphi (x;y_{i})$ . We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of φ and vice versa. The main results are a characterization of NIP and of simplicity in terms of persistence of configurations in the characteristic sequence. Specifically, we show that (...) some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence property manifest themselves in the persistence of complicated configurations under localization. (shrink)

The characteristic sequence of hypergraphs Pn:n<ω associated to a formula φ, introduced in Malliaris [5], is defined by Pn=i≤nφ. We continue the study of characteristic sequences, showing that graph-theoretic techniques, notably Szemerédi’s celebrated regularity lemma, can be naturally applied to the study of model-theoretic complexity via the characteristic sequence. Specifically, we relate classification-theoretic properties of φ and of the Pn to density between components in Szemerédi-regular decompositions of graphs in the characteristic sequence. In addition, we use Szemerédi regularity to calibrate (...) model-theoretic notions of independence by describing the depth of independence of a constellation of sets and showing that certain failures of depth imply Shelah’s strong order property SOP3; this sheds light on the interplay of independence and order in unstable theories. (shrink)

This article develops an account of the nature and limits of the state’s legislative authority that closely attends to the challenge of harmonizing Kant’s ethical and juridical theories. It clarifies some key Kantian concepts and terms, then explains the way in which the state’s three interlocking authorities – legislative, executive, and judicial – are metaphysically distinct and mutually dependent. It describes the emergence of the Kantian state and identifies the preconditions of its authority. Then it offers a metaphysical model of (...) the Kantian state and uses it to argue that the activity of juridical lawgiving is an act of the omnilateral will itself. Legislative authority is limited in the sense that it does not include the capacity to create juridical laws that are conceptually incompatible with the idea of universal external freedom. I argue that my proposed account of the legislative authority is wholly consistent with that authority’s exclusive lawgiving capacity and does not threaten the possibility of ‘distributive justice’ – the legal finality that is the sine qua non of a civil condition. (shrink)

A new interpretation of quantum theory is proposed. It coincides in a number of points with the orthodox interpretation, the main difference being that the projection of the state vector can occur without the intervention of any observer.

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

In spite of his post-World War II works on international law, which seems more purely juridical, Hans Kelsen continues to put forward in his vast body of work an implicit – and sometimes even explicit – juridical objectivism and pacifism. Especially before and during the second World War he makes – by means of many moral-political writings – an effort for a more effective assurance of international peace. The fact that Kelsen regards the law as the pre-eminent means to achieve (...) the end of peace, is – in view of the tradition running from Hobbes to Kant – still not very innovating. But the primary and central role he assigns to the judiciary in order to guarantee international peace is on the other hand really original. To bring out Kelsen’s juridical objectivism and pacifism, I restrict myself in this article to his plea before and during the second World War for the judicial primacy in the international legal order. In that plea, which is spread over many writings and founded by several arguments, I distinguish however three main convincing arguments – namely an evolutionary, a technical and a moral-political argument – for the establishment of an international court with compulsory jurisdiction as the ‘guardian of international peace’. The fact that Kelsen’s original plea is still relevant to our times, is already evident from the post-World War II UN-system of peace-enforcement, which still functions little satisfactorily and of which the existing plans of reform go no further than strengthening the position of the Security Council, the current hardly effective ‘maintainer of world peace’. (shrink)

PURPOSE: To evaluate the effects of social support on comprehension and recall of consent form information in a study of Parkinson disease patients and their caregivers.DESIGN and METHODS: Comparison of comprehension and recall outcomes among participants who read and signed the consent form accompanied by a family member/friend versus those of participants who read and signed the consent form unaccompanied. Comprehension and recall of consent form information were measured at one week and one month respectively, using Part A of the (...) Quality of Informed Consent Questionnaire .RESULTS: The mean age of the sample of 143 participants was 71 years . Analysis of covariance was used to compare QuIC scores between the intervention group and control group . In the 1-week model, no statistically significant intervention effect was found . However, the intervention status by patient status interaction was statistically significant . In the 1-month model, no statistically significant intervention effect was found . Again, however, the intervention status by patient status interaction was statistically significant . At both time periods, intervention group patients scored higher on the QuIC than did intervention group caregivers, and control group patients scored lower on the QuIC than did control group caregivers.IMPLICATIONS: Social support played a significant role in enhancing comprehension and recall of consent form information among patients. (shrink)

ABSTRACTThere are two distinct types of legal wrongdoing: civil and criminal. This article demonstrates in three ways that Immanuel Kant's Universal Principle of Right, properly interpreted, offers a plausible and resilient account of this important distinction. First, Kant's principle correctly identifies attempted crimes as crimes themselves even when they do not violate the rights of any individual. Second, it justifies our treatment of reckless endangerment as a crime by distinguishing it from ordinary negligence, traditionally thought to be only civilly wrong. (...) Third, it explains and justifies differences between the features of traditional criminal punishments and the features of civil remedies. Moreover, the Universal Principle of Right yields a Kantian standard for criminal wrongdoing that is compelling enough to inform future philosophical inquiries into the nature and limits of the state's criminal lawmaking authority. (shrink)

Synaesthesia is a condition in which one type of stimulation evokes the sensation of another, as when the hearing of a sound produces photisms, i.e. mental percepts of colours. R is a 20 year old colour blind subject who, in addition to the relatively common grapheme-colour synaesthesia, presents a rarely reported cross modal perception in which a variety of visual stimuli elicit aura-like percepts of colour. In R, photisms seem to be closely related to the affective valence of stimuli and (...) typically bring out a consistent pattern of emotional responses. The present case study suggests that colours might be an intrinsic category of the human brain. We developed an empirical methodology that allowed us to study the subject's otherwise inaccessible phenomenological experience. First, we found that R shows a Stroop effect elicited by photisms despite the fact that he does not show a regular Stroop with real colours. Secondly, by manipulating the colour context we confirmed that colours can alter R's emotional evaluation of the stimuli. Furthermore, we demonstrated that R's auras may actually lead to a partially inverted emotional spectrum where certain stimuli bring out emotional reactions opposite to the normal ones. These findings can only be accounted for by considering R's subjective colour experience or qualia. Therefore the present paper defends the view that qualia are a useful scientific concept that can be approached and studied by experimental methods. (shrink)

Interactions entail a tangled mix of emotional states that emerge between the people who are communicating. Being capable of comprehending these states help us to adapt to our partner’s needs enhancing the interaction. In the same fashion, we believe that robots capable of such skills would be better integrated in society. Hence, this paper tackles the internal state that focuses on the unfolding of any social exchange: Comfortability. It explores whether a humanoid robot can have an impact on humans Comfortability (...) and explores the way people might behave. To this aim, the iCub robot interviewed 29 non-HRI researchers for a real column of the IIT Opentalk online magazine. During the interview the robot complimented, ignored, interrupted, and insulted the participant with the intention of making them feel opposite Comfortability levels. The results concluded that a humanoid robot can affect people’s Comfortability highlighting that not everyone perceives, assimilates, and reacts to the same situations in the same way. The findings suggest that self-reports and Valence/Arousal estimations are not reliable measures to determine someone’s Comfortability and that external factors (e.g., attitude towards robots or the robot’s perception) might affect it. On top of that, a list of 28 visual features associated with low Comfortability levels is included, providing support to keep unraveling Comfortability in further studies. (shrink)

LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and nice description (...) (see Figure 2) while the latticeL(V 0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V 0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with free generators. Each of the quasivarietiesV 0,V 1, andV 2 is generated by a 2-element algebra inD 2. (shrink)