The technique of forcing is almost ubiquitous in set theory, and it seems to be based on technicalities like the concepts of genericity, forcing names and their evaluations, and on the recursively defined forcing predicates, the definition of which is particularly intricate for the basic case of atomic first order formulas. In his [3], the first author has provided an axiomatic framework for set forcing over models of $\mathrm {ZFC}$ that is a collection of (...) guiding principles for extensions over which one still has control from the ground model, and has shown that these axiomatics necessarily lead to the usual concepts of genericity and of forcing extensions, and also that one can infer from them the usual recursive definition of forcing predicates. In this paper, we present a more general such approach, covering both class forcing and set forcing, over various base theories, and we provide additional details regarding the formal setting that was outlined in [3]. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)

ArgumentThis paper investigates the conceptual treatment and mathematical modeling of force in Newton's Principia. It argues that, contrary to currently dominant views, Newton's concept of force is best understood as a physico-mathematical construct with theoretical underpinnings rather than a “mathematical construct” or an ontologically “neutral” concept. It uses various philosophical and historical frameworks to clarify interdisciplinary issues in the history of science and draws upon the distinction between axiomatic systems in mathematics and physics, as well as discovery patterns in (...) science. It also dwells on Newton's “philosophy” of mathematics, described here in terms of mathematical naturalism. This philosophy considers mathematical quantities to be physically significant quantities whose motions are best mapped by geometry. It then shows that to understand the epistemic status of force in the Principia, it is important to scrutinize both Newton's mathematical justificatory strategies and his background assumptions about force – without constructing, however, an overarching metaphysical framework for his science. Finally, the paper studies scientific attempts to redefine or eliminate force from science during the period between Newton and Laplace. From a philosophical standpoint, the paper implicitly suggests that questions about the reality of force be distinguished from questions about the validity of force, and that both sets of questions be distinguished from questions about the utility of the concept of force in science. (shrink)

This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these (...) theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic (...) event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

We propose an account of dynamic predicates which draws on the notion of force, eliminating reference to events in the linguistic semantics. We treat dynamic predicates as predicates of forces, represented as functions from an initial situation to a final situation that occurs ceteris paribus, that is, if nothing external intervenes. The possibility that opposing forces might intervene to prevent the transition to a given final situation leads us to a novel analysis of non-culminating accomplishment predicates in a variety of (...) languages, including the English progressive. We then apply the force-theoretic framework to the composition of basic Vendlerian eventuality types within a lexical-decomposition syntax. The difference between predicates of forces and predicates of situations is argued to underlie the dynamic/stative contrast, and also to allow for a formal treatment of the difference between be and stay. Consequences for the relationship between language and cognition are discussed. (shrink)

We present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF . It allows the use of set terms, but provides a static check of their validity. Like the inconsistent “ideal calculus” for set theory, it is essentially based on just two set-theoretical principles: extensionality and comprehension (to which we add ∈-induction and optionally the axiom of choice). Comprehension is formulated as: x ∈ {x | ϕ} ↔ (...) ϕ, where {x | ϕ} is a legal set term of the theory. In order for {x | ϕ} to be legal, ϕ should be safe with respect to {x}, where safety is a relation between.. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic (...) event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

The new system of axioms we propose is based on the foundational theory of De Giorgi et al. Scuola Normale Superiore di Pisa, Preprints di Matematica 26: 1 (1996) slightly modified. In that paper (which is dedicated to a new axiomatic framework for mathematics, informatics and logic) the authors use two kinds of primitive notions: relations and qualities. Since their system is based on the distribution paradigm, they start from distinction. We propose to shift the perspective and to (...) start from unity and then from within unity to pass to distinction; to this end we apply ideas of Lesniewski, Nijhoff International Philosophy Series 44 (1992). We introduce only one kind of entity as a primitive notion, namely relations, and treat qualities as articulations of relations. The new concept of "primary relation" permits the introduction of a dynamic, non-standard form of identity, which we hope will find application in various fields where self-referential structures are required. (shrink)

Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change through experiences: taste for Mozart changes through listening to it, sympathy for another player through observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework (...) for defining, analysing and comparing rival models of change. I show that seemingly basic postulates on modelling change together have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This is a step towards placing the modelling of change on solid axiomatic grounds and enabling non-arbitrary incorporation of change into economic models. (shrink)

The horizon for feminists studying horror films appears bleak. Since _Psycho_'s infamous shower scene, the big screen has treated us to Freddie's long razor-nails emerging between Nancy's legs in the bathtub (_A Nightmare on Elm Street I_), De Palma's exhibitionist heroine being power-drilled into the floor (_Body Double_), and Leather-face hanging women from meat hooks (_The Texas Chain Saw Massacre_). Even in a film with a strong heroine like _Alien_, any feminist point is qualified by the monstrousness of the alien (...) mother, the objectification of Sigourney Weaver in her underwear, and her character Ripley's forced assumption of a maternal role. Despite all this, there has been some feminist work on horror, and I believe there is room for more. In the first part of this paper I shall survey and criticize currently dominant psychodynamic feminist approaches to horror. In the second part, I propose an alternative framework for constructing feminist interpretations of horror films by critically interrogating their gender ideologies. My proposal focuses less on the psychology of viewers than on the nature of films as artifacts with particular structures and functions. In the third part I illustrate my recommended framework by sketching readings of _Jurassic Park_ (Spielberg 1993), _The Fly_ (Cronenberg 1986), and _Repulsion_ (Polanski 1965). (shrink)

An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.

Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change through experiences: taste for Mozart changes through listening to it, sympathy for another player through observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework (...) for defining, analysing and comparing rival models of change. I show that seemingly basic postulates on modelling change together have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This is a step towards placing the modelling of change on solid axiomatic grounds and enabling non-arbitrary incorporation of change into economic models. (shrink)

In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér’s theorem to the theory of symmetry (...) in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions. (shrink)

This study explores the way that belief systems, interactions with social or experimental environments, and skills at the “control” level in decision‐making shape people's behavior as they solve problems. It is argued that problem‐solvers' beliefs (not necessarily consciously held) about what is useful in mathematics may determine the set of “cognitive resources” at their disposal as they do mathematics. Such beliefs may, for example, render inaccessible to them large bodies of information that are stored in long‐term memory and that are (...) easily retrieved in other circumstances. In other cases, individuals' reactions to an experimental setting (fear of failure, or the desire to “look mathematical” while being videotaped) may induce behavior that is almost pathological—and at the same time, so consistent that it can be modeled. In general, such “environmental” factors establish the context within which individuals access and utilize the information potentially at their disposal.Protocols illustrating these points are presented and discussed. A model based on an axiomatization of students' beliefs about plane geometry is outlined, and is shown to correspond closely to their problem‐solving performance. A framework is offered for analyzing problem‐solving performance at three qualitatively different levels: access to cognitive resources stored in LTM, executive or control decision‐making, and belief systems. (shrink)

Scientific research in the formal sciences comes in multiple degrees of formality: fully formal work; rigorous proofs that practitioners know to be formalizable in principle; and informal work like rough proof sketches and considerations about the advantages and disadvantages of various formal systems. This informal work includes informal and semi-formal debates between formal scientists, e.g. about the acceptability of foundational principles and proposed axiomatizations. In this paper, we propose to use the methodology of structured argumentation theory to produce a formal (...) model of such informal and semi-formal debates in the formal sciences. For this purpose, we propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate natural deduction style arguments and explanations. We illustrate the applicability of the framework to debates in the formal sciences by presenting a simple model of some arguments about proposed solutions to the Liar paradox, and by discussing a more extensive—but still preliminary—model of parts of the debate that mathematicians had about the Axiom of Choice in the early twentieth century. (shrink)

When research concludes, post-trial access to the trial intervention or standard healthcare can be crucial for participants who are ill such as those in resource-poor countries with inadequate healthcare, British participants testing ‘last-chance drugs’ unavailable on the National Health Service and underinsured US participants. Yet, many researchers are unclear about their obligations regarding the post-trial period, and many research ethics committees do not know what to require of researchers. Consequences include participants who reasonably expect but lack PTA to the trial (...) intervention, unplanned financial liabilities for NHS Trusts forced to fund this, negative press and potential to undermine public trust.1–3,iOne reason for the lack of clarity is controversy over whether and when participants should have access, after the study, to the study intervention. At one extreme is the view that continued access should be ensured when the intervention has benefited the participant or when it has proven safe and effective for the participant population, irrespective of the cost and burden of ensuring continued access. At the other extreme is the view that continued access need never be provided so long as non-availability of the study intervention post-trial was adequately disclosed when participants were invited to participate.6 There is also disagreement about when poststudy access to the study intervention should be considered beneficial for participants. The spectrum ranges from the view that the intervention should be regarded as beneficial for a proposed use only after the …. (shrink)

An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.

Many different but related arguments developed in the Caritas in Veritate converge on one central, yet not clearly stated, conclusion or thesis: economic and business activities are ‘incomplete’. This article will explore the above-mentioned ‘incompleteness’ thesis or argument from three different perspectives: the role, the practice and the purpose of economic and business activities in contemporary societies. In doing so, the paper will heavily draw on questions and, still not fully learned, lessons derived from the present financial and economic crisis. (...) Caritas in Veritate provides an appealing moral framework in which many of these lessons take a deeper sense and a more comprehensive meaning. The notion of ‘incompleteness’ is applied here to economic and business theory and practice in the sense derived from Gödel’s theorems. They state in terms of logical and mathematical demonstrations that no system of axiomatic statements can provide a proof of its own consistency. Such a proof requires the use of statements belonging to another (higher) level system. In the case of economics or business theory and practice these ‘higher level’ statements are value judgments. By stressing the importance of ethics and moral philosophy for daily life, Caritas in Veritate strongly reminds us that neither economy nor business are self-sufficient either in organisational and social, practical or moral terms. (shrink)

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system (...) the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...) propose a very general and powerful framework based on quantifier-free predicate language extended by a new modality, which packs exactly ∃x◻ together. We show that the resulting language, though much more expressive, shares many good properties of the basic propositional modal logic over arbitrary models, such as finite-tree-model property and van Benthem-like characterization w.r.t.\ first-order modal logic. We axiomatize the logic over S5 frames with intuitive axioms to capture the interaction between the new modality and know-that operator in an epistemic setting. (shrink)

We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision (...) rules and these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule?mnx?mnx in the classical framework of choice under complete uncertainty. (shrink)

The objective of this research programme is to contribute to the establishment of the emerging science of Formal Ontology in Information Systems via a collaborative project involving researchers from a range of disciplines including philosophy, logic, computer science, linguistics, and the medical sciences. The re­searchers will work together on the construction of a unified formal ontology, which means: a general framework for the construction of ontological theories in specific domains. The framework will be constructed using the axiomatic-deductive (...) method of modern formal ontology. It will be tested via a series of applications relating to on-going work in Leipzig on medical taxonomies and data dictionaries in the context of clinical trials. This will lead to the production of a domain-specific ontology which is designed to serve as a basis for applications in the medical field. (shrink)

This paper proposes a framework for understanding and analysing online social resistance movements based on Hilde Lindemann’s concept of counterstories (Damaged Identities, Narrative Repair, 2003). This framework is based on the premise that we shape our identities in shared social spaces, and that such shared spaces are structured according to so-called ‘master narratives’. Master narratives define the ‘realm of possible identities’ that we can assume, and form the basis for either recognizing or denying recognition to various social groups (...) in specific roles that they might occupy. Social oppression occurs when master narratives preclude or forbid a certain form of self-expression, or alternatively force members of a specific social group into a determinate societal role (say, women who receive recognition only in the roles of mother or housewife). Counterstories serve as a corrective to these aspects of oppression by challenging the oppressive facets of master narratives. Based on this framework, I propose an interpretation of the #MeToo movement as a counterstory that aims to change the oppressive aspects of the patriarchal master narrative that (partially) structures many shared social spaces in the modern Western world. I end this paper by applying the framework to consider potential obstacles #MeToo may encounter as a distinctively online movement. (shrink)

This paper introduces the model of Utilitarian Principlism as a framework for crisis healthcare ethics. In modern Western medicine, during non-crisis times, principlism provides the four guiding principles in biomedical ethics—autonomy, nonmaleficence, beneficence, and justice; autonomy typically emerges as the decisive principle. The physician–patient relationship is a deontological construct in which the physician’s primary duty is to the individual patient and the individual patient is paramount. For this reason, we term the non-crisis ethical framework that guides modern medicine (...) Deontological Principlism. During times of crisis, resources become scarce, standards of care become dynamic, and public health ethics move to the forefront. Healthcare providers are forced to work in non-ideal conditions, and interactions with individual patients must be considered in the context of the crisis. The COVID-19 pandemic has forced healthcare to shift to a more utilitarian framework with a greater focus on promoting the health of communities and populations. This paper puts forth the notion of Utilitarian Principlism as a framework for crisis healthcare ethics. We discuss each of the four principles from a utilitarian perspective and use clinical vignettes, based on real cases from the COVID-19 pandemic, for illustrative purposes. We explore how Deontological Principlism and Utilitarian Principlism are two ends of a spectrum, and the implications to healthcare as we emerge from the pandemic. (shrink)

From the viewpoint of the constitutional crisis in Europe, slow UN reforms, difficulties implementing the Kyoto Protocol and the International Criminal Court, and tensions between human rights and trade, Mireille Delmas-Marty's 'journey through the legal landscape' of the early years of the 21st century shows it to be dominated by imprecision, uncertainty and instability. The early 21st century appears to be the era of great disorder: in the silence of the market and the fracas of arms, a world overly fragmented (...) by anarchical globalisation is being unified too quickly through hegemonic integration. How, she asks, can we move beyond the relative and the universal to build order without imposing it, to accept pluralism without giving up on a common law? Neither utopian fusion nor illusory autonomy, Ordering Pluralism is her answer: both an epistemological revolution and an art, it means creating a common legal area by progressive adjustments that preserve diversity. Since an immutable world order is impossible, the imaginative forces of law must be called upon to invent a flexible process of harmonisation that leaves room for believing we can agree on - and protect - common values. 'The book is timely and relevant to the practical concerns of those who work with, and within, the legal system. We must thank Professor Delmas-Marty for her fine work.' From the foreword, Stephen Breyer, Washington, DC. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can (...) be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

The UN Convention on the Rights of Persons with Disabilities (CRPD) was passed in 2006 and came into force in 2008. It sets out a number of core values, including dignity, individual autonomy, non-discrimination, participation and community inclusion. Although the CRPD has been recognised as an important step forward by many disabled people and their supporters and provides the foundation for building a good life, the author argues that it does not necessarily equate with it. The underpinning Western values of (...) choice, independence and control are important, but leave out groups of marginalised people for whom these goals may not be achievable. They also present challenges and dilemmas for those involved in supporting/caring roles. In this paper, the author reflects on the implications of the CRPD for the lives of people with learning disabilities, in particular those with profound needs and explores whether it provides a genuinely coherent framework for an inclusive society. (shrink)

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version (...) of the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory. (shrink)

In the article, we elaborate an interdisciplinary methodological framework that enables us to study and prepare the grounds for the development of organizational practices through discourse perspectives. The framework differs from mainstream monological and complexity reducing tendencies within organizational studies in that it argues for an approach that takes in historical, broad, and situational power relations and discourses into consideration when we engage in ethical organizational development. We place the framework within organizational discourse studies (ODS) and discuss (...) how the intersection of Bakhtinian and Foucauldian ideas and concepts, as well as their diverse analytical strategies and focuses, contributes to the field. The combination entails taking a dissensus approach to organizational discursive phenomena that we view as dynamic features that are historically and locally (re)created through battles of unifying (centripetal) and diversifying (centrifugal) force relations. Following similar ideas of Deleuze and Bakhtin, we argue that dialogue and every (organizational) situation is seen as a plurivocal, open-ended, and unique time-space in which subjects have agency to change and transform the power relations and lines of subjectification that they are embedded in. We arrive at a methodological framework that bridges the gulf that often exists between discourse perspectives that tend to either focus on situated or more abstract and historical discursive dimensions. Furthermore, the frame involves an ethics of dispositif and dialogue that insists that organizational discourse scholars engage in organizational discourse activism furthering local change processes. (shrink)

Estimating the effects of introducing a range of smart mobility solutions within an urban area is a crucial concern in urban planning. The lack of a simulator for the assessment of mobility initiatives forces local public authorities and mobility service providers to base their decisions on guidelines derived from common heuristics and best practices. These approaches can help planners in shaping mobility solutions; however, given the high number of variables to consider, the effects are not guaranteed. Therefore, a solution conceived (...) respecting the available guidelines can result in a failure in a different context. In particular, difficult aspects to consider are the interactions between different mobility services available in a given urban area and the acceptance of a given mobility initiative by the inhabitants of the area. In order to fill this gap, we introduce Tangramob, an agent-based simulation framework capable of assessing the impacts of a smart mobility initiative within an urban area of interest. Tangramob simulates how urban traffic is expected to evolve as citizens start experiencing newly offered traveling solutions. This allows decision makers to evaluate the efficacy of their initiatives, taking into account the current urban system. In this paper, we provide an overview of the simulation framework along with its design. To show the potential of Tangramob, three mobility initiatives are simulated and compared in the same scenario. This demonstrates how it is possible to perform comparative experiments so as to align mobility initiatives to the user goals. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola (1995, Erkenntnis, 43, 81–109) by outlining a pragmatic logic for assertions (...) and hypotheses. On the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

The term “epistemic shifts” refers to a widely recognized phenomenon that knowledge ascribers would ascribe different epistemic statuses to the same belief under different internal/external conditions. Mainstream theories explaining shifts can all be assimilated into a probabilistic framework, according to which the epistemic status of a belief P can be at least partially evaluated in terms of the strength of the link between this belief and its normal truth-maker, namely, a P-corresponding fact, and the strength of this link can (...) be further probabilistically measured in terms of the knowledge-undermining force of an “abnormal” truth-maker of P, namely, a P-inducing fact which itself is not a P-corresponding fact simpliciter. I will further claim that by accepting my framework, a theorist of shifts has to tolerate a pluralist view of the etiology of shifts on the philosophical level, and mainstream theories explaining shifts are flawed in the sense that they all attempt to exaggerate one single and particular factor underpinning shifts by ignoring others. (shrink)

Shortages of generic, injectable chemotherapeutics have been increasing in prevalence since 2006. Due to the lack of access to first-line, lifesaving treatments, physicians have been forced to ration chemotherapy between patients. Although the scarcity has been managed with good intentions, it has been done in an ad hoc manner, without the benefit of an ethically grounded and standardized schema. Using an approach based on the “accountability for reasonableness” method by Daniel and Sabin, I establish a framework and protocol for (...) rationing that is specific to chemotherapy. Prior to the state of true shortage, I present guidelines for the use of an adequate supply of chemotherapy with knowledge of upcoming scarcity. Within the rationing framework itself, I first prioritize emergency use of chemotherapeutics and those already receiving treatment at the time of shortage. I advocate for stratifying patients based on the prognostic indicators of their cancer type, using a combination of clinical-trial-based initial response and longer term survival, followed by the patients’ line of treatment. All patients who are not able to receive their “best” treatment must receive a sequent, next-best treatment, and their treatment team must have the ability to appeal to a rationing committee in special circumstances. I reject the ideas of stratification based on the intention of the treatment, perceived quality of life, pre-existing condition not impacting performance status, the classical “sickest first” argument, and giving preference to pediatric cases. Lastly, I advocate for any system of rationing to be transparent to those it affects and acknowledge the difficulties it presents to patients and physicians alike. (shrink)

There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated by (...) a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction $$(\phi \wedge \phi )$$ with that stated by its conjunct $$\phi $$. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy. (shrink)

The zone of proximal development (ZPD) is defined as an overarching concept that integrates the main tenets of Vygotsky’s theory of human development. The conceptualization of the ZPD begins with its social, cultural, and historical context and traces its development as a spatial and temporal metaphor that reflects the sociogenetic root of all human mental functioning. Beyond the explication of sociogenesis, the ZPD is reconceptualized to include the notions of voice and dialogicality. The insights gained from the fields of semiotics (...) and discourse studies allow a broader understanding of the ZPD by bringing to light participant structures and institutional and historical forces that may not have been included in the dominant interpretations of the ZPD. (shrink)

Can recognition theories distinguish legitimate from illegitimate claims to recognition put forward by social movements? This paper identifies an under-theorised problem of recognition theories: in viewing struggles for recognition as a force for social progress in the mould of the New Social Movements of the 1960s and 1970s, existing accounts have trouble identifying and ruling out illegitimate claims to recognition as formulated by contemporary counter-movements like white supremacists or men’s rights activists. I refer to this issue as the symmetry problem (...) of recognition since it amounts to difficulties in identifying grounds for excluding illegitimate claims to recognition that do not also symmetrically justify the exclusion of legitimate ones (and vice versa). I argue that criteria for telling apart legitimate from illegitimate claims to recognition need to include interpretation issues as a dimension of analysis, which consequently requires incorporating democratic deliberation as a necessary component of recognition theory. (shrink)

We present a general framework for forcing on ω2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω2, adding a nonreflecting stationary subset of, and adding an ω1‐Kurepa tree.

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.

It is shown by means of general principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of compressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure of charged elementary particles, the speed of light propagation, relativistic phenomena, the inertia of matter, the expansion of the universe, and the physical nature of time. (...) New avenues and opportunities for fundamental theoretical research are thereby illuminated. (shrink)

We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite (...) conditions while preserving CH, solving a problem of Friedman [Forcing with finite conditions, in Set Theory: Centre de Recerca Matemática, Barcelona, 2003–2004, Trends in Mathematics, pp. 285–295.]. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On the (...) basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and (...) problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)

Social science requires a dual ontology: one for the physical realm, and one for the symbolic realm of meaning. Much research produced in social science remains based in an old paradigm, which entirely neglects the symbolic realm. While social scientists attempting to forge a new paradigm have embraced a discursive approach, this approach lacks a coherent framework that can be systematically applied in the analysis of meaning. This paper presents the positioning diamond as a framework that can be (...) employed in discourse analysis across social science disciplines. The four facets of the diamond—storylines, identities, rights and duties, and the social force of acts—can be analyzed at three levels of discourse: the content, narrator-interlocutor, and ideological levels. The framework can be employed to provide explanations of most types of human thought and action. (shrink)