Philosophy of mathematics is moving in a new direction: away from a foundationalism in terms of formal logic and traditional ontology, and towards a broader range of approaches that are united by a focus on mathematical practice. The scientific research network PhiMSAMP (Philosophy of Mathematics: Sociological Aspects and Mathematical Practice) consisted of researchers from a variety of backgrounds and fields, brought together by their common interest in the shift of philosophy of mathematics towards mathematical practice. Hosted by the Rheinische Friedrich- (...) Wilhelms-Universitat Bonn and funded by the Deutsche Forschungsgemeinschaft (DFG) from 2006-2010, the network organized and contributed to a number of workshops and conferences on the topic of mathematical practice. The refereed contributions in this volume represent the research results of the network and consists of contributions of the network members as well as selected paper versions of presentations at the network's mid-term conference, "Is mathematics special?" (PhiMSAMP-3) held in Vienna 2008. (shrink)

Logicians and theoretical physicists will also benefit from this book.

Affective congruency effects in the evaluation task can be explained by either spreading of activation or response competition. Eliminating effects of response compatibility by using other tasks (semantic categorisation, naming task) typically also eliminates affective congruency effects. However, there is no need for processing the affective information of the stimuli in these tasks either, which could be necessary for an affectively mediated spreading of activation (Spruyt et al., 2007, 2009, 2012). We introduced a new task to further test this hypothesis. (...) The valent/neutral-categorisation task does not confound affective congruency with response compatibility, but still requires a processing of the stimuli's valence. No affective congruency effect was obtained with this task in two experiments, disfavouring a conditional spreading activation account. On the other hand, a significant priming effect was found for associated word pairs in Experiment 1, providing evidence for the sensitivity of the task to detect spreading activation processes. (shrink)

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

C-systems were defined by Cartmell as models of generalized algebraic theories. B-systems were defined by Voevodsky in his quest to formulate and prove an initiality conjecture for type theories. They play a crucial role in Voevodsky’s construction of a syntactic C-system from a term monad. In this work, we construct an equivalence between the category of C-systems and the category of B-systems, thus proving a conjecture by Voevodsky.

In this paper we discuss Brandom's definition of necessity, which is part of the incompatibility sematnics he develops in his fifth John Locke Lecture. By comparing incompatibility semantics to standard Kripkean possible worlds semantics for modality, we motivate an alternative definition of necessity in Brandom's own terms. Our investigation of this alternative necessity will show that - contra to Brandom's own results - incompatibility semantics does not necessarily lead to the notion of necessity of the modal logic S5.

Panentheism seems to be an attractive alternative to classical theism. It is not clear, though, what exactly panentheism asserts and how it relates to classical theism. By way of clarifying the thesis of panentheism, I argue that panentheism and classical theism differ only as regards the modal status of the world. According to panentheism, the world is an intrinsic property of God – necessarily there is a world – and according to classical theism the world is an extrinsic property of (...) God – it is only contingently true that there is a world. Therefore, as long as we do not have an argument showing that necessarily there is a world, panentheism is not an attractive alternative to classical theism. (shrink)

The advent of ChatGPT by OpenAI has prompted extensive discourse on its potential implications for science and higher education. While the impact on education has been a primary focus, there is limited empirical research on the effects of large language models (LLMs) and LLM-based chatbots on science and scientific practice. To investigate this further, we conducted a Delphi study involving 72 researchers specializing in AI and digitization. The study focused on applications and limitations of LLMs, their effects on the science (...) system, ethical and legal considerations, and the required competencies for their effective use. Our findings highlight the transformative potential of LLMs in science, particularly in administrative, creative, and analytical tasks. However, risks related to bias, misinformation, and quality assurance need to be addressed through proactive regulation and science education. This research contributes to informed discussions on the impact of generative AI in science and helps identify areas for future action. (shrink)

A common assumption within the migration ethics literature is that it is only states that have the power to admit foreigners to their territory. However, this assumption misses something important. While it is true that it is states that have the ultimate power to admit, other actors can possess a derivative power from the laws that states put in place. By establishing a system of work visas, for instance, states lend private corporations, and other employers, the power to nominate foreigners (...) for admission by making job offers. For many foreigners, a job offer is what they require to start a new life in a new country. The question then arises how corporations should use this derivative power? One might assume that they should use it as they typically do: to pursue their business interests and by doing so (we hope) benefit their stakeholders including the state and its citizens. However, could there not be other reasons, besides profit seeking, to offer refugees a visa-conferring job? If hiring refugees does not greatly harm their business, it is arguable that corporations could be obliged to use their derivative power to do so on humanitarian grounds. Moreover, some corporations also seem to be obliged to use this power on grounds of corrective justice. This paper advances these possibilities. It has three sections. First, I will look at how much discretion corporations have in terms of employment and migration laws in some European countries. Second, I will present an argument for why corporations are morally permitted to facilitate admission for refugees by offering them a visa-conferring job. In the final section, I will then defend a stronger claim, namely that corporations are possibly obliged to do so on humanitarian grounds or on grounds of corrective justice. (shrink)

In transformation research of late, accounts on the relation between intentionality and agency on the one hand, and the more routinised and structured side of social co-existence on the other, are increasingly nuanced. However, we observe a deficiency in the way arguments are set up by the interlocutors: both, scholars who grant intentionality a central role and those who emphasise its limitations generally do so at the level of ontology – debating degrees of human capacity for conscious planning versus a (...) largely unconscious reproduction. We wish to shift this question from an ontological to a pedagogical one, exploring possibilities to cultivate and learn intentionality. We do so by developing the concept of consciousness-in-nature that we derive from, and contextualise in, the traditions of deep ecology and (Westernised) Buddhism which both view human beings as inseparable from nature and one another. With consciousness-in-nature we refer to an understanding of humans as a part of nature that has developed the capacity for (self-) reflection and deliberation – a capacity that is not static or firm but can be nurtured and cultivated or clouded over and subdued. From this standpoint, we lay out an understanding of the role of (re)learning consciousness for processes of social change and explore potentials for its nurturing. (shrink)

Long‐term modification of synaptic strength is thought to be the basic mechanism underlying the activity‐dependent refinement of neural circuits and the formation of memories engrammed on them. Studies ranging from cell culture preparations to humans subjects indicate that the decision of whether a synapse will undergo strengthening or weakening critically depends on the temporal order of presynaptic and postsynaptic activity. At many synapses, potentiation will be induced only when the presynaptic neuron fires an action potential within milliseconds before the postsynaptic (...) neuron fires, whereas weakening will occur when it is the postsynaptic neuron that fires first. Such processes might be important for the remodeling of neural circuits by activity during development and for network functions such as sequence learning and prediction. Ultimately, this synaptic property might also be fundamental for the cognitive process by which we structure our experience through cause and effect relations. BioEssays 24:212–222, 2002. © 2002 Wiley Periodicals, Inc.; DOI 10.1002/bies.10060. (shrink)

In climate science, climate models are one of the main tools for understanding phenomena. Here, we develop a framework to assess the fitness of a climate model for providing understanding. The framework is based on three dimensions: representational accuracy, representational depth, and graspability. We show that this framework does justice to the intuition that classical process-based climate models give understanding of phenomena. While simple climate models are characterized by a larger graspability, state-of-the-art models have a higher representational accuracy and representational (...) depth. We then compare the fitness-for-providing understanding of process-based to data-driven models that are built with machine learning. We show that at first glance, data-driven models seem either unnecessary or inadequate for understanding. However, a case study from atmospheric research demonstrates that this is a false dilemma. Data-driven models can be useful tools for understanding , specifically for phenomena for which scientists can argue from the coherence of the models with background knowledge to their representational accuracy and for which the model complexity can be reduced such that they are graspable to a satisfactory extent. When citing this paper, please use the full journal title Studies in History and Philosophy of Science. (shrink)

We show that the theories ZF and ZFU are synonymous, answering a question of Visser.

We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.

ABSTRACTDot-probe studies usually find an attentional bias towards threatening stimuli only in anxious participants, but not in non-anxious participants. In the present study, we conducted two experiments to investigate whether attentional bias towards angry faces in unselected samples is moderated by the extent to which the current task requires social processing. In Experiment 1, participants performed a dot-probe task involving classification of either socially meaningful targets or meaningless targets. Targets were preceded by two photographic face cues, one angry and one (...) neutral. Angry face cues only produced significant cueing scores with socially meaningful targets, not with meaningless targets. In Experiment 2, participants classified only meaningful targets, which were either socially meaningful or not. Again, mean cue... (shrink)

We investigate the possibility of arguing for or against the philosophical position that mathematics is an _epistemic exception_ on the basis of agreement data from the mathematical peer review process and argue that Cohen’s \(\kappa \), the standard agreement measure used for inter-rater agreement, is unable to detect epistemic exceptionality from peer review data.

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

Enlightenment thought and its contemporary followers usually support two contradictory principles simultaneously. The first is universality. Truth is universal because it is truth for all. Claims to universality are made in logic and science, but also in areas that are culturally or politically controversial. Recently, universalism has become a key term to express a fundamental critique of identity politics. For much of European history, Christianity provided such a universal truth. But with the decline of its cultural hegemony and the rise (...) of particular nation-states, conflicting truth claims became weapons in violent conflicts, leading Hobbes to argue that dangerous truth claims must be neutralized by robust political power. In the eighteenth century, rationalism became more optimistic, interpreting universalism as cosmopolitanism based on universal reason and progress through history. The second principle is historicism, which is the self-reflexive look at the historical origins of universal claims and theories. Historicism emerged in the nineteenth century as a response to the application of rationalism to history. It challenged the universal claims of the French Revolution, emphasizing instead the unique value of each historical entity. This revealed a fundamental paradox: when universalism becomes self-reflexive, it recognizes that it has non-universal historical origins, thereby undermining itself. After the devastation of World War II and the Holocaust, the Universal Declaration of Human Rights (1948) represented a significant effort toward a new universalism. It sought to establish human rights as universal principles for the emerging world order. But history repeated itself: Historicism once again weakened confidence in human rights. The enemies of human rights take advantage of this weakness. We therefore have to live with the paradox that universalism is necessary because humanity shares a single world, but that historical self-reflection is also unavoidable. In other words, the Enlightenment principle of universalism must accept historicism as an integral part of itself. (shrink)

Police officers often encounter potentially dangerous situations in which they strongly rely on their ability to identify threats quickly and react accordingly. Previous studies have shown that practical experience and targeted training significantly improve threat detection time and decision-making performance in law enforcement situations. We applied 90-min traditional firearms training as a control condition and a specifically developed intervention training to police cadets. The intervention training contained theoretical and practical training on tactical gaze control, situational awareness, and visual attention, while (...) the control training focused on precision and speed. In a pre- and posttest, we measured decision-making performance as well as response preparation and execution to evaluate the training. Concerning cognitive performance training, the number of correct decisions increased from pre- to posttest. In shoot scenarios, correct decisions improved significantly more in the intervention group than in the control group. In don’t-shoot scenarios, there were no considerable differences. Concerning the training of response preparation and execution in shoot scenarios, the intervention group’s response time, but not hit time, decreased significantly from pre- to posttest. The control group was significantly faster than the intervention group, with their response and hit time remaining constant across pre- and posttest. Concerning the training of tactical action control, the intervention group performed significantly better than the control group. Moreover, the intervention group improved the tactical handling of muzzle position significantly. The results indicate that a single 90-min session of targeted gaze control and visual attention training improves decision-making performance, response time, and tactical handling of muzzle position in shoot scenarios. However, these faster response times do not necessarily translate to faster hit times – presumably due to the motor complexity of hitting an armed attacker with live ammunition. We conclude that theory-based training on tactical gaze control and visual attention has a higher impact on police officers’ decision-making performance than traditional firearms training. Therefore, we recommend law enforcement agencies include perception-based shoot/don’t-shoot exercises in training and regular tests for officers’ annual firearm requalification. (shrink)

We study classes of ultrafilters on ω defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.

Commercial success of big data has led to speculation that big-data-like reasoning could partly replace theory-based approaches in science. Big data typically has been applied to ‘small problems’, which are well-structured cases characterized by repeated evaluation of predictions. Here, we show that in climate research, intermediate categories exist between classical domain science and big data, and that big-data elements have also been applied without the possibility of repeated evaluation. Big-data elements can be useful for climate research beyond small problems if (...) combined with more traditional approaches based on domain-specific knowledge. The biggest potential for big-data elements, we argue, lies in socioeconomic climate research. (shrink)

We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small restrictions (...) on the semi-linear sets considered. (shrink)

This work deals with the expressive power of logics on finite graphs with access to an additional "arbitrary" linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph (...) is complex -unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results. (shrink)

Transhumanism conceives itself as the next phase of humanism, postulating to leave behind most of its allegedly outdated features and paradigms. To that purpose, transhumanism has recently developed its own philosophy to get to a concrete social ideology, on which political action can be based. This philosophy has been first concentrated in the best-selling book “The Transhumanist Wager”. We discuss the basic elements of the social philosophy of transhumanism in its attempt to overcome traditional humanism both in the social sphere (...) and in politics, including the innovative elements and the contradictions inbuilt in its current self-concept and thought. (shrink)

We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justification in mathematics, in a context dependent way.

This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also (...) including the promotion of related non-scientific fields such as philosophy and history of computing. (shrink)

The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy.

After 30 years of research, the mechanisms underlying the evaluative priming effect are still a topic of debate. In this study, we tested whether the evaluative priming effect can result from associative relatedness rather than evaluative congruency. Stimuli that share the same evaluative connotation are more likely to show some degree of non-evaluative associative relatedness than stimuli that have a different evaluative connotation. Therefore, unless associative relatedness is explicitly controlled for, evaluative priming effects reported in earlier research may be driven (...) by associative relatedness instead of evaluative relatedness. To address this possibility, we performed an evaluative priming study in which evaluative congruency and associative relatedness were manipulated independently from each other. The valent/neutral categorisation task was used to ensure evaluative stimulus processing in the absence of response priming effects. Results showed an effect of associative relatedness but no effect of evaluative congruency. Our findings highlight the importance of controlling for associative relatedness when testing for evaluative priming effects. (shrink)

We study relations between measure-theoretic classes of ultrafilters, such as the Property M ultrafilters of [4], with other well-known ultrafilter classes. We define several classes of measure theoretic ultrafilters, of which the Property M ultrafilters are the strongest. We show which containments are provable in ZFC between these measure-theoretic ultrafilters and boolean combinations of well-known ultrafilters such as the selective, semi-selective, and P-point ultrafilters. We also list some of the containment results between measure-theoretic ultrafilters and several other ultrafilter classes, such (...) as the Arrow and Property C ultrafilters. (shrink)

We give characterizations for the sentences "Every $\Sigma^1_2$-set is measurable" and "Every $\Delta^1_2$-set is measurable" for various notions of measurability derived from well-known forcing partial orderings.

We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.

The so-called “conciliatory” norm in epistemology and meta-ethics requires that an agent, upon encountering peer disagreement with her judgment, lower her confidence about that judgment. But whether agents actually abide by this norm is unclear. Although confidence is excessively researched in the empirical sciences, possible effects of disagreement on confidence have been understudied. Here, we target this lacuna, reporting a study that measured confidence about moral beliefs before and after exposure to moral discourse about a controversial issue. Our findings indicate (...) that participants do not abide by the conciliatory norm. Neither do they conform to a rival “steadfast” norm that demands their confidence to remain the same. Instead, moral discourse seems to boost confidence. Interestingly, we also find a confidence boost for factual beliefs, and a correlation between the extremity of moral views and confidence. One possible explanation of our findings is that when engaging in moral discourse participants become more extreme in their opinions, which leads them to become more confident about them, or vice versa: they become more confident and in turn more extreme. Although our work provides initial evidence for the former mechanism, further research is needed for a better understanding of confidence and moral discourse. (shrink)

The existence of God is once again the focus of vivid philosophical discussion. From the point of view of analytic theology, however, people often talk past each other when they debate about the putative existence or nonexistence of God. In the worst case, for instance, atheists deny the existence of a God, which no theists ever claimed to exist. In order to avoid confusions like this we need to be clear about the function of the term 'God' in its different (...) contexts of use. In what follows, I distinguish between the functions of 'God' in philosophical contexts on the one hand and in theological contexts on the other in order to provide a schema, which helps to avoid confusion in the debate on the existence or non-existence of God. (shrink)

An important task of philosophy is to provide substantial arguments concerning the basic structure of reality and its relation to the ultimate source of everything. Sometimes, philosophers are convinced that there is an absolutely certain starting point within philosophy. More often, however, they suppose that we start with certain intuitions about empirical reality and its source. Based on these intuitions, philosophers try to develop sound arguments with an intelligible logical structure. By this very fact, they place themselves in the realm (...) of public discussion and criticism. There are, though, different kinds of criticism. Good criticism shows that at least one premise in an argument is not true—which is to say that the argument is not sound—or it shows that the premises could be true while the conclusion is false—which is to say that the argument is not valid. Then, there is criticism that is beside the point. It seems to me that the reply to my paper by Latester belongs to the ki .. (shrink)

Should or shouldn’t Christians endorse the transhumanist agenda of changing human nature in ways fitting to one’s needs? To answer this question, we first have to be clear on what precisely the thesis of transhumanism entails that we are going to evaluate. Once this point is clarified, I argue that Christians can in principle fully endorse the transhumanist agenda because there is nothing in Christian faith that is in contradiction to it. In fact, given certain plausible moral assumptions, Christians should (...) endorse a moderate enhancement of human nature. I end with a brief case study that analyses the theological implications of the idea of immortal Christian cyborgs. I argue that the existence of Christian cyborgs who know no natural death has no impact on the Christian hope of immortality in the presence of God. (shrink)

Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issues raised by Hamkins. Our work brings (...) to light additional structural issues that we also discuss. (shrink)

We attempt to identify and evaluate the association between key characteristics of not-for-profit hospitals and market concentration, as measured by the Herfindahl–Hirschman Index, using data available from the American Hospital Association, the Centers for Medicare and Medicaid Services, and the Internal Revenue Service Form 990. Our goal is to provide decision support to policy makers on factors that contribute to market competitiveness, which has been linked to improvements in efficiency, costs, and access to health care. We find that contributions are (...) positively associated with market concentration. This could indicate that well-run NP hospitals are rewarded both financially as well as with increased market share. We also find that a higher percentage of Medicare patients is positively correlated with market concentration. This could be explained by the fact that Medicare reimbursement rates are generally lower than those paid by private insurers ; thus, hospitals might not necessarily choose to operate in areas with high Medicare populations. Further, median income is negatively associated with market concentration. One explanation for this effect could be the fact that a population with a higher median income is in a better position to pay for services, making them attractive to hospitals as a potential market. Finally, we find that the presence of managers with voting rights on the boards of directors has no significant impact. (shrink)

We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”. This answers a question of Tony Martin.

The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this (...) article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. (shrink)

There is a close systematic relationship between panentheism, as a metaphysical theory about the relation between God and the world, and transhumanism, the ethical demand to use the means of the applied sciences to enhance both human nature and the environment. This relationship between panentheism and transhumanism provides a ‘cosmic’ solution to the problem of evil: on panentheistic premises, the history of the world is the one infinite life of God, and we are part of the one infinite divine being. (...) We ourselves are therefore responsible for the future development of the life of the divine being. We should therefore use the means provided by the natural sciences to develop the history of the world in such a way that the existence of evil shall be overcome and shall no longer be part of the divine being in whom we move and live and have our being. The metaphysics of panentheism leads to the ethics of transhumanism. (shrink)

The Tria Opuscula by the Late Antique Neoplatonist Proklos are accessible in full in the translation into medieval Latin by Wilhelm von Moerbeke, as well as in fragments in the Greek texts of Late Antique and Byzantine authors. Using the form of a commentary on passages, this work assesses what we can learn from these sources about the original Greek text of the three works. At the same time the commentary serves the elucidation of the first complete Greek retroversion of (...) the Tria Opuscula, which is published here. (shrink)

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games (...) with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature. (shrink)

We define a parametrised choice principle PCP which is equivalent to the Axiom of Determinacy. PCP describes the difference between these two axioms and could serve as a means of proving Martin's conjecture on the equivalence of these axioms.

We generalize Solovay's unfolding technique for infinite games and use an Unfolding Theorem to give a uniform method to prove that all analytic sets are in the $\sigma$ -algebras of measurability connected with well-known forcing notions.

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

Recent evidence suggests that probabilistic grammars may be modulated by communication mode and genre. Accordingly, the question arises how complex language users’ lectal competence is, where complexity is proportional to the extent to which choice-making processes depend on the situation of language use. Do probabilistic constraints vary when we talk to a friend compared to when we give a speech? Are differences between spoken and written language larger than those within each mode? In the present study, we aim to approach (...) these questions systematically. Guided by theorizing in cognitive (socio)linguistics and using logistic regression based on corpus materials, we analyzed the dative alternation with give (The government gives farmers money vs. The government gives money to farmers) in four broad registers of English: spoken informal, spoken formal, written informal, and written formal. Corpus analysis was supplemented with a scalar rating experiment. Results suggest that language users’ probabilistic grammars vary as a function of register. (shrink)

The human masticatory system is a complex functional unit characterized by a multitude of skeletal components, muscles, soft tissues, and teeth. Muscle activation dynamics cannot be directly measured on live human subjects due to ethical, safety, and accessibility limitations. Therefore, estimation of muscle activations and their resultant forces is a longstanding and active area of research. Reinforcement learning (RL) is an adaptive learning strategy which is inspired by the behavioral psychology and enables an agent to learn the dynamics of an (...) unknown system via policy-driven explorations. The RL framework is a well-formulated closed-loop system where high capacity neural networks are trained with the feedback mechanism of rewards to learn relatively complex actuation patterns. In this work, we are building on a deep RL algorithm, known as the Soft Actor-Critic, to learn the inverse dynamics of a simulated masticatory system, i.e., learn the activation patterns that drive the jaw to its desired location. The outcome of the proposed training procedure is a parametric neural model which acts as the brain of the biomechanical system. We demonstrate the model’s ability to navigate the feasible three-dimensional (3D) envelope of motion with sub-millimeter accuracies. We also introduce a performance analysis platform consisting of a set of quantitative metrics to assess the functionalities of a given simulated masticatory system. This platform assesses the range of motion, metabolic efficiency, the agility of motion, the symmetry of activations, and the accuracy of reaching the desired target positions. We demonstrate how the model learns more metabolically efficient policies by integrating a force regularization term in the RL reward. We also demonstrate the inverse correlation between the metabolic efficiency of the models and their agility and range of motion. The presented masticatory model and the proposed RL training mechanism are valuable tools for the analysis of mastication and other biomechanical systems. We see this framework’s potential in facilitating the functional analyses aspects of surgical treatment planning and predicting the rehabilitation performance in post-operative subjects. (shrink)

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.