This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts in which (...) problem-solving procedures and strategies are studied. We represent proof-events as problem-centred spatio-temporal processes by means of the language of the calculus of events, which adequately captures certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a “loose” semantics for the proof events by means of Kolmogorov’s calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving. (shrink)

In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in history of mathematics. In this framework, proof is understood not as a purely syntactic object, but as a social process that involves at least two agents; this highlights the communicational aspect of proving. We claim that historians of mathematics essentially study proof-events in their research, since the mathematical proofs they face in the extant sources involve many informal (...) components, often not completely formalizable, and convey some kind of semantic content calling for understanding and verification. We illustrate the application of this methodological approach in some outstanding historical cases, paying particular attention to the process of proof interpretation that makes a proof-event alive. Finally, we suggest a classification of proof-events, according to the conditions imposed upon problem-solving. This enables us to speak about broad classes of proof-events in history of mathematics that share a common characteristic. (shrink)

Neospora caninum infection, one of the major causes of abortions in dairy cattle, has brought a huge loss to farmers worldwide. In this study, we develop a six-compartment susceptible-infected model of N. caninum transmission which is later reduced to a two-equation system. Potential controls including medication, test-and-cull, and vaccination are proposed and analyzed, and the corresponding reproduction numbers are derived. The conditions for the global stabilities of disease-free and endemic equilibria are investigated with analytical solutions and geometric approach. Furthermore, uncertainty (...) and sensitivity analysis shows that three control strategies are effective towards the varied environment, whereas the effectiveness of each measure highly depends on parameters related to control actions. Dynamics of reproduction numbers illustrate that disease elimination can be achieved by three types of controls: adopting medication with medicine efficacy higher than 0.4 to prevent vertical transmission, implementing test-and-cull with culling coverage larger than 0.3, and taking vaccine with coverage larger than 0.1. Numerical results suggest that preventive measures should at least include the prevention of access of other hosts, such as dogs, to cattle; otherwise, these control measures will lose effectiveness. Our presented study provides guidance for decision-making on N. caninum infected farm management. (shrink)

Seit dem 2. Nachchristlichen Jahrhundert werden die Schriften von Aristoteles kommentiert. DIese Ausgabe enthalt griechische Kommentare zu seinem Werk vom 3. Bis 8. JAhrhundert n. CHr., u. A. Von Alexander von Aphrodiensias, Themistios, Joh. PHiloponus, Simplicius in griechischer Sprache.

Seit dem 2. nachchristlichen Jahrhundert werden die Schriften von Aristoteles kommentiert. Diese Ausgabe enthält griechische Kommentare zu seinem Werk vom 3. bis 8. Jahrhundert n. Chr., u. a. von Alexander von Aphrodiensias, Themistios, Joh. Philoponus, Simplicius in griechischer Sprache.

In this paper, we approach the problem of the relationship between Greek mathematics and Eleatic philosophy from a new perspective, which leads us to a reappraisal of Szabó’s hypothesis about the origin of mathematics out of Eleatic philosophy. We claim that Parmenidean philosophy, particularly its semantic core, has possibly been shaped by reflexion on the Pythagoreans’ mathematical practice, particularly in arithmetic. Furthermore, Pythagorean arithmetic originates not from another domain outside mathematics but from counting, i.e., it has its roots in man’s (...) practical activity. This interpretation restores the historically inverse relationship between mathematics and philosophy, refuting the attribution of mathematics’ origin to a field outside mathematics, for which Szabó’s hypothesis has been criticised. Moreover, Parmenidean theory of truth is viewed not as a defective predecessor of Aristotle’s classical theory of truth that needs to be remedied but as a semantic conception coordinated with the mathematics of Parmenides’ times. (shrink)

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical (...) Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way. (shrink)

This book explores the way in which the fear of enemies shapes political groups at their founding and helps to preserve them by consolidating them in times of crisis. It develops a theory of “negative association” that examines the dynamics captured by the maxim “The enemy of my enemy is my friend” and then traces its role in the history of political thought, demonstrating that the fear of external threats is an essential element of the formation and preservation of political (...) groups and that its absence renders political association unsustainable. (shrink)

In nature validation for physiological and emotional bonding becomes a mode for supporting social connectivity. Similarly, in the blockchain ecosystem, cryptographic validation becomes the substrate for all interactions. In the dialogue between human and artificial intelligence (AI) agents, between the real and the virtual, one can distinguish threads of physical or mental entanglements allowing different modes of participation. One could even suggest that in all types of realities there exist frameworks that are to some extent equivalent and act as validation (...) mechanisms for behavioural interweaving. Relevant to our own experience as an Editorial Organism, in this issue of Technoetic Arts we explore modes of participation and collaboration through different lenses by including guest-edited sections and stand-alone articles. (shrink)

This article focuses on an analysis and evaluation of the importance Derrida's work may have for a theory of the social. It is argued that both his earlier and his later works are important in this respect, albeit at a high level of abstraction. In his early work the social is seen as an open `field of meaning' while in later work differentations within this field, such as the level of the `phantasmatic', are introduced. This is a direction of theorization (...) that has to be developed, although the way the `openness' of this field is to be conceived needs to be re-elaborated. However, Derrida's account in recent work of the structure of ethical/political action, based on `emancipatory promises', is not satisfactory and runs the danger of regressing to subjectivism. Instead, the existence of structural determinations - of a `history' - within the subject has to be theorized without reducing the subject to a form of self-presence. This history, alongside the contextuality of the moment of action, delineates the framework for ethical/political action. (shrink)

Providing interpretations and drawing critically from classical and modern social theory, post-structuralism, and psychoanalytic theory, this original study offers an alternative way of thinking about the social and the individual. It offers critical analyses of, among others, Marx, Giddens, Bourdieu, Derrida, Laclau and Mouffe, Castoriadis, Freud and modern psychoanalytic theorists, and considers their roles in advancing our present-day conceptualization of the social and the self. In theorizing that behaviour is both socially determined and autonomous, it avoids the impasses of either (...) individualist or structuralist approaches. (shrink)

We investigate the impact of perceived greenwashing on customer satisfaction. Unlike prior research that largely examines customer perceptions associated with irresponsible behavior, we focus on cases where firms overcommit and/or do not deliver on promised socially responsible actions. We theorize that this type of greenwashing is associated with lower customer satisfaction because customers perceive greenwashing through the lens of corporate hypocrisy. Using data from the American Customer Satisfaction Index (ACSI) for U.S. companies during the period 2008–2016, we document a negative (...) link between perceived greenwashing related to green product innovation (GPI) and the ACSI index. We demonstrate that this effect is primarily triggered by corporate policies exceeding the corresponding implementation actions and not by lower levels of implementation. We also show that a firm’s capability reputation mitigates the negative effect of greenwashing on customer satisfaction. Moreover, we conduct an experiment and provide evidence confirming that GPI greenwashing is in fact perceived by customers as corporate hypocrisy. (shrink)

Even though aesthetics and affordances are two important factors based on which designers provide effective ways of interaction through their artifacts, there is no study or theoretical model that relates these two aspects of design. We suggest a theoretical explanation that relates the underlying functionality of aesthetics, in particular, of interaction aesthetics and of affordances in the design process. Our claim is that interaction aesthetics are one among other factors that allow users to enhance the detection of action possibilities and (...) consequently, the detection of affordances. Our aim is first to discuss the role of interaction aesthetics in the design process, and second to suggest an explanation for their role in the detection of affordances when users interact with artifacts. (shrink)

A stalwart view in the philosophy of science holds that, even when broadly construed so as to include theoretical auxiliaries, theories cannot make direct contact with observations. This view owes much to Bogen and Woodward’s influential distinction between data and phenomena. According to them, data are typically the kind of things that are observable or measurable like "bubble chamber photographs, patterns of discharge in electronic particle detectors and records of reaction times and error rates in various psychological experiments". Phenomena are (...) physical processes that are typically unobservable. Examples of the latter category include "weak neutral currents, the decay of the proton, and chunking and recency effects in human memory". Theories, in Bogen and Woodward’s view, are utilised to systematically explain, infer and predict phenomena, not data. The relationship between theories and data is rather indirect. Data count as evidence for phenomena and the latter in turn count as evidence for theories. This view is becoming increasingly influential, Stathis Psillos and Mauricio Suárez ). In this paper I argue contrary to this view that in various significant and well-known cases theories do make direct contact with the help of suitable auxiliaries. (shrink)

In the context of a viral outbreak and necessary physical distancing, the emergence of new or the evolution of older artistic behavioural schemes becomes evident. We correlate the isolation space of the artist with the cockpit of a spaceship and the navigation and communication interfaces used by an astronaut. The cybernetic domain between physical space(s) and artist(s) can be thought of as consisting of many ‘organs’. It includes a core (black box), many-layered limits: skin, walls, mental and digital borders as (...) well as mechanisms of connectivity with external entities (other astronauts in art spaceships). This space could be a bedroom, a studio, an office or any different location the artist uses as an isolated bubble of information sharing and manipulation (material and immaterial). For the construction of such an (astronaut, artist) ontology we use metaphors, etymological references, transformed concepts and creative analogies between the actual and the subjective space. As one case study for this paradigm, we experimented with a telematic performance of Heiner Müller’s Hamlet Machine titled, I want to be 171. (shrink)

Exploring emotions, in terms of their evolutionary origin; their basic neurobiological substratum, and their functional significance in autonomous agents, we propose a model of minimal functionality of emotions. Our aim is to provide a naturalized explanation – mostly based on an interactivist model of emergent representation and appraisal theory of emotions – concerning basic aesthetic emotions in the formation of aesthetic judgment. We suggest two processes the Cognitive Variables Subsystem (CVS) which is fundamental for the accomplishment of the function of (...) heuristic learning; and Aesthetic Appraisal Subsystem (AAS) which primarily affects the elicitation of aesthetic emotional meanings. These two subsystems (CVS and AAS) are organizationally connected and affect the action readiness of the autonomous agent. More specifically, we consider the emotional outcome of these two subsystems as a functional indication that strengthens or weakens the anticipation for the resolution of the dynamic uncertainty that emerges in the particular interaction. (shrink)

Diarmuid Costello has recently argued that, contra received opinion, Kant’s aesthetics can accommodate conceptual art, as well as all other art. Costello offers an interpretation of Kant’s art theory that demands from all art a minimal structure involving three basic “players” and three basic “actions” corresponding to those “players.” The article takes issue with the “action” assigned by Costello’s Kant to the artwork’s recipient, namely that her imagination generates a multitude of playful thoughts deriving from or in any other way (...) relating to the concept or idea that the artist has instilled in the artwork and that the artwork transmits to the recipient. It is argued that the “proper” recipient of conceptual art may very well have a multitude of thoughts that are all irrelevant to the concept or idea the artist has instilled in the artwork, even if the artwork has transmitted that concept or idea to the recipient. This shows that Kant’s art theory, as presented by Costello, cannot accommodate conceptual art. I conclude by suggesting that either one of two amendments to the theory’s account of the recipient’s experience could enable it to accommodate conceptual art. (shrink)

Aesthetic perception is one of the most interesting topics for philosophers and scientists who investigate how it influences our interactions with objects and states of affairs. Over the last few years, several studies have attempted to determine “how aesthetics is represented in an object,” and how a specific feature of an object could evoke the respective feelings during perception. Despite the vast number of approaches and models, we believe that these explanations do not resolve the problem concerning the conditions under (...) which aesthetic perception occurs, and what constitutes the content of these perceptions. Adopting a naturalistic perspective, we here view aesthetic perception as a normative process that enables agents to enhance their interactions with physical and socio-cultural environments. Considering perception as an anticipatory and preparatory process of detection and evaluation of indications of potential interactions, we argue that the minimal content of aesthetic perception is an emotionally valued indication of interaction potentiality. Aesthetic perception allows an agent to normatively anticipate interaction potentialities, thus increasing sense making and reducing the uncertainty of interaction. This conception of aesthetic perception is compatible with contemporary evidence from neuroscience, experimental aesthetics, and interaction design. The proposed model overcomes several problems of transcendental, art-centered, and objective aesthetics as it offers an alternative to the idea of aesthetic objects that carry inherent values by explaining “the aesthetic” as emergent in perception within a context of uncertain interaction. (shrink)

Nowadays, aesthetics are generally considered as a crucial aspect that affects the way we confront things, events, and states of affairs. However, the functional role of aesthetics in the interaction between agent and environment has not been addressed effectively. Our objective here is to provide an explanation concerning the role of aesthetics, and especially, of the aesthetic experience as a fundamental bodily and emotional activity in the respective interactions. An explanation of the functional role of the aesthetic experience could offer (...) new orientations to our understanding of embodied cognition and of aesthetics as a fundamental part of it. We argue that aesthetic experience, especially its emotional dimension, is an evaluative process that influences the anticipation for stable and successful interactions with the environment. In other words, aesthetics facilitates sense-making as they affect what might be anticipated by an action tendency with respect to an environment. (shrink)

Wonder is undoubtedly a term that floats around in today’s academic discussion both on ancient philosophy and on philosophy of education. Back in the 4th century B.C., Aristotle underlined the fact that philosophy begins in wonder, without being very specific about the conditions and the effects of its emergence. He focused a great deal on children’s education, emphasizing its fundamental role in human beings’ moral fulfillment, though he never provided a systematic account of children’s moral status. The aim of this (...) paper is to examine, on the one hand, if, to what extent, and under what conditions, Aristotle allows for philosophical wonder to emerge in children’s souls, and, on the other hand, how his approach to education may shed light to the link between wonder and the ultimate moral end, i.e. human flourishing. We will, thus, 1) try to offer a unified outlook of the philosopher’s views on children’s special cognitive and moral state, and 2) illustrate how wonder contributes in overcoming their imperfect state of being. (shrink)

The plague of 541–542 ad started in Pelusium, a town in Egypt, and reached Constantinople in 542 ad. The following series summarizes the event and its repeated appearance until 746 ad.

In June 2018 the Texan philosopher and distinguished bioethicist Tristram Engelhardt, Jr. crossed the great divide to meet his maker, as he would probably put it. His work remains till now the most systematic effort to fully revise Bioethics based on the doctrines of the Orthodox Christian theology, while it is also apreciseaccount ofEthics and Bioethics in the “after God” era. Engelhardt was anexcellent master of ancient Greek, medieval, western and eastern philosophy, and after heconverted from the Roman Catholic to (...) the Eastern Orthodox Church – officially the Orthodox Catholic Church – he indulged in the works of the Holy Fathers andbecame greatly influenced by them. This is clearlymanifest in his views and continuous reference to Fathers and Ecclesiastical Writers. His conversion crucially influenced not only his bioethical views, but also his entire philosophical system. This magnificent journey obviously turned the Texan philosopher into a true Theologist – not in the academic sense, but in the one the Orthodox Catholic Church accepts, according to which “a Theologist is a person of God, from God, before God and speaks to praise God”. Engelhardt was not the first to deal with bioethical issues under the spectrum of Orthodox Theology, but he was the first to unravel both secular and Western-Church Bioethics and suggest a totally different version of Bioethicsbased on the principles of Orthodox ethics, the ceremonial and esoteric life of the Orthodox Church, having previously made himself a true communicant of both the paternal tradition and dogmatic teaching. (shrink)

Emilios Christodoulidis’ The Redress of Law: Globalisation, Constitutionalism and Market Capture is a rare work in its magnitude and ambition. More than on an argument, the book centres on an impas...

This is the first part of a study on cardinals that are characterizable by Scott sentences. Building on previous work of Hjorth, Malitz, and Baumgartner, we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$ but no models of size $\kappa^{+}$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions, and countable products. We (...) also prove that if $\aleph_{\alpha}$ is characterized by a Scott sentence, at least one of $\aleph_{\alpha}$, $\aleph_{\alpha+1}$, or $$ is homogeneously characterizable. Based on an argument of Shelah, we give counterexamples that characterizable cardinals are not closed under predecessors or cofinalities. (shrink)

The linguistic foundations of science and technology include many terms that have been borrowed from ancient languages. In the case of terms with origins in the Greek language, the modern meaning can often differ significantly from the original one. Here we use the PubMed database to demonstrate the prevalence of words of Greek origin in the language of modern science, and call for scientists to exercise care when coining new terms.