Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case on which (...) to focus in analyzing mathematical depth. After introducing the theorem, four accounts of mathematical depth will be considered. (shrink)

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and (...) proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used (...) several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project. (shrink)

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...) school. For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them. (shrink)

In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay (...) identified for his characterization of degrees of models of arbitrary completions of PA cannot be dropped (I showed that these conditions cannot be simplified in the paper. (shrink)

When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject accordingly.

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this “crisis” as (...) follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano. (shrink)

This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The term ‘modern’ (or ‘modernism’) is used widely in the humanities to describe the era since about 1900, exemplified by Picasso or Kandinsky in the visual arts, Rilke or Pound in poetry, or Le Corbusier or Loos in architecture (a building (...) by the latter graces the cover of this book’s dust jacket). (shrink)

Why do mathematics often give several proofs of the same theorem? This is the question raised in this article, introducing the notion of an epistemic ideal and discussing two such ideals, the explanatoriness and purity of proof.

La ciudad y los perros ha sido expuesta para el análisis de la comunidad hermenéutica durante más de cincuenta años. En ese sentido, es insoslayable recurrir al criterio sistematizador que fundamenta Hans-Georg Gadamer en su texto Verdad y método, que es de utilidad para catalogar y criticar condicionalmente las propuestas que se han desarrollado en torno a la diversidad de representaciones literarias que han sido manifestadas en este libro. Para la efectividad de este trabajo, se asume que este objeto de (...) estudio está comprendido en función de los siguientes tratamientos: la percepción de la realidad real en la obra literaria, su clasificación autobiográfica, la articulación del lenguaje como estilo, la ironía como estrategia discursiva y canalizadora de la violencia y, para terminar, la técnica del final abierto con respecto a la muerte del personaje Ricardo Arana (el Esclavo). Con estos seis planteamientos enfocados desde lo hermenéutico, se pretende producir la confrontación y el diálogo intertextual con los aportes referenciados, con el propósito de que resulte utópica la configuración de un panorama exégeta de la primera novela de Mario Vargas Llosa. (shrink)

Review of Dowek, Gilles, Computation, Proof, Machine, Cambridge University Press, Cambridge, 2015. Translation of Les Métamorphoses du calcul, Le Pommier, Paris, 2007. Translation from the French by Pierre Guillot and Marion Roman.

We review Solomon Feferman's 1998 essay collection In The Light of Logic (Oxford University Press).

Al final de su libro “La conciencia inexplicada”, Juan Arana señala que la nomología, explicación según las leyes de la naturaleza, requiere de una nomogonía, una consideración del origen de las leyes. Es decir, que el orden que observamos en el mundo natural requiere una instancia previa que ponga ese orden específico. Sabemos que desde la revolución científica la mejor manera de explicar dicha nomología ha sido mediante las matemáticas. Sin embargo, en las últimas décadas se han presentado algunas (...) propuestas basadas en modelos matemáticos que fundamentarían muchos aspectos de la realidad. Dos claros ejemplos provienen de Roger Penrose y Max Tegmark. Esto lleva a pensar en una posición no solo nomológica sino además nomogónica de la matemática. ¿Puede la Naturaleza estar fundada por las matemáticas como señalan algunos físico-matemáticos? Y en ese caso, ¿sería pertinente buscar una nomo-génesis de esta índole en la constitución de la conciencia? -/- At the end of his book “La conciencia inexplicada”, Juan Arana points out that nomology, explanation according to the laws of nature requires a nomogony, an account of the origin of the laws. This means that the order that we can observe in the natural World demands something prior to posit that specific order. Since the scientific revolution we know that the best way to explain that nomology has been through mathematics. Anyway, in recent decades a number of proposals based on mathematical models that found many aspects of reality has been offered. Two clear examples come from Roger Penrose and Max Tegmark. This drives us to think of a position of mathematics as not only nomological but also nomogonical. Can Nature be founded by mathematics as some physicists and mathematicians point out? And, in this case, would be relevant this kind of approach to search a nomo-genesis in the constitution of consciousness? (shrink)

Today, the Internet is a rich source of study materials, and Google Scholar offers free access to a large number of scientific articles. There are excellent research publications available in many more databases. Students have the option of easily copying the material. Reusing, paraphrasing, patchwriting, and ghostwriting without citing the original documents are plagiarism. Plagiarism is increasing in academics, particularly in research. This study aims to study the awareness of plagiarism and to analyze the reasons for plagiarism. The study samples (...) are the student teachers in India. For this study, we used a survey method, and the author prepared a questionnaire to collect data from the student teachers. Study respondents are the student teachers of the Regional Institute of Education Mysore; Purposive sampling was used to select samples. The total number of study respondents is 207. The findings of the study revealed that over 70 per cent of respondents mentioned reasons for plagiarism as lack of relevant literature studying, lack of preparation and time, difficulty checking every piece of work, do not know the manual citation style, lack of knowledge about bibliographic management software and also they stated that getting easily available materials on the internet is also a reason for plagiarism. The study recommends that teachers teach or conduct awareness programs on plagiarism, avoiding plagiarism, citation style, and software. (shrink)

The paper offers a model of Kant's claim that unity of consciousness entails objectivity of experience. This claim has nothing especially to do with thought, language or the categories but is a general truth about arbitrary signaling systems of the sort modeled in the paper. In conclusion I draw some consequences for various forms of idealism.

As a member of the so-demarcated 'Generation Z,' I have been blessed/damned with a front-row seat to the technological evolution kicked off by the COVID-19 Pandemic of 2020, and have succeeded to varying degrees in recognizing its effects and responding to them with the efficiency and care that my neurological soul deserves. Jean-Paul Sartre's conception of bad faith provides an excellent scalpel for the dissection of such a quasi-biological progression, and in this paper, I analyze the third dimension of bad (...) faith that has become possible in the 21st century, that of the digital realm. I wish whoever has read this far immense luck in their personal voyage across the 70,000 fathoms of the internet, an electrical space organized for the mechanized transfusion of suffering into profit. Delete Instagram if you are not using it to proliferate wealth yourself. Go outside and lay in the grass. -/- "Remember being happy in our silence." -Warning, Bridges. (shrink)

Sample chapter from H. Asgeirsson, The Nature and Value of Vagueness in the Law (Hart Publishing, 2020), in which I present and partially defend a version of what has come to be called the communicative-content theory of law. Book abstract: Lawmaking is – paradigmatically – a type of speech act: people make law by saying things. It is natural to think, therefore, that the content of the law is determined by what lawmakers communicate. However, what they communicate is sometimes vague (...) and, even when it is clear, the content itself is sometimes vague. The monograph examines the nature and consequences of these two linguistic sources of indeterminacy in the law with the aim of providing plausible answers to three related questions: In virtue of what is the law vague? What might be good about vague law? How should courts resolve cases of vagueness? (shrink)

“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, philosophy and history of (...) science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

The study aims to identify the efficiency of the university education performance from the perspective of postgraduate and undergraduate students in international and Palestinian universities. The analytical descriptive approach was used for this purpose and the questionnaire was used as a main tool for data collection. The study community consists of: post graduate students, (23850) graduate students and (146355) undergraduate students. The sample of the study was 378 graduate students and 383 undergraduate students. The random stratified sample was used. The (...) Statistical Package of Social Sciences (SPSS) was also used for data analysis. The study reached a number of results, the most important of which are: The level of efficiency of educational performance in Palestinian and international universities from the point of view of postgraduate and undergraduate students was high. And that there are significant differences between the average views of the sample of the study on the efficiency of educational performance in Palestinian and international universities attributed to the University and to the benefit of international universities. The study concluded many recommendations, the most important of which is the necessity of continuing to develop e-learning strategies that affect the efficiency of educational performance and research commensurate with the university's position in the local and international community, which puts it on the best classification between local and international universities through e-learning. (shrink)

Background If trials of therapeutic interventions are to serve society's interests, they must be of high methodological quality and must satisfy moral commitments to human subjects. The authors set out to develop a clinical - trials compendium in which standards for the ethical treatment of human subjects are integrated with standards for research methods. Methods The authors rank-ordered the world's nations and chose the 31 with >700 active trials as of 24 July 2008. Governmental and other authoritative entities of the (...) 31 countries were searched, and 1004 English-language documents containing ethical and/or methodological standards for clinical trials were identified. The authors extracted standards from 144 of those: 50 designated as ‘core’, 39 addressing trials of invasive procedures and a 5% sample of the remainder. As the integrating framework for the standards we developed a coherent taxonomy encompassing all elements of a trial's stages. Findings Review of the 144 documents yielded nearly 15 000 discrete standards. After duplicates were removed, 5903 substantive standards remained, distributed in the taxonomy as follows: initiation, 1401 standards, 8 divisions; design, 1869 standards, 16 divisions; conduct, 1473 standards, 8 divisions; analysing and reporting results, 997 standards, four divisions; and post-trial standards, 168 standards, 5 divisions. Conclusions The overwhelming number of source documents and standards uncovered in this study was not anticipated beforehand and confirms the extraordinary complexity of the clinical trials enterprise. This taxonomy of multinational ethical and methodological standards may help trialists and overseers improve the quality of clinical trials, particularly given the globalisation of clinical research. (shrink)

Do thay đổi chính sách Journal Citation Reports (JCR) 2023 có vài cải tiến. Các ấn phẩm trong Core Collections đều được công bố Journal Impact Factor (JIF).

Abstract: Heart diseases are increasing daily at a rapid rate and it is alarming and vital to predict heart diseases early. The diagnosis of heart diseases is a challenging task i.e. it must be done accurately and proficiently. The aim of this study is to determine which patient is more likely to have heart disease based on a number of medical features. We organized a heart disease prediction model to identify whether the person is likely to be diagnosed with a (...) heart disease or not using the medical features of the person. We used many different algorithms of machine learning such as Gaussian Mixture, Nearest Centroid, MultinomialNB, Logistic RegressionCV, Linear SVC, Linear Discriminant Analysis, SGD Classifier, Extra Tree Classifier, Calibrated ClassifierCV, Quadratic Discriminant Analysis, GaussianNB, Random Forest Classifier, ComplementNB, MLP Classifier, BernoulliNB, Bagging Classifier, LGBM Classifier, Ada Boost Classifier, K Neighbors Classifier, Logistic Regression, Gradient Boosting Classifier, Decision Tree Classifier, and Deep Learning to predict and classify the patient with heart disease. A quite helpful approach was used to regulate how the model can be used to improve the accuracy of prediction of heart diseases in any person. The strength of the proposed model was very satisfying and was able to predict evidence of having a heart disease in a particular person by using Deep Learning and Random Forest Classifier which showed a good accuracy in comparison to the other used classifiers. The proposed heart disease prediction model will enhances medical care and reduces the cost. This study gives us significant knowledge that can help us predict the person with heart disease. The dataset was collected from Kaggle depository and the model is implemented using python. (shrink)

The problem of divine hiddenness discussed among both theist and non- theist circles. From an atheistic perspective the existence of people who are sincerely looking for God but cannot reach Him is a supportive point for atheism. On the other side, same problem supports agnosticism since there are equal evidence from both side for the existence of God from an agnostic perspective. The theists who are belonging to different religion have tried to find some solutions to this problem. For instance; (...) there is a theistic understanding which claims hiddenness of God provides us freedom to believe and another one says it is the only way to have personal relationship with God. A different position brings solution from the Jewish idea that chosen people of God. In this article, I have evaluated those different approaches. In the first section, I have indicated that there is no agreement on the implication of divine hiddenness problem even amongst non-theistic positions by shortly introducing atheistic and agnostic approaches. In the second section, I dealt with theistic approaches and the problems that they produced while trying to provide a solution to the problem. After an inquiry on how we are supposed to understand hiddenness, I have tried to show the problem has nothing new since premises of the divine hiddenness problem are not verifiable by everyone. As a conclusion I have offered postponing the divine hiddenness problem and discussing existence of God on a rational ground by presenting a counterargument. (shrink)

This chapter uncovers a less investigated aspect of the relationship between the two most important scholastic schools of the Renaissance, Thomism and Scotism: the influence of Scotist literature on distinctions as seen in some sixteenth-century Thomists. The chapter has a primary focus on Chrysostomus Javelli’s engagement in his discussion of divine attributes with the Scotist doctrine of distinctions, but also considers other Thomist sources. First, the beginnings of the highly specialised Scotist literature on distinctions are traced back to the start (...) of the fourteenth century; I show how some early followers of Duns Scotus, in particular Francis of Meyronnes and Petrus Thomae, systematised Scotus’ ontology of the various grades of being by compiling lists of subtle distinctions to be applied to various levels of reality. I give some indications as to the later reception of these models of distinctions in the Scotist school. Special attention is paid to Étienne Brulefer, since his summary of Petrus Thomae’s model of seven distinctions was Javelli’s source for the Scotist doctrine. I then investigate how Javelli worked with Brulefer’s summary, and how he sought to integrate the Scotist doctrine into his own discussion of divine attributes. Thomists traditionally allowed only a rational or mental kind of distinction among divine attributes, and between them and the divine essence. Javelli, however, endeavours to show how the Thomist position may be reconciled with the Scotist doctrine of a formal or ex natura rei distinction. He did not always endorse this conciliatory approach; I hypothesise that he changed his mind on the subject over time. Finally, I show how other Renaissance Thomists reacted to the Scotist system of distinctions; in particular, I draw attention to the Thomists Andreas Bodenstein von Karlstadt, Bartolomeo Manzoli, and Mattia Gibboni da Aquario, who all wrote treatises on Thomist distinction theory modelled on the Scotist system of distinctions. In some of this literature, lists of distinctions based on Thomist metaphysics were compiled in order to replace the Scotist system. I argue that Javelli’s approach is more conciliatory and, in fact, has some overlap with the concordist thought of Giovanni Pico della Mirandola, who himself considered Scotus and Aquinas to be in fundamental agreement as regards the distinction between divine attributes. (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

Should a principle of charity be applied to the interpretation of the colour concepts exercised in visual experience? We think not. We shall argue, for one thing, that the grounds for applying a principle of charity are lacking in the case of colour concepts. More importantly, we shall argue that attempts at giving the experience of colour a charitable interpretation either fail to respect obvious features of that experience or fail to interpret it charitably, after all. Charity to visual experience (...) is therefore no motive for resisting the natural, Galilean response to a scientific understanding of light and vision. The best interpretation of colour experience ends up convicting it of widespread and systematic error. (shrink)

We approach the notion of general (global) human intelligence as a prominently multifaceted concept which can be tested in at least seventy specific scenarios. We say that an agent has Artificial Global Intelligence (AGLI), if it is able to perform in an intelligent manner for at least the collection of tasks defining the former scenarios. In particular, based on Gartner's multiple intelligences theory, we describe the design of a concrete test for AGLI made in such a way that an ‘average’ (...) young human being should, per diffinitionem, pass it. We compare our holistic test with several highly representative human and artificial intelligence tests for deducing that our AGLI test is the one with the broader scope of the whole range of intelligence. However, we claim as a plausible hypothesis and based on the wide thematic spectrum of the test that the most outstanding inventions of AI currently available are far from getting a high score on it. Finally, we open a discussion about the fact that, although there are artificial agents being able to simulate intelligent behaviour at a perfect level for several local tasks, this seems not to be the case for AGLI. This would imply, in particular, a kind of practical implausibility of the notion of intelligence explosion coming from philosophy of AI. (shrink)

The general methodology of "algebraizing" logics is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved.

This study aims to understand the perceptions and opinions of academicians towards ChatGPT-3 by collecting and analyzing social media comments, and a survey was conducted with library and information science professionals. The research uses a content analysis method and finds that while ChatGPT-3 can be a valuable tool for research and writing, it is not 100% accurate and should be cross-checked. The study also finds that while some academicians may not accept ChatGPT-3, most are starting to accept it. The study (...) is beneficial for academicians, content developers, and librarians. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in time, He does not (...) know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

1st to date [partial yet irrefutable] proof of this creed well-foundedness.

People’s health is hugely affected by where they live, their occupational status and their socio-economic position. It has been widely argued that the presence of such social determinants in health provides good reasons to reject luck egalitarianism as a theory of distributive justice in health. The literature provides different reasons why this responsibility-sensitive theory of distributive justice should not be applied to health. The critiques submit that the social circumstances undermine or remove people’s responsibility for their health; responsibility sensitive health (...) policies would adversely affect those who are worst off and; the luck egalitarian approach to health distracts from the important task of rectifying socio-economic influences on people's health and provides individualistic solutions to collective problems. But for each of these variants of the critique luck egalitarianism provides suitable answers. The literature on social determinants is no detriment to the project of applying luck egalitarianism to health. (shrink)

Crowdfunding is a way to fund a project by pooling incremental investments from a large number of funders. This can be a great way to fund OA publications, especially for projects that lack traditional funding sources.

We present a multidisciplinary, universal a pragmatic theory of causation based explicitly on five methodological causal seminal dimensions. The first one is called formal-mathematical-idealist theory and emerges as a meta-conceptual fusion of several existing causal theories. The second one is essentially based on a global, scientific and technical perspective. In fact, this can be considered as a meta-dimension encompassing a huge number of academic disciplines. The third dimension arises once more as combination of former approaches having the mind and its (...) laws as the central paradigm. The fourth one is structurally related with our subjective phenomenological world and its objective impact on the external universe. And, finally, the fifth dimension is closely related with the first one, but more oriented toward the global implicit purpose of the universe and what this implies causally on the events in nature. We give several concrete examples elucidating the explanatory range of our theory. (shrink)

A new formulation of the Fine-Tuning Argument (FTA) for the existence of God is offered, which avoids a number of commonly raised objections. I argue that we can and should focus on the fundamental constants and initial conditions of the universe, and show how physics itself provides the probabilities that are needed by the argument. I explain how this formulation avoids a number of common objections, specifically the possibility of deeper physical laws, the multiverse, normalisability, whether God would fine-tune at (...) all, whether the universe is too fine-tuned, and whether the likelihood of God creating a life-permitting universe is inscrutable. (shrink)

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

Abstract Most discussions of risk are developed in broadly consequentialist terms, focusing on the outcomes of risks as such. This paper will provide an alternative account of risk from a virtue ethical perspective, shifting the focus to the decision to take the risk. Making ethical decisions about risk is, we will argue, not fundamentally about the actual chain of events that the decision sets in process, but about the reasonableness of the decision to take the risk in the first place. (...) A virtue ethical account of risk is needed because the notion of the ‘reasonableness’ of the decision to take the risk is affected by the complexity of the moral status of particular instances of risk-taking and the risk-taker’s responsiveness to these contextual features. The very idea of ‘reasonable risk’ welcomes judgments about the nature of the risk itself, raises questions about complicity, culpability and responsibility, while at its heart, involves a judgement about the justification of risk which unavoidably focuses our attention on the character of the individuals involved in risk making decisions. Keywords: Risk; ethics; morality; responsibility; virtue; choice; reasons . (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of generalizations, (...) not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

Alain Badiou is one of the world's most influential living philosophers. Few contemporary thinkers display his breadth of argument and reference, or his ability to intervene in debates critical to both analytic and continental philosophy. Alain Badiou: Key Concepts presents an overview of and introduction to the full range of Badiou's thinking. Essays focus on the foundations of Badiou's thought, his "key concepts" - truth, being, ontology, the subject, and conditions - and on his engagement with a range of thinkers (...) central to his philosophy, including Plato, Descartes, Spinoza, Heidegger and Deleuze. (shrink)

There is a type of metaphysical picture that surfaces in a range of philosophical discussions, is of intrinsic interest, and yet remains ill-understood. According to this picture, the world contains a range of standpoints relative to which different facts obtain. Any true representation of the world cannot but adopt a particular standpoint. The aim of this paper is to propose a regimentation of a metaphysics that underwrites this picture. Key components are a factive notion of metaphysical relativity, a deflationary notion (...) of adopting standpoints, and two kinds of valid inference, one that allows one to abandon standpoints and one that does not. To better understand how theories formulated in terms of this framework are situated in dialectical space, I sketch a theory in the philosophy of time that admits both temporal and atemporal standpoints. (shrink)

I propose a distinct type of robustness, which I suggest can support a confirmatory role in scientific reasoning, contrary to the usual philosophical claims. In model robustness, repeated production of the empirically successful model prediction or retrodiction against a background of independentlysupported and varying model constructions, within a group of models containing a shared causal factor, may suggest how confident we can be in the causal factor and predictions/retrodictions, especially once supported by a variety of evidence framework. I present climate (...) models of greenhouse gas global warming of the 20th Century as an example, and emphasize climate scientists’ discussions of robust models and causal aspects. The account is intended as applicable to a broad array of sciences that use complex modeling techniques. (shrink)

We describe (essential features and an axiomatization of) a new metamathematical (cognitive) ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions, and playing a fundamental role in Artificial Mathematical Intelligence (or Cognitive-computational metamathematics). Furthermore, we present an initial (first-order) formalization of this mechanism together with its characterizing relation with classic notions like primitive positive definability and Diophantiveness. Additionally, we analyze the semantic variability of functional conceptual substratum when small syntactic modifications are done. Finally, (...) we describe cognitively natural inference rules for (mathematical) definitions inspired by functional conceptual substratum and we show that they are sound and complete w.r.t.\ standard calculi. (shrink)

The boundless nature of the natural numbers imposes paradoxically a high formal bound to the use of standard artificial computer programs for solving conceptually challenged problems in number theory. In the context of the new cognitive foundations for mathematics' and physics' program immersed in the setting of artificial mathematical intelligence, we proposed a refined numerical system, called the physical numbers, preserving most of the essential intuitions of the natural numbers. Even more, this new numerical structure additionally possesses the property of (...) being a bounded object allowing us to work with quite similar axioms like the classic Peano axioms, but in a finite environment and with an enriched physical dimension. Finally, we present several enlightening examples and we conclude that the physical numbers provide a natural formal setting for approaching classic problems in number theory from a more hybrid perspective, i.e. with a potential participation in the generation of solutions, not only of working mathematicians but also of more sophisticated artificial interactive (mathematical) intelligent agents (within the context of cognitive-computational metamathematics or artificial mathematical intelligence) and more controlled by physically-inspired principles. Finally, this paper addresses a highly new, bottom-up and paradigm-shifting approach to the foundations of physics: One should refine and improve the conceptual formal setting of the language that we use for understanding physical phenomena (e.g. the mathematical grounding concepts and theories) for being able to understand better more subtle and complex physical phenomena. (shrink)

Abstract This chapter addresses the meta-ethical and psychological implications of Murdoch’s epistemic internalism—her claim that moral responsiveness is a condition of reliable and accurate moral evaluations. Part 1 examines Murdoch’s view that moral judgments feature a quasi-experiential phenomenology analogous to that of certain perceptual ones. Focussing on the phenomenology of our perception-based judgments of certain aspectual properties (e.g., pictorial and musical ones) it argues that such judgments support both Murdoch’s analogy and the internalism she takes it to imply. In Part (...) 2 this chapter considers Murdoch’s internalism as a psychological thesis, assessing it in view of several empirical studies of psychopathic subjects. It argues that the psychopath’s distinctive complex of cognitive and motivational deficits supports Murdoch’s conviction that moral judgment and moral motivation are interdependent. Just as Murdoch believed, many of our ordinary, non-pathological moral beliefs seem to be the natural progeny of our responsiveness to other persons, and so inherit the intrinsic power that others have to move us. (shrink)