A famous theorem by van der Waerden states the following: Given any finite coloring of the integers, one color contains arbitrarily long arithmetic progressions. Equivalently, for every q,k, there is an N = N(q,k) such that for every q-coloring of an interval of length N one color contains a progression of length k. An obvious question is what is the growth rate of N = N(q,k). Some proofs, like van der Waerden's combinatorial argument, answer this question directly, while the topological (...) proof by Furstenberg and Weiss does not. We present an analysis of (Girard's variant of) Furstenberg and Weiss's proof based on monotone functional interpretation, both yielding bounds and providing a general illustration of proof mining in topological dynamics. The bounds do not improve previous results by Girard, but only—as is also revealed by the analysis—because the combinatorial proof and the topological dynamics proof in principle are identical. (shrink)

In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach , Oxford University Press, Oxford, 1996, pp. 225–260) to analyze Cheney's simplification 189) of Jackson's original proof 320) of the uniqueness of the best L1-approximation of continuous functions fC[0,1] by polynomials pPn of (...) degree n. Cheney's proof is non-effective in the sense that it is based on classical logic and on the non-computational principle WKL . The result of our analysis provides the first effective uniform modulus of uniqueness . Moreover, the extracted modulus has the optimal ε-dependency as follows from Kroó 331). The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed fC[0,1] with arbitrary precision. The second author uses this result to give a complexity upper bound on the computation of the best L1-approximation in Oliva 66–77). (shrink)

We obtain an equivalent implicit characterization of Lp Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for such spaces into a higher order logical system, the kind of which is used in proof mining, a research program that aims to obtain the hidden computational content of mathematical proofs using tools from mathematical logic. As an aside, we obtain a concrete way of formalizing Lp spaces in positive-bounded logic. The axiomatization is followed (...) by a corresponding metatheorem in the style of proof mining. We illustrate its use with the derivation for this class of spaces of the standard modulus of uniform convexity. (shrink)

Hilbert’s program: • Formalize abstract, infinitary, nonconstructive mathematics. • Prove consistency using only finitary methods.

It is well-known that an element of a commutative ring with identity is nilpotent if, and only if, it lies in every prime ideal of the ring. A modification of this fact is amenable to a very simple proof mining analysis. We formulate a quantitative version of this modification and obtain an explicit bound. We present an application. This proof mining analysis is the leitmotif for some comments and observations on the methodology of computational extraction. In (...) particular, we emphasize that the formulation of quantitative versions of ordinary mathematical theorems is of independent interest from proof mining metatheorems. (shrink)

In view of an enhancement of our implementation on the computer, we explore the possibility of an algorithmic optimization of the various proof-theoretic techniques employed by Kohlenbach for the synthesis of new effective uniform bounds out of established qualitative proofs in Numerical Functional Analysis. Concretely, we prove that the method of “colouring” some of the quantifiers as “non-computational” extends well to ε-arithmetization, elimination-of-extensionality and model-interpretation.

We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research programme that aims to obtain the hidden computational content of ordinary mathematical proofs using tools from proof theory.

In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...) this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice. (shrink)

\noindent\textbf{Introduction} Online interventions hold great potential for Therapeutic Change Process Research (TCPR), a field that aims to relate in-therapeutic change processes to the outcomes of interventions. Online a client is treated essentially through the language their counsellor uses, therefore the verbal interaction contains many important ingredients that bring about change. TCPR faces two challenges: how to derive meaningful change processes from texts, and secondly, how to assess these complex, varied and multi-layered processes? We advocate the use text mining and (...) multi-level models (MLMs): the former offers tools and methods to discovers patterns in texts; the latter can analyse these change processes as outcomes that vary at multiple levels. \noindent\textbf{Method} We (re-)used the data from \cite{Lamers2015} because it includes outcomes and the complete online intervention for clients with mild depressive symptoms. We used text mining to obtain basic text-variables from e-mails, that we analysed through MLMs. \noindent\textbf{Results} We found that we could relate outcomes of interventions to variables containing text-information. We conclude that we can indeed bridge text mining and MLMs for TCPR as it was possible to relate text-information (obtained through text mining) to multi-levelled TCPR outcomes (using a MLM). \noindent\textbf{Discussion} Text mining can be helpful to obtain change processes, which is also the main challenge for TCPR. We showed how MLMs and text mining can be combined, but our proposition leaves open how to obtain the most relevant textual operationalization of TCPR concepts. That requires interdisciplinary collaboration and discussion. The future does look bright: based on our proof-of-concept study we conclude that MLMs and text mining can indeed advance TCPR. (shrink)

西洋哲学に対峙した日本の二人の思索者は無や直観、時間や場所などの主題をめぐり何を共有し、どうすれ違ったのか。明晰な最新研究。.

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by (...) the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

オリンピック招致問題、部活絶対主義、スポーツへの逃避、無気力試合...... スポーツにかかわる問題の解決に求められている姿勢とは?スポーツに関して、自分の意見に会わない人や新しい情報に接し、自分とは違う考えを取り入れることが、スポーツを理解する素晴らしいヒントになる。複雑な真 実から目をそらさず、学びを止めない姿勢が、今、求められている。.

The task of this article is to propose an alternative method for adjudicating truth claims between various paradigms. Informed by sources such as Augustine, Aquinas, Heidegger, Gadamer, and Kuhn, I argue for a form of reasoning which aspires to credibility, plausibility, and explanatory capacity, rather than absolute proof. Instead of representing a flight from scientific standards, I argue that such an approach ultimately represents the best hope of safeguarding the essence of science and rationality as such.

Early Childhood and Neuroscience is a practical guide to understanding the complex and challenging subject of neuroscience and its use (and misapplication) in early childhood policy and practice. The 2nd edition has been updated throughout and includes three new chapters on: - the effects of childhood trauma - school readiness - neurodiversity It also includes a new Foreword by Laura Jana (Penn State University, USA). The book provides a balanced overview of the debates by weaving discussion on the opportunities of (...) using neuroscience in early childhood practice with examination of the limitations and ethical implications throughout the chapters. This enables students to inform their own opinions about the discipline and its use in their future practice. Clear explanations of the main terms and theories are complemented with illustrative case studies of cutting-edge research from around the world, a glossary of key terms and suggestions for further reading. Reflective discussion questions give students the chance to apply their theoretical knowledge to real-world contexts. (shrink)

Having a good grasp of theories of child development and what these look like in practice, can make a positive difference to how you understand babies and children and the ways in which they learn. This guide offers easy access to a wide range of concepts, as well as traditional and current theories, of how babies and children learn. Each chapter offers clear guidance on how to recognise the theory in action within the setting and suggests ways to test these (...) ideas out in early years' settings, supporting the development of reflective practice. Case studies are included throughout, along with questions to guide thinking and encourage readers to develop their practice. Summaries conclude each chapter offering a quick reference of the theory examined and the benefits of applying it to practice. An essential guide for those looking to develop their practice in supporting child development within the Early Years. (shrink)

This paper proposes an agent community based information retrieval method, which uses agent communities to manage and look up information related to users. An agent works as a delegate of its user and searches for information that the user wants by communicating with other agents. The communication between agents is carried out in a peer-to-peer computing architecture. In order to retrieve information related to a user query, an agent uses two histories : a query/retrieved document history(Q/RDH) and a query/sender agent (...) history(Q/SAH). The former is a list of pairs of a query and retrieved documents, where the queries were sent by the agent itself. The latter is a list of pairs of a query and sender agents and shows ``who sent what query to the agent''. This is useful to find a new information source. Making use of the Q/SAH is expected to cause a collaborative filtering effect, which gradually creates virtual agent communities, where agents with the same interests stay together. Our hypothesis is that a virtual agent community reduces communication loads to perform a search. As an agent receives more queries, then more links to new knowledge are achieved. From this behavior, a ``give and take''(or positive feedback) effect for agents seems to emerge. We implemented this method with Multi-Agents Kodama which has been developed in our laboratory, and conducted preliminary experiments to test the hypothesis. The empirical results showed that the method was much more efficient than a naive method employing 'broadcast' techniques only to look up a target agent. (shrink)

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.

Bringing together an international collection of experts, this work explores various philosophical issues surrounding modern music recordings. With perspectives from practicing musicians, musicologists, sound artists, and recordings engineers, this reference asks how theoretical issues related to their work relate to the context of making and using recordings. Additional questions asked by this study include What kind of “spatiality” is generated through recordings, and by what means? What is the nature of “recorded space”? Do recordings reflect musical reality or create one? (...) and What are the philosophical bases of an “ethics” of recording? (shrink)

Abstract“Natural syllogisms” are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants (Politzer, 2011) have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy (known as ecthesis in classic logic) and an operational use of the concept of inclusion (the recognition that an element that belongs to a subset must belong to the (...) set but not vice versa), it was hypothesized that these syllogisms would be within the grasp of non‐adult participants, provided they have acquired the notion of deductive validity. Here, 11‐year‐old children were presented with natural syllogisms embedded in short dialogs. The first experiment showed that their performance was equivalent to adults' highest level of performance in standard experiments on syllogisms. The second experiment, while confirming children's proficiency in solving natural syllogisms, showed that they outperformed children who solved non‐natural matched syllogisms in the same experimental setting. The results are also in agreement with the argumentation theory of reasoning. (shrink)

Objective To compare assessments of the decision-making competencies of psychiatric inpatients as provided by physicians, nurses, relatives and an assessment tool.Methods This study was carried out at the psychiatry clinic of Kocaeli University Hospital from June 2007 to February 2008. The decision-making competence of the 83 patients who participated in the study was assessed by physicians, nurses, relatives and MacCAT-T.Results Of the 83 patients, the relatives of 73.8% of them, including the parents of 47.7%, were interviewed during the study. A (...) moderately good consistency between the competency assessments of the nurses versus those of the physicians, but a poor consistency between the assessments of the physicians and nurses versus those of the patients’ relatives, was determined. The differences in the competency assessment obtained with the MacCAT-T versus the evaluations of the physicians, nurses and patients’ relatives were statistically significant.Conclusions Our findings demonstrate those physicians, nurses and the patients’ relatives have difficulty in identifying patients lacking decision-making competence. Therefore, an objective competence assessment tool should be used along with the assessments of physicians and nurses, both of whom can provide clinical data, as well as those of relatives, who can offer insights into the patient's moral values and expectations. (shrink)

O presente ensaio tem por objetivo contribuir com o debate sobre o valor e universalidade da democracia para a emancipação humana. Propõe pensar a compreensão da universalidade da democracia no enfoque abrangente da cultura argumentativa, a partir de Amartya Sen e Jürgen Habermas. Entende que as abordagens metodológicas, pragmática de um e pragmática formal do outro dos autores são complementares. Nesta perspectiva procura demonstrar que a democracia, além de suas raízes institucionais modernas, vincula-se também a expressões culturais da Índia, África (...) e América pré-colombiana. Portanto não é mera expressão de domínio cultural e político ocidental, mas desenvolvimento de uma tendência profunda de governo mediante a discussão e razão pública. O que permite recepcionar de um ponto de vista mais amplo a contribuição do pensamento de Habermas que explicita o nexo interno entre Justiça, Direitos Humanos e Democracia, na perspectiva procedimental de uma esfera pública crítica com uma racionalidade pública que inclui a todos. Apresenta o desenvolvimento das capacidades políticas e sociais, bem como o papel instrumental da democracia, na construção da compreensão dos direitos e da cultura que permitem o aprendizado, a emancipação e o desenvolvimento da própria identidade. (shrink)

O presente ensaio com metodologia de pesquisa reconstrutiva questiona como a interação entre democracia, direitos humanos, justiça e imperativos globais é disposta no pensamento de Habermas. Seu objetivo é a explicitação racional de seus nexos internos. Expõe como Habermas, a partir da reconstrução da esfera pública e agir comunicativo aborda a justiça e o direito. A dialética entre facticidade e validade, entrelaça filosofia e sociologia para desenvolver sua abordagem normativa do direito e do Estado, conectando direito e democracia através do (...) paradigma discursivo do direito. Conecta jurisdição constitucional, direito, política, sociedade civil e esfera pública. (shrink)

We will apply the methods developed in the field of ‘proof mining’ to the Bolzano-Weierstraß theorem BW and calibrate the computational contribution of using this theorem in proofs of combinatorial statements. We provide an explicit solution of the Gödel functional interpretation as well as the monotone functional interpretation of BW for the product space Πi ∈ℕ[–ki, ki] . This results in optimal program and bound extraction theorems for proofs based on fixed instances of BW, i.e. for BW applied (...) to fixed sequences in Πi ∈ℕ[–ki, ki]. (shrink)