The theory of Yin and Yang and the Five Movements is based on the concept of cyclical time. This ancient cosmological model postulates that when expansive energy reaches its apex, mutual life-saving relations prevail over mutually conflictual societal relations, and that this cycle repeats. This cosmic change model was first presented in ancient Korea and China, by Hado-Nakseo, via numerological configurations and symbols. The Hado diagram was drawn by a Korean thinker, Bok-hui (?-BC3413), also known as Great Empeor Fuzi or (...) Fu-hsi in Chinese mythology. Confucius once recognized him as the father of I Ching (Book of Changes). The Eastern cosmology was further developed by King Wen and the Duke of Zhou and compiled by Confucius (BC551?-BC 479) during the Spring and Autumn Period and the Warring States Period. Nakseo diagram was first discovered by the famous King Wu of China, who founded the Xia dynasty. In contrast to the harmonious mathematical matrix of Hado, Nakseo symbolizes the conflictual and dynamic expansion of the universe. In the Nakseo world, masculine energy is structurally greater than feminine energy, continuously breeding disequilibrium and conflict. The Yin and Yang model suggests that everything in the universe exists as a combination of opposing dynamics. At any given time, one of the two dynamics grows while the other declines. When Yang energy is at its peak, Yin energy is at its nadir; then, a reversal occurs; and envetually the whole cycle repeats. It would thus be logical to express that when conflictual energy has reached its apex harmonious energy begins to wax. It can be argued that since the state of disequilibrium within the universe represented by Nakseo cannot indefinitely sustain its dynamic of expansion, harmonious international relationships eventually come to pervade the world. This argument represents a unique applicationof the concept of Yin and Yang logic to international arms race and arms control. This cyclical dynamics can explain the long-term process of arms build-up followed by eventually by nuclear standoff and subsequent nuclear arms control regimes as NPT, CTBT, MTCR, SALT, START, PSI and etc. One can boldly claim that Yin and Yang logic offers a clue to creating a theory of structural peace by discovering a constructivist element in the model. The esoteric matrixes of ancient Korea and China thus provide humanity with an new vision for nuclear disarmament and a sustainable peace. (shrink)

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis (...) of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

I discuss a stochastic model of language learning and change. During a syntactic change, each speaker makes use of constructions from two different idealized grammars at variable rates. The model incorporates regularization in that speakers have a slight preference for using the dominant idealized grammar. It also includes incrementation: The population is divided into two interacting generations. Children can detect correlations between age and speech. They then predict where the population’s language is moving and speak according to that prediction, which (...) represents a social force encouraging children not to sound out-dated. Both regularization and incrementation turn out to be necessary for spontaneous language change to occur on a reasonable time scale and run to completion monotonically. Chance correlation between age and speech may be amplified by these social forces, eventually leading to a syntactic change through prediction-driven instability. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. (...) Several attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

The philosophy of linguistics is a rich philosophical domain which encompasses various disciplines. One of the aims of this thesis is to unite theoretical linguistics, the philosophy of language, the philosophy of science and the ontology of language. Each part of the research presented here targets separate but related goals with the unified aim of bringing greater clarity to the foundations of linguistics from a philosophical perspective. Part I is devoted to the methodology of linguistics in terms of scientific modelling. (...) I argue against both the Conceptualist and Platonist interpretations of linguistic theory by means of three grades of mathematical involvement for linguistic grammars. Part II explores the specific models of syntactic and semantics by an analogy with the harder sciences. In Part III, I develop a novel account of linguistic ontology and in the process comment on the type-token distinction, the role and connection with mathematics and the nature of linguistic objects. In this research, I offer a structural realist interpretation of linguistic methodology with a nuanced structuralist picture for its ontology. This proposal is informed by historical and current work in theoretical linguistics as well as philosophical views on ontology, scientific modelling and mathematics. (shrink)

The relevance of exchange effects for the stability of superheavy nuclei is examined within a linear QHD-II model by comparing Hartree-Fock with meanfield results. To allow a scan of the complete superheavy regime the recently developed local density approximation (LDA) for the exchange potential is employed for the Hartree-Fock level calculations. It turns out that, while many nuclear properties obtained with the LDA approach differ significantly from the corresponding mean-field results, the predictions of the two methods for shell closures (...) are very similar. Furthermore, a comparison with a nonlinear variant of QHD-II shows that many nuclear properties obtained with the LDA in the framework of linear QHD-II are somewhere in-between the corresponding linear and nonlinear mean-field results. This indicates that the LDA exchange partially includes nonlinear contributions, which supports the interpretation of the meson self-coupling as a parametrization of many-body effects. (shrink)

A holobiont is a composite organism consisting of a host together with its microbiome, such as a coral with its zooxanthellae. To explain the often intimate integration between hosts and their microbiomes, some investigators contend that selection operates on holobionts as a unit and view the microbiome’s genes as extending the host’s nuclear genome to jointly comprise a hologenome. Because vertical transmission of microbiomes is uncommon, other investigators contend that holobiont selection cannot be effective because a holobiont’s microbiome is (...) an acquired condition rather than an inherited trait. This disagreement invites a simple mathematical model to see how holobiont selection might operate and to assess its plausibility as an evolutionary force. This paper presents two variants of such a model. In one variant, juvenile hosts obtain microbiomes from their parents (vertical transmission). In the other variant, microbiomes of juvenile hosts are assembled from source pools containing the combined microbiomes of all parents (horizontal transmission). According to both variants, holobiont selection indeed causes evolutionary change in holobiont traits. Therefore, holobiont selection is plausibly an effective evolutionary force with either mode of microbiome transmission. The modeling employs two distinct concepts of inheritance, depending on the mode of microbiome transmission: collective inheritance whereby juveniles inherit a sample of the collected genomes from all parents, as contrasted with lineal inheritance whereby juveniles inherit the genomes from only their own parents. A distinction between collective and lineal inheritance also features in theories of multilevel selection. (shrink)

The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most (...) important cause of cyclical crises stems from strong structural disproportions that develop during economic booms. These are not only disproportions between different economic sectors, but also disproportions between different societal subsystems; at present these are also disproportions within the World System as a whole. The proposed model of business cycle is based on its subdivision into four phases: – recovery phase (which could be subdivided into the start sub-phase and the acceleration sub-phase); – upswing/prosperity/expansion phase (which could be subdivided into the growth sub-phase and the boom/overheating sub-phase); – recession phase (within which one may single out the crash/bust/acute crisis subphase and the downswing sub-phase); – depression/stagnation phase (which we could subdivide into the stabilization subphase and the breakthrough sub-phase). The article provides a detailed qualitative description of macroeconomic dynamics at all the phases; it specifies driving forces of cyclical dynamics and the causes of transition from one phase to another (including psychological causes); a special attention is paid to the turning point from the peak of overheating to the acute crisis, as well as to the turning point from the downswing to recovery. The proposed mathematical model of Juglar cycle takes into account the following effects that are typical for the market economy: • positive feedbacks between various economic processes; • presence of a certain inertia, time lags in reactions of the economic subsystem to the change in conditions; • amplification by the financial subsystem of positive feedbacks and time lags in the economic subsystem; • excessive reaction to changing conditions during the acute crisis sub-phase. The authors suggest that the current crisis turns out to be rather similar to classical Juglar crises; however, there is also a significant difference, as the current crisis occurs at a truly global scale. Yet, due to this truly global scale of the current crisis, the possibilities of regulation with the national state's measures have turned out to be ineffective,whereas the suprastate regulation of financial processes hardly exists. It is shown that all these have led to the reproduction of the current crisis according to a classical Juglar scenario. (shrink)

Microgames are rapidly gaining increased attention and are highly being considered because of the technology-based media that enhances students’ learning interests and educational activities. Therefore, this study aims to develop a new construct through confirmatory factor analysis, to comprehensively understand the factors influencing the use of microgames in mathematics class. Participants of the study were the secondary school teachers in West Java, Indonesia, which had a 1-year training in microgames development. We applied a quantitative approach to collect the data via (...) online questionnaires through google form. Structural Equation Modelling with AMOS software was used to analyze the proposed model. Empirical results confirmed the perceived easy to use and subjective norm influence relationship with teachers’ microgame usage behaviors and intentions. In this condition, SN was found to have the initial significant influence on behavioral intention, as attitude, BI, and facilitating conditions also correlated with the actual use of microgames. Furthermore, the largest influential factor was BI, with the results subsequently showing that TPACK had no significant influence on the actual use of microgames. This report is expected to help bridge the gap across several previous studies, as well as contribute to the explanation and prediction of the factors influencing the teachers’ mathematical utilization of the study’s program. Besides this, it also helps to increase the use of microgames in teaching and learning activities. (shrink)

The objective of the study was to develop a structural model that explores the relationship between Mathematics Performance and students’ self-regulated learning skills, grit, and expectancy-value towards science, technology, engineering and mathematics (STEM). The research collected survey data from 664 senior high school students from 17 STEM high schools, and conducted a covariance-based structural equation modeling (SEM) analysis. The results of the SEM analysis indicate that the Re-specified Self-Regulated Learning Skill – Expectancy-Value towards STEM – Grit – Mathematics Performance (Re-specified (...) SRL-EV-GR-MP) model is the most parsimonious fit, offering the best empirical support for the theoretical model of the study. The research findings suggest that the mathematics performance of senior high school students in STEM curriculum is attributed to their high expectancies for success and perceived values of the STEM tasks, high grit, and high self-regulated learning skills. Moreover, the research also observed evidence of mediating and moderating grit effects in the concurrent effects of expectancy-values towards STEM and self-regulated learning skills towards students’ mathematics performance. (shrink)

Legal scholarship exploring the nature of evidence and the process of juridical proof has had a complex relationship with formal modeling. As evident in so many fields of knowledge, algorithmic approaches to evidence have the theoretical potential to increase the accuracy of fact finding, a tremendously important goal of the legal system. The hope that knowledge could be formalized within the evidentiary realm generated a spate of articles attempting to put probability theory to this purpose. This literature was both insightful (...) and frustrating. Much light was shed on the legal system, but it also quickly became evident that the tools of probability theory were in many ways ill-constructed for the task. Fundamental incompatibilities between the structure of legal decision making and the extant formal tools were identified, and it became evident that many of the purported explanations of legal phenomena were internally inconsistent. As a consequence, interest in this type of formal modeling declined, and attention was directed toward different kinds of explanations of the phenomena. Perhaps under the influence of a recent trend toward various types of formal modeling in legal scholarship, a recent burst of articles, rather than attempting to explain the macro structure of trials, which was the previous object of interest, attempts to quantify the probative value of various items of evidence in ways consistent with the formal features of various probability theories, and then to study decision making from that perspective. For example, the value of evidence is often purported to be its likelihood ratio, that is, the probability of discovering or receiving the evidence given a hypothesis (e.g., the defendant did it) divided by the probability of discovering or receiving the evidence given the negation of the hypothesis (the defendant didn't do it). Alternatively, the value of evidence is purported (more contextually) to be the information gain it provides, defined as the increase in probability it provides for a hypothesis above the probability of the hypothesis based on the other available evidence. Both conceptions then assume that all of the various probability assessments conform or ought to conform to the dictates of Bayes' theorem (that maintains consistency among such assessments); empirical studies are then done testing the extent to which this is so and proposing how the law can increase the probability that it is so. The general criticisms of using Bayes' theorem as a formal model of juridical proof are well known and were integral to the last wave of interest in formal modeling of the evidentiary process. This paper thus for the most part puts aside that more general issue, and focuses specifically on mathematical modeling of the value of particular items of evidence. The paper demonstrates that formal modeling has only limited value in explaining the value of legal evidence, much more limited than those constructing and discussing the models assume, and thus that the conclusions they draw about the value of evidence are unwarranted. This is done through a discussion of four recent examples that attempt to quantify evidence relating to, respectively, carpet fibers, infidelity, DNA random-match evidence, and character evidence used to impeach a witness. This article thus makes two contributions. First, and most importantly, it is another demonstration of the complex relationship between algorithmic tools and legal decision making. Second, at a minimum it points out serious pitfalls for analytical or empirical studies of juridical proof. (shrink)

We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial (...) equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource. (shrink)

In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, namely, that which sees them as non-individuals, then (...) there would be strong reasons to ask for a different mathematical framework for describing the structures that would be the models of the corresponding theory. In departing from the standard frameworks, we hope to bring to the scene, within the scope of the semantic approach, the importance of paying attention to some fundamental concepts usually only superficially touched by philosophers of science. (shrink)

A general equation is derived describing the concentration of all possible complexes of a central molecule with a set of ligands bound to the central molecule. This deduction allows the reaction rate constants for the binding of a given molecule to the central molecule to depend on the species of molecules already bound and the location of the molecules already bound. The model thus allows for structural alteration of the central molecule by binding. Functions describing the concentration dependence of any (...) effect whatever depending on the distribution of complexes are deduced. Possible applications and methods of application are indicated.II est dérivé une équation qui décrit la concentration des toutes les complexes d'une molécule centrale avec une collection de ligands connectés à la molécule centrale. La déduction montre comme les coefficients de la rapidité de reaction entre la molécule centrale et les molécules de la collection dépend de l'espèce et de la location des molécules déjà connectées.La modèle dérivée de l'équation montre les changements structurelles par la connection. Les functions qui décrivent la dependence de chaque effet à la concentration, sont dérivés. Ces effects dépendent aussi à la distribution des complexes. Des applications et des méthodes sont indiqués.Eine allgemeine Vergleichung hat man bekommen welche die Konzentration aller möglichen Komplexen eines zentralen Moleküles mit einer Reihe von „Ligands” verbunden mit dem zentralen Molekül beschreibt. Diese Folgerung gestattet dass die Reaktiongeschwindigkeit Konstanten für die Bindung eines gegebenen Moleküles mit dem zentralen Molekül abhÄngt von den Arten schon gegebenen Molekülen und die Ortsbestimmung der schon gebundenen Molekülen. Das Model zeigt die strukturelle Änderungen des zentralen Moleküls durch Bindung. Funktionen, die die Konzentrationband jedes Effektes beschreiben dass abhÄngt von der Distribution der Komplexen, sind abgeleitet.Mögliche Anwendungen und Methoden von Anwendung sind dargelegt. (shrink)

We provide a detailed history of the concepts of atomic number and isotopy before the discovery of protons and neutrons that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing on research by Frederick Soddy and Ernest Rutherford, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role of the periodic table led to a relatively (...) coherent notion of atomic number. Subsequent attention to valency, still neglected in the secondary literature, and to nuclear charge led to a decoupling of the concepts of elemental identity and weight and allowed for a coherent concept of isotopy. This concept received motivation from empirical investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards. After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly accepted explanatory relations. It is an episode of scientific collaboration and partial integration without simple, wholesale gestalt switches or chemical revolutions. (shrink)

Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive (...) arguments which, by virtue of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects. (shrink)

Statistical learning refers to the ability to identify structure in the input based on its statistical properties. For many linguistic structures, the relevant statistical features are distributional: They are related to the frequency and variability of exemplars in the input. These distributional regularities have been suggested to play a role in many different aspects of language learning, including phonetic categories, using phonemic distinctions in word learning, and discovering non-adjacent relations. On the surface, these different aspects share few commonalities. Despite (...) this, we demonstrate that the same computational framework can account for learning in all of these tasks. These results support two conclusions. The first is that much, and perhaps all, of distributional statistical learning can be explained by the same underlying set of processes. The second is that some aspects of language can be learned due to domain-general characteristics of memory. (shrink)

Projections of future climate change cannot rely on a single model. It has become common to rely on multiple simulations generated by Multi-Model Ensembles (MMEs), especially to quantify the uncertainty about what would constitute an adequate model structure. But, as Parker points out (2018), one of the remaining philosophically interesting questions is: “How can ensemble studies be designed so that they probe uncertainty in desired ways?” This paper offers two interpretations of what General Circulation Models (GCMs) are and how (...) MMEs made of GCMs should be designed. In the first interpretation, models are combinations of modules and parameterisations; an MME is obtained by “plugging and playing” with interchangeable modules and parameterisations. In the second interpretation, models are aggregations of expert judgements that result from a history of epistemic decisions made by scientists about the choice of representations; an MME is a sampling of expert judgements from modelling teams. We argue that, while the two interpretations involve distinct domains from philosophy of science and social epistemology, they both could be used in a complementary manner in order to explore ways of designing better MMEs. (shrink)

We examine two very different approaches to formalising real computation, commonly referred to as “Computable Analysis” and “the BSS approach”. The main models of computation underlying these approaches—bit computation and BSS, respectively—have also been put forward as appropriate foundations for scientific computing. The two frameworks offer useful computability and complexity results about problems whose underlying domain is an uncountable space. Since typically the problems dealt with in physical sciences, applied mathematics, economics, and engineering are also defined in uncountable domains, it (...) is fitting that we choose between these two approaches a foundational framework for scientific computing. However, the models are incompatible as to their results. What is more, the BSS model is highly idealised and unrealistic; yet, it is the de facto implicit model in various areas of computational mathematics, with virtually no problems for the everyday practice. This paper serves three purposes. First, we attempt to delineate what the goal of developing foundations for scientific computing exactly is. We distinguish between two very different interpretations of that goal, and on the separate basis of each one, we put forward answers about the appropriateness of each framework. Second, we provide an account of the fruitfulness and wide use of BSS, despite its unrealistic assumptions. Third, according to one of our proposed interpretations of the scope of foundations, the target domain of both models is a certain mathematical structure. In a clear sense, then, we are using idealised models to study a purely mathematical structure. The third purpose is to point out and explain this intriguing phenomenon and attempt to make connections with the typical case of idealised models of empirical domains. (shrink)

In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories with first-order structures, and which are studied in standard model theory. All of us are, of course, bound to make abuses of language even in putatively precise (...) contexts. This is not a problem—in fact, it is part of scientific and philosophical practice. But it is important to be sensitive to the dierent uses that structure, model, and language have. In this paper, we examine these topics in the context of classical logic; only in the last section we touch upon briefly on non-classical ones. (shrink)

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book (...) describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore (...) as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined. (shrink)

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of four years as a variable. The sampled students were (...) initially assessed by means of an Early Numeracy Test (ENT), and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence (TILE). The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 to 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. (shrink)

The specificity of eukaryotic DNA organization into loops fixed to the nuclear matrix/chromosomal scaffold has been studied for more than fifteen years. The results and conclusions of different authors remain, however, controversial. Recently, we have elaborated a new approach to the study of chromosomal DNA loops. Instead of characterizing loop basements (nuclear matrix DNA), we have concentrated our efforts on the characterization of individual loops after their excision by DNA topoisomerase II‐mediated DNA cleavage at matrix attachment sites. In (...) this review the results of applying this mapping approach are compared with the results and conclusions from studies of nuclear matrix DNA. An attempt is also made to reconsider all data about the specificity of DNA interactions with the nuclear matrix and to suggest a model of spatial organization of the eukaryotic genome which resolves apparent contradictions between these data. (shrink)

A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which (...) is continuous with the modern structural approach in mathematics. (shrink)

We propose an infrastructure for collaborative content management and version control for structured mathematical knowledge. This will enable multiple users to work jointly on mathematical theories with minimal interference. We describe the API and the functionality needed to realize a cvs-like version control and distribution model. This architecture extends the cvs architecture in two ways, motivated by the specific needs of distributed management of structured mathematical knowledge on the Internet. On the one hand the one-level client/server model (...) of cvs is generalized to a multi-level graph of client/server relations, and on the other hand the underlying change-detection tools take the math-specific structure of the data into account. (shrink)

Gene regulatory networks are intensively studied in biology. One of the main aims of these studies is to gain an understanding of how the structure of genetic networks relates to specific functions such as chemotaxis and the circadian clock. Scientists have examined this question by using model organisms such as Drosophila and mathematical models. In the last years, synthetic models—engineered genetic networks—have become more and more important in the exploration of gene regulation. What is the potential of this (...) new approach in the investigation of gene network structures? How do synthetic models relate to model organisms and mathematical models? (shrink)

Based on the paper [4] we show that true second‐order arithmetic is interpretable over the real‐algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras.

The nominalistic ontology of Kotarbinski, Slupecki and Tarski does not provide any direct interpretations of the sets of higher types which play important roles in type theory and in set theory. For this and other reasons I will interpret those theories as descriptions of some finite structures which are actually constructed in human imaginations and stored in their memories. Those structures will be described in this lecture. They are hinted by the idea of Skolem functions and Hilbert's -symbols, and they (...) constitute a finitistic modification of Tarski's concept of a model. They suggest also a form of the evolutionary process which leads to the development of human intelligence and language. (shrink)

A new diagnostic modeling system for automatically synthesizing a deep‐structure model of a student's misconceptions or bugs in his basic mathematical skills provides a mechanism for explaining why a student is making a mistake as opposed to simply identifying the mistake. This report is divided into four sections: The first provides examples of the problems that must be handled by a diagnostic model. It then introduces procedural networks as a general framework for representing the knowledge underlying a skill. (...) The challenge in designing this representation is to find one that facilitates the discovery of misconceptions or bugs existing in a particular student's encoding of this knowledge. The second section discusses some of the pedagogical issues that have emerged from the use of diagnostic models within an instructional system. This discussion is framed in the context of a computer‐based tutoring/gaming system developed to teach students and student teachers how to diagnose bugs strategically as well as how to provide a better understanding of the underlying structure of arithmetic skills. The third section describes our uses of an executable network as a tool for automatically diagnosing student behavior, for automatically generating “diagnostic” tests, and for judging the diagnostic quality of a given exam. Included in this section is a discussion of the success of this system in diagnosing 1300 school students from a data base of 20.000 test items. The last section discusses future research directions. (shrink)

Inference to the best explanation (IBE) is the principle of inference according to which, when faced with a set of competing hypotheses, where each hypothesis is empirically adequate for explaining the phenomena, we should infer the truth of the hypothesis that best explains the phenomena. When our theories correctly display this principle, we call them our ‘best’. In this paper, I examine the explanatory role of mathematics in our best scientific theories. In particular, I will elucidate the enormous utility of (...) mathematical structures. I argue from a reformed indispensability argument that mathematical structures are explanatorily indispensable to our best scientific theories. Therefore, IBE scientific realism entails mathematical realism. I develop a naturalistic, neo-Quinean ontology, which grounds physical and mathematical entities in structures. Mathematical structures are the truthmakers for the entities of our quantificational discourse. I also develop an ‘ontic conception’ of explanation, according to which explanations exist in the world, whether or not we discover and model them. I apply the ontic account to mathematical structures, arguing that these structures are the explanations for particles, forces, and even the conservation laws of physics. As such, mathematical structures provide the fundamental grounding for ontological commitment. I conclude by reviewing the evidence from modern physics for the existence of mathematical structures. (shrink)

A study of stage structured model of fish population is presented. This model focuse on the anchovy population in the Bay of Biscay (Engraulis encrasicolus L.) is presented. The method of study is based on an intermediate complexity mathematical model, taking into account the spatialisation, the environmental conditions and the stage-structure of the fishes. First, to test the model, we show mathematical properties, such as unicity of the solution of structural stability. Then we provide numerical simulations, to (...) validate the model and to test the dynamics according to the variations of the parameters. (shrink)

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic (...) is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background. (shrink)

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A,O and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and (...) combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence and parental aspirations when comparing children with and without MLD. In addition, A, O and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. (shrink)

In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and categories of meaning spaces. Here, we give a mathematical foundation, referred to as DisCoCirc, for how sentences interact in texts in order to produce the meaning of that text. First we revisit DisCoCat. While in DisCoCat all meanings are (...) fixed as states, in DisCoCirc word meanings correspond to a type, or system, and the states of this system can evolve. Sentences are gates within a circuit which update the variable meanings of those words. Like in DisCoCat, word meanings can live in a variety of spaces e.g. propositional, vectorial, or cognitive. The compositional structure are string diagrams representing information flows, and an entire text yields a single string diagram in which word meanings lift to the meaning of the entire text. While the developments in this paper are independent of a physical embodiment, both the compositional formalism and suggested meaning model are highly quantum-inspired, and implementation on a quantum computer would come with a range of benefits. We also praise Jim Lambek for his role in mathematical linguistics in general, and the development of the DisCo program more specifically. (shrink)

Remarkable advances in cold fusion, known also as LENR, raised the hope for a safer and cheaper nuclear energy. The results, however, cannot be explained from the point of view of current physical understanding of nuclear fusion. This is an obstacle for research investment in this field. The present book suggests a new approach for analysis of the experimental results and practical recommendations based on the models of atomic nuclei derived in the BSM-Supergravitation Unified theory (BSM-SG). The book (...) provides: (1) a method for analysis of the LENR experiments using the BSM-SG atomic models; (b) a selection of isotopes suitable for a more efficient energy yield with a minimum of radioactive byproducts; (c) practical considerations for selection of the technical method and the reaction environment. (shrink)

Two views of scientific theories dominated the philosophy of science during the twentieth century, the syntactic view of the logical empiricists and the semantic view of their successors. I show that neither view is adequate to provide a proper understanding of the connections that exist between theories at different times. I outline a new approach, a hybrid of the two, that provides the right structural connection between earlier and later theories, and that takes due account of the importance of the (...) mathematical models of a theory and of the various distinct formulations that pick out these models. (shrink)

An important epistemic issue in climate modelling concerns structural uncertainty: uncertainty about whether the mathematical structure of a model accurately represents its target. How does structural uncertainty affect our knowledge and predictions about the climate? How can we identify sources of structural uncertainty? Can we manage the effect of structural uncertainty on our knowledge claims? These are some of the questions that an epistemology of structural uncertainty faces, and these questions are also important for climate scientists and policymakers. (...) I develop three desiderata for an epistemological account of structural uncertainty. In my view, an account of structural uncertainty should identify sources of structural uncertainty, explain how these sources limit the applicability of a model, and show how the severity of structural uncertainty depends on the questions that can be asked of a model. I argue that analyzing structural uncertainty by paying attention to the details of model building can satisfy these desiderata. I focus on parametrizations, which are representations of important processes occurring at scales that are not resolved by climate models. Parametrizations are often thought to be ad-hoc, but I show that some important parametrizations are theoretically justified by explicit or implicit scale separation assumptions. These assumptions can also be supported empirically. Analyzing these theoretical and empirical justificatory roles of the scale separation assumptions can provide insights into how parametrizations contribute to structural uncertainty. I conclude by sketching how my approach can satisfy the desiderata I set out at the beginning, highlighting its importance for policy-relevant scientific statements about the climate. (shrink)

Approaches to the interpretation of physical theories provide accounts of how physical meaning accrues to the mathematical structure of a theory. According to many standard approaches to interpretation, meaning relations are captured by maps from the mathematical structure of the theory to statements expressing its empirical content. In this article I argue that while such accounts adequately address meaning relations when exact models are available or perturbation theory converges, they do not fare as well for models (...) that give rise to divergent perturbative expansions. Since truncations of divergent perturbative expansions often play a critical role in establishing the empirical adequacy of a theory, this is a serious deficiency. I show how to augment state-space semantics, a view developed by Beth and van Fraassen, to capture perturbatively evaluated observables even in cases where perturbation theory is divergent. This new semantics establishes a sense in which the calculations that underwrite the empirical adequacy of a theory are both meaningful and true, but requires departure from the assumption that physical meaning is captured entirely by the exact models of a theory. (shrink)

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et al., as well as the Quantum IIT introduced by Zanardi (...) et al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background. (shrink)

The classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, (...) I argue that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification. (shrink)

Exploration of a hypothetical model of the structure of the Emergent Event. -/- Key Words: Emergent Event, Foundational Mathematical Categories, Emergent Meta-system, Orthogonal Centering Dialectic, Hegel, Sartre, Badiou, Derrida, Deleuze, Philosophy of Science.

‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this (...) assumption as a working hypothesis about applied mathematics? In order to do so, we examine the role played by mathematics in the multiscalar modelling of sea ice melting behaviour and examine whether we can indeed capture the mathematics involved in the kind of mathematical structure employed by the mapping account. Along the way, we note that the cases of applied mathematics that appear in discussions of mapping accounts almost exclusively involve the employment of a single clearly circumscribed mathematical field or domain. While the core assumption of mapping accounts may appear plausible in such situations, we ultimately suggest that the mapping account is not able to handle the important added complexities involved in our sea ice case study. In particular, the notion of mathematical structure around which such accounts are framed does not seem to be able to capture the way in which some applications of mathematics require that very different pieces of mathematics be related to one another on the basis of both mathematical and empirical information. (shrink)

Climate modelling plays a crucial role for understanding and addressing the climate challenge, in terms of both mitigation and adaptation. It is therefore of central importance to understand to what extent climate models are adequate for relevant purposes, such as providing certain kinds of climate change projections in view of decision-making. In this perspective, the issue of the stability of climate models under small relevant perturbations in their structure seems particularly important. Within this framework, a debate has emerged in (...) the philosophy of science literature about the relevance for climate modelling of the mathematical notion of structural stability. This paper adresses several important foundational and epistemological questions that arise in this context, in particular about the the role of abstract mathematical considerations of a qualitative nature for concrete modelling projects with mainly quantitative purposes. (shrink)