Causal claims in physics may have two familiar kinds of support: theoretical and experimental. This paper claims that a rigorous mathematical derivation in a realistic model is necessary, though not sufficient, for full theoretical support. The support is not provided by the derivation itself; but rather it comes from a detailed back-tracing through the derivation, matching the mathematical dependencies, point by point, with details of the causal story. This back-tracing is not enough to pick out the correct causal (...) story, however; a good deal of background causal knowledge is required as well. These claims are illustrated by a detailed example of what causes the Lamb dip in gas lasers. (shrink)

Spinoza is most often seen as a stern advocate of mechanistic efficient causation, but examining his philosophy in relation to the Aristotelian tradition reveals this view to be misleading: some key passages of the Ethics resemble so much what Surez writes about emanation that it is most natural to situate Spinoza's theory of causation not in the context of the mechanical sciences but in that of a late scholastic doctrine of the emanative causality of the formal cause; as (...) taking a look at the seventeenth-century philosophy of mathematics reveals, this is in consonance also with Spinoza's geometrical cast of mind. Against this background, I examine Spinoza's essentialist model of causation according to which each thing has a formal character determined by the thing's essence and what follows from that essence. In the case of real things this essential causal architecture results in efficacy, i.e. in bringing about real effects, the key idea being that without the essential, formally structured causal thrust there would be no efficacy in the first place. I also explain how this model accounts for efficient causation taking place between finite things. (shrink)

Salmon has argued that science provides explanations by describing a causal nexus: For Salmon, this nexus is a network of processes and interactions. I argue that this picture of the causal nexus is insufficient for an account of scientific explanation: a taxonomy of causal relevance is also needed. ;Probabilistic theories of causation seem to provide such a taxonomy in their dichotomy between promoting and inhibiting causes. However, standard probabilistic theories are beset by a difficulty called the problem of disjunctive (...) factors. According to such theories, an effect is more probable in the presence of a cause than in its absence . But there are many ways in which a particular cause may come about, and many in which it may be absent; these ways need not confer the same probabilities upon the effect. Thus, there is no direct comparison of two probabilities to be made. My solution is to abandon the oversimplified dichotomy between promoting and inhibiting causes. Causal claims convey qualitative information about more complex probabilistic relationships. Interestingly, this picture of causation meshes naturally with extant theories of explanation. ;I show how this framework may be employed in resolving several outstanding problems in the theories of causation and explanation, such as the relationship between singular and general causal claims, and the role of contrastive stress in causal and explanatory claims. ;Finally, I show how my account of causal explanation can be connected with the semantic conception of scientific theories. According to this conception, a theory is characterized in terms of a class of mathematical models. I describe the relationship between these mathematical models and the probabilistic relationships that are described by causal explanations. These ideas are illustrated in an extended discussion of causation and explanation in evolutionary theory. (shrink)

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

This paper articulates an account of causation as a collection of information-theoretic relationships between patterns instantiated in the causal nexus. I draw on Dennett’s account of real patterns to characterize potential causal relata as patterns with specific identification criteria and noise tolerance levels, and actual causal relata as those patterns instantiated at some spatiotemporal location in the rich causal nexus as originally developed by Salmon. I develop a representation framework using phase space to precisely characterize causal relata, including their (...) degree of counterfactual robustness, causal profiles, causal connectivity, and privileged grain size. By doing so, I show how the philosophical notion of causation can be rendered in a format that is amenable for direct application of mathematical techniques from information theory such that the resulting informational measures are causal informational measures. This account provides a metaphysics of causation that supports interventionist semantics and causal modeling and discovery techniques. (shrink)

Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

ABSTRACT Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

In 1949 the great logician Kurt Gödel constructed the first mathematical models of the universe in which travel into the past is, in theory at least, possible. Within the framework of Einstein’s general theory of relativity Gödel produced cosmological solutions to Einstein’s field equations which contain closed time-like curves, that is, curves in spacetime which, despite being closed, still represent possible paths of bodies. An object moving along such a path would travel back into its own past, to (...) the very moment at which it “began” the journey. More generally, Gödel showed that, in his “universe”, for any two points P and Q on a body’s track through spacetime, such that P temporally precedes Q, there is a timelike curve linking P and Q on which Q temporally precedes P. This means that, in principle at least, one could board a “time machine” and travel to any point of the past. Gödel inferred, in consonance with the views of Parmenides, Kant and the modern idealists, that under these circumstances there could be no such thing as an objective lapse of time, that time or, more generally, change, is an illusion arising from our special mode of perception. For consider an observer initially at point P. At point Q he boards a time machine and travels back to point P, taking time t′′ to do so. In that case, according to his own clock, t′ – t + t′′ > 0 seconds have elapsed, and yet an identical clock left at P would show that 0 seconds have elapsed. In short, there has been no “objective” lapse of time at all. Gödel remarks that in his universe this situation is typical: for every possible definition of an “objective” time one could travel into regions which are past according to that definition. He continues. (shrink)

This paper argues that scale-dependence of physical and biological processes offers resistance to reductionism and has implications that support a specific kind of downward causation. I demonstrate how insights from multiscale modeling can provide a concrete mathematical interpretation of downward causation as boundary conditions for models used to represent processes at lower scales. The autonomy and role of macroscale parameters and higher-level constraints are illustrated through examples of multiscale modeling in physics, developmental biology, and systems biology. (...) Drawing on these examples, I defend the explanatory importance of constraining relations for understanding the behavior of biological systems. (shrink)

Contrary to common belief, acceptance of Newtonian causation does not commit one to a mechanistic, materialistic, or deterministic understanding of the world. I argue that the Newtonian view can be assimilated to contemporary theoretical alternatives in psychology. This means that, given the Newtonian understanding of causation, it is possible for such alternatives to be scientific - to treat of causes - without requiring either mechanism, materialism, or mathematical formalizations. I argue that we best understand Newtonian causation (...) as formal causation. I do this by discussing the history of Newton's theory of causation and comparing his theory to Bacon's. I also compare Newton's theory of causation to Aristotle's, arguing that when we speak of formal causes we speak of our descriptions rather than the nature of things. We may accurately impute various elements of our scientific descriptions to the nature of things, but when we speak of formal causes, we are speaking of the patterns we use to describe the changes we observe rather than the nature of things themselves. Since any science must use such patterns, even alternative psychologies use Newtonian causation - if they are genuinely scientific alternatives. However, mathematics is not the only discipline that offers such patterned explanations. Moral explanations offer an alternate model for causal explanation. (shrink)

The action language C+ of Giunchiglia, Lee, Lifschitz, McCain and Turner is a high-level, logical formalism for the representation of domains involving action and change. However, one cannot directly express relationships which hold between states more than one time-step distant, or even say that one action determines another at the next time. We present C+timed, a generalization of C+ which removes these limitations. As for C+, translations to the language of causal theories are given. We also define a new kind (...) of transition system called a ‘run system’ to provide a graphical semantics. Finally, we show how domains involving prohibition and permission can be modelled, by incorporating the ideas of another extension of C+. (shrink)

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea (...) of closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The system can be regenerated from the set of food components plus a single intermediate, and maintain itself in that state indefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in prebiotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctuations in the numbers of molecules need to be taken into account. With the stochastic approach there is no non-trivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after sufficient time. However, the average time before collapse is so long for volumes greater than $10^{-19}\;{\textsc{l}}$ (much smaller than the volume of the order of $10^{-15}\;{\textsc{l}}$ for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally. (shrink)

A key challenge for probabilistic causal models is to distinguish non-causal probabilistic dependencies from true causal relations. To accomplish this task, causal models are usually required to satisfy several constraints. Two prominent constraints are the causal Markov condition and the faithfulness condition. However, other constraints are also needed. One of these additional constraints is the causal sufficiency condition, which states that models must not omit any direct common causes of the variables they contain. In this paper, I (...) argue that the causal sufficiency condition is problematic: (1) it is incompatible with the requirement that the variables in a model must not stand in non-causal necessary dependence relations, such as mathematical or conceptual relations, or relations described in terms of supervenience or grounding, (2) it presupposes more causal knowledge as primitive than is actually needed to create adequate causal models, and (3) if models are only required to be causally sufficient, they cannot deal with cases where variables are probabilistically related by accident, such as Sober’s example of the relationship between bread prices in England and the sea level in Venice. I show that these problems can be avoided if causal models are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. I give a definition of this monotonicity condition and conclude that causal models should be required to be monotonic rather than causally sufficient. (shrink)

The statistical community has brought logical rigor and mathematical precision to the problem of using data to make inferences about a model’s parameter values. The TETRAD project, and related work in computer science and statistics, aims to apply those standards to the problem of using data and background knowledge to make inferences about a model’s specification. We begin by drawing the analogy between parameter estimation and model specification search. We then describe how the specification of a structural equation model (...) entails familiar constraints on the covariance matrix for all admissible values of its parameters; we survey results on the equivalence of structural equation models, and we discuss search strategies for model specification. We end by presenting several algorithms that are implemented in the TETRAD II program. (shrink)

The choice of emphasis in kinship studies has often resulted in incompatible theoretical models of kinship that are mutually undermining and contradictory. Jones' attempts to reconcile disparate approaches to kinship using OT is useful, however; seeing kinship as a specialized system for representing genealogy may be unwarranted in the light of recent advances in mathematical approaches to kinship terminologies.

Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.

I argue that the contrast between models and theories is important for public policy issues. I focus especially on the way a mathematical model explains just one aspect of the data.

Mathematical models of biological patterns are central to contemporary biology. This paper aims to consider what these models contribute to biology through the detailed consideration of an important case: Hamilton’s selfish herd. While highly abstract and idealized, Hamilton’s models have generated an extensive amount of research and have arguably led to an accurate understanding of an important factor in the evolution of gregarious behaviors like herding and flocking. I propose an account of what these models (...) are able to achieve and how they can support a successful scientific research program. I argue that the way these models are interpreted is central to the success of such programs. (shrink)

Nineteenth-century medical advances were entwined with a conceptual innovation: the idea that many cases of disease which were previously thought to have diverse causes could be explained by the action of a single kind of cause, for example a certain bacterial or parasitic infestation. The focus of modern epidemiology, however, is on chronic non-communicable diseases, which frequently do not seem to be attributable to any single causal factor. This paper is an effort to resolve the resulting tension. The paper criticises (...) the monocausal model of disease, so successful in the nineteenth century. It also argues that a multifactorial model of disease can only be satisfactory if it amounts to more than a mere rejection of the monocausal model. A third alternative, the contrastive model, is proposed and defended on the grounds that it links the notions of disease and of general explanation, while avoiding the philosophical naiveties and practical difficulties of the monocausal model. (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)

A reasoned argument or tarka is essential for a wholesome vāda that aims at establishing the truth. A strong tarka constitutes of a number of elements including an anumāna based on a valid hetu. Several scholars, such as Dharmakīrti, Vasubandhu and Dignāga, have worked on theories for the establishment of a valid hetu to distinguish it from an invalid one. This paper aims to interpret Dignāga’s hetu-cakra, called the wheel of grounds, from a modern philosophical perspective by deconstructing it into (...) a simple probabilistic mathematical model. The objective is to understand how and why a vāda based on a probabilistically weaker hetu can degrade into a Jalpa or vitaṇḍā. To do so, the paper maps the concept of ‘Bounded Rationality’ onto the hetu-cakra. Bounded Rationality, an idea coined by the management thinker Herbert Simon, is often employed in understanding decision-making processes of rational agents. In the context of this paper, the concept would state that the prativādin and ālocaka (debater) may not hold unbounded information to back their pratijñā (proposition). The paper argues that within the probabilistically deconstructed hetu-cakra model, most people argue in the ‘Zone of Bounded Rationality’, and thus, the probability of a debate degrading into Jalpa or vitaṇḍā is high. -/- . (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)

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)

Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That series (...) rises to an absolutely infinite degree of that perfection. God has that absolutely infinite degree. We focus on the perfections of knowledge, power, and benevolence. Our model of divine infinity thus builds a bridge between mathematics and theology. (shrink)

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a (...) central role, namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

"This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. (...) To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory's resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism"--. (shrink)

John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy (...) of mathematics, logic, and philosophy of language. (shrink)

A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section (...) I. Many modifications of Turing machines cum quantum ones are researched in Section II for the Halting problem and completeness, and the model of two independent Turing machines seems to generalize them. Then, that pair can be postulated as the formal definition of reality therefore being complete unlike any of them standalone, remaining incomplete without its complementary counterpart. Representation is formal defined as a one-to-one mapping between the two Turing machines, and the set of all those mappings can be considered as “language” therefore including metaphors as mappings different than representation. Section III investigates that formal relation of “reality”, “representation”, and “language” modeled by (at least two) Turing machines. The independence of (two) Turing machines is interpreted by means of game theory and especially of the Nash equilibrium in Section IV. Choice and information as the quantity of choices are involved. That approach seems to be equivalent to that based on set theory and the concept of actual infinity in mathematics and allowing of practical implementations. (shrink)

We review mathematical models of HIV dynamics, disease progression, and therapy. We start by introducing a basic model of virus infection and demonstrate how it was used to study HIV dynamics and to measure crucial parameters that lead to a new understanding of the disease process. We discuss the diversity threshold model as an example of the general principle that virus evolution can drive disease progression and the destruction of the immune system. Finally, we show how mathematical (...) models can be used to understand correlates of long‐term immunological control of HIV, and to design therapy regimes that convert a progressing patient into a state of long‐term non‐progression. BioEssays 24:1178–1187, 2002. © 2002 Wiley‐Periodicals, Inc. (shrink)

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of (...) mathematics to informal reality is not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed. (shrink)

We have developed a simple mathematical model with three physiologically significant states to describe the changes in intrauterine pressure associated with a contraction during human parturition. The myometrium is modelled as a set of smooth muscle cells, each of which is in one of three states (quiescent, contracted, refractory) at a given time. These states are occupied according to a cycle governed by three temporal parameters. The solutions of the equations describing the model show an oscillatory behavior for particular (...) values of these parameters, which is very similar to the time dependant development of intrauterine pressure during labor. Due to its non-linear terms, our model could lead to chaotic oscillations (in the mathematical sense), whose clinical counterpart may occur in cases of dystocia. Despite its simplicity, this model appears to be a useful guide to further investigations of the oscillatory behavior of the myometrium, or other smooth muscles, in normal and pathological situations. (shrink)

Open peer commentary on the article “Info-computational Constructivism and Cognition” by Gordana Dodig-Crnkovic. Upshot: I propose a mathematical approach to the framework developed in Dodig-Crnkovic’s target article. It points to an important property of natural computation, called the multiplicity principle (MP), which allows the development of increasingly complex cognitive processes and knowledge. While local dynamics are classically computable, a consequence of the MP is that the global dynamics is not, thus raising the problem of developing more elaborate computations, perhaps (...) with the help of Turing oracles. (shrink)

Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is computed and used to investigate the local stability of the model’s steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable Lyapunov (...) function. Sensitivity analysis shows that the basic reproduction number is most sensitive to the model parameters related to the contaminated environment, namely: shedding rate of cercariae by snails, cercariae to miracidia survival probability, snails-miracidia effective contact rate and natural death rate of miracidia and cercariae. Numerical results show that when no intervention measures are implemented, there is an increase of the infected classes, and a rapid decline of the number of susceptible and exposed bovines and snails. Effects of the variation of some of the key sensitive model parameters on the schistosomiasis dynamics as well as on the initial disease transmission threshold parameter R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} are graphically depicted. (shrink)

The shape of hooks is of a taxonomic significance for cestoda. In order to characterize shape through numbers, a mathermatical model of drawings in two-dimensional space is proposed. This model is a synthetic one: first, it uses a large number of points on the edge of a hook-drawing as data; secondly, it enables to draw a specific hook by means of a computer after the parameters have been extracted from the data. The method does not use landmarks and therefore avoids (...) the difficulty of locating them. The ensuing discussion concerns description in common parlanceversus mathermatical language, the genesis of hooks and description in three-dimensional space. (shrink)

This article looks at the way people determine the antecedent of a pronoun in sentence pairs, such as: Albert invited Ron to dinner. He spent hours cleaning the house. The experiment reported here is motivated by the idea that such judgments depend on reasoning about identity . Because the identity of an individual over time depends on the causal-historical path connecting the stages of the individual, the correct antecedent will also depend on causal connections. The experiment varied how likely it (...) is that the event of the first sentence would cause the event of the second for each of the two individuals . Decisions about the antecedent followed causal likelihood. A mathematical model of causal identity accounted for most of the key aspects of the data from the individual sentence pairs. (shrink)

This article contributes to the revision of the procedure of robustness analysis of mathematical models in epistemic democracy using the systematic review method. It identifies the drawbacks of robustness analysis in epistemic democracy in terms of sample universality and inference from samples with the same results. To exemplify the effectiveness of systematic review, this article conducted a pilot review of diversity trumps ability theorem models, which are mathematical models of deliberation often cited by epistemic democrats. (...) A review of nine models extracted from 352 papers exemplifies the effectiveness of robustness analysis supplemented by systematic review in epistemic democracy. (shrink)

[v. 1. Basic theories]--v. 2. Applications.--v. 3. Theory of plants and other essays.

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)

John P. Burgess, Mathematics, Models, and Modality: Selected Philosophical Essays. Cambridge: Cambridge University Press, 2008. xiii + 301 pp. $90.00, £50.00. ISBN 978-0-521-88034-3. Adobe eBook, $...

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective — thepoliheuristic theory of decision-making — as an alternative to the rational actor and cybernetic paradigms in international relations. (...) This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective -- the poliheuristic theory of decision-making -- as an alternative to the rational actor and cybernetic paradigms in international (...) relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. (...) 11 EUCh. These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)