We present a framework for model theoretic forcing in a non first order context, and present some applications of this framework to Banach space theory.

Two of Hilary Putnam's model-theoretic arguments against metaphysical realism are examined in detail. One of them is developed as an extension of a model-theoretic argument against mathematical realism based on considerations concerning the so-called Skolem-Paradox in set theory. This argument against mathematical realism is also treated explicitly. The article concentrates on the fine structure of the arguments because most commentators have concentrated on the major premisses of Putnam's argument and especially on his treatment of metaphysical realism. (...) It is shown that the validity of Putnam's arguments is doubtful and that realists are by no means forced to accept the theses Putnam ascribes to them. It is concluded that Putnam fails to give convincing arguments for rejecting mathematical or metaphysical realism. Furthermore, Putnam's internal realism is discussed critically. (shrink)

In the United Kingdom, the debate about how best to meet the shortfall of organs for transplantation has persisted on and off for many years. It is often presumed that the answer is simply to alter the law to a system of presumed consent. Acting perhaps on that presumption in his annual report launched in July, the Chief Medical Officer, Sir Liam Donaldson, advocated a system of organ donation based on presumed consent, the so-called “opt-out” system.1 He is calling for (...) a change in the law in England and Wales whereby consent to organ donation is presumed, making a person’s organs automatically available for transplantation after death, unless they registered objections to this while alive. Subsequently, the British Medical Association lent its support to the introduction of such a system.2 The BMA contends that “the practice of presumed consent legislation has had a significant effect on the number of cadaveric donors per million population.”2It is often taken for granted that there must be a correlation between the enactment of legislation on presumed consent and an increase in organ donation and procurement. However, the correlation is not as straightforward as it might seem. It may be that other practical measures to encourage organ donation could be implemented without changing the Human Tissue Act 2004, an Act which has been in force for barely a year.An analysis by Abadie and Gay demonstrated that “presumed consent legislation has a positive and sizeable effect on organ donation rates”,3 but they themselves admitted that the correlation between rates of donation and presumed consent legislation is “not completely unequivocal”.3 It is true that among the most successful cases in procurement rates are countries with presumed consent legislation . However, since some of the …. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, inertial (...) or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

This paper investigates the relationship between generic statements and the expression, transmission and persistence of social norms. The author presents the concept of normativity and its importance in the decision-making process in the context of social reality and social norms that comprise it (Bicchieri, 2006, 2016; Bicchieri et al., 2018). The paper analyses the idea of “what is normal” (Haslanger, 2014) to show how social norms are triggered by particular generic constructions relating to “social kinds”, represented by noun phrases denoting (...) “dual character concepts” (Knobe et al., 2013; Prasada et al., 2013; Leslie, 2015). DCCs are shown as effectively serving their persuasive and explanatory function due to their polysemous nature (Leslie, 2015) rather than to different pragmatics (Leslie, forthcoming). Special focus is placed on gender terms as particularly salient social kinds; this salience can be explained by a culturally pivotal role of social constructs of manhood and womanhood and by linguistic potential of generics in the development of social beliefs and legitimizing norm-driven behaviours. (shrink)

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic (...) behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Montaigne and the Coherence of EclecticismPierre ForceSince the publication of Pierre Hadot's essays on ancient philosophy by Arnold Davidson in 1995,2 Michel Foucault's late work on "the care of the self"3 has appeared in a new light. We now know that Hadot's work was familiar to Foucault as early as the 1950s.4 It is also clear that Foucault's notion of "techniques of the self" is very close to what (...) Hadot calls "spiritual exercises." At the same time, there are important differences between the views of these two philosophers, and Hadot has often expressed his regret that Foucault's untimely death prevented them from exploring these differences.5 One important point of disagreement was the status of eclecticism. In Foucault's interpretation of ancient philosophy, the "constitution of the self" implied a personal choice among disparate philosophical references: "Writing as a personal exercise done by the self and for the self, is an art of disparate truth."6 In a 1989 article Hadot argued from a historical point of view that, so far as Stoicism and Epicureanism were concerned, [End Page 523] eclecticism had no place in a mature practice of philosophy. Foucault's favorite example, Seneca's Letters to Lucilius, in which Stoic arguments were invoked along with Epicurean arguments, was a work for beginners. In a mature practice of Stoicism, one would stick to the arguments of the Stoic school, choose them for their coherence, and instead of trying to forge a spiritual identity for oneself through writing, one would "liberate oneself from one's individuality in order to raise oneself up to universality."7 Hadot added that "it is only in the New Academy—in the person of Cicero, for instance—that a personal choice is made according to what reason considers as most likely at a given moment."8 This discussion of Foucault may give the impression that Hadot was somewhat dismissive of eclecticism. Yet in a 2001 interview Hadot claimed that he had always admired Cicero's intellectual independence, and he proposed a reappraisal "of an attitude that has always had a bad reputation: eclecticism."9Something very similar is a stake in the work of Alexander Nehamas, as Lanier Anderson and Joshua Landy showed in their study of his Art of Living. In the conception of philosophy as a "way of life" (Hadot) or "care of the self" (Foucault) or "self-fashioning" (Nehamas), a central issue is the relationship between theoretical coherence and the coherence of the person who theorizes. Elaborating on Nehamas's chapter on Montaigne, Anderson and Landy argue that there is a move in Montaigne away from doctrinal coherence and towards a coherence of the self. As they put it, "the harmonious whole Montaigne commends [... ] is not a coherent body of fact or theory; it is the unified self of the theorizer."10 Anderson and Landy show that this brings up all kinds of difficulties: can this unified self be other than a fiction? If that is the case, how can philosophy be a way of life? Nehamas's answer is very much in the spirit of the late Foucault: there is a coherence of the self in Montaigne, and this coherence is the product of writing as a philosophical activity. The self is fashioned through writing.Because Montaigne writes in the ancient tradition of philosophy as a way of life, one may recall Hadot's suggestion that Foucault's notion of [End Page 524] "writing the self" is an intriguing but historically inaccurate description of ancient philosophical practice. But perhaps Hadot agrees with Foucault after all, since in his most recent interviews, he speaks favorably of eclecticism, a notion that is central to Foucault's analysis of self-fashioning through writing. The case of Montaigne is particularly interesting for these purposes, not only because the Essays seem to be the prototypical example of "writing the self," but also because eclecticism is both discussed and practiced throughout the Essays. I propose to take a fresh look at this issue by investigating the status of eclecticism in Montaigne's Essays. This must start with an examination of the philosophical tradition most closely associated with... (shrink)

Sagoff (2016) criticizes widely used “theoretical” methods in ecology; arguing that those methods employ models that rely on problematic metaphysical assumptions and are therefore uninformative and useless for practical decision-making. In this paper, I show that Sagoff misconstrues how such model-based methods work in practice, that the main threads of his argument are problematic, and that his substantive conclusions are consequently unfounded. Along the way, I illuminate several ways the model-based inferential methods he criticizes can be, and have (...) been, usefully informative. (shrink)

We show that certain model-theoretic forcing arguments involving subsystems of second-order arithmetic can be formalized in the base theory, thereby converting them to effective proof-theoretic arguments. We use this method to sharpen the conservation theorems of Harrington and Brown-Simpson, giving an effective proof that WKL+0 is conservative over RCA0 with no significant increase in the lengths of proofs.

We use model theoretic forcing to study and generalize the construction of ()-generic models introduced by Kueker and Laskowski. We characterize the ()-generic models in terms of forcing and introduce a more general class of models, called essential forcing generics, which have many of the same properties.

Model theoretic considerations purportedly show that a certain version of structural realism, one which articulates the nvtion of structure via Ramsey sentences, is in fact trivially true. In this paper we argue that the structural realist is by no means forced to Ramseyfy in the manner assumed in the formal proof. However, the structural realist's reprise is short-lived. For, as we show, there are related versions of the model theoretic argument which cannot be so easily blocked (...) by the structural realist. We examine various ways in which the structural realist may respond, and conclude that the best way of blocking the model theoretic argument involves formulating his Ramseyfied theories using intensional operators. Introduction The model theoretic arguments On Ramseyfying away predicates The model theoretic argument bites back Restricting the second order quantifiers 5.1 Naturalness 5.2 Intrinsic 5.3 Qualitative 5.4 Contingent and causal Intensional operators and relations between properties Conclusion. (shrink)

Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will (...) discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.

There are many social psychological theories regarding the nature of prejudice, but only one major theory of prejudice reduction: under the right circumstances, prejudice between groups will be reduced with increased contact. On the one hand, the contact hypothesis has a range of empirical support and has been a major force in social change. On the other hand, there are practical and ethical obstacles to any large-scale controlled test of the hypothesis in which relevant variables can be manipulated. Here we (...) construct a spatialized model that tests the core hypothesis in a large array of game-theoretic agents. Robust results offer a new kind of support for the contact hypothesis: results in simulation do accord with a hypothesis of reduced prejudice with increased contact. The spatialized game-theoretic model also suggests a deeper explanation for at least some of the social psychological phenomena at issue. (shrink)

The Hardy–Weinberg equilibrium has been argued by Sober, Stephens and others to represent the zero-force state for evolutionary biology understood as a theory of forces. I investigate what it means for a model to involve forces, developing an explicit account by defining what the zero-force state is in a general theoretical context. I use this account to show that Hardy–Weinberg equilibrium is not the zero-force state in biology even in the contexts in which it applies, and argue based on (...) this that drift should not be understood as an evolutionary force. (shrink)

My chief aim has been to convey the thought that the application of model theoretic techniques to natural languages needn't force a distortion of intentional phenomena. I hope that at least I have succeeded in accomplishing this.

How environmental mechanical forces affect cellular functions is a central problem in cell biology. Theoretical models of cellular biomechanics provide relevant tools for understanding how the contributions of deformable intracellular components and specific adhesion conditions at the cell interface are integrated for determining the overall balance of mechanical forces within the cell. We investigate here the spatial distributions of intracellular stresses when adherent cells are probed by magnetic twisting cytometry. The influence of the cell nucleus stiffness on the simulated nonlinear (...) torque-bead rotation response is analyzed by considering a finite element multi-component cell model in which the cell and its nucleus are considered as different hyperelastic materials. We additionally take into account the mechanical properties of the basal cell cortex, which can be affected by the interaction of the basal cell membrane with the extracellular substrate. In agreement with data obtained on epithelial cells, the simulated behaviour of the cell model relates the hyperelastic response observed at the entire cell scale to the distribution of stresses and strains within the nucleus and the cytoskeleton, up to cell adhesion areas. These results, which indicate how mechanical forces are transmitted at distant points through the cytoskeleton, are compared to recent data imaging the highly localized distribution of intracellular stresses. (shrink)

We present a simple and completely model-theoretical proof of a strengthening of a theorem of Ajtai: The independence of the pigeonhole principle from IΔ0. With regard to strength, the theorem proved here corresponds to the complexity/proof-theoretical results of [10] and [14], but a different combinatorics is used. Techniques inspired by Razborov [11] replace those derived from Håstad [8]. This leads to a much shorter and very direct construction.

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane (J Appl Physiol 63(3):951–961, 1987 ) and introduce some dynamic properties of the respiratory system. The passive elements (rib cage and abdomen) are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles (active) force is applied to both compartments. Parameters of the model are (...) identified in using experimental data of airflow signal measured by pneumotachography and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R 2 ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing. (shrink)

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane :951–961, 1987) and introduce some dynamic properties of the respiratory system. The passive elements are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles force is applied to both compartments. Parameters of the model are identified in using experimental data of airflow signal measured (...) by pneumotachography and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R2 ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing. (shrink)

The operation of fundamental forces in quantum field theory is explicated here as the exchange of particles, consistently with the standard methodology of particle physics. The particles involved are seen to bear little relation to any classical particle but, rather, comprise unified collections of compresent, conserved quantities indicated by propagators. The exchange particles, which supervene upon quantum fields, are neither more fundamental than fields nor replace them as has often previously been assumed in models of exchange forces. It is argued (...) that this explication of quantum field-theoretic exchange forces definitively improves upon its predecessors. (shrink)

This paper is devoted to an analysis of some aspects of Bas van Fraassen’s views on representation. While I agree with most of his claims, I disagree on the following three issues. Firstly, I contend that some isomorphism between the representor and what is represented is a universal necessary condition for the success of any representation, even in the case of misrepresentation. Secondly, I argue that the so-called “semantic” or “model-theoretic” construal of theories does not give proper due (...) to the role played by true propositions in successful representing practices. Thirdly, I attempt to show that the force of van Fraassen’s pragmatic - and antirealist - “dissolution” of the “loss of reality objection” loses its bite when we realize that our cognitive contact with real phenomena is achieved not by representing but by expressing true propositions about them. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which (...) are generally either S4.2 or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account. (shrink)

This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians.

We study notions of genericity in models of, inspired by lines of inquiry initiated by Chatzidakis and Pillay and continued by Dolich, Miller and Steinhorn in general model‐theoretic contexts. These papers studied the theories obtained by adding a “random” predicate to a class of structures. Chatzidakis and Pillay axiomatized the theories obtained in this way. In this article, we look at the subsets of models of which satisfy the axiomatization given by Chatzidakis and Pillay; we refer to these (...) subsets in models of as CP‐generics. We study a more natural property, called strong CP‐genericity, which implies CP‐genericity. We use an arithmetic version of Cohen forcing to construct (strong) CP‐generics with various properties, including ones in which every element of the model is definable in the expansion, and, on the other extreme, ones in which the definable closure relation is unchanged. (shrink)

We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set (...) theoretical level of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

A general duality connecting the level of a formal theory and of a metatheory is proposed. Because of the role of natural numbers in a metatheory the existence of a dual theory is conjectured, in which the natural numbers become formal in the theory but in formalizing non-formal natural numbers taken from the dual metatheory these numbers become nonstandard. For any formal theory there may be in principle a dual theory. The dual shape of the lattice of projections over separable (...) Hilbert space is exhibited. The crucial ingredient of this dual theory is set-theoretical (Cohen) forcing. Then, some attempts have been made to exhibit the dual shape of the exotic smooth (small) structures on topological ℝ4. There are striking similarities of both pictures. Nonstandard solutions of the equations of motion of 10-dimensional superstring of IIB type are described as a model theoretic extension of standard ones. Based on Brans conjecture one can predict the existence of sources of gravity in 4 dimensions. By their dual origins they carry quantum information as well. The generalized Maldacena conjecture appears naturally, which sheds light on a definition of background independent string theory. (shrink)

In the 1960s, theoretical biologist Richard Levins criticised modellers in his own discipline of population biology for pursuing the “brute force” strategy of building hyper-realistic models. Instead of exclusively chasing complexity, Levins advocated for the use of multiple different kinds of complementary models, including much simpler ones. In this paper, I argue that the epistemic challenges Levins attributed to the brute force strategy still apply to state-of-the-art climate models today: they have big appetites for unattainable data, they are limited by (...) computational tractability, and they are incomprehensible to the human modeller. Along the lines Levins described, this uncertainty generates a trade-off between realistic, precise models with predictive power and simple, highly idealised models that facilitate understanding. In addition to building ensembles of highly complex dynamical models, climate modellers can address model uncertainty by comparing models of different types, such as dynamical and data-driven models, and by systematically comparing models at different levels of what climate modellers call the model hierarchy. Despite its age, Levins’ paper remains incredibly insightful and should be considered an important entry into the philosophy of computational modelling. (shrink)

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force (...) of the model is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs to show how Newton's (...) method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the 'autonomy of the models'. (shrink)

In this paper, I adopt the view that if general forces or processes can be detected in ecology, then the principles or models that represent them should provide predictions that are approximately correct and, when not, should lead to the sorts of intervening factors that usually make trouble. I argue that Lotka–Volterra principles do not meet this standard; in both their simple “strategic” and their complex “tactical” forms they are not approximately correct of the findings of the laboratory experiments and (...) historical studies most likely to confirm them; nor do they instruct ecologists where to look for likely intervening factors. Evidence drawn from long-term case studies and other available data sets suggests that the populations of predators and their prey are not regulated by an interaction between them but are controlled by transient, contingent, and accidental events that affect each animal and each population individualistically. This paper argues that the presence of general forces or processes in ecology should be determined by comparing competing models of these forces not just to each other or to a null model but also to case studies that may challenge theoretical approaches with convincing individualistic causal accounts of the phenomena. (shrink)

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize (...) these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs. (shrink)

The impact of our desires and preferences upon our ordinary, everyday beliefs is well-documented [Gilovich, T. . How we know what isn’t so: The fallibility of human reason in everyday life. New York: The Free Press.]. The influence of such motivational factors on delusions, which are instances of pathological misbelief, has tended however to be neglected by certain prevailing models of delusion formation and maintenance. This paper explores a distinction between two general classes of theoretical explanation for delusions; the motivational (...) and the deficit. Motivational approaches view delusions as extreme instances of self-deception; as defensive attempts to relieve pain and distress. Deficit approaches, in contrast, view delusions as the consequence of defects in the normal functioning of belief mechanisms, underpinned by neuroanatomical or neurophysiological abnormalities. It is argued that although there are good reasons to be sceptical of motivational theories , recent experiments confirm that motives are important causal forces where delusions are concerned. It is therefore concluded that the most comprehensive account of delusions will involve a theoretical unification of both motivational and deficit approaches. (shrink)

This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their (...) deeper subjectively founded content and also their influence in reaching relative consistency results by the forcing method. In this perspective, the present approach may be seen as offering an alternative view of the consistency results of K. Gödel and P. Cohen in mathematical foundations reaching a subjective level that may be taken as ultimately conditioning the non-decidability of key infinity statements on the level of formal theory. (shrink)

In a (2016) paper in this journal, I defuse allegations that theoretical ecological research is problematic because it relies on teleological metaphysical assumptions. Mark Sagoff offers a formal reply. In it, he concedes that I succeeded in establishing that ecologists abandoned robust teleological views long ago and that they use teleological characterizations as metaphors that aid in developing mechanistic explanations of ecological phenomena. Yet, he contends that I did not give enduring criticisms of theoretical ecology a fair shake in my (...) paper. He says this is because enduring criticisms center on concerns about the nature of ecological networks and forces, the instrumentality of ecological laws and theoretical models, and the relation between theoretical and empirical methods in ecology that that paper does not broach. Below I set apart the distinct criticisms Sagoff presents in his commentary and respond to each in turn. (shrink)

This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce (...) models as new entities. In conclusion, I argue for a view that takes both sets and models to be fundamental entities in set theory. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles (...) each express a form of width reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

Since the days of classical Montague Grammar, formal semantics is frequently characterised as intensional, type-logical and model-theoretic. This paper takes a closer look of some less obvious changes these three key concepts have undergone since the appearance of English as a Formal Language. While intensions used to be crucial for resolving substitution puzzles, they are now giving way to more general constructions of index-dependant denotations. Types, on the other hand, were promoted from handy taxonomic devices to driving forces (...) in meaning composition. Finally, the rôle of models was overestimated in the early days of formal semantics, but appears to have lost its importance. (shrink)

Solovay’s random-real forcing [R.M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory , Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428] is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay’s model that do not follow from the existence of real-valued measurability.

This bibliographical review of the modelling of the mitotic apparatus covers a period of one hundred and twenty years, from the discovery of the bipolar mitotic spindle up to the present day. Without attempting to be fully comprehensive, it will describe the evolution of the main ideas that have left their mark on a century of experimental and theoretical research. Fol and Bütschli's first writings date back to 1873, at a time when Schleiden and Schwann's cell theory was rapidly gaining (...) ground throughout Germany. Both mitosis and chromosomes were to be discovered within the space of thirty years, along with the two key events in the animal and plant reproductive cycle, namely fecondation and meiosis. The mitotic pole, a term still in use to this day, was employed to describe a morphological fact which was noted as early as 1876, namely that the lines and the dots of the karyokinetic figure, with its spindle and asters, looks remarkably like the lines of force around a bar magnet. This was to lead to models designed to explain the movements of chromosomes which take place when the cell nucleus appears to cease to exist as an organelle during mitosis. The nature of those mechanisms and the origin of the forces behind the chromosomes' ordered movements were central to the debate. Auguste Prenant, in a remarkable bibliographical synthesis published in 1910, summed up the opposing viewpoints of the vitalists, on the one hand, who favoured the theory of contractility or extensility in spindle fibres, and of those who believed in models based on physical phenomena, on the other. The latter subdivided into two groups: some, like Bütschli, Rhumbler or Leduc, referred to diffusion, osmosis and superficial tension, whilst the others, led by Gallardo and Hartog, focussed on the laws of electromagnetism. Lillie, Kuwada and Darlington followed up this line of research. The mid-20th century was a major turning point. Most of the modelling mentioned above was criticized and fell into disuse after disappearing from research publications and textbooks.This marked the onset of a new era, as electron microscopes made possible the materialization and detailed study of the macromolecular elements of the fibres, filaments and microtubules of the cytoskeleton. The successive phases of (a) de Harven and Bernhard's 1956 discovery of the centriole's ultrastructure, (b) its identification with the basal body of the cilia and flagella, confirming the theory set out by Henneguy and von Lenhossek (1898–99), (c) the universal presence of microtubules in animal, vegetal and eukaryotic protist cells, (d) the polymerization-depolymerization induced reversible transformations of the tubulin pool in mitosing cells (Inoue, 1960), (e) ultrastructural comparative studies of the mitotic apparatus of eukaryotes illustrating the Pickett-Heaps integrating concept of the MTOC (microtubule-organizing centre), (f) the possibility ofin vitro experiments on mtocs or on microtubules, brings us upon the present day, which has seen the focus placed on the concept of motor-proteins (kinesin, dynein) and on cell cycle models. The latter are based on a close coincidence between the observable modifications of the mitotic apparatus and the periodic variations in intracellular concentrations of calcium or of certain enzymes (cyclins, Cdc2) during the main transitions of the cell cycle. (shrink)

This essay is, first, a theoretical and historical study of some classical scientific ways of studying human being in the world. The more readily accessible and more commonly discussed "models" of being human were chosen for review here, but structuralism is included because I believe it will have ,the same impact in America as it has had in France, and I hope that American readers might be forewarned about what may be ideologically at stake before the technical, and fruitful, aspects (...) of the movement become an academic fad in the United States. The subjects included are mainline experimental psychology from Wundt to Skinner, with its relatively shortlived functionalist and Watsonian-behaviorist formulations; holistic psychology from Brentano through Stumpf, Husserl, and Goldstein to Maslow, Rogers, and contemporary "third force" psychology; and the psychoanalytic model, for which the only paradigm is Freud himself. Preeminence is given to psychological paradigms, since their subject matter lies closest to the classical philosophical tradition from which "philosophical anthropology" emerged. (This book is, in the final analysis, a prolegomenon to an articulated philosophical anthropo logy. ) Sociological models are also considered: the "classical" tradition from Comte to the present, and Marxist anthropology from the manu scripts of 1844 to the present. The structuralist model, from Durkheim to Chomsky, is also considered, since it cuts across and gives new dimensions to all the foregoing models. The essay is, second, a phenomenological critique of these historico theoretical considerations. (shrink)

The gap between the metatheoretical inquiries of the analytical philosophy of history, formulated in terms of general principle, and the actual research practices of the historical discipline needs to be bridged. This investigation of the determinants -preconditions, causes, factors, forces - of technological development during the Industrial Revolution makes explicit the range of theoretical instruments used in such studies. The methodologically unavoidable plurality of aspects and perspectives for each concrete inquiry precludes any generally binding model for technological development. Discussion (...) of epistemological presuppositions, by comparing various approaches, can serve to make fully conscious these presuppositions and make them accessible to analysis and criticism. (shrink)

Theoretical models of schizophrenia have traditionally emphasized the biological social, and environmental forces that lead to the dysfunction that characterizes this disorder. However important these aspects may be, an understanding of schizophrenia is incomplete without attention to the first-person perspective of those who continue to struggle to find meaning and security in the midst of this disorder. Encouragingly, an interest has grown steadily in recent years in understanding subjective experience in schizophrenia, and can be found within a range of bodies (...) of research, including.. (shrink)

The phenomenon of self-healing forces has again and again challenged doctors in the different historical periods of medical science. They relied on effects of self-healing forces in diagnosis and therapy. They also tried to explain these effects based on the current model of organism. The understanding of this phenomenon has always influenced the understanding of therapy and played a role in defining the concept of health and disease. In the 17th and 18th century the idea of self-healing force was (...) interpreted as a phenomenon related to the organic forces, whereas in the 19th century the explanation was reduced to a materialistic mechanism. Nowadays the knowledge of heath-shock-proteins open the way of a new understanding of the organic defense mechanisms. (shrink)

This research note proposes the Bass Model as an empirical tool for analyzing the diffusion of new product and service innovations in Base of the Pyramid markets. This approach allows researchers to test whether factors that seem theoretically relevant to the speed and trajectory of adoption actually matter empirically. The authors model the growth of three BoP success stories using the Bass Model: Patrimonio Hoy, e-Choupal, and Grameen’s Village Phone. In two of the three cases considered, the (...) Bass Model estimates confirm Diffusion Theory predictions, but generate additional insight by quantifying the strength of the identified effects. In the case of PH, the Bass Model estimates conflict with the predictions of Diffusion Theory. Sorting out this paradox demonstrates the Bass Model’s potential to identify conflicting influences on consumer adoption, and measure how the relative strength of these competing forces nets out to determine the course of consumer adoption. (shrink)

Although chemical phenomena are primarily associated with electrons in atoms, ions, and molecules, the masses, charges, spins, and other properties of the nuclei in these species contribute significantly as well. Isotopes, for instance, have proven invaluable in chemistry, in particular the elucidation of reaction mechanisms. Elements with unstable nuclei, for example carbon-14 undergoing beta decay, have enriched chemistry and many other scientific disciplines. The nuclei of all elements have a much more subtle and largely unknown effect on chemical phenomena. All (...) nuclei are innately chiral and, because electrons can penetrate nuclei, all atoms and molecules are likewise chiral. This article describes in considerable detail the discovery of chiral nuclei, how this unusual chirality may influence the chemical behavior of atoms and molecules, and how atomic chirality may have been responsible for the synthesis of optically active molecules in the pre-biotic world. (shrink)