A volume of papers inspired by the work of George E. Smith on confirmation and evidence in advanced science—from Newton's gravitation theory to the physics of molecules.

This chapter looks at Euler’s relation to Newton, and at his role in the rise of ‘Newtonian’ mechanics. It aims to give a sense of Newton’s complicated legacy for Enlightenment science, and to raise awareness that some key ‘Newtonian’ results really come from Euler.

The author proposes in this practical guide for both problem and non-problem gamblers a new pragmatic, conceptual approach of gambling mathematics. The primary aim of this guide is the adequate understanding of the essence and complexity of gambling through its mathematical dimension. The author starts from the premise that formal gambling mathematics, which is hardly even digestible for the non-math-inclined gamblers, is ineffective alone in correcting the specific cognitive distortions associated with gambling. By applying the latest research results in this (...) field, the author blends the gambling-mathematics concepts with the epistemology of applied mathematics and cognitive psychology for providing gamblers the knowledge required for rational and safe gambling. (shrink)

Much early modern metaphysics grew with an eye to the new science of its time, but few figures took it as seriously as Emilie du Châtelet. Happily, her oeuvre is now attracting close, renewed attention, and so the time is ripe for looking into her metaphysical foundation for empirical theory. Accordingly, I move here to do just that. I establish two conclusions. First, du Châtelet's basic metaphysics is a robust realism. Idealist strands, while they exist, are confined to non-basic regimes. (...) Second, her substance realism seems internally coherent, so her foundational project appears successful.I have two aims in this paper. Historically, I show that du Châtelet's main source of inspiration was Christian... (shrink)

In this article, I examine the discourse around evil from the perspective of philosophical anthropology. Through an analysis of the religious symbolism of evil and an associated quest for a complete study of being, I intend in this article to explore fresh ways of establishing the relation between our rhetorical practices of evil and moral responsibility. I draw on Ricoeur’s work on the primary symbols of evil, which can be seen as a means for clarifying and extending our understanding of (...) evil and moral responsibility. I employ the concept of “the double intentionality of symbol” to advance an expressive-performative model of speaking about the full shape of moral responsibility. At stake in my paper is the possibility of recognizing the need to valorise subordinate resources of knowledge that might prevent us from studying and responding to the elusive reality of evil in intellectual abstraction. (shrink)

The problem of trickster leadership is discussed in this chapter in the context of the Romanian experience of modernity. This experience has emerged as a Post-Byzantine condition; it was strongly marked by the forty years of communist regimes and was loaded with a high amount of duplicity and ambivalence. The chapter argues that the communist type of trickster leadership in Romania was the outcome of a clash between two types of corruption: a domestic one and a global one. The idea (...) of ‘forms without substance’, coined in 1868 by the historian Titu Maiorescu, is shown to be indicative of the exilic condition in which Romanians remained caught even after their country became independent. The description of this paradoxical condition is followed by a review of the main eras of Romania as a modern state, arguing that this condition has led to an accumulation of disharmony and the absurd in the social fabric of the people. (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)

The article addresses the necessity of increasing the role of mathematics in the psychological intervention in problem gambling, including cognitive therapies. It also calls for interdisciplinary research with the direct contribution of mathematics. The current contributions and limitations of the role of mathematics are analysed with an eye toward the professional profiles of the researchers. An enhanced collaboration between these two disciplines is suggested and predicted.

My thesis in this paper is: the modern concept of laws of motion—qua dynamical laws—emerges in 18th-century mechanics. The driving factor for it was the need to extend mechanics beyond the centroid theories of the late-1600s. The enabling result behind it was the rise of differential equations. -/- In consequence, by the mid-1700s we see a deep shift in the form and status of laws of motion. The shift is among the critical inflection points where early modern mechanics turns into (...) classical mechanics as we know it. Previously, laws of motion had been channels for truth and reference into mechanics. By 1750, the laws lose these features. Instead, now they just assert equalities between functions; and serve just to entail (differential) equations of motion for particular mechanical setups. This creates two philosophical problems. First, it’s unclear what counts as evidence for the laws of motion in the Enlightenment. Second, it’s a mystery whether these laws retain any notion of causality. That subverts the early-modern dictum that physics is a science of causes. (shrink)

In light of the observations and research design presented in the previous reports, the current technical report is focused on the relationship between the quality and specificity of the content of the gambling sites and the site’s SEO and marketing policy. This relationship is dependent upon the category of the gambling site and the difference in content quality, and the degree to which the mathematical dimension of gambling is reflected in this content is explained by this dependence.

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I (...) argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy by (...) giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

The current technical report presents the partial results of the quantitative analysis of the research project, after the review of 247 gambling websites. It is focused on and discusses the usage of the math terms specific to gambling in the reviewed sample. In particular, the fifth technical report discusses the usage of math terms associated with the game of slots, as found in the reviewed sample.

The core insight of neutral monism is that there might be something underlying both mind and matter which is neither and of which mind and matter could be seen as particular manifestations. In this paper, I shall present some directions for developing neutral monism as a metaphysical position on the mind-brain problem and argue that its core insight may be applied to other debates in philosophy of mind, in particular debates about the metaphysics of phenomenologies, such as the phenomenology of (...) thought and cognitive phenomenologies. (shrink)

Accountability for corporate social responsibility (CSR) and its societal challenges is undetermined, and it is unclear whether business or society should carry these responsibilities. Despite severe criticism from some, many organizations continue to invest in and promote CSR. The purpose of this multiple-case study was to increase the understanding of the phenomenon from the perspective of a purposeful sample of participants who contribute to CSR execution and who were representatives of the 10 organizations identified as active promoters. The participant corporations (...) (case studies), in Europe and North America, were mainly in the telecommunications industry. Study data came from 11 face-to-face, semistructured interviews with chief executive officers (CEOs) and other CSR key participants, a review of corporate archival records, and a review of other sources regarding the effective implementation of CSR in these organizations. The conceptual framework consisted of Carroll’s constructs of CSR based on economic, legal, social, and discretionary elements. The constant comparative method was used to analyze the interview data and identify factors leading corporations to continue to engage in CSR. These factors were economic, social impact, legal compliance, or good reputation, sponsored by transformational or adaptive leaderships and endorsed by visionary CEOs. The findings may enlighten and motivate other organizations to engage in CSR programs and connect stakeholders’ contribution to a broadened positive social change. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with this study describe (...) the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

Much scholarship has claimed the physics of Emilie du Châtelet’s treatise, Institutions de physique, is Newtonian. I argue against that idea. To do so, I distinguish three strands of meaning for the category ‘Newtonian science,’ and I examine her book against them. I conclude that her physics is not Newtonian in any useful or informative sense. To capture what is specific about it, we need better interpretive categories.

Philosophy and Phenomenological Research, EarlyView.

Richard Rorty is well known as a propagandist of pragmatism and of a "post-philosophical" culture in which many traditional philosophical debates are dismissed as outrightly fruitless. The paper is mainly concerned with Rorty's dismissal of the realism-antirealism debate. The shift from argument to propaganda which is typical of much of Rorty's reasoning is critically investigated from different perspectives. In particular, it is argued that Rorty cannot convincingly establish a pragmatist position beyond realism and antirealism, and that pragmatism seems to be (...) inadequate with respect to scientific practice. Finally, the fruitfulness of the realism-antirealism debate is defended. (shrink)

This paper examines the young Kant’s claim that all motion is relative, and argues that it is the core of a metaphysical dynamics of impact inspired by Leibniz and Wolff. I start with some background to Kant’s early dynamics, and show that he rejects Newton’s absolute space as a foundation for it. Then I reconstruct the exact meaning of Kant’s relativity, and the model of impact he wants it to support. I detail (in Section II and III) his polemic engagement (...) with Wolffian predecessors, and how he grounds collisions in a priori dynamics. I conclude that, for the young Kant, the philosophical problematic of Newton’s science takes a back seat to an agenda set by the Leibniz-Wolff tradition of rationalist dynamics. This results matters, because Kant’s views on motion survive well into the 1780s. In addition, his doctrine attests to the richness of early modern views of the relativity of motion. (shrink)

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by Newton's Continental followers, such as (...) Leonhard Euler, who made novel attempts to defend his mechanical foundations against the pro-Leibnizian attack. This examination grants us deeper insight into the fate of Newton's mechanics on the Continent during the early eighteenth century and, more specifically, sheds needed light on the conflicts and tensions that characterized the reception of Newton's philosophy of mechanics among the Leibnizians. (shrink)

This book offers a theoretical investigation into the general problem of reality as a multiplicity of ‘finite provinces of meaning’, as developed in the work of Alfred Schutz. A critical introduction to Schutz’s sociology of multiple realities as well as a sympathetic re-reading and reconstruction of his project, Experiencing Multiple Realities traces the genesis and implications of this concept in Schutz’s writings before presenting an analysis of various ways in which it can shed light on major sociological problems, such as (...) social action, social time, social space, identity, or narrativity. (shrink)

I argue that the key dynamical concepts and laws of Newton's Principia never gained a solid foothold in Germany before Kant in the 1750s. I explain this absence as due to Leibniz. Thus I make a case for a robust Leibnizian legacy for Enlightenment science, and I solve what Jonathan Israel called “a meaningful historical problem on its own,” viz. the slow and hesitant reception of Newton in pre-Kantian Germany.

The current technical report of the research project investigating how the mathematical dimension of gambling is reflected in the communication and texts associated with the gambling industry raises the problem of the adequacy of sampling and proposes a new approach in this respect. The qualitative analysis of the reviewed websites is extended to a deeper analysis of language and also to the organization and structure of websites’ content. Although not stated as a goal of the initial project, the research will (...) also try to identify relationships between the specificity of content relative to the mathematical dimension of gambling, and the management and marketing of the website. An overview of the results of the statistical analysis of the current sample is also presented. (shrink)

This article is a study on Paul’s mystical experiences using an interpretive framework that relies on multiple grounds: Alfred Schutz’s phenomenology of the “multiple realities” applied to the problem of religion, political anthropology and general scholarship on Paul. The aim of this study is also multiple: I seek to draw an interpretive insight into those mystical experiences that have been traditionally attributed to Paul by using a hermeneutic lens provided by Schutzian phenomenology, to clarify this hermeneutic method as such and (...) explore its interpretive potential for the phenomenology of religion in general, and to interpret the results of this analysis from the reflexive-historical perspective of political anthropology. (shrink)

This second technical report shows some partial results for the variables of the proposed statistical analysis and a discussion about some changes in sampling. In what concerns the qualitative analysis of content, the report presents the general predominant tendencies that get contoured with the first two samples.

I examine here if Kant’s metaphysics of matter can support any late-modern versions of classical mechanics. I argue that in principle it can, by two different routes. I assess the interpretive costs of each approach, and recommend the most promising strategy: a mass-point approach.

I uncover here a conflict in Kant’s natural philosophy. His matter theory and laws of mechanics are in tension. Kant’s laws are fit for particles but are too narrow to handle continuous bodies, which his doctrine of matter demands. To fix this defect, Kant ultimately must ground the Torque Law; that is, the impressed torque equals the change in angular momentum. But that grounding requires a premise—the symmetry of the stress tensor—that Kant denies himself. I argue that his problem would (...) not arise if he had kept his early theory of matter as made of mass points, or “physical monads.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did Hans (...) Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

I explain and assess here Huygens’ concept of relative motion. I show that it allows him to ground most of the Law of Inertia, and also to explain rotation. Thereby his concept obviates the need for Newton’s absolute space. Thus his account is a powerful foundation for mechanics, though not without some tension.

Newton had a fivefold argument that true motion must be motion in absolute space, not relative to matter. Like Newton, Kant holds that bodies have true motions. Unlike him, though, Kant takes all motion to be relative to matter, not to space itself. Thus, he must respond to Newton’s argument above. I reconstruct here Kant’s answer in detail. I prove that Kant addresses just one part of Newton’s case, namely, his “argument from the effects” of rotation. And, to show that (...) rotation is relative to matter, Kant changes the meaning of ‘relative motion.’ However, that change puts Kant’s doctrine in deep tension with Newton’s science. Based on my construal, I correct earlier readings of Kant by John Earman and Martin Carrier. And, I argue that we need to revise Michael Friedman’s influential view of Kant. Kant’s struggle, I conclude, illustrate the difficulties that early modern relationists faced as they turned down Newtonian absolute space ; and it typifies their selective engagement with Newton’s case for it. (shrink)

I examine here if Kant can explain our knowledge of duration by showing that time has metric structure. To do so, I spell out two possible solutions: time’s metric could be intrinsic or extrinsic. I argue that Kant’s resources are too weak to secure an intrinsic, transcendentally-based temporal metrics; but he can supply an extrinsic metric, based in a metaphysical fact about matter. I conclude that Transcendental Idealism is incomplete: it cannot account for the durative aspects of experience—or it can (...) do so only with help from a non-trivial metaphysics of material substance. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the principles (...) that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these (...) formal constructions and discusses them as an argument for the alternative semantic and propositional-structure accounts of the applicability of mathematics. (shrink)

Research on interdisciplinarity has been concentrated on the methodological and educational aspects of this complex phenomenon and less on its theoretical nature. Within a theoretical framework specific to the philosophy of science, I propose a structural scheme of how interdisciplinary processes go, focusing on the concepts of availability of the methods, concept linking, and theoretical modeling. In this model, the challenges interdisciplinarity is claimed to pose to its practitioners are of the same nature as the challenges scientists encounter within the (...) evolution of their own disciplines. (shrink)

This paper is an exploration of the multiple meanings that the invention of the brick – this simple artefact that has permitted the raising of complex and durable buildings – has brought to civilisation and to humans in their relationship with the world. I suggest that bricks may have brought a number of novel experiences to society, whose meanings are important for the understanding of the modern condition and its emphasis on rationalism, replicability, precision, standardisation and modularity among other principles. (...) I also point out that bricks, along with rectangular types of packaging, are eminently liminal objects that entail a peculiar form of violence. (shrink)

The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.

In book X, Plato's rejection of mimetic poetry can be read as a parallel to rejecting the conventions of the poetic style contemporary to his time. This rejection can, owing to the premises derived and the analyses made in this paper, further be read as to suggest that Plato presses for a reformation of the poetic vocabulary. That is, as to suggest that Plato proposes that the non-rational imagistic tradition, embodied in mimetic poetry, get replaced by a rational and noetic-aspiring (...) rhetoric that opts for knowledge and truth. (shrink)

Modern philosophy of physics debates whether motion is absolute or relative. The debate began in the 1600s, so it deserves a close look here. Primarily, it was a controversy in metaphysics, but it had epistemic aspects too. I begin with the former, and then touch upon the latter at the end.

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

The attempts of theoretically solving the famous puzzle-dictum of physicist Eugene Wigner regarding the “unreasonable” effectiveness of mathematics as a problem of analytical philosophy, started at the end of the 19th century, are yet far from coming out with an acceptable theoretical solution. The theories developed for explaining the empirical “miracle” of applied mathematics vary in nature, foundation and solution, from denying the existence of a genuine problem to structural theories with an advanced level of mathematical formalism. Despite this variation, (...) methodologically fundamental questions like “Which is the adequate theoretical framework for solving Wigner’s conjecture?” and “Can the logico-mathematical formalism solve it and is it entitled to do it?” did not receive answers yet. The problem of the applicability of mathematics in the physical reality has been treated unitarily in some sense, with respect to the semantic-conceptual use of the constitutive terms, within both the structural and non-structural theories. This unity (of consistency) applied to both the referred objects and concepts per se and the aims of the investigations. For being able to make an objective study of the possible alternatives of the existent theories, a foundational approach of them is needed, including through semantic-conceptual distinctions which to weaken the unity of consistency. (shrink)

This work is a critical introduction to Alfred Schutz’s sociology of the multiple reality and an enterprise that seeks to reassess and reconstruct the Schutzian project. In the first part of the study, I inquire into Schutz’s biographical con- text that surrounds the germination of this conception and I analyse the main texts of Schutz where he has dealt directly with ‘finite provinces of meaning.’ On the basis of this analysis, I suggest and discuss, in Part II, several solutions to (...) the shortcomings of the theoretical system that Schutz drew upon the sociological problem of multiple reality. Specifically, I discuss problems related to the struc- ture, the dynamics, and the interrelationing of finite provinces of meaning as well as the way they relate to the questions of narrativity, experience, space, time, and identity. (shrink)

On an influential view, Newton's mechanics is built into Kant's very theory of exact knowledge. However, Newtonian dynamics had serious explanatory limits already known by 1750. Thus, we might worry that Kant's Analytic is too narrow to ground enough exact knowledge. In this paper, I draw on Enlightenment dynamics to show that Kant's notion of determinate objecthood is sufficiently broad, non-trivial, and still relevant to the present.

I emphasize two merits of Eric Watkins’ account in "Kant on Laws": the strong evidential support it has, and the central place it gives to Kant’s laws of mechanics. Then, I raise two questions for further research. 1. What kind of evidential reasoning confirms a Kantian law? 2. Do natures explain Kantian laws? If so, how?

Aceasta nu este o carte de matematică, ci una despre matematică, care se adresează elevului sau studentului, dar şi dascălului său, cu un scop cât se poate de practic, anume acela de a iniţia şi netezi calea către înţelegerea completă a matematicii predate în şcoală. Tradiţia predării matematicii într-o abordare preponderent procedural-formală a avut ca efect o viziune deformată a elevilor asupra matematicii, ca fiind ceva strict formal, instrumental şi calculatoriu. Pierzând contactul cu baza conceptuală a matematicii, elevii dezvoltă pe (...) parcurs o "anxietate matematică" şi renunţă la a mai căuta înţelegerea matematicii, care devine "duşmanul tradiţional" din şcoală. Această lucrare şi-a propus materializarea rezultatelor cercetărilor inter- şi trans-disciplinare având ca obiect înţelegerea matematicii, care au concluzionat că domeniile care au potenţialul de a contribui în acest fel la educaţia matematicii, unificând abordările procedurală şi conceptuală, sunt epistemologia şi filosofia matematicii şi ştiinţei, precum şi fundamentele şi istoria matematicii. Aceste rezultate susţin teza că teama de matematică poate fi înlăturată prin abordarea conceptuală, iar un elev cu o bună înţelegere conceptuală va fi un rezolvitor de probleme mai bun. Autorul a identificat acele zone şi concepte aparţinând acestor discipline, care pot fi adaptate şi prelucrate în vederea familiarizării elevului sau studentului cu acest tip de cunoştinţe, care să însoţească conţinutul tradiţional al matematicii şcolare. Lucrarea a fost astfel organizată încât să contureze cititorului o imagine unificatoare asupra complexităţii naturii matematicii, precum şi o perspectivă conceptuală necesară, în final, înţelegerii de tip holistic a matematicii şcolare. Autorul vorbeşte despre matematică, pentru a convinge că a înţelege matematica înseamnă mai întâi să o înţelegem ca întreg, dar şi ca parte a unui întreg. Natura matematicii, conceptele sale primare (cum ar fi numerele şi mulţimile), structurile, limbajul, metodele, rolurile şi aplicabilitatea matematicii, sunt prezentate în conţinutul lor esenţial, iar explicarea conceptelor non-matematice este făcută într-un limbaj accesibil, însoţită de multe exemple relevante. Cartea este o unitate didactică concepută să reprezinte punctul de plecare şi un ghid de orientare către dobândirea înţelegerii de tip holistic a matematicii (pentru elev sau student) şi (pentru dascăl) către o predare de tip epistemic-conceptual, în care înţelegerea conceptuală este la fel de importantă ca antrenarea abilităţilor procedural-aplicative. (shrink)

Lucrarea tratează unul dintre “misterele” filosofiei analitice şi ale raţionalităţii însăşi, anume aplicabilitatea matematicii în ştiinţe şi în investigarea matematică a realităţii înconjurătoare, a cărei filosofie este dezvoltată în jurul sintagmei – de acum paradigmatice – ‘eficacitatea iraţională a matematicii’, aparţinând fizicianului Eugene Wigner, problemă filosofică etichetată în literatură drept “puzzle-ul lui Wigner”. Odată intraţi în profunzimea acestei probleme, investigaţia nu trebuie limitată la căutarea unor răspunsuri explicative la întrebări precum “Ce este de fapt aplicabilitatea matematicii?”, “Cum explicăm prezenţa în (...) natură a conceptelor matematice simple şi complexe?” sau “Cum explicăm rata de succes uriaşă a aplicaţiilor matematice, care presupun modele aproximativ false ale unei realităţi idealizate?”, ci extinsă în plan metateoretic către căutarea unei justificări teoretice a utilizării metodei matematice în practica ştiinţifică, independent de succesul acestei metode. Aceste întrebări şi probleme sunt abordate în detaliu în lucrarea de faţă. Lucrarea, care va continua cu un al doilea titlu, dedicat modelelor teoretice ale aplicabilităţii şi alternativelor structurale ale acestora, se adresează în special – dar nu exclusiv – matematicienilor, fizicienilor, filosofilor ştiinţei, filosofilor limbajului şi epistemologilor, dar şi studenţilor acestor discipline. (shrink)