An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the (...) issue under study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

This Hackett edition, first published in 1981, is an unabridged and unaltered republication of the seventh edition as published by Macmillan and Company, Limited. From the forward by John Rawls: In the utilitarian tradition Henry Sidgwick has an important place. His fundamental work, The Methods of Ethics, is the clearest and most accessible formulation of what we may call 'the classical utilitarian doctorine.' This classical doctrine holds that the ultimate moral end of social and individual action is the greatest net (...) sum of the happiness of all sentient beings. Happinesss is specified by the net balance of pleasure over pain, or, as Sidgwick preferred to say, as the net balance of agreeable over disagreeable consciousness.... (shrink)

Written in the 1960s, TRUTH AND METHOD is Gadamer's magnum opus. Looking behind the self-consciousness of science, he discusses the tense relationship between truth and methodology. In examining the different experiences of truth, he aims to "present the hermeneutic phenomenon in its fullest extent.

The article addresses some aspects of Gava’s book, highlighting two main points: (1) the notion of philosophy in a cosmic sense; (2) its connection with the meaning of the concept of method. Regarding (1) I show how Gava’s interpretation of the systematic concept of philosophy does not account adequately for the scholastic concept. This has consequences for the notion of philosophy in a cosmic sense itself; its nature as an objective archetype and its personification in the ideal of a (...) master of wisdom are not properly emphasized. These features are closely related to Kant’s claim that philosophy cannot be learned, which is connected with Kant’s peculiar idea of method. Regarding (2), I argue that ‘method’ for Kant does not concern only the construction of scientific systems, but also the establishment of a way of thinking, a stance embracing thought and action. The meaning of the postulates and the notion of ‘faith’ thus acquire a ‘weaker’ connotation, as an attitude, habitus, aimed at the establishment and promotion of a ‘life-structuring’ rationality, and not as an alternative route to a theoretical ‘commitment’. (shrink)

Written in the 1960s, TRUTH AND METHOD is Gadamer's magnum opus.

Introduction: An ethnographer among the anthropologists -- The world at hand: between scientific and literary inquiry -- A method of experience: reading, writing, teaching, fieldwork -- For the humanity yet to come: politics, art, fiction, ethnography -- Coda: The anthropologist as critic.

Method of Medicine, a systematic and comprehensive account of the principles of treating injury and disease and one of Galen's greatest and most influential works.

This article focuses on the main methods used in analytic metaphysics. It first considers five important sources of constraints on metaphysical theorizing: linguistic and conceptual analysis, consulting intuitions, employing the findings of science, respecting folk opinion, and applying theoretical virtues in metaphysical theory choice such as preferring simpler theories, or preferring more explanatory theories. It then examines the role of formal methods in metaphysics as well as the role of metaphysical communities, traditions, and the place of the history of metaphysics (...) in contemporary work. It also discusses the issue of whether metaphysics should be seen as an enterprise that will yield knowledge of metaphysical matters or whether it should have more modest epistemic goals. Finally, it explores the question of how much of metaphysics is a priori. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

In this paper, we first briefly survey the main responses to the challenge that experimental philosophy poses to the method of cases, given the common assumption that the latter is crucially based on intuitive judgments about cases. Second, we discuss two of the most popular responses in more detail: the expertise defense and the mischaracterization objection. Our take on the expertise defense is that the available empirical data do not support the claim that professional philosophers enjoy relevant expertise in (...) their intuitive judgments about cases. In contrast, the mischaracterization objection seems considerably more promising than its largely negative reception has suggested. We argue that the burden of proof is thus on philosophers who still hold that the method of cases crucially relies on intuitive judgments about cases. Finally, we discuss whether conceptual engineering provides an alternative to the method of cases in light of the challenge from experimental philosophy. We argue that this is not clearly the case, because conceptual engineering also requires descriptive information about the concepts it aims to improve. However, its primarily normative perspective on our concepts makes it largely orthogonal to the challenge from experimental philosophy, and it can also benefit from the empirical methods of the latter. (shrink)

Renaissance logician, philosopher, humanist, and teacher, Peter Ramus (1515-72) is best known for his attack on Aristotelian logic, his radical pedagogical theories, and his new interpretation for the canon of rhetoric. His work, published in Latin and translated into many languages, has influenced the study of Renaissance literature, rhetoric, education, logic, and--more recently--media studies. Considered the most important work of Walter Ong's career, Ramus, Method, and the Decay of Dialogue is an elegant review of the history of Ramist scholarship (...) and Ramus's quarrels with Aristotle. A key influence on Marshall McLuhan, with whom Ong enjoys the status of honorary guru among technophiles, this challenging study remains the most detailed account of Ramus's method ever published. Out of print for more than a decade, this book--with a new foreword by Adrian Johns--is a canonical text for enthusiasts of media, Renaissance literature, and intellectual history. (shrink)

Argumentation, which can be abstractly defined as the interaction of different arguments for and against some conclusion, is an important skill to learn for everyday life, law, science, politics and business. The best way to learn it is to try it out on real instances of arguments found in everyday conversational exchanges and legal argumentation. The introductory chapter of this book gives a clear general idea of what the methods of argumentation are and how they work as tools that can (...) be used to analyze arguments. Each subsequent chapter then applies these methods to a leading problem of argumentation. Today the field of computing has embraced argumentation as a paradigm for research in artificial intelligence and multi-agent systems. Another purpose of this book is to present and refine tools and techniques from computing as components of the methods that can be handily used by scholars in other fields. (shrink)

Introduction: "a matter so obscure, so difficult, and likewise so new . . ." -- Argument, narrative, and methods discourse -- Many, many experiments -- Trying again -- Newtonian poison: a mechanical account of viper venom -- Experiment as the only guide -- Thousands of experiments -- Practical criticisms -- Controlling experiment -- Unobservables -- Fragmentation and modularity: notes on crotoxin -- Conclusion: about methods.

As is well known, Plato was a significant influence on Gadamer’s thought. Nevertheless, Gadamer’s interpretation of Plato changed through the years, and he became increasing sympathetic towards Plato in his later works after 1960’s Truth and Method. This article will examine how Gadamer’s writings on Plato after Truth and Method may inform our interpretation of his magnum opus. I will present the case that this not only leads to rethinking Gadamer’s relation to Plato, but also has wider implications (...) for his hermeneutics and for potential reconsiderations of key aspects of the text. I point to the possibility that if we do not sufficiently appreciate these changes in Gadamer’s interpretation of Plato, this may not only distort our understanding of Gadamer’s reading of Plato, but perhaps more importantly neglect how Platonic conceptions may inform his own hermeneutic project as it is outlined in Truth and Method. (shrink)

Plato’s Theaetetus, Sophist, and Statesman exhibit several related dialectical methods relevant to Platonic education: maieutic in Theaetetus, bifurcatory division in Sophist and Statesman, and non-bifurcatory division in Statesman, related to the ‘god-given’ method in Philebus. I consider the nature of each method through the letter or element paradigm, used to reflect on each method. At issue are the element’s appearances in given contexts, its fitness for communing with other elements like it in kind, and its own nature (...) defined through its relations to others. These represent stages of inquiry for the Platonic student inquiring into the sources of knowledge. (shrink)

Both individually and as a collection, these essays will promote understanding and provoke further debate amongst students and established scholars alike.

By focusing on the nineteenth-century debate between William Whewell and Augustus De Morgan on the nature and scope of scientific method and induction, this article captures an important episode in the history of Baconianism. More specifically, it sheds new light on the social and intellectual construction of Francis Bacon as an emblem of modern science and on British Baconianism as part of the creation of a vision of the modern enterprise. A critic of Whewell’s renovated Baconianism and an advocate (...) of an alternative anti-Baconian (or pro-Newtonian) view of science, De Morgan is presented for the first time as a philosopher of science (or metascientist), one who pioneered the application of probability theory to scientific reasoning. (shrink)

This title presents a comprehensive guide to interpretative phenomenological analysis (IPA) which is an increasingly popular approach to qualitative inquiry taught to undergraduate and postgraduate students today.

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

" Vivid . . . immense clarity . . . the product of a brilliant and extremely forceful intellect." — Journal of the Royal Naval Scientific Service "Still a sheer joy to read." — Mathematical Gazette "Should be read by any student, teacher or researcher in mathematics." — Mathematics Teacher The originator of algebraic topology and of the theory of analytic functions of several complex variables, Henri Poincare (1854–1912) excelled at explaining the complexities of scientific and mathematical ideas to lay (...) readers. Science and Method, written in 1908, has been appreciated by a wide audience of nonprofessionals and translated into many languages. It defines the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition. Translated by Francis Maitland. (shrink)

This book gives a comprehensive account of methods in philosophy of education, it also examines their application in the 'real world' of education. It will therefore be of interest to philosophers and educators alike.

The method of mathematical induction: The method of mathematical induction -- Examples and exercises -- The proof of induction of some theorems of elemetary algebra -- Solutions.

The method of reflective equilibrium (MRE) is a method of justification popularized by John Rawls and further developed by Norman Daniels, Michael DePaul, Folke Tersman, and Catherine Z. Elgin, among others. The basic idea is that epistemic agents have justified beliefs if they have succeeded in forming their beliefs into a harmonious system of beliefs which they reflectively judge to be the most plausible. Despite the common reference to MRE as a method, its mechanisms or rules are (...) typically expressed in a metaphorical or simplified manner and are therefore criticized as too vague. Recent efforts to counter this criticism have been directed towards the attempt to provide formal explications of MRE. This paper aims to supplement these efforts by providing an informal working definition of MRE. This approach challenges the view that MRE can adequately be characterized only in the negative as a set of anti-essentialisms. I argue that epistemic agents follow MRE iff they follow four interconnected rules, which are concerned with a minimalistic form of foundationalism, a minimalistic form of fallibilism, a moderate form of holism, and a minimalistic form of rationality. In the critical spirit of MRE, the corresponding working definition is, of course, provisional and revisable. In general, the aim is to contribute to a reflective equilibrium (RE) concerning MRE. If it is successful, this working definition provides a better grasp of the most basic elements of the method and thereby enhances our understanding of it. (shrink)

The goal of chapter 2 is to analyse Socrates’ method. Firstly, it is argued that theSocratic method is not able to reach definitive conclusions. Secondly, it is shown that this occurs because of the use of real rather than nominal definitions. Finally, it is noted that, although this method cannot provide any proper knowledge, it constitutes a very good starting point to address moral problems with great care.

Socratic Method in the Euthyphro can be fruitfully analysed as a method of irony interpretation. Socrates' method – the irony of irony interpretation – is to pretend that Euthyphro is an ironist in order to transform him into a self-ironist. To be a self-ironist is to ironize one's knowledge of virtue in order to bring an intuitive and unarticulated awareness of virtue to mind. The exercise of the capacity for self-irony is then a mode of striving for (...) the good. (shrink)

"Dr. Montessori was par excellence the great interpreter of the child; and though she herself has passed on from the scene of her labours her work will still go on."-- Westminster Cathedral Chronicle One of the landmark books in the history of education--and one of the least expensive editions now available--this volume describes a new system for educating youngsters. Based on a radical concept of liberty for the pupil and highly formal training of separate sensory, motor, and mental capacities, the (...) system enabled youngsters to master reading, writing, and arithmetic rapidly and substantially. Included are discussions of scientific pedagogy; discipline; the importance of proper diet, gymnastics, and manual labor; and many other topics. Unabridged reprint of the classic 1912 edition. (shrink)

"Science et méthode" de Henri Poincaré. Mathématicien, physicien et philosophe français (1854-1912).

The aim of the article is to intervene in debates about the digital and, in particular, framings that imagine the digital in terms of epochal shifts or as redefining life. Instead, drawing on recent developments in digital methods, we explore the lively, productive and performative qualities of the digital by attending to the specificities of digital devices and how they interact, and sometimes compete, with older devices and their capacity to mobilize and materialize social and other relations. In doing so, (...) our aim is to explore the implications of digital devices and data for reassembling social science methods or what we call the social science apparatuses that assemble digital devices and data to ‘know’ the social and other relations. Building on recent work at CRESC on the social life of methods, we recommend a genealogical approach that is alive to the ways in which digital devices are simultaneously shaped by social worlds, and can in turn become agents that shape those worlds. This calls for attending to the specificities of digital devices themselves, how they are varied and composed of diverse socio-technical arrangements, and are enrolled in the creation of new knowledge spaces, institutions and actors. Rather than exploring what large-scale changes can be revealed and understood through the digital, we argue for explorations of how digital devices themselves are materially implicated in the production and performance of contemporary sociality. To that end we offer the following nine propositions about the implications of digital data and devices and argue that these demand rethinking the theoretical assumptions of social science methods: transactional actors; heterogeneity; visualization; continuous time; whole populations; granularity; expertise; mobile and mobilizing; and non-coherence. (shrink)

At the beginning of his Metaphysics, Aristotle attributed several strange-sounding theses to Plato. Generations of Plato scholars have assumed that these could not be found in the dialogues. In heated arguments, they have debated the significance of these claims, some arguing that they constituted an 'unwritten teaching' and others maintaining that Aristotle was mistaken in attributing them to Plato. In a prior book-length study on Plato's late ontology, Kenneth M. Sayre demonstrated that, despite differences in terminology, these claims correspond to (...) themes developed by Plato in the Parmenides and the Philebus. In this book, he shows how this correspondence can be extended to key, but previously obscure, passages in the Statesman. He also examines the interpretative consequences for other sections of that dialogue, particularly those concerned with the practice of dialectical inquiry. (shrink)

Can ethical character be stimulated and enabled? Cognitive understanding of organizational ethics issues is important and necessary, but not sufficient. Ethical behavior does not emerge automatically. Effective political method is necessary. While it may be difficult to teach ethical character, nonetheless, skill development with respect to joined ethics understanding and action-learning methods can help us develop the skills and confidence we need to actualize our ethical characters and social concerns. An action-learning approach to organizational ethics can help stimulate and (...) enable ethical character. (shrink)

Nous présentons ici la traduction d’une conférence donnée par Ernst Cassirer au Cercle linguistique de New York en 1945, intitulée « Le structuralisme dans la linguistique moderne ». Dans ce texte, Cassirer propose une généalogie de l’approche structurale dans la linguistique moderne, en faisant remonter la problématique aux débats épistémologiques des xviii e et xix e siècles sur la constitution des sciences du vivant. La conférence de Cassirer revêt ainsi à nos yeux un double intérêt : d’une part, elle rend (...) compte de l’unité de l’œuvre cassirerienne, puisque l’auteur y mobilise des concepts dont il a posé les premiers jalons dès 1910 dans _Substance et fonction_ ; d’autre part, elle permet de rendre compte de la spécificité méthodologique des sciences de la culture, à partir d’une généalogie conceptuelle de la méthode en train de naître dans les cercles linguistiques de l’époque. Nous tâcherons de présenter les différentes étapes de l’argumentation de Cassirer, allant d’une redéfiniti... (shrink)

This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried (...) to naturalize mathematics by relying on evolutionism. But several difficulties arise when we try to do this. This chapter suggests that, in order to naturalize mathematics, it is better to take the method of mathematics to be the analytic method, rather than the axiomatic method, and thus conceive of mathematical knowledge as plausible knowledge. (shrink)

Paul Feyerabend's globally acclaimed work, which sparked and continues to stimulate fierce debate, examines the deficiencies of many widespread ideas about scientific progress and the nature of knowledge. Feyerabend argues that scientific advances can only be understood in a historical context. He looks at the way the philosophy of science has consistently overemphasized practice over method, and considers the possibility that anarchism could replace rationalism in the theory of knowledge. -- Amazon.com.

This paper explores the distinctive features of the critical agenda associated with the ‘Social Life of Methods’. I argue that although this perspective can be associated with the increasing interest, often associated with scholars in Science and Technology Studies, to reflect on how methods can become objects of inquiry, it also needs to be rooted in the current crisis of positivist methods. I identify the challenge for positivism in terms of the decreasing ability of its procedures to effectively organize increasingly (...) ‘lively’ sources of standardized data, which can now be assembled using aesthetic registers. In developing this argument, I dispute the idea that this development is due to historical shifts linked to the way that methodological devices are playing an increasingly significant role in contemporary social life, which might be argued by writers such as Thrift or Castells. I also argue that by opening up issues of method to the aesthetic, we also recast the relationship between theory and method, pointing to the exhaustion of a certain kind of cultural theory within the social sciences. I contextualize these issues by considering how methods are implicated in the intellectual differentiation between scientific and humanities expertise. Rather than conceiving the ‘Social Life of Methods’ in terms of the rise of instrumentalist modes of governance, it is preferable to place it within the dialectic of transparency and the relationship between the implicit and explicit. These issues are addressed through introducing the papers in the special issue. (shrink)

The core argument of chapter 9 is the thesis that the epistemological distinction between knowledge and beliefs introduced in the Meno plays a crucial role in the consideration of virtues. Thanks to this distinction, Plato can indeed dismiss the theory according to which virtues are only instrumental. Therefore, it is demonstrated that the theory of virtue of the early dialogues is the result of having knowledge of the importance of virtues but not a proper and true knowledge of them.