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)

This essay is an examination of the relationship between phenomenology and analytic method in the philosophy of law. It proceeds by way of a case study, the requirement of compliance in Raz’s theory of mandatory norms. Proceeding in this way provides a degree of specificity that is otherwise neglected in the relevant literature on method. Drawing on insights from the philosophy of art and cognitive neuroscience, it is argued that the requirement of compliance is beset by a range (...) of epistemological difficulties. The implications of these difficulties are then reviewed for method and normativity in practical reason. A topology of normativity emerges nearer the end of the paper, followed by a brief examination of how certain normative categories must satisfy distinct burdens of proof. (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.

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

In 1900 David Hilbert announced his famous list of then-opened mathematical problems; the problem number 6 in this list is axiomatization of physical theories. Since then a lot of systematic efforts have been invested into solving this problem. However the results of these efforts turned to be less successful than the early enthusiasts of axiomatic method expected. The existing axiomatizations of physical and biological theories provide a valuable logical analysis of these theories but they do not constitute anything like (...) their standard presentation,which can be used for transmission, evaluation, and justification of physical and biological knowledge. This state of theart in the axiomatization of physics is strong evidence that the standard notion of axiomatic theory stemming from Hilbert and Tarski is not appropriate for thet ask. However in the recent years in mathematics there emerged a new axiomatic approach best represented by the Homotopy Type theory (HoTT). We argue that the constructive axiomatic architecture used in HoTT has better chances to be successfully applied in physics as well as in computer science and engineering. (shrink)

Feyerabrend argues that intellectual progress relies on the creativity of the scientist, against the authority of science.

1. Overview and organizing themes 2. Historical Review: Aristotle to Mill 3. Logic of method and critical responses 3.1 Logical constructionism and Operationalism 3.2. H-D as a logic of confirmation 3.3. Popper and falsificationism 3.4 Meta-methodology and the end of method 4. Statistical methods for hypothesis testing 5. Method in Practice 5.1 Creative and exploratory practices 5.2 Computer methods and the ‘third way’ of doing science 6. Discourse on scientific method 6.1 “The scientific method” in (...) science education and as seen by scientists 6.2 Privileged methods and ‘gold standards’ 6.3 Scientific method in the court room 6.4 Deviating practices 7. Conclusion Bibliography Academic Tools Other Internet Resources Related Entries . (shrink)

The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, the philosophical (...) fruitfulness of the new method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

This paper provides a systematic literature review, analysis and discussion of methods that are proposed to practise ethics in research and innovation. Ethical considerations concerning the impacts of R&I are increasingly important, due to the quickening pace of technological innovation and the ubiquitous use of the outcomes of R&I processes in society. For this reason, several methods for practising ethics have been developed in different fields of R&I. The paper first of all presents a systematic search of academic sources that (...) present and discuss such methods. Secondly, it provides a categorisation of these methods according to three main kinds: ex ante methods, dealing with emerging technologies, intra methods, dealing with technology design, and ex post methods, dealing with ethical analysis of existing technologies. Thirdly, it discusses the methods by considering problems in the way they deal with the uncertainty of technological change, ethical technology design, the identification, analysis and resolving of ethical impacts of technologies and stakeholder participation. The results and discussion of our literature review are valuable for gaining an overview of the state of the art and serve as an outline of a future research agenda of methods for practising ethics in R&I. (shrink)

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that (...) standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect. (shrink)

Experimental philosophers rely almost exclusively on quantitative surveys that potentially misrepresent participants’ multifarious judgments. To assess the efficacy of qualitative methods in experimental philosophy and reveal limitations with quantitative surveys, a study was conducted on the Kantian principle that ‘ought implies can’, which limits moral obligation to actions that agents can do. Specifically, the think aloud method and a follow-up interview were employed in a modified version of a prominent experiment that recorded participants’ judgments of ability, blame, and obligation (...) using quantitative surveys. The modified version produced quantitative results similar to the original experiment along with qualitative data that reveal that the surveys fundamentally misrepresented participants’ judgments. The qualitative transcripts from 40 participants are analyzed to show that ‘ought implies can’ judgments are complex and multifarious, that ‘ought implies can’ judgments are misrepresented by quantitative survey questions, and that the majority of participants uphold or preserve ‘ought implies can.’ The results suggest that experimental philosophers can more accurately capture judgments by using qualitative methods, and that studies which rely on quantitative surveys possibly misrepresent participants’ judgments. (shrink)

Given the prominent position Habermas' philosophy has gained, it is surprising that his method, rational reconstruction, has not caused more debate. This article clarifies what this method consists of, and shows how it is used in two of Habermas' research programs. The method is an interesting, but problematic way of confronting some of the basic epistemological questions in the social sciences. It represents an alternative to both the empirical-analytical and the hermeneutic tradition. On the basis of this (...) methodology, Habermas' work is situated between the transcendental and the empirical approach. A fundamental problem is that it remains unclear how to test the hypothesis put forward through rational reconstruction. (shrink)

Introduction -- Ethics and politics -- Ethical judgments -- Pleasure and desire -- Free will -- Ethical principles and methods -- Egoism and self-love -- Chapter viii-intuitionism -- Good -- Book II: Egoism -- The principle and method of egoism -- Empirical hedonism -- Empirical hedonism (continued) -- Objective hedonism and common sense -- Happiness and duty -- Deductive hedonism -- Book III: Intuitionism -- Intuitionism -- Virtue and duty -- The intellectual virtues -- Benevolence -- Justice -- Laws (...) and promises -- Classification of duties. truth -- Other social duties and virtues -- Self-regarding virtues -- Courage, humility, etc. -- Review of the morality of common sense -- Motives or springs of action as subjects of moral judgment -- Philosophical intuitionism -- Ultimate good -- Book IV: Utilitarianism -- The meaning of utilitarianism -- The proof of utilitarianism -- The relation of utilitarianism to the morality of common sense -- The method of utilitarianism -- The method of utilitarianism (continued) -- Concluding chapter: The mutual relations of the three methods. (shrink)

Many philosophers claim to employ intuitions in their philosophical arguments. Others contest that no such intuitions are used frequently or at all in philosophy. This article suggests and defends a conception of intuitions as part of the philosophical method: intuitions are special types of philosophical assumptions to which we are invited to assent, often as premises in argument, that may serve an independent function in philosophical argument and that are not formed through a purely inferential process. A series of (...) philosophical case studies shows that intuitions in these arguments contain the relevant features. The view has implications for philosophical method, offering a compromise between opponents on the divisive debate of the merits of experimental philosophy: experimental philosophy provides an especially useful role in philosophical assumption analysis. (shrink)

Devitt has developed an interesting defense of realism against the threats posed by the Pessimistic Induction and the Argument from Unconceived Alternatives. Devitt argues that the best explanation for the success of our current theories, and the fact that they are superior to the theories they replaced, is that they were developed and tested with the aid of better methods than the methods used to develop and test the many theories that were discarded earlier in the history of science. It (...) is no surprise that theories developed earlier in the history of science needed to be replaced. But our current theories are different, having been developed and tested with the aid of these more recently developed superior methods. I critically analyze Devitt’s defense of realism. I argue that recent developments in methodology cannot support the claims Devitt makes. I present an argument I call the “Argument from Unconceived Methods.” Given the history of science, it seems likely that scientists will continue to develop new methods in the future. And some of these methods will enable scientists to generate data that cannot be reconciled with the currently accepted theories. Consequently, it seems that our current best theories are not immune from being replaced in the future by radically different theories. (shrink)

(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)

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)

Science is founded on a method based on critical thinking. A prerequisite for this is not only a sufficient command of language but also the comprehension of the basic concepts underlying our understanding of reality. This constraint implies an awareness of the fact that the truth of the World is not directly accessible to us, but can only be glimpsed through the construction of mod- els designed to anticipate its behaviour. Because the relationship between models and reality rests on (...) the interpretation of founding postulates and in- stantiations of their predictions (and is therefore deeply rooted in language and culture), there can be no demarcation between science and non-science. However, critical thinking is essential to ensure that the link between models and reality is gradually made more adequate to reality, based on what has already been established, thus guaranteeing that science progresses on this basis and excluding any form of relativism. (shrink)

This paper is an essay based on many years of reviewing journal submissions and discussions with business ethics scholars on a range of themes regarding methods. To some extent, it contains condensed thoughts from two experienced scholars in the field, which we hope will be useful, especially to emerging scholars who, to some extent, may still be wrestling with some of the issues raised in the paper. The validity and reliability of research methods in business ethics research is discussed in (...) terms of legitimate methods to employ in the discipline, the epistemic challenges in the discipline, the debate between qualitative and quantitative methods, and some considered comments on ‘researching well’ in this discipline. Within each theme, we attempt to convey our distilled thoughts in the hope that methods employed in future studies will avoid some of the failures we have observed in the past. (shrink)

Principlism : the Borg of bioethics -- A common morality for hedgehogs : Bernard Gert -- Getting down to cases : the revival of casuistry in bioethics -- Nice story but so what : narrative and justification in ethics -- Dewey and Rorty's pragmatism and bioethics -- Freestanding pragmatism in bioethics and law -- A method in search of a purpose : the internal morality of medicine -- Method to rule them all? Reflective equilibrium in bioethics -- Concluding (...) reflections : method in bioethics : the very idea. (shrink)

Scientific methods are heuristic in nature. Heuristics are simplifying, incomplete, underdetermined and fallible problem-solving rules that can nevertheless serve certain goals in certain contexts better than truth-preserving algorithms. Because of their goal- and context-dependence, a framework is needed for systematic choosing between them. This is the domain of scientific methodology. Such a methodology, I argue, relies on a form of instrumental rationality. Three challenges to such an instrumentalist account are addressed. First, some authors have argued that the rational choice of (...) at least some methods, namely those supporting belief formation, is not goal-dependent. Second, some authors have observed that some method choices seem intuitively rational, even though relevant goals are lacking. Thirdly, some authors have argued that instrumental rationality itself depends on a goal-independent form of rationality. It is the heuristic nature of scientific methods that affords me the arguments against these challenges. This heuristic-instrumentalist account provides the means-ends analysis needed to evaluate heuristic method choice. The paper thus offers the conceptual basis for a scientific methodology that is both compatible with the heuristic nature of actual scientific practice and also normatively relevant for assessing method choice. (shrink)

What is the relation between method and truth? Are we justified in accepting a theory that satisfies the rules of scientific method as true? Such questions divide realism from anti-realism in the philosophy of science. Scientific realists take the methods of science to promote the realist aim of correspondence truth. Anti-realists either claim that the methods of science promote lesser epistemic goals than realist truth, or else they reject the realist conception of truth altogether. In this paper, I (...) propose a realist theory of the relation between method and truth. The theory consists of three basic elements: (a) a naturalistic treatment of epistemic normativity, (b) an instrumentalist conception of the nature of methodological rules, and (c) an abductive argument for the truth-conduciveness of the rules of scientific method. (shrink)

The method of hermeneutics first became prominent as a method of biblical exegesis. The method Schleiermacher proposes for this is twofold: it has what he calls a grammatical and a psychological moment. Wilhelm Dilthey wanted to develop hermeneutics as a methodology for the humanities. The critique of method in Heidegger and Gadamer was directed against a particular kind of method prevailing in the Cartesian tradition of scientific knowledge. Hans‐Georg Gadamer continues this late Heideggerian line of (...) thought in his philosophical hermeneutics. Paul Ricoeur follows Heidegger and Gadamer in their ontological reorientation of hermeneutics, but deepens hermeneutics further by what we might call a critical turn. Recent developments seem to open up new possibilities for a hermeneutics in which method is neither abolished nor reduced to an instrument designed to find a historical truth, nor understood as a guideline for proceeding within a realm of interpretations or dialogues without exteriority. (shrink)

The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets’ behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.

Methods have been a controversial element in theories of knowledge for the last 40 years. Recent developments in theories of justification, concerning the identification and individuation of belief-forming processes, can shed new light on methods, solving some longstanding problems in the theory of knowledge. We needn’t and shouldn’t shy away from methods; rather, methods, construed as psychological processes of belief-formation, need to play a central role in any credible theory of knowledge.

The paper aims to contribute to the ongoing conversation on critical phenomenology with reflections on its method. The key argument is that critical phenomenology should be understood as a form of historico-transcendental inquiry and therefore it cannot forgo the phenomenological reduction. Rather, this methodological step should be centered in critical phenomenology, and appropriated in problematized and rethought forms. The methodological assessment of critical phenomenology has implications also for how we read its canon. The paper shows that while Simone de (...) Beauvoir did not adopt the phenomenological reduction in its full Husserlian meaning, her analyses of experience did not remain on the level of personal or experiential description either. The contention is that if we want to read her as a critical phenomenologist, we should focus on her seminal modification of the historico-transcendental method of phenomenology. (shrink)

Use of argumentation methods applied to legal reasoning is a relatively new field of study. The book provides a survey of the leading problems, and outlines how future research using argumentation-based methods show great promise of leading to useful solutions. The problems studied include not only these of argument evaluation and argument invention, but also analysis of specific kinds of evidence commonly used in law, like witness testimony, circumstantial evidence, forensic evidence and character evidence. New tools for analyzing these kinds (...) of evidence are introduced. (shrink)

Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...) to try to put some order in the present logical jungle. Thus Cl91], Ep90] and Wo88] are three recent books in which an attempt is made to develop a general theoretical framework for the study of logics. On the more pragmatic side, several systems have been developed with the goal of providing a computerized logical framework in which many di erent logical systems can be implemented in a uniform way. An example is the Edinburgh LF( HHP91]). (shrink)

Pluralism about scientific method is more-or-less accepted, but the consequences have yet to be drawn out. Scientists adopt different methods in response to different epistemic situations: depending on the system they are interested in, the resources at their disposal, and so forth. If it is right that different methods are appropriate in different situations, then mismatches between methods and situations are possible. This is most likely to occur due to method bias: when we prefer a particular kind of (...) method, despite that method clashing with evidential context or our aims. To explore these ideas, we sketch a kind of method pluralism which turns on two properties of evidence, before using agent-based models to examine the relationship between methods, epistemic situations, and bias. Based on our results, we suggest that although method bias can undermine the efficiency of a scientific community, it can also be productive through preserving a diversity of evidence. We consider circumstances where method bias could be particularly egregious, and those where it is a potential virtue, and argue that consideration of method bias reveals that community standards deserve a central place in the epistemology of science. (shrink)

'Behavioral Methods in Consciousness Research' is the first book of its kind, providing an overview of methods and approaches for studying consciousness. The chapters are written by leading researchers and experts who describe the methods they actually use in their own studies, along with their pitfalls, problems, and difficulties.

The four principles approach to medical ethics plus specification is used in this paper. Specification is defined as a process of reducing the indeterminateness of general norms to give them increased action guiding capacity, while retaining the moral commitments in the original norm. Since questions of method are central to the symposium, the paper begins with four observations about method in moral reasoning and case analysis. Three of the four scenarios are dealt with. It is concluded in the (...) “standard” Jehovah’s Witness case that having autonomously chosen the authority of his religious institution, a Jehovah’s Witness has a reasonable basis on which to refuse a recommended blood transfusion. The author’s view of the child of a Jehovah’s Witness scenario is that it is morally required—not merely permitted—to overrule this parental refusal of treatment. It is argued in the selling kidneys for transplantation scenario that a fair system of regulating and monitoring would be better than the present system which the author believes to be a shameful failure. (shrink)

The paper aims to contribute to the ongoing conversation on critical phenomenology with reflections on its method. The key argument is that critical phenomenology should be understood as a form of historico-transcendental inquiry and therefore it cannot forgo the phenomenological reduction. Rather, this methodological step should be centered in critical phenomenology, and appropriated in problematized and rethought forms. The methodological assessment of critical phenomenology has implications also for how we read its canon. The paper shows that while Simone de (...) Beauvoir did not adopt the phenomenological reduction in its full Husserlian meaning, her analyses of experience did not remain on the level of personal or experiential description either. The contention is that if we want to read her as a critical phenomenologist, we should focus on her seminal modification of the historico-transcendental method of phenomenology. (shrink)

Experimental emotion inductions provide the strongest causal evidence of the effects of emotions on psychological and physiological outcomes. In the present qualitative review, we evaluated five common experimental emotion induction techniques: visual stimuli, music, autobiographical recall, situational procedures, and imagery. For each technique, we discuss the extent to which they induce six basic emotions: anger, disgust, surprise, happiness, fear, and sadness. For each emotion, we discuss the relative influences of the induction methods on subjective emotional experience and physiological responses. Based (...) on the literature reviewed, we make emotion-specific recommendations for induction methods to use in experiments. (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)

While introspective methods went out of favour with the decline of Titchener’s analytic school, many important questions concern the rehabilitation of introspection in contemporary psychology. Hatfield rightly points out that introspective methods should not be confused with analytic ones, and goes on to describe their “ineliminable role” in perceptual psychology. Here I argue that certain methodological conventions within psychophysics reflect a continued uncertainty over appropriate use of subjects’ perceptual observations and the reliability of their introspective judgements. My first claim is (...) that different psychophysical methods do not rely equally on the introspective capabilities of experimental subjects. I contrast “minimally-introspective” tasks with “introspection-heavy” ones. It is only in the latter, I argue, that introspection can be said to have a non-trivial role in the subjects’ performance. My second claim is that my rough-and-ready distinction maps onto a number of important “dichotomies” in vision science. Not coincidentally, the introspection-heavy categorisation captures many of the tasks typically considered less able to yield useful information regarding the processes underlying visual sensation. (shrink)

This is an introductory overview of theories of scientific method.

Reliabilism is an intuitive and attractive view about epistemic justification. However, it has many well-known problems. I offer a novel condition on reliabilist theories of justification. This method coherence condition requires that a method be appropriately tested by appeal to a subject’s other belief-forming methods. Adding this condition to reliabilism provides a solution to epistemic circularity worries, including the bootstrapping problem.

This paper is the introduction to the Special Issue “Philosophical Methods”. The Special Issue will be published by Synthese.