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)

This is an introductory overview of theories of scientific method.

This paper provides a critical review of the debate over the philosophical foundations of mixed methods research and examines the notion of philosophical foundations. It distinguishes axiology-oriented from ontology-oriented philosophical foundations. It also identifies three different senses of philosophical foundations of mixed methods research. The weak sense of philosophical foundations (e.g., pragmatism) merely allows the possibility of the integration of both quantitative and qualitative methods/data/designs. The moderate sense of philosophical foundations (e.g., transformativism) provide a good reason to use mixed methods (...) in (at least some) social scientific research. The strong sense of philosophical foundations (e.g., dialectical pluralism) justifies a normative thesis that mixed methods research should be encouraged in (at least some) social scientific research. (shrink)

Why scientists reach an agreement on new experimental methods when there are conflicts of interest about the evidence they yield? I argue that debiasing methods play a crucial role in this consensus, providing a warrant about the impartiality of the outcome regarding the preferences of different parties involved in the experiment. From a contractarian perspective, I contend that an epistemic pre-requisite for scientists to agree on an experimental method is that this latter is neutral regarding their competing interests. I present (...) two medical experiments (on smallpox inoculation and Mesmerism) in which debiasing procedures such as blinding and data tabulation provided warrants of impartiality that made people agree on the experimental design even if they disagreed on the outcome. (shrink)

According to the sensitivity account of knowledge, S knows that p only if S’s belief in p is sensitive in the sense that S would not believe that p if p were false. The sensitivity condition is usually relativized to belief-formation methods to avoid putative counterexamples. A remaining issue for the account is where methods should be mentioned in sensitivity subjunctives. In this paper, I argue that if methods are mentioned in the antecedent, then the account is too strong to (...) accommodate inductive knowledge; if methods are mentioned in the consequent, then the account is too weak to eliminate some luckily true beliefs from the realm of knowledge. Therefore, the strategy to relativize the sensitivity condition is undermined by inductive knowledge and some luckily true beliefs. (shrink)

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)

Philosophy is a subject which does not concerned only to an expert or specialist. It appears that there is probably no human being who does not philosophise. Good philosophy expands one’s imagination as some philosophy is close to us, whoever we are. Then of course some is further away, and some is further still, and some is very alien indeed. We raise questions about the assumptions, presuppositions, or definitions upon which a field of inquiry is based, and these questions can (...) be concerned with the meaning, significance, or integration of the results discovered or proposed by a field of inquiry. We find Karmic, Bhaktic and Jnanic interpretations of an ancient text in Indian philosophy because of different approaches adopted to inquire the text. This paper is an attempt to draw an outline of Upanishadic methods of inquiry in Indian philosophical tradition. Several methods like Enigmatic, Aphoristic, Etymological, Mythical, Analogical, Dialectical, Synthetic, Monologic, Temporising and Regressive methods etc. we can find in Upanishads. (shrink)

This paper examines whether, and how, Foucauldian genealogy travels to contexts and problematizations beyond the method's European site of articulation. Our particular focus is on the work of Colombian philosopher Santiago Castro-Gómez, whose work includes both a systematic defense of the usefulness of Foucauldian inquiry for decolonial study and genealogical inquiry in a Foucauldian spirit but in a context beyond Foucault's own horizon of study. We show that taking up Foucault's work in the context of Latin America leads Castro-Gómez to (...) significantly change Foucauldian concepts, categories, and methods. We further survey the potential synergies of decolonial thought and Foucauldian critique, while also highlighting how their joint mobilization requires a revision and problematization of key commitments of both approaches. (shrink)

Recent breakthroughs in artificial intelligence have primarily resulted from training deep neural networks (DNNs) with vast numbers of adjustable parameters on enormous datasets. Due to their complex internal structure, DNNs are frequently characterized as inscrutable ``black boxes,'' making it challenging to interpret the mechanisms underlying their impressive performance. This opacity creates difficulties for explanation, safety assurance, trustworthiness, and comparisons to human cognition, leading to divergent perspectives on these systems. This chapter examines recent developments in interpretability methods for DNNs, with a (...) focus on interventionist approaches inspired by causal explanation in philosophy of science. We argue that these methods offer a promising avenue for understanding how DNNs process information compared to merely behavioral benchmarking and correlational probing. We review key interventionist methods and illustrate their application through practical case studies. These methods allow researchers to identify and manipulate specific computational components within DNNs, providing insights into their causal structure and internal representations. We situate these approaches within the broader framework of causal abstraction, which aims to align low-level neural computations with high-level interpretable models. While acknowledging current limitations, we contend that interventionist methods offer a path towards more rigorous and theoretically grounded interpretability research, potentially informing both AI development and computational cognitive neuroscience. (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 chapter presents a new argument for thinking of traditional ethical theories as methods that can be used in first-order ethics - as a kind of deliberation procedures rather than as criteria of right and wrong. It begins from outlining how ethical theories, such as consequentialism and contractualism, are flexible frameworks in which different versions of these theories can be formulated to correspond to different first-order ethical views. The chapter then argues that, as a result, the traditional ethical theories cannot (...) be evaluated in terms of their truth or correctness. Instead, I will suggest that these theories should be understood as providing different kind of ways of thinking about difficult moral problems. I then recommend a certain form of pragmatic pluralism - it may well be that different moral problems are better approached through different ethical theories. (shrink)

In this paper, I argue that the method of cases (namely, the method of using intuitive judgments elicited by intuition pumps as evidence for and/or against philosophical theories) is not a reliable method of generating evidence for and/or against philosophical theories. In other words, the method of cases is unlikely to generate accurate judgments more often than not. This is so because, if perception and intuition are analogous in epistemically relevant respects, then using intuition pumps to elicit intuitive judgments is (...) like using illusions to elicit perceptual judgments. In both cases, judgments are made under bad epistemic circumstances. (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)

In order to have an effective and reliable understanding of the basic moral concepts, moral propositions and moral reasoning in Daoist ethical thoughts, it is necessary to use the methods of doing philosophy and doing ethics to engage in research work, and thus draw an intellectual conclusion about Daoist ethics. The methods of Daoist ethics mainly include analysis, explanation and comparison. The method of analysis focuses on logical analysis and language analysis of moral language in the classic texts of Daoist (...) ethics. The method of interpretation focuses on effective translation and understanding of moral language with unclear meaning in Daoist ethics. The method of comparison focuses on critical dialogue between ancient Daoist ethical thoughts and contemporary ethical theories and comparison between Confucian, Buddhist and Daoist ethics. Explaining the method of doing Daoist ethics clearly will promote the dialogue and understanding between Daoist ethics and contemporary ethics. (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)

This selective and opinionated overview of English-language scholarship on the philosophical method(s) of Plato's Socrates discusses whether this Socrates has any expertise or method, how he examines others and why, and how he exhorts others to care about wisdom and the state of their soul.

Darwin’s treatment of morality in The Descent of Man has generated a wide variety of responses among moral philosophers. Among these is the dismissal of evolution as irrelevant to ethics by Darwin’s contemporary Henry Sidgwick; the last, and arguably the greatest, of the Nineteenth Century British Utilitarians. This paper offers a re-examination of Sidgwick’s response to evolutionary considerations as irrelevant to ethics and the absence of any engagement with Darwin’s work in Sidgwick’s main ethical treatise, The Methods of Ethics . (...) This assessment of Sidgwick’s response to Darwin’s work is shown to have significance for a number of ongoing controversies in contemporary metaethics. (shrink)

The method of contrast is used within philosophy of perception in order to demonstrate that a specific property could be part of our perception. The method is based on two passages. I argue that the method succeeds in its task only if the intuition of the difference, which constitutes the core of the first passage, has two specific traits. The second passage of the method consists in the evaluation of the available explanations of this difference. Among the three outlined options, (...) I will demonstrate that only in the third option – as we shall see, the case of the scenario that remains the same but is perceived in two different ways by the same perceiver – the intuition purports a difference that posses the necessary characteristics, namely being immediately evident and extremely complex and multifaceted, which determine its tensive nature. The application within auditory perception of this third option will generate two cases, a diachronic one and a synchronic one, which clearly show that we can auditorily perceive causality as a link between two sonorous episodes. The causal explanation is the only possible explanation among the many evaluated within the second passage of the method of contrast. (shrink)

The aim of the article is to develop the existing methodological approaches to assessing the military and economic capabilities of the country in conditions of war and peace. To achieve the purpose of the study, its decomposition was carried out and the following were investigated: existing approaches to assessing the military and economic potential of the country, the country's power and national power; the concept of critical load of the national economy is revealed; the generally accepted norms on financing of (...) defense needs are resulted; the experience of financing the needs of defense by the leading countries of the world - in the conditions of the Second World War is given; a methodical approach to assessing the military and economic capabilities of the country is proposed. The article proposes a methodical approach to assessing the military and economic capabilities of the country. According to the results of the research, the existing theory of military economy has been improved in the context of understanding the allowable burden on the country's economy in conditions of war and the development of methodological approaches to assessing the country's military and economic capabilities. The proposed methodological approach is the development of existing military-economic thought and capability-based military-economic planning. The proposed methodological approach allows to assess the ability of the national economy to meet military and economic needs in wartime by industry and type of military support, taking into account the critical load of the national economy, which will help simplify and improve the process of military policy decisions. The practical value of the study is that the proposed method of assessing the military and economic capabilities of the country allows to identify critical sectors of the economy, assess their ability to provide resources for military needs in wartime, based on which to form and make appropriate management decisions. The results of the study can be used in further studies of the development of military and economic potential of the country, balancing military and civilian economic needs in war, as well as military-economic planning based on capabilities. A limitation of the study is the use of publicly available sources. Future research is seen in the further development of methodological approaches to assessing and developing the military and economic potential of the country. (shrink)

This paper argues that whereas philosophical discussions of first-person methods often turn on the veridicality of first-person reports, more attention should be paid to the experimental circumstances under which the reports are generated, and to the purposes of designing such experiments. After pointing to the ‘constructedness’ of first-person reports in the science of perception, I raise questions about the criteria by which to judge whether the reports illuminate something about the nature of perception. I illustrate this point with a historical (...) debate between Gestalt psychologist and atomists, both of whom used first-person methods to investigate perception. (shrink)

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.

It is a common view that arguments from analogy can only be evaluated on a case-by-case basis. However, while this reflects an important insight, I propose instead a relatively simple method for their evaluation based on just (i) their general form and (ii) four core questions. One clear advantage of this proposal is that it does not depend on any substantial (and controversial) view of similarity, unlike influential current alternative methods, such as Walton’s. Following some initial clarification of the notion (...) of analogy and similarity, I demonstrate the strength of this method by analysing and evaluating three prominent arguments from analogy. (shrink)

This article argues that, suitably modified, the method of reflective equilibrium is a plausible way of selecting moral principles. The appropriate conception of the method is wide and radical, admitting consideration of a full range of moral principles and arguments, and requiring the enquiring individual to consider others' views and undergo experiences that may offset any formative biases. The individual is not bound by his initial considered judgments, and may revise his view in any way whatsoever. It is appropriate to (...) describe the method as a balance between coherentism and fallibilist foundationalism. With these points in mind, various criticisms, including the claims that considered judgments are not initially credible and are shaped by prejudice, and that the method itself fails to determine principle selection, are challenged. (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)

The main objective of this paper is to address the problem of the philosophical method, which consists of the lack of consensus among philosophers regarding the proper procedure to carry out this human activity. In this sense, it examines a few methodological proposals put forward by some representatives of contemporary philosophy, emphasizing the impact that the development of modern science has had on such views. In addition, the plausibility of such proposals is assessed.

Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction method (...) and natural deduction method were developed and practiced. In this paper, both of these methods are briefly discussed with an emphasis on their historical, groundbreaking significance for logic. The axiomatic method by means of rejection (proposed by Jan Łukasiewicz – a co-creator of the WSL), which is the method of the so-called rejection proof (rejection/refutation method) in logical systems and the proving method of generalized natural deduction, which is a hybrid deduction–refutation method of proving theorems, are also outlined in the paper. The author discusses their historical significance. This paper also contains a brief mention of the most significant results which the application of the discussed methods introduced into contemporary scientific research, not only logical one. (shrink)

In this article I offer an opinionated overview of the central elements of Kant’s philosophical methodology during the critical period. I begin with a brief characterization of how Kant conceives of the aims of human inquiry – focusing on the idea that inquiry ideally aims at not just cognition (Erkenntnis), but also the more demanding cognitive achievements that Kant labels insight (Einsehen) and comprehension (Begreifen). Then I explore the implications of this picture for philosophy — emphasizing Kant’s distinction between critical (...) and doctrinal phases of philosophical inquiry, with the first of these playing both a negative and a positive role with respect to the second. Then, I will argue that this positive role is possible, according to Kant, only insofar as philosophy follows what I call a “capacities-first” methodology – that is, one that treats basic cognitive capacities (such as reason) and their self-conscious activities as fundamental (in both a cognitive sense and in an explanatory sense) for the sort of philosophy human beings are capable of. It is this methodology, I will argue, that allows Kant to introduce the first principles that philosophy in its doctrinal phase requires in a manner that is neither arbitrary nor (at least obviously) incompatible with Kant’s own critical restrictions on cognition. I conclude by discussing some of the implications of this methodological picture – including the methodological significance of self-consciousness and regressive or “transcendental” arguments, Kant’s distinction between analytic and synthetic methods in philosophy, and Kant’s conception of reason as autonomous. (shrink)

Descartes' methodical doubt is being criticized by naïve realists and others who don't find doubt as a good starting point for metaphysical thought, however, the philosophical achievements of his method have been absorbed in all later philosophies. The objective of this paper is to demonstrate how an inevitable question concerning the foundation of Descartes' mathesis universalis, which led him to investigate this foundation by applying this very method in Metaphysics, has finally enabled him to discover his most important philosophical principle, (...) i.e., the necessary relation between being and reason in the identity of the "I". To demonstrate this, after summarizing the fundamental ideas of mathesis uneversalis, and showing the inner necessity of introducing the methodical doubt to fortify these ideas, the decisive role of metaphysical doubt as the third step of the methodical doubt, and malicious demon as its second phase would be highighted. It would also become clear that the metaphysical doubt has a great importance as a turning point from different aspects: as a knot that ties mathesis universalis with its underlying Metaphysics; as a bridge from within the psychological "I" to the metaphysical "I". (shrink)

Notwithstanding diverse opinions and debates about mixing methods, mixed methods research (MMR) is increasingly being used in sport and exercise psychology. In this paper, we describe MMR trends within leading sport and exercise psychology journals and explore critical realism as a possible underpinning framework for conducting MMR. Our meta-study of recent empirical mixed methods studies published in 2017–2019 indicates that eight (36%) of the 22 MMR studies explicitly stated a paradigmatic position (five drew on pragmatism, two switched paradigms between qualitative (...) and quantitative elements of the study, and one was situated in relativist-interpretivism). The remaining 14 (64%) studies did not report their underpinning research philosophical assumptions. Evaluating the merits and limitations of these positions against critical realist assumptions suggests that several paradigmatic disagreements are potentially reconcilable. These include (a) maintaining that ontological and epistemological concerns are important for methodological integrity of a mixed methods study; (b) switching between paradigms in the same study is problematic; and (c) refuting the qualitative-quantitative incommensurability thesis, therefore allowing mixed methods research without compromising philosophical coherence. From a critical realist position, we suggest that both quantitative and qualitative designs are justifiable in a mixed methods study because (1) they help corroborate, refine, or refute plausible explanations of phenomena (epistemological), but (2) with different methodologies utilised to perform different tasks in the same research design related to different psycho-social system features (ontological). We call for a collaborative engagement by researchers across paradigmatic positions to work towards the advancement of methodological pluralism in our research community. (shrink)

The research aims to identify the reality of modern methods applied in the process of performance assessments of employees in the municipalities of Gaza-strip, Complete Census method of community study was used, (571) questionnaires were distributed to all members of the community study, (524) questionnaires were recovery with rate of (91.76%). The most important findings of the study: There were statistically significant relationship differences between the applications of modern methods in the performance assessments of employees in the municipalities of Gaza-strip. (...) There was statistically significant relationship between the evaluation criteria that fit the required performance and the application of standards evaluations on performance of employees in the municipalities of Gaza-strip. There was statistically significant relationship between the use of methods, models for the evaluation of appropriate functions and the application of the performance assessments of employees in the municipalities of Gaza-strip. There was statistically significant relationship between the feedback and the application of performance assessments of employees in the municipalities of Gaza-strip. There was statistically significant relationship between the efficient, professional assessors and the application of the performance assessments of employees in the municipalities of Gaza-strip. There was statistically significant relationship between the extent of awareness of subordinates, participation in the evaluation of their performance and the application of the performance assessments of employees in the municipalities of Gaza-strip. The research also concluded a series of recommendations, including: that the design of evaluation models must be done with the participation of the employees and inform them of it, and that a date must be set to provide feedback and discuss the results with them, that they should be allowed grievance in front of an ad hoc committee in accordance with the known system. Direct manager must inform employees of their performance assessment date, discuss the results of the evaluation with them, and others should be involved with the direct manager of employees in their performance evaluation. The application of modern methods of performance evaluation through the good and purposeful planning should be used, analyzing and employing the results in administrative decisions regarding the employees, and the application of modern methods must be used in an effective and efficient performance evaluation. (shrink)

The aim of this paper is to argue that intuitive methods of moral decision making are objective tools on the grounds that they are reasons based. First, I will conduct a preliminary analysis in which I highlight the acceptance of methodological pluralism in the practice of medical ethics. Here, the point is to show the possibility of using intuitive methods given the pluralism framework. Second, I will argue that the best starting point of elaborating such methods is a bottom-up perspective. (...) Third, I will address the worry of subjectivism. Under the influence of certain rationalist positions and recent developments in cognitive science and moral psychology, one might think that intuitive methods of moral decision making are essentially subjective and emotion based. If moral intuitions are the result of emotional reactions and intuitive reasoning is emotionally driven, then there are reasons to believe intuitive methods are subjective and relative to particular psychological constitution. Against this picture, I will argue that intuitive methods of moral decision making are essentially reasons-based. A Wittgensteinian approach will show that intuitive methods of moral decision making are conceptually linked with criteria of morality. (shrink)

The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially pedagogically in teaching (...) basic logic and critical reasoning skills at all levels of scientific education. I propose in this essay to build on Beardsley diagramming techniques to refine and supplement their structural tools for visualizing logical relationships in a number of categories not originally accommodated by Beardsley diagramming, including circular reasoning, reductio ad absurdum arguments, and efforts to dispute and contradict arguments, with applications and analysis. (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)

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

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.

How does experimental philosophy address philosophical questions and problems? That is: What projects does experimental philosophy pursue? What is their philosophical relevance? And what empirical methods do they employ? Answers to these questions will reveal how experimental philosophy can contribute to the longstanding ambition of placing philosophy on the ‘secure path of a science’, as Kant put it. We argue that experimental philosophy has introduced a new methodological perspective – a ‘meta-philosophical naturalism’ that addresses philosophical questions about a phenomenon by (...) empirically investigating how people think about this phenomenon. This chapter asks how this novel perspective can be successfully implemented: How can the empirical investigation of how people think about something address genuinely philosophical problems? And what methods – and, specifically, what methods beyond the questionnaire – can this investigation employ? We first review core projects of experimental philosophy and raise the question of their philosophical relevance. For ambitious answers, we turn to experimental philosophy’s most direct historical precursor, mid-20th century ordinary language philosophy, and discuss empirical implementations of two of its research programmes that use experimental methods from psycholinguistics and corpus methods from the digital humanities. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. Several possible solutions (...) are explored and rejected. (shrink)

Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.

Here, we try to show that the method used in -/- Theory of Fuzzy Time Computation(TC * vs TC, TQC). 2023. ￿hal-04330281￿ -/- is a general method that sheds light on various types of problems. The author choose the navier stocks problem, to check the possibility of solving this problem by this method. This text is a guideline of possible proof of this problem.

In Aristotle's cosmology, the nature of the elements is defined by their place in the Totality. Their cosmic motions keep the whole in motion, and this is their nature. Thus, the cosmos is an organized whole, a single substance directed to the good; this body constitutes together with its Prime Mover a composite substance that can be regarded as a self-mover.

This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives (...) of user-friendliness, reliability (in the sense that misuse is less likely), educational efficiency and realism. This means that they offer very considerable potential for simplifying the mathematical syllabus underlying many areas of applied mathematics such as management science and statistics: crunchier methods can provide the same, or greater, technical power, flexibility and insight, while requiring only a fraction of the mathematical conceptual background needed by their cleverer brethren. (shrink)

Mixing methods is a well-known innovative meth- odologic proposal for research in the second half of the 20th century social sciences. Reading literature about it, I observed the aspect that justifies this paper: Authors of theoretical contributions on mixing methods recognized that this was known to be a practice already in use many centuries ago. Some of them even have re-examined the whole history of the scientific method to search precedents. They are however individual and theoretical precedents. I add in (...) this paper the practical projection of these and other methodological theories on people’s training from Greek classical times. My hypothesis is that liberal arts was the basic syllabus in Western -and westernized- educaion for more than a millennium in such a way that results of their training precisely involved to mixing methods. In return, to understand the liberal arts in the light of mixing methods shows new aspects of their historical interest. I study the theoretical basis of this syllabus from Cicero to Alcuin. More important for future research, I conclude that Alcuin’s thesis about the correspondence between the gifts of the Holy Spiritu and the seven liberal arts can be extended to the Aristotelian dianoethics habits and to Dilthey’s 20th-century sciences of mind. (shrink)

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)

Research in experimental philosophy has increasingly been turning to corpus methods to produce evidence for empirical claims, as they open up new possibilities for testing linguistic claims or studying concepts across time and cultures. The present article reviews the quasi-experimental studies that have been done using textual data from corpora in philosophy, with an eye for the modeling and experimental design that enable statistical inference. I find that most studies forego comparisons that could control for confounds, and that only a (...) little less than half employ statistical testing methods to control for chance results. Furthermore, at least some researchers make modeling decisions that either do not take into account the nature of corpora and of the word-concept relationship, or undermine the experiment's capacity to answer research questions. I suggest that corpus methods could both provide more powerful evidence and gain more mainstream acceptance by improving their modeling practices. (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 elite sport, the advantages demonstrated by expert performers over novices are sometimes due in part to their superior physical fitness or to their greater technical precision in executing specialist motor skills. However at the very highest levels, all competitors typically share extraordinary physical capacities and have supremely well-honed techniques. Among the extra factors which can differentiate between the best performers, psychological skills are paramount. These range from the capacities to cope under pressure and to bounce back from setbacks, to (...) the knowledge of themselves, opponents, and the domain, which experts access and apply in performance. In the companion chapter on breadth and depth of knowledge in expert sport (see Chapter 11), we discussed the forms or kinds of knowledge deployed by elite athletes, and described some lines of research which seek to tap and study such expert knowledge (McPherson & MacMahon, 2008; McRobert, Ward, Eccles & Williams, 2011). In this chapter we focus more directly on questions about methods for measuring or more accurately assessing expert knowledge, in particular addressing a wider range of methods to help us understand what experts know. Suggesting that sport researchers can productively adopt and adapt existing qualitative methodologies for integration with more standard quantitative methods, we introduce and survey a number of areas of qualitative research in psychology. (shrink)

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to work (...) with the exact values of the derivatives, instead of their approximations. (shrink)

In this paper I discuss a set of problems concerning the method of cases as it is used in applied ethics and in the metaphysical debate about personal identity. These problems stem from research in social psychology concerning our access to the data with which the method operates. I argue that the issues facing ethics are more worrying than those facing metaphysics.