Dung’s argumentation frameworks are formalisms widely used to model interaction among arguments. Although their study has been profusely developed in the field of Artificial Intelligence, it is not common to see its treatment among those less connected to computer science within the logical-philosophical community. In this paper we propose to bring to that audience a proof-theory for argument justification based on tableaux, very similar to those the Logic students are familiar with. The tableaux enable to calculate whether an (...) argument or subset of arguments are accepted or rejected in accordance to Dung’s preferred and grounded extension-based semantics. Soundness and completeness results regarding those semantics are provided. (shrink)

Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and (...) knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi. (shrink)

Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It (...) combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued (...) first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...) the hierarchy of Paracomplete Propositional Calculi Pn (0 ≤ n ≤ ω). In “Logics that are both paraconsistent and paracomplete” (1989), Newton da Costa proposed a system with approximate characteristics to what we are looking for. In the hierarchy of Non-Alethical Propositional Calculi Nn (0 ≤ n ≤ ω), only one negation is introduced (as primitive), called a “non-alethic” (¬n), whose operation preserves the properties of classical, or paraconsistent or paracomplete negation -- depending on the well or ill behavior of the formula connected to it. However, as we shall see, in the hierarchy Nn we can not reiterate negations with different behaviors in a same formula (e.g., ¬p¬cα or ¬q¬c¬p α), or even analyze a formula like ¬cα → ¬pα. In view of these problems, can we really say that the hierarchy Nn allows us to understand the relationships and interactions of the three types of negations? In order to deal with this, given the initial problem, we will present four axiomatic systems (KG) in which, unlike Nn, the three negations are directly introduced -- offering a semantics and a method of proofs by analytic tableaux. Through the KG Systems we will show how the negations interact, obtaining non-demonstrable theorems in LPC, Cn, Pn, and Nn (0 ≤ n ≤ ω). Finally, we will also offer a first-order extension for the KG Systems. (shrink)

This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this (...) constructive method to non-classical fragments equipped with weaker implications (that avoid Curry's objection). This is the case, for example, of Jan Lukasiewicz's n-valued logics and Wilhelm Ackermann's logic of restricted implication. Besides such problems, both Henkin's method and the triviality phenomenon enable us to propose a new positive tableau proof system which uses only positive meta-linguistic resources, and to mo- tivate a new discussion concerning the role of negation in logic proposing the concept of paratriviality. In this way, some relations between positive reasoning and infinity, the possibilities to obtain a ¯first-order positive logic as well as the philosophical connection between truth and meaning are dis- cussed from a conceptual point of view. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This (...) dissertation focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six. (shrink)

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

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.

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)

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.

Some basic methods of philosophizing as an introduction to philosophy.

The author considers the model-theoretic character of proofs and disproofs by means of attempted counterexample constructions, distinguishes this proof format from formal derivations, then contrasts two approaches to semantic tableaux proposed by Beth and Lambert-van Fraassen. It is noted that Beth's original approach has not as yet been provided with a precisely formulated rule of closure for detecting tableau sequences terminating in contradiction. To remedy this deficiency, a technique is proposed to clarify tableau operations.

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)

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)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

There seems to be a difficulty in the practice of metaphysics, in that any methodology used in metaphysical study relies on certain presuppositions, whereby it seems that metaphysical results are relative to those presuppositions. What is needed is a methodology that can yield objective metaphysical results that are not limited by the presuppositions of that methodology. This paper argues for a way to triangulate on stable metaphysical results by using existing methodologies as perspectives on metaphysical topics, and by reducing the (...) differences between those perspectives to non-perspectival truths, if possible. (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)

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)

Engineering failure investigations seek to reconstruct the actual causes of major engineering failures. The investigators need to establish the existence of certain past events and the actual causal relationships that these events bear to the failures in question. In this paper, I examine one method for reconstructing the actual causes of failure events, which I call "feature dependence". The basic idea of feature dependence is that some features of an event are informative about the features of its causes; therefore, (...) the investigators can use the features of a known failure event to reconstruct details of its causes. I make explicit the structure of feature dependence and the evidential basis of its key premises, and show how feature dependence works in the investigation of the American Airlines Flight 191 accident. (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)

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)

Xenophon’s conception of the dialectical method shares many similarities with Antisthenes’ point of view regarding the relation between language and reality. The key element supporting this reading is the parallel between Xenophon’s method of dialegein kata genē and Antisthenes’ method of episkepsis tōn onomatōn. In this paper, I claim that a correct understanding of both methods yields a clear structural proximity between the two Socratics on the issue of dialectics. Although they present some significant differences, which I (...) will also explore, I will argue that both variants express a single Socratic motive with regard to dialectics. That is that dialectics, in its basic structure, consists of organizing reality through discourse in order to make it comprehensible. In particular, this is done through establishing unified instances capable of comprehending a multiplicity. This nuclear position could also be extended to include middle Plato’s concept of dialectics. This concurrence takes up different forms in Plato, Xenophon and Antisthenes. Nevertheless, they share the same structure, which indicates quite plausibly a major characteristic of Socratic philosophies, as opposed to previous attempts by the Presocratics and the Sophists. (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)

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 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.

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 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)

This paper offers a practical argument for metaphysical emergence. The main message is that the growing reliance on so-called irrational scientific methods provides evidence that objects of science are indecomposable and as such, are better described by metaphysical emergence as opposed to the prevalent reductionistic metaphysics. I show that a potential counterargument that science will eventually reduce everything to physics has little weight given where science is heading with its current methodological trend. I substantiate my arguments by detailed examples from (...) biological engineering, but the conclusions are extendable beyond that discipline. (shrink)

Experimental philosophy has focused attention on the role that intuitive responses to philosophical cases play in philosophical argumentation. The method of appealing to such cases has been dubbed the “method of cases,” and, in recent work, Edouard Machery has both defended its prevalence and uniformity in philosophical practice, and criticized its epistemic value. In this paper, I argue that there is no single method of cases, but rather a set of methods of cases. To defend this claim, (...) I distinguish and articulate these different methods and argue that they better explain several paradigmatic appeals to cases. This result not only challenges the homogeneity of the method of cases; it also stocks our methodological toolbox with additional interpretive tools which help us to not only better understand philosophical arguments, but to better understand the significance of experimental work. (shrink)

This essay argues that a black radical Kantianism proposes a Kantian theory of justice in the circumstances of injustice. First, I describe BRK’s method of political critique and explain how it builds on Kant’s republicanism. Second, I argue that Kant’s original account of public right is incomplete because it neglects that a situated citizenry’s adoption of an ideal contributes to its refinement. Lastly, with the aid of W.E.B. Du Bois’s analysis of American Reconstruction and his proposal of an “abolition (...) democracy,” I offer my refined universalizable standard for political critique. Du Bois reconceptualizes the requirements of justice to protect the political liberties and productive powers of black freedmen and the working poor. While originating with the political demands of black freedmen during the Reconstruction era, the universal protection of political liberties and productive powers offers a novel public standard for political judgment that should still anchor deliberation today. (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 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)

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)

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)

A variety of philosophical positions have been proposed and developed to motivate, justify, and guide mixed methods research. This chapter provides a brief overview of the main positions in the debate over the philosophical foundations of mixed methods research. It shows that ‘philosophical foundations’ means differently while different positions provide ‘philosophical foundations’ in different senses. It also highlights the significance of the collaboration between researchers and philosophers in the examination of the philosophical foundations of mixed methods research.

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 the 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)

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)

One of the vibrant topics of debate among African and non-African scholars in the 20th and 21st centuries centered on the existence of African philosophy. This debate has been described as unnecessary. What is necessary is, if African philosophy exists, we should show it, do it and write it rather than talking about it, or engaging in endless talks about it. A popular position on the debate is that what is expected to be shown, done and written is philosophy tailored (...) along the stereotyped and paradigmatic sense peculiar to Western philosophy. Interestingly, a non-African scholar, Barry Hallen argues that using the method of ordinary language philosophy, African philosophy is philosophy per se, and should be recognised as such. The focus of this paper is to analyse what Hallen refers to as ordinary language philosophy and explain how it authenticates African philosophy as unique ‘species’ of philosophy, thus, putting an end to the controversy on the ontology of African philosophy. (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)

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.

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)

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)