(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)

Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that the proportion of papers using logical methods remained more or less constant over that (...) time period but the proportion of papers using probabilistic methods was approximately three times higher in the late 2010s than it was in the late 2000s. Further analyses explored this change by looking more closely at specific methods, specific levels of technical engagement, and specific subdisciplines within philosophy. These analyses indicate that the increasing proportion of papers using probabilistic methods was pervasive, not confined to particular probabilistic methods, levels of sophistication, or subdisciplines. (shrink)

This commentary is a reflection on a collaboration with the artist Rossella Biscotti and comments on how artistic research and logico-mathematical methods can be used to contribute to the development of critical perspectives on contemporary data practices.

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

Two interconnected surveys are presented, one of artifacts and one of designometry. Artifacts are objects, which have an originator and do not exist in nature. Designometry is a new field of study, which aims to identify the originators of artifacts. The space of artifacts is described and also domains, which pursue designometry, yet currently doing so without collaboration or common methodologies. On this basis, synergies as well as a generic axiom and heuristics for the quest of the creators of artifacts (...) are introduced. While designometry has various areas of applications, the research of methods to detect originators of artificial minds, which constitute a subgroup of artifacts, can be seen as particularly relevant and, in the case of malevolent artificial minds, as contribution to AI safety. (shrink)

Published with great thanksgiving for Yaohushua, the living One Yahowah, "Jesus Christ." -/- In previous work, Formalizing Mechanical Analysis Using Sweeping Net Methods I, sweeping net methods have been extended to complex analysis, relying on the argument of complex functions defined on the unit circle. In this paper, we reformulate these methods purely within a real-valued and geometric framework, avoiding the use of complex analysis. By redefining the sweeping net constructs and the associated theorems using real functions (...) and geometric interpretations on the unit circle, we demonstrate how singularities and their approximations can be effectively analyzed without the need for imaginary numbers. This approach provides intuitive geometric insights and broadens the applicability of sweeping net methods in mathematical analysis. (shrink)

Changes in an upper level ontology have obvious conse-quences for the domain ontologies that use it at lower levels. It is therefore crucial to document the changes made between successive versions of ontologies of this kind. We describe and apply a method for tracking, explaining and measuring changes between successive versions of upper level ontologies such as the Basic Formal Ontology (BFO). The proposed change-tracking method extends earlier work on Realism-Based Ontology Versioning (RBOV) and Evolutionary Terminology Auditing (ETA). We (...) describe here the application of this evaluation method to changes between BFO 1.0, BFO 1.1, and BFO 2.0. We discuss the issues raised by this application and describe the extensions which we added to the original evaluation schema in order to account for changes in an ontology of this type. Our results show that BFO has undergone eight types of changes that can be systematically explained by the extended evaluation schema. Finally, we discuss problematic cases, possible pitfalls and certain limits of our study that we propose to address in future work. (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria (...) for such formalizations, and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

Over the last decade, multi-agent systems have come to form one of the key tech- nologies for software development. The Formal Approaches to Multi-Agent Systems (FAMAS) workshop series brings together researchers from the fields of logic, theoreti- cal computer science and multi-agent systems in order to discuss formal techniques for specifying and verifying multi-agent systems. FAMAS addresses the issues of logics for multi-agent systems, formal methods for verification, for example model check- ing, and formal approaches (...) to cooperation, multi-agent planning, communication, coordination, negotiation, games, and reasoning under uncertainty in a distributed environment. In 2007, the third FAMAS workshop, FAMAS'007, was one of the agent workshops gathered together under the umbrella of Multi-Agent Logics, Languages, and Organ- isations - Federated Workshops, MALLOW'007, taking place from 3 to 7 September 2007 in Durham. This current special issue of the Logic Journal of the IGPL gathers together the revised and updated versions of the five best FAMAS'007 contributions. (shrink)

As conceived by analytic philosophers ontology consists in the application of the methods of mathematical logic to the analysis of ontological discourse. As conceived by realist philosophers such as Meinong and the early Husserl, Reinach and Ingarden, it consists in the investigation of the forms of entities of various types. The suggestion is that formal methods be employed by phenomenological ontologists, and that phenomenological insights may contribute to the construction of adequate formal-ontological languages. The paper sketches (...) an account of what might be involved in this new discipline, an account which is illustrated in application to the formal-ontological problems raised by negative states of affairs. (shrink)

This essay presents Husserl’s Formal and Transcendental Logic (1929) in three main sections following the layout of the work itself. The first section focuses on Husserl’s introduction where he explains the method and the aim of the essay. The method used in FTL is radical Besinnung and with it an intentional explication of proper sense of formal logic is sought for. The second section is on formal logic. The third section focuses on Husserl’s “transcendental logic,” which is (...) needed to make Husserl’s conception complete, i.e., to understand what makes Besinnung radical, how the proper sense of formal logic has been reached and how all this relates to transcendental constitution of an object in the world. Husserl’s work is connected to his context (in exact sciences) and the relevance of his views for the contemporary approaches is discussed. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results (...) from formal epistemology have been used fruitfully to advance epistemically-relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (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)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. (...) Then, we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results (...) from formal epistemology have been used fruitfully to advance epistemically‐relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (shrink)

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal (...) semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

Since the beginning of the 20th Century to the present day, it has rarely been doubted that whenever formal aesthetic methods meet their iconological counterparts, the two approaches appear to be mutually exclusive. In reality, though, an ahistorical concept is challenging a historical analysis of art. It is especially Susanne K. Langer´s long-overlooked system of analogies between perceptions of the world and of artistic creations that are dependent on feelings which today allows a rapprochement of these positions. Krois’s (...) insistence on a similar point supports this analysis. - I - Unbestritten bis heute gilt, formwissenschaftliche und ikonologische Methoden scheinen sich grundsätzlich auszuschließen, da die ersteren auf ahistorischen und die letzteren auf historischen Grundlagen aufbauen. Dem entgegen soll mit diesem Beitrag gezeigt werden, wie insbesondere die Forschungen Susanne K. Langers und ergänzend diejenigen von John M. Krois eine Annäherung beider Positionen ermöglichen. (shrink)

There are two fundamentally distinct kinds of biological theorizing. "Formal biology" focuses on the relations, captured in formal laws, among mathematically abstracted properties of abstract objects. Population genetics and theoretical mathematical ecology, which are cases of formal biology, thus share methods and goals with theoretical physics. "Compositional biology," on the other hand, is concerned with articulating the concrete structure, mechanisms, and function, through developmental and evolutionary time, of material parts and wholes. Molecular genetics, biochemistry, developmental biology, (...) and physiology, which are examples of compositional biology, are in serious need of philosophical attention. For example, the very concept of a "part" is understudied in both philosophy of biology and philosophy of science. ;My dissertation is an attempt to clarify the distinction between formal biology and compositional biology and, in so doing, provide a clear philosophical analysis, with case studies, of compositional biology. Given the social, economic, and medical importance of compositional biology, understanding it is urgent. For my investigation, I draw on the philosophical fields of metaphysics and epistemology, as well as philosophy of biology and philosophy of science. I suggest new ways of thinking about some classic philosophy of science issues, such as modeling, laws of nature, abstraction, explanation, and confirmation. I hint at the relevance of my study of two kinds of biological theorizing to debates concerning the disunity of science. (shrink)

Usual narratives among prehistoric archaeologists consider typological approaches as part of a past and outdated episode in the history of research, subsequently replaced by technological, functional, chemical, and cognitive approaches. From a historical and conceptual perspective, this paper addresses several limits of these narratives, which (1) assume a linear, exclusive, and additive conception of scientific change, neglecting the persistence of typological problems; (2) reduce collective developments to personal work (e.g. the “Bordes’” and “Laplace’s” methods in France); and (3) presuppose (...) the coherence and identity of these “methods” over time. It explores the case of the “Structural and analytical typology” method, developed in France, Spain, and Italy from the 1950s to the 2000s by Georges Laplace and his collaborators for lithic implements. This paper (1) provides a detailed historical account of the evolving content of this collective endeavour over five decades; (2) it addresses the epistemological question of what makes the identity and unity of a scientific method, demonstrating that the core component of the “analytical typology” lies in its particular way to represent real-world phenomena through its notation system; and (3) it reveals how this little known but significant episode of advances in the methods and theory of archaeology, contemporary but independent of the “New Archaeology” trend in English-speaking archaeology, was instrumental in the continuation of evolutionary perspectives in France and in the development of quantitative and formal methods in archaeology in southwestern Europe, foreseeing crucial knowledge representation issues raised today by digital methods in archaeology and data curation. (shrink)

The paper presents a new method for generating typologies of formal-ontological relations. The guiding idea is that formal relations are those sorts of relations which hold between entities which are constituents of distinct ontologies. We provide examples of ontologies (in the spirit of Zemach’s classic “Four Ontologies” of 1970), and show how these can be used to give a rich typology of formal relations in a way which also throws light on the opposition between threeand four-dimensionalism.

This paper explicates Husserl’s usage of what he calls “radical Besinnung” in Formale und transzendentale Logik. Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical (...) Besinnung and transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological framework within which transcendental phenomenological descriptions are used to criticize historically given goal-directed practices. (shrink)

The construction of complex ontologies can be facilitated by adapting existing vocabularies. There is little clarity and in fact little consensus as to what modifications of vocabularies are necessary in order to re-engineer them into ontologies. In this paper we present a method that provides clear steps to follow when re-engineering a thesaurus. The method makes use of top-level ontologies and was derived from the structural differences between thesauri and ontologies as well as from best practices in modeling, some of (...) which have been advocated in the biomedical domain. We illustrate each step of our method with examples from a re-engineering case study about agricultural fertilizers based on the AGROVOC thesaurus. Our method makes clear that re-engineering thesauri requires far more than just a syntactic conversion into a formal language or other easily automatable steps. The method can not only be used for re-engineering thesauri, but does also summarize steps for building ontologies in general, and can hence be adapted for the re-engineering of other types of vocabularies or terminologies. (shrink)

Customer behavior, market dynamics, and technological advances have made it challenging for marketing theorists to provide comprehensive explanations and actionable insights. Although there are numerous substantive marketing frameworks, no formal marketing theory exists. This study aims to develop the first formal grounded theory in marketing by incorporating artificial intelligence and Forde's conceptual framework as a guiding lens. Charmaz's constructivist grounded theory tradition and Forde's conceptual framework and data analysis strategy were employed for this purpose. The data analysis strategy (...) used with grounded theory’s constant compare-and-contrast method comprises holistic and systems thinking, dramaturgical and situational analysis, perspective-taking, and deconstruction. To evaluate Glaser’s assertion that all is data, artificial intelligence was incorporated into the research as the data source for retrieving the theoretical samples to address the primary research question: How can Forde's conceptual framework and artificial intelligence be leveraged to develop a formal marketing theory grounded in evidence? Of significance was the emergence of democratic marketing behaviors and the normalization of anti-democratic marketing approaches leveraged to manipulate buyers or gain access to segments of customers. Buyers and sellers can simultaneously benefit from and be prejudiced by marketing exchange dynamics. This finding lends credibility to the newly emerged framework of strategic actions where empowerment and disempowerment are leveraged to achieve specific goals. Considering this finding, it is suggested that businesses view marketing as a symbiotic relationship between two power centers, buyers and sellers, who respectively strive to maintain human dignity and sustainability. Researchers are encouraged to apply the framework across substantive areas, international markets, public relations, political campaigns, and others. (shrink)

A central aim for philosophers of science has been to understand scientific theory change, or more specifically the rationality of theory change. Philosophers and historians of science have suggested that not only theories but also scientific methods and standards of rational inquiry have changed through the history of science. The topic here is methodological change, and what kind of theory of rational methodological change is appropriate. The modest ambition of this paper is to discuss in what ways results in (...) formal theories of belief revision can throw light on the question of what an appropriate theory of methodological change would look like. (shrink)

The paper discusses Husserl’s method of historical reflection, radical Besinnung, as defined and used in Formale und transzendentale Logik (1929). Whereas Formal and Transcendental Logic introduces and displays Husserl’s usage of Besinnung in the context of the exact sciences, the paper seeks to develop it as a more general critical method with which to approach any rational goal-directed activity. Husserl defines Besinnung as a method that enables understanding agents and their actions by explicating agents’ typically implicit goals. It leads (...) to the inclusion of historical-teleological activities as part of Husserl’s natural understanding of the world. The transcendental reflection radicalizes Besinnung by clarifying the kinds of evidence sought for in activities and then suggesting revisions to the concepts and principles used. The result is inner critique, which means that the activities are criticized against the norms that arise from reflection on these activities themselves, and not from a comparison with external standards or measures. (shrink)

In a historiographical and methodological comparison of Formal Aesthetics and Iconology with the method of Affordance, the latter is to be introduced as a new method in Visual Cultural Studies. In extension ofepistemologically relevant aspects relatedtostyle and history of the artefacts, communicative and furthermoreaction and decisionrelevant aspects of artefacts become important. In this respect, it is the share of artefacts in life that the new method aims to uncover. The basis for this concern is the theory and methodological tools (...) of Visual Semiotics, which I have already presented. A direct comparison of the three methods based on the same example should clarify the points of contact and the respective performance of the methods. For this purpose, theChrist among the Doctorsof Albrecht Dürer from 1506 will be used, which was already examined in 1905 and indirectly in 1915 by the prominent representative of Formal Aesthetics Heinrich Wölfflin,and in 1914 and finally in1943by the founder of Iconology Erwin Panofsky. With the new method thecommunicative-actionand decision relevant aspects and thus their share in life should be shown. (shrink)

This paper introduces a novel interpretation of Wittgenstein’s Tractatus, a work widely held to be one of the most intricate in the philosophical canon. We understand the Tractatus not as the development of a theory but as the advancement of a new logical symbolism (a new instrument) that enables one to “recognize the formal properties [the logic] of propositions by mere inspection of propositions themselves” (6.122). Moreover, the Tractarian conceptual notation stands to instruct us in a better way to (...) follow the logic of language, and by that token, enhances our ability to think. Upon acquiring the thinking skills that one can develop by working with this symbolism, one can “throw away [this] ladder” (6.54), as it were, and move on. (shrink)

As engineering applications require management of ever larger volumes of data, ontologies offer the potential to capture, manage, and augment data with the capability for automated reasoning and semantic querying. Unfortunately, considerable barriers hinder wider deployment of ontologies in engineering. Key among these is lack of a shared top-level ontology to unify and organise disparate aspects of the field and coordinate co-development of orthogonal ontologies. As a result, many engineering ontologies are limited to their scope, and functionally difficult to extend (...) or interoperate with other engineering ontologies. This paper demonstrates how the use of a top-level ontology, specifically the Basic Formal Ontology (BFO), greatly facilitates interoperability of multiple engineering-related ontologies. We constructed a system of formal linked ontologies by re-engineering legacy ontologies to be conformant with BFO and developing new BFO-conformant ontologies to capture knowledge in the engineering design, enterprise, human factors, manufacturing, and application domain of additive manufacturing. The resulting Integrated Framework for Additively Manufactured Products (IFAMP), including the body knowledge instantiated on its basis, serve as the basis for a proposed Design with Additive Manufacturing Method (DWAM), which we believe can support the design of innovative products with semantically enhanced ideation tools and enhanced access to application domain knowledge. The method and its facilitation through the ontological framework are demonstrated using a case study in medicine. (shrink)

Reciprocal Ethics is a novel ethical framework rooted in praxeology, the study of purposeful action. It represents an entirely new paradigm in moral philosophy, placing interaction at the core of universal ethics. Traditional ethical theories often divorce thought from action. Reciprocal Ethics contends that they are two aspects of the same phenomenon in the human experience, removing the traditional boundary between theoretical and practical ethics. The system categorizes all social interaction as either “self-directed” or “other-directed”, and by introducing the concept (...) of "normative signaling" it also exerts legitimate prescriptive power. The theory is a self-consistent, purely descriptive approach to ethics, that suggests that one's actions serve as semiotic signs that signal one's ethical stance in social interaction. Hence actions do not only define individual moral profiles, but also the moral ecosystem within which one actually operates. The theory operates in real time, adapting to the complexity of reality by taking into account uncertainty, incomplete data and social asymmetries. Reconciling elements of consequentialism and deontological theories, Reciprocal Ethics delivers a streamlined, yet comprehensive ethical system for social interaction, offering tangible insights for navigating complex moral dilemmas. By synthesizing descriptive metaethics and normative moral philosophy into one comprehensive formal theory, a bold assertion arises: Reciprocal Ethics becomes the Formal Science of Ethics. (shrink)

John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus from G. W. (...) Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations. (shrink)

Looks into evaluation of information provision probability from different sources, based on use of linguistic variables. Formation of functions appurtenant for its unclear variables provides for adoption of decisions by the decision maker, in conditions of nonprobabilistic equivocation. The development of market relations in Ukraine increases the independence and responsibility of enterprises in justifying and making management decisions that ensure their effective, competitive activities. As a result of the analysis, it is determined that the condition of economic facilities can be (...) described and determined by the decision-maker, in the presence of the necessary information. The confidence of the decision-maker in the information received is different and the decisions made have a correspondingly different level of information risk. It is important to substantiate the procedure for assessing the numerical extent of information risk in decision-making based on the information obtained in conditions of uncertainty. The use of a linguistic variable in the processing of expert data presented in the form of a matrix of binary relations of values of the membership function, which allowed to move to further processing of knowledge to support decision-making in the management of industrial, commercial, financial and other activities. As a mathematical model for estimating the numerical measure of information risk when making decisions based on the information obtained in conditions of non-stochastic uncertainty, a model has been developed to model natural language uncertainties, which differs from existing ones by formalizing knowledge taking into account uncertainty of input information. Making such a clear decision in a fuzzy environment has appropriate values of effectiveness and risk. The paper proposes all the functions and accessories of indicators of both quantitative nature and qualitative nature to bring their values in the field of definition to one scale. Then the indicator of the effectiveness of decision-making will be a measure of the clarity of the cross-section of fuzzy subsets, which correspond to the introduced indicators of information risk. The condition of economic facilities can be described and determined by the decision-maker, if the necessary information is available. Decision-making on thenumerical measure of information risk must be determined by a set of basic indicators, which can be both quantitative and qualitative in nature. Predictive values of indicators should be determined in conditions of nonstochastic uncertainty. In this case, the indicators of a quantitative nature can be determined by fuzzy triangular numbers, which implement a high level of confidence in the subjective judgments of experts. Indicators of qualitative nature should be presented in linguistic variables. The values of the indicators of qualitative nature that are predicted must be considered for all fuzzy variable terms-sets of linguistic variables introduced into consideration. For any fuzzy variable, the introduction to the consideration of a clear set of values as carriers of the α-level of its membership function allows to reduce to a single interpretation of the predicted values of indicators of quantitative and qualitative nature in terms of non-stochastic uncertainty. (shrink)

Introduction to the Special Volume, “Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy,” edited by Scott Edgar and Lydia Patton. At its core, analytic philosophy concerns urgent questions about philosophy’s relation to the formal and empirical sciences, questions about philosophy’s relation to psychology and the social sciences, and ultimately questions about philosophy’s place in a broader cultural landscape. This picture of analytic philosophy shapes this collection’s focus on the history of the philosophy of mathematics, physics, and psychology. The following (...) essays uncover, reflect on, and exemplify modes of philosophy that are engaged with these allied disciplines. They make the case that, to the extent that analytic philosophers are still concerned with philosophy’s ties to these disciplines, we would do well to pay attention to neo-Kantian views on those ties. (shrink)

Copi's method of deduction is formalized and shown to be complete.

Along with “epoché” or his “reductions”, Husserl’s “noema” and “noesis”, being neologisms invented by him, are main concepts in phenomenology able to represent its originality. Following the trace of a recent paper (Penchev 2021 July 23), its formal and philosophical approach is extended to both correlative notions, in the present article. They are able to reveal the genesis of the world from consciousness in a transcendental method relevant to Husserl, but furthermore described formally as a process of how subjective (...) temporality appears being isomorphic to objective temporality of the “world by itself” (an abstraction meaning it out of consciousness or transcendental consciousness): thus, it shares the same mathematical structure, which is embodied in the physical process of decoherence by the physical quantity of quantum information. The temporal world is able to appear naturally (rather as a ridiculous effect of the mythical “Big Bang”). The same process translated by formal and mathematical tools as interpreted in terms of “noema”, “noesis”, or transcendental consciousness is isomorphic to how “Self” (including in an individual and psychological sense) appears in virtue of transcendental consciousness. (shrink)

The philosophy of science of Patrick Suppes is centered on two important notions that are part of the title of his recent book (Suppes 2002): Representation and Invariance. Representation is important because when we embrace a theory we implicitly choose a way to represent the phenomenon we are studying. Invariance is important because, since invariants are the only things that are constant in a theory, in a way they give the “objective” meaning of that theory. Every scientific theory gives a (...) representation of a class of structures and studies the invariant properties holding in that class of structures. In Suppes’ view, the best way to define this class of structures is via axiomatization. This is because a class of structures is given by a definition, and this same definition establishes which are the properties that a single structure must possess in order to belong to the class. These properties correspond to the axioms of a logical theory. In Suppes’ view, the best way to characterize a scientific structure is by giving a representation theorem for its models and singling out the invariants in the structure. Thus, we can say that the philosophy of science of Patrick Suppes consists in the application of the axiomatic method to scientific disciplines. What I want to argue in this paper is that this application of the axiomatic method is also at the basis of a new approach that is being increasingly applied to the study of computer science and information systems, namely the approach of formal ontologies. The main task of an ontology is that of making explicit the conceptual structure underlying a certain domain. By “making explicit the conceptual structure” we mean singling out the most basic entities populating the domain and writing axioms expressing the main properties of these primitives and the relations holding among them. So, in both cases, the axiomatization is the main tool used to characterize the object of inquiry, being this object scientific theories (in Suppes’ approach), or information systems (for formal ontologies). In the following section I will present the view of Patrick Suppes on the philosophy of science and the axiomatic method, in section 3 I will survey the theoretical issues underlying the work that is being done in formal ontologies and in section 4 I will draw a comparison of these two approaches and explore similarities and differences between them. (shrink)

Reflective equilibrium (RE) is often regarded as a powerful method in ethics, logic, and even philosophy in general. Despite this popularity, characterizations of the method have been fairly vague and unspecific so far. It thus may be doubted whether RE is more than a jumble of appealing but ultimately sketchy ideas that cannot be spelled out consistently. In this paper, we dispel such doubts by devising a formal model of RE. The model contains as components the agent’s commitments and (...) a theory that tries to systematize the commitments. It yields a precise picture of how the commitments and the theory are adjusted to each other. The model differentiates between equilibrium as a target state and the dynamic equilibration process. First solutions to the model, obtained by computer simulation, show that the method allows for consistent specification and that the model’s implications are plausible in view of expectations on RE. In particular, the mutual adjustment of commitments and theory can improve one’s commitments, as proponents of RE have suggested. We argue that our model is fruitful not only because it points to issues that need to be dealt with for a better understanding of RE, but also because it provides the means to address these issues. (shrink)

This chapter outlines a new theoretical method, which I call “dancing-with,” emerging from the process of writing my dissertation and the book manuscript that followed it. Defined formally, a given theorist X can be said to “dance-with” with a second theorist Y insofar as X “choreographs” an interpretation of Y which is both true to Y and Y’s historical communities, and also meaningful and actionable (i.e. facilitating social justice) for X and X’s historical communities. In this pursuit, the method of (...) dancing-with involves both (1) a creative “torsion” of Y’s thought (particularly in the direction of unconscious, embodied and political factors at work in Y’ texts), and (2) a resultant, sympathetic torsion of X’s thought toward Y. In other words, X and Y “meet in the middle,” like two dancers walking onto the dance floor, to explore the promise of a flourishing artistic partnership. In this partnership, each must attend to the way that political meanings are inscribed on the other’s raced/sexed/etc. body, both to react maximally justly, and to maximize the aesthetic movement options that can be brought into play. As the method of dancing-with is thus modeled on an ideal comportment for improvisational social dance (such as the contemporary Latin dance called “salsa”), I envision the end-goal of dancing-with as what I call “poetic social justice.” By this, I mean the “poetic justice” of two theorists’ mutually empowering each other for maximal social good. Though this process is admittedly more difficult between some theorists, in part as a function of their respective embodiments and sociohistorical positions, at least a move or two together is always possible. (shrink)

The fact that the same equations or mathematical models reappear in the descriptions of what are otherwise disparate physical systems can be seen as yet another manifestation of Wigner's “unreasonable effectiveness of mathematics.” James Clerk Maxwell famously exploited such formal similarities in what he called the “method of physical analogy.” Both Maxwell and Hermann von Helmholtz appealed to the physical analogies between electromagnetism and hydrodynamics in their development of these theories. I argue that a closer historical examination of the (...) different ways in which Maxwell and Helmholtz each deployed this analogy gives further insight into debates about the representational and explanatory power of mathematical models. (shrink)

This study aims to present how a religious education is given in the formal education institutions while Turkish Cypriots are under British administration. In this context, studies were conducted to clarify the issue by using the method of documentation based on the supplied documents from the archives of Turkey and the TRNC and printed works, periodicals and reports. The educational institutions of the Turkish Cypriots continued the tradition that they obtained from the Ottoman Empire under the British administration. During (...) this period, sıbyan schools-primary schools, rushdiyyeh-secondary schools, idadi-high schools and madrasahs constitute the formal education institutions of Turkish Cypriots. Religious education courses were taught in the primary schools of these formal education institutions until the end of the British administration. In secondary and high schools, while religion courses were given for many years, this course was removed from the curriculum after 1942-1943 academic year. The madrasahs, another formal education institution of the period, have lost their effectiveness with the increase of the rushdiyyeh-secondary schools as of the beginning of the 20th century and in the 1920s, all of them were closed except the Peristerona Madrasah. With the death of the teacher of the Peristerona Madrasah in 1940, this madrasah also vanished. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on a (...) case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

The purpose of the research is to develop a new methodological basis for identifying, analyzing and solving problems of international corporations export-import activities and to ground the directions for ensuring their business excellence. The approach originality provides introduction of a conceptual model that aims to eliminate the negative symptoms of international corporations export-import activities based on the results of comprehensive market research, effectiveness of export-import activities and calculation of the integrated indicator of business excellence. The leading corporations of Slovakia and (...) India in the production of bi-axially oriented polypropylene (BOPP) films were the primary basis for this study. The results of the research showed the need to implement a system of managerial innovation for reasoning the directions of ensuring international corporations business excellence. This is achieved because of using logically formalized methods and provides the improvement of organizational and structural interaction of management entities in the process of solving export-import activity problems. Important factors for ensuring business excellence are also the optimization of export and import costs, as well as an increase in export revenue for Slovak companies, and an increase in market share and cost optimization for Indian companies. The practical value of the obtained results is to develop a set of managerial innovations that can improve the efficiency of export-import activities and improve international corporations business. (shrink)

Although McMillan recognizes that moral theory has its place, he suggests that by setting bioethics up as a discipline whose predominant issues are to do with theory, not only are students insulated from the broadness of its scope and the diversity of its methods, but the subject comes across as largely inaccessible to those without some formal train- ing in normative ethics and of limited practical signifi- cance to those dealing with concrete issues.

The criticism of Hilbert's axiomatic system of geometry by Mate Meršić (Merchich, 1850-1928), presented in his work "Organistik der Geometrie" (1914, also in "Modernes und Modriges", 1914), is analyzed and discussed. According to Meršić, geometry cannot be based on its own axioms, as a logical analysis of spatial intuition, but must be derived as a "spatial concretion" using "higher" axioms of arithmetic, logic, and "rational algorithmics." Geometry can only be one, because space is also only one. It cannot be reduced (...) to manipulation with symbols but has to deal with concepts and provide real knowledge. According to Meršić, aiming at some particular proof of the consistency of the whole axiomatic system is meaningless because the consistency follows from the truth of individual axioms based on spatial intuition. It is impossible, according to Meršić, for the geometric axioms to be mutually independent because they must be interconnected as essential parts of a whole. Although Meršić did not recognize all the advantages of Hilbert's formalization of geometry, he clearly pointed out some crucial limitations of the axiomatic method. (shrink)

E-waste, also known as waste from electrical and electronic equipment, is a solid waste that accumulates quickly due to high demand driven by the market for replacing newer electrical and electronic products. The global e-waste generation is estimated to be between 53.6 million tons, and it is increasing by 3–5% per year. Metals make-up approximately 30% of e-waste, which contains precious elements Au, Ag, Cu, Pt, and other high-value elements, valued at USD 57 billion, which is driving the e-waste recycling (...) industry. It is noteworthy that the recycling of precious elements from e-waste has emerged as a profitable enterprise in several parts of developing nations. E-waste contains 50–100 times higher levels of precious metals compared to natural ores, making it suitable for mining. E-waste recycling in developing nations, mostly occurs through the informal sector comprising manual collection, crushing, segregation and selling of precious elements, such as Au, Ag, Cu, Pb, Pt, and other rare elements (Nd, In, and Ga). The organized sector, on the other hand, mostly employs mechano-chemical methods, such as pyrometallurgy, hydrometallurgy, and bio-hydrometallurgy, which have serious environmental consequences. Both the informal and formal sectors of e-waste processing lead to the leaching of toxic elements into groundwater and soils. Owing to the lesser efficiency of greener technologies, such as phytoremediation and bioremediation, their use in precious metal extraction is very limited. However, this review explores several hyper-accumulating and tolerant plants viz. Brassica juncea and Berkheya coddii, which holds great potential in phytomining of precious metal from e-waste. Thus, the state of the art in precious metal extraction from e-waste as well as the advantages and disadvantages of different metal extraction technologies has been reviewed. (shrink)

Philosophy of science in the 20th century is to be considered as mostly characterized by a fundamentally systematic heuristic attitude, which looks to mathematics, and more generally to the philosophy of mathematics, for a genuinely and epistemologically legitimate form of knowledge. Rooted in this assumption, the book provides a formal reconsidering of the dynamics of scientific theories, especially in the field of the physical sciences, and offers a significant contribution to current epistemological investigations regarding the validity of using (...) class='Hi'>formal (especially: model-theoretic) methods of analysis, as developed principally by Stegmüller, Sneed, Suppes, Moulines, “to bring the airy flights of analytical philosophy back down to earth”, to borrow Stephan Hartmann’s provocative statement. At the same time, the volume represents a comprehensive account of the epistemic content of physical theories, the logic of theory change in science, and specific (inter-)theoretical core aspects of scientific progress, particularly in the form suggested informally by Thomas Kuhn. As C. Ulises Moulines writes in the preface, “there is no other example in present-day literature (in any language) on this topic, i.e. the formal analysis of the ideographic characterization of the dynamics of theories between Kuhn’s theory of science and structural epistemology, that is as systematic and complete as Perrone’s work”. (shrink)

This chapter presents the core challenge before Hamlet as that of achieving authenticity in the face of inner multiplicity. Authenticity—which this chapter will take to mean (1) acting on the (2) knowledge of (3) what one truly is, beneath one’s various masks and social roles—becomes a particularly pressing need under conditions of (early) modernity, when traditional forms of action-guidance are at least halfway off the table. But authenticity is highly problematic when the self that is discovered turns out to be (...) multiple. Which self, exactly, should one be true to? Hamlet’s solution, this chapter suggests, is an “actor’s ethos,” in which each of his aspects is given its day in the sun, granted full commitment by means of what we now call “method acting.” That is what Hamlet learns from the players—and that too is what we stand to learn from _Hamlet_: not an idea but a method. (shrink)

The classical theory of computation does not represent an adequate model of reality for simulation in the social sciences. The aim of this paper is to construct a methodological perspective that is able to conciliate the formal and empirical logic of program verification in computer science, with the interpretative and multiparadigmatic logic of the social sciences. We attempt to evaluate whether social simulation implies an additional perspective about the way one can understand the concepts of program and computation. We (...) demonstrate that the logic of social simulation implies at least two distinct types of program verifications that reflect an epistemological distinction in the kind of knowledge one can have about programs. Computer programs seem to possess a causal capability (Fetzer, 1999) and an intentional capability that scientific theories seem not to possess. This distinction is associated with two types of program verification, which we call empirical and intentional verification. We demonstrate, by this means, that computational phenomena are also intentional phenomena, and that such is particularly manifest in agent-based social simulation. Ascertaining the credibility of results in social simulation requires a focus on the identification of a new category of knowledge we can have about computer programs. This knowledge should be considered an outcome of an experimental exercise, albeit not empirical, acquired within a context of limited consensus. The perspective of intentional computation seems to be the only one possible to reflect the multiparadigmatic character of social science in terms of agent-based computational social science. We contribute, additionally, to the clarification of several questions that are found in the methodological perspectives of the discipline, such as the computational nature, the logic of program scalability, and the multiparadigmatic character of agent-based simulation in the social sciences. (shrink)

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)