In the search of new approaches to the problem of emergence and evolution of natural languages, Mathematics, Theoretical Computer Science, as well as Molecular Biology and Neuroscience, both deeply penetrated and profoundly inspired by concepts originated in Mathematics and Computer Science, represent today the richest pools of formal concepts, structures, and methods to borrow and to adapt.

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type (...) of Alexandroff spaces was used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...) and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical (...) atomism and monism with theaid of topological separation axioms. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be (...) useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and (...) combinatoric spaces; (5) Gottfried Leibniz’s development of compositional analysis and synthesis as a general modelling method and a paradigm for ars inveniendi; (6) Fritz Zwicky’s revival of the morphological method of analysis and construction, and its subsequent computerised applications. (shrink)

The Controversy over the Existence of the World (henceforth Controversy) is the magnum opus of Polish philosopher Roman Ingarden. Despite the renewed interest for Ingarden’s pioneering ontological work whithin analytic philosophy, little attention has been dedicated to Controversy's main goal, clearly indicated by the very title of the book: finding a solution to the centuries-old philosophical controversy about the ontological status of the external world. -/- There are at least three reasons for this relative indifference. First, even at the time (...) when the book was published, the Controversy was no longer seen as a serious polemical topic, whether it was disqualified as an archaic metaphysical pseudo-problem, or taken to be the last remnant of an antiscientific approach to philosophy culminating in idealism and relativism. Second, Ingarden’s reasoning on the matter is highly complex, at times misleading, and even occasionally faulty. Finally, his analysis is not only incomplete – Controversy being unachieved – but also arguably aporetic. -/- One may wonder, then, why it is still worth excavating this mammoth treatise to study an issue apparently no longer relevant to contemporary philosophy. Aside from historical and exegetical purposes, which are of course very interesting in their own right, Ingarden’s treatment of the Controversy remains one of the most detailed and ambitious ontological undertakings of the twentieth century. Not only does it lay out an incredibly detailed map of possible solutions to the Controversy, but it also tries to show why the latter is a genuine and fundamental problem that owes its hasty disqualification to various oversimplifications over the course of the history of philosophy. -/- In this chapter, I first give an overview of Ingarden’s method, which relies mainly on a combinatorial analysis. Then, I summarize his examination of possible solutions to the Controversy, and determine which ones can be ruled out on ontological grounds. Finally, I explain why this ambitious project ultimately leads to a theoretical impasse, leaving Ingarden unable to come up with a definitive solution to the Controversy – regardless of the fact that the book is unachieved. I argue that his analysis of the problem yields a more modest but nonetheless valuable result. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

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

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all (...) inductive formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

In parts of his Notebooks, Tractatus and in “Lecture on Ethics”, Wittgenstein advanced a new approach to the problems of the meaning of life. It was developed as a reaction to the explorations on this theme by Bertrand Russell. Wittgenstein’s objective was to treat it with a higher degree of exactness. The present paper shows that he reached exactness by treating themes of philosophical anthropology using the formal method of topology.

What is the philosophical significance of Heidegger’s interpretation of the Japanese notion of kotoba (言葉) for Japanese philosophy? Was his conversation with Tezuka Tomio a real dialogue or not? To answer to these correlated questions, I elucidate Heidegger’s 1954 essay “A Dialogue on Language” by following a topological mode of thinking, and I inquire into the way-making of a “thinking conversation”. First, I problematize whether Heidegger engaged in a genuine dialogue with Tezuka. To that end, I distinguish the hermeneutic (...) horizon of the actual encounter between Tezuka and Heidegger from Heidegger’s essay which places Tezuka (the Japanese) and Heidegger (the Inquirer) in a fictional philosophical conversation. Second, I argue that Heidegger’s topological method of interpretating kotoba can be read as a poetic means of thematizing East-West dialogue. Third and finally, exploring the topological sense of kotoba, I engage with third generation Kyoto School thinker Ueda Shizuteru’sideaof“hollow words” of language, situated in a twofold view of the world. I conclude that the true character of Heidegger’s conversation with Tezuka can be identified neither in Heidegger’s “actual” encounter with Tezuka, nor merely in Heidegger’s “hollow” essay. Departing from Ueda’s account of kotoba, it appears that a genuine conversation with language can be located in the dialogue of actuality and hollowness, which finds it expression in poetic language. (shrink)

Human language, hominin tool production modes, and multimodal communications systems of primates and other animals are currently well-studied for how they display compositionality or combinatoriality. In all cases, the former is defined as a kind of hierarchical nesting and the latter as a lack thereof. In this article, I extend research on combinatoriality and compositionality further to investigations of everyday primate skills. Daily locomotion modes as well as behaviors associated with subsistence practices, hygiene, or body modification rely on the hierarchical (...) nesting of different behavioral and cognitive actions into complex skills. I introduce a scheme which uses hierarchical organization to differentiate combinatorial from compositional skills. Combinatorial skills are defined either as aggregational or linearly hierarchical depending on whether the skill occurs momentarily in space or unfolds sequentially over time. Compositional skills are defined either as nested or interactionally hierarchical depending on whether the skill results in new constructs or in new interactions between existing constructs. The methodology I propose combines epistemological hierarchy theory with data from primatological field research and experimental and comparative psychological research and provides a means to integrate current constructionist and extended views on cognition and action with older research on behavioral logics in psychology and operational chain thinking in anthropology. The approach furthermore synchronizes with ongoing research on teleonomy, intentionality, and creativity. -/- . (shrink)

Combinatorial behavior involves combining different elements into larger aggregates with meaning. It is generally contrasted with compositionality, which involves the combining of meaningful elements into larger constituents whose meaning is derived from its component parts. Combinatoriality is commonly considered a capacity found in primates and other animals, whereas compositionality often is considered uniquely human. Questioning the validity of this claim, this multidisciplinary special issue of the International Journal of Primatology unites papers that each study aspects of combinatoriality and compositionality (...) found in primate and bird communication systems, tool use, skills, and human language. The majority of authors conclude that compositionality is evolutionarily preceded by combinatoriality and that neither are uniquely human. This introduction briefly introduces readers to the major findings and issues raised by the contributors. -/- . (shrink)

The purpose of this paper is to review and critique Wessel Reijers and Bert Gordijn’s paper Moving from value sensitive design to virtuous practice design. In doing so, it draws on recent literature on developing value sensitive design (VSD) to show how the authors’ virtuous practice design (VPD), at minimum, is not mutually exclusive to VSD. This paper argues that virtuous practice is not exclusive to the basic methodological underpinnings of VSD. This can therefore strengthen, rather than exclude the VSD (...) approach. Likewise, this paper presents not only a critique of what was offered as a “potentially fruitful alternative to VSD” but further clarifies and contributes to the VSD scholarship in extending its potential methodological practices and scope. It is concluded that VPD does not appear to offer any original contribution that more recent instantiations of VSD have not already proposed and implemented. (shrink)

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that (...) class='Hi'>topological predictions can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone. (shrink)

Karl Christian Friedrich Krause and Georg Wilhelm Friedrich Hegel are two representatives of German Idealism, both of whom developed impressing category systems. At the core of both systems is the question of the relation of the Absolute to its determinations and the determinations of finite beings. Both idealists try to deduce their respective category systems from the immediacy of the Absolute. Both use combinatorial methods to get from known to new categories or constellations in the system, which then (...) unfold in the world. Krause is thereby considered the eponym of so-called panentheism, the doctrine that “Everything is in God.” Hegel is also often referred to as a panentheist. Through a comparison of the two systems of categories, in this essay the thesis will be advocated that Hegel was in no sense a panentheist. Krause is and remains the gold standard of panentheism. (shrink)

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the properties (...) of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

General Morphological Analysis (GMA) is a method for structuring a conceptual problem space – called a morphospace – and, through a process of existential combinatorics, synthesizing a solution space. As such, it is a basic modelling method, on a par with other scientific modelling methods including System Dynamics Modelling, Bayesian Networks and various types graph-based “influence diagrams”. The purpose of this article is 1) to present the theoretical and methodological basics of morphological modelling; 2) to situate GMA within a (...) broader modelling theoretical framework by developing a (morphological) model representing different modelling methods, and 3) to demonstrate some of the basic modelling techniques that can be carried out with GMA using dedicated computer support. (shrink)

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

The hope of finding new methods of predicting the course of historical processes could be connected with the recent developments of the theory of self-organisation, also called synergetics. It provides us with knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general (...) and local instability of development is increasing. The social world seems to go towards a unity, a sustainable commonwealth through pulsations rather than monotonously. It goes via alternation of disintegration, even if partial, and getting more powerful integrations of structures. There is a path of multiple reduction of temporal and material expenses, a path of a resonant excitation of desirable and — no less important — feasible in a given social system structure. In the case of the right topology of integration of geopolitical structures an arising whole organisation can accelerate its tempo of evolution. 1999 Elsevier Science Ltd. All rights reserved. (shrink)

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists might prefer diagrammatic representations of topological information to sentential equivalents nor how such representations might facilitate important processes of explanatory (...) reasoning unavailable to scientists who restrict themselves to sentential representations. Accordingly, relying upon a case study about immune system vulnerability to attacks on CD4+ T-cells, I argue that diagrams group together information in a way that avoids repetition in representing topological structure, facilitate identification of specific topological properties of those structures, and make available to controlled processing explanatorily salient counterfactual information about topological structures, all in ways that sentential counterparts of diagrams do not. (shrink)

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can (...) be used to prove a completeness theorem for S4.1. Further, it is shown that the McKinsey algebra MKX of a space X endoewed with an alpha-topologiy satisfies Esakia's GRZ axiom. (shrink)

The being is derived by a difference in Lacanian ontology. This difference is the basic element in Lacanian theory that grounds the unconscious subject. Because according to Lacan, the existence of the subject can not be self-proclaimed and it is represented by a signifier. Lacan gives the name "object a" to this paradoxical being which is distinguished by this difference or lack, and uses some topological transformations in order to be able to explain the structural paradoxes in the psychological (...) theory. The aim of this study is to explore the ontology of these paradoxical situations and try to decipher the function of topology in Lacan's theory. (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)

Ontologies of living things are increasingly grounded on the concepts and practices of current life science. Biological development is a process, undergone by living things, which begins with a single cell and (in an important class of cases) ends with formation of a multicellular organism. The process of development is thus prima facie central for ideas about biological individuality and organismality. However, recent accounts of these concepts do not engage developmental biology. This paper aims to fill the gap, proposing the (...) lineage view of stem cells as an ontological framework for conceptualizing organismal development. This account is grounded on experimental practices of stem cell research, with emphasis on new techniques for generating biological organization in vitro. On the lineage view, a stem cell is the starting point of a cell lineage with a specific organismal source, time-interval of existence, and ‘tree topology’ of branch-points linking the stem to developmental termini. The concept of ‘enkapsis’ accommodates the cell-organism relation within the lineage view; this hierarchical notion is further explicated by considering the methods and results of stem cell experiments. Results of this examination include a (partial) characterization of stem cells’ developmental versatility, and the context-dependence of developmental processes involving stem cells. (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.

The paper concentrates on an appreciation of W.V. Quine’s thought on meaning and how it escalates beyond the meaning holism and confirmation holism, thereby paving the way for a ‘meaning nihilism’ and ‘confirmation rejectionism’. My effort would be to see that how could the acceptance of radical naturalism in Quine’s theory of meaning escorts him to the indeterminacy thesis of meaning. There is an interesting shift from epistemology to language as Quine considers that a person who is aware of linguistic (...) trick can be the master of referential language. Another important question is that how could Quine’s radical translation thesis reduce into semantic indeterminacy that is a consequence of his confirmation method. I think that the notion and the analysis of meaning became hopelessly vague in Quine’s later work. I further argue on Quine’s position of meaning that I call, following Hilary Putnam, ‘meaning nihilism’. It seems to me that Quine had no belief like ‘meaning consists in’, or ‘meaning depends on’ something. Through this argument, I would like to challenge the confirmation holism that was foisted by Fodor on Quine’s thesis. My attempt would be to scrutinize Putnam’s point of view that Quine was neither a confirmation holist nor a meaning holist. I think that both Putnam and Quine denied the concept of constitutive connection of meaning as a second grade notion not only from the realm of semantic, but also from the perspective of epistemology. So, linguistic meaning cannot be formed by any sample of its uses. For Quine, the concept of meaning in metaphysics is heuristic and need not be taken seriously in any ‘science worthy’ literature. (shrink)

Although current educational priorities tend to avoid strong moral positions, one of the world's most venerable yet persistently influential moral traditions not only lays out a number of major moral principles but also incorporates them into its pedagogy. Confucius teaches us about the importance of seeking knowledge, learning how to learn, applying ancient wisdom to contemporary situations, valuing virtue over material gain, following the Golden Rule, and living by our principles. He also has ways of assessing his own students' progress (...) in these matters. Confucius' pedagogy is an interesting model to consider and contrast with contemporary models. This chapter introduces these principles and assessments from the Analects and draws out some comparisons to and contrasts with two alternative theories in western moral thought, Augustine and John Dewey. -/- The accepted version of the paper is included here. Pagination does not match the published version. (shrink)

Here, I examine the epistemic relation between beliefs about the nature of sexual orientation (e.g., beliefs concerning whether orientation is dispositional) and beliefs about the taxonomy of orientation categories (e.g., beliefs concerning whether polyamorous is an orientation category). Current philosophical research gives epistemic priority to the former class of beliefs, such that beliefs about the taxonomy of orientation categories tend to be jettisoned or revised in cases of conflict with beliefs about the nature of sexual orientation. Yet, considering the influence (...) of ideology on beliefs about socially significant phenomena, I argue for an epistemic reversal. (shrink)

The use of "levels of abstraction" in philosophical analysis (levellism) has recently come under attack. In this paper, we argue that a refined version of epistemological levellism should be retained as a fundamental method, which we call the method of abstraction. After a brief introduction, in section two we make clear the nature and applicability of the (epistemological) method of levels of abstraction. In section three, we show the fruitfulness of the new method by applying it to five case studies: (...) the concept of agenthood, the Turing test, the definition of emergence, quantum observation and decidable observation. In section four, we further characterise and support the method by distinguishing it from three other forms of "levellism": (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In this context, we also briefly address the problems of relativism and antirealism. In the conclusion, we indicate 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)

Dialectica: Mathematica and Physica, Truth and Justice, Trick and Life. Mathematica as the Constructive Metaphysica and Ontology. Mathematica as the constructive existential method. Сonsciousness and Mathematica: Dialectica of "eidos" and "logos". Mathematica is the Total Dialectica. The basic maternal Structure - "La Structure mère". Mathematica and Physica: loss of existential certainty. Is effectiveness of Mathematica "unreasonable"? The ontological structure of space. Axiomatization of the ontological basis of knowledge: one axiom, one principle and one mathematical object. The main ideas and concepts (...) of the ontological construction/ "Point with a vector germ" and "heavenly triangle". "Ordo geometricus" and "Ordo onto-topological". Architecture of the onto-topological basis of knowledge: general framework structure, carcass and foundation. The absolute space and the absolute field. The absolute (natural) system of coordinates of Universum. Eidos of "idea of ideas", the symbol and the "formula of Justice". (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

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

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

Philosophical methodology is the central focus of pragmatism’s founding documents. The early works of Peirce, James, and Dewey examine methodological questions such as ‘how do we make philosophical ideas clear?’, ‘what is the best method for fixing belief?’ and ‘how do we know whether a philosophical question is answerable?’. Thus, many consider pragmatism inherently methodological – as a metaphilosophy, a view about how philosophy should or must be done (e.g. Talisse 2017). Any summary of pragmatist methods is therefore a (...) summary of pragmatism itself. Given such an impossibly broad remit, this chapter does only three things. First, it provides four broad claims common to pragmatist approaches to philosophical methodology, claims reflecting its underlying theory of inquiry. Second, it briefly examines three core pragmatist methods – for conceptual clarification, for fixing belief, and for settling or dissolving philosophical disputes. Third, it briefly describes differences between the Classical figures regarding each method. This is merely a brief sketch – the reader should consider all entries in this volume relevant to pragmatism qua philosophical method. (shrink)

Progress in the last few decades in what is widely known as “Chaos Theory” has plainly advanced understanding in the several sciences it has been applied to. But the manner in which such progress has been achieved raises important questions about scientific method and, indeed, about the very objectives and character of science. In this presentation, I hope to engage my audience in a discussion of several of these important new topics.

The aim of the paper is to give a description of the development of understanding scientific method in the history of science and philosophy of science. The thesis is defended that crucial changes in understanding scientific method had fundamental consequences for the development in scientific knowledge, for the position of science in the system of knowledge and for its role in human culture. Basic attitudes to scientific method in contemporary philosophy and philosophy of science are shortly outlined and the rationality (...) of scientific method is defended. (shrink)

This paper argues that naturalistic philosophy does not meet its own empiricist mandate. It argues from an empiricist perspective. Naturalists either claim that philosophy is like science in significant ways, or they claim that philosophy ought to be like science. This paper, being chiefly focused on the former claim, argues that naturalistic philosophy is nothing like science. Using Papineau’s markers for the similarities between naturalistic philosophy and science, I argue, counter Papineau, that the method employed in naturalistic philosophy is not (...) a posteriori and its claims are certainly not synthetic in the same way as that of science. This methodological distinction between science and philosophy is one made by Carnap. To show how the methods are distinct I compare two papers; I compare the method employed by Andy Clark in his philosophical paper on the brain as a prediction error minimisation machine with that employed by Rees and Haynes in their neuroscientific paper on mental content. (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)

Whether some condition is equivalent to a conjunction of some conditions has been a major issue in analytic philosophy. Examples include: knowledge, acting freely, causation, and justice. Philosophers have striven to offer analyses of these, and other concepts, by showing them equivalent to such a conjunction. Timothy Williamson offers a number of arguments for the idea that knowledge is ‘prime’, hence not equivalent to or composed by some such conjunction. I focus on one of his arguments: the requirement that such (...) conjuncts must be freely recombinable. Although there has been a great deal of discussion of Williamson's arguments, the flaw I describe has gone unnoticed. Williamson's argument is expressed in terms of conditions, and cases of the condition. Does the condition include specific information, or is the specific information only part of the case? His argument equivocates between more and less general specifications of the conditions. Once this distinction is clarified, his argument can be seen to be vitiated by this conflation. Neither option yields a sound argument for Williamson's desired conclusion. (shrink)

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

Entrepreneurship education is among the key drivers of the country’s economy, and teachers are primarily responsible for its integration into teaching and finding the best and most useful method. The purpose of this research is to determine the level of entrepreneurial competence and teaching methods among entrepreneurship education teachers. Focusing on the concept of entrepreneurial competencies combining conceptual, human relations, strategic, commitment, opportunity, organizational and strategic competencies. Using quantitative – descriptive survey, the study tested its significant difference and relationship (...) when grouped with the profile variables. The findings indicate a significant correlation between the variables particularly, with the technical competence which has the strongest correlation. The paper sheds some light concerning the status of the current entrepreneurial competence of the teachers in the division and recommends training curriculum to develop their competencies in handling the subject. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...) point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Alsted was a foremost encyclopedist of the early seventeenth century. He provided both a complete presentation of all the subjects of philosophy (of which encyclopedia consisted) and a method to learn them. This method was an original synthesis of the dialectic of Petrus Ramus, the combinatorial art of memory of Raimond Lull and Giordano Bruno, and the method of presentation of philosophical disciplines of Bartholomäus Keckermann. Alsted’s encyclopedism was intended as a remedy to the postlapsarian condition of man and (...) was functional to the pedagogical reform pursued at the Academy of Herborn; this was, in turn, an essential part of the Calvinist state reform of the county of Nassau-Dillenburg. In theology, the importance of Alsted consists of having introduced millenarianism in the Reformed Europe, though his early, optimistic views on the imminent end of the world would change to pessimistic as a consequence of the Thirty Years’ War. (shrink)

[English] This paper aims to discuss ten traditional and contemporary methodological paradigms in African philosophy, and demonstrates how they may apply to African environmental ethics research. The methods include: Ethno-philosophy, Sage Philosophy, Conversational Philosophy, Conceptual Mandelanization, Eco-Afrocentricism, Indigenous Language Analysis, Eco-Afro-feminism, Conceptual Decolonization, Storytelling Philosophy, and Cultural Adaptationism. The significance and limitations of the methodologies are highlighted. The concept and principles of African environmental ethics are analyzed and discussed to facilitate an understanding of the conceptual frameworks that underpin the (...) methodologies. In conclusion, the discourse demonstrates that environmental ethics research in Africa should be based on African philosophical methodologies so as to facilitate production of research that will be relevant in African contexts. -/- [Annang] N̄wed nduongo ami ayem ibene nwọ́d mme n̄kaan nne mfa usung unam nduongo ke vilọsọvi Afrịke , nne nte amọ ekeme iwam unam nduongo mbanga ido ukpeme nkan-nkuk ke Afrịke. Mme usung unam nduongo ami nsehe ade ami: vilọsọvi mben ufọk, vilọsọvi n̄kan ideen, vilọsọvi nneme, vilọsọvi Mandela, “Eco-Afrocentricism”, nduongore usem utiit ajid, vilọsọvi ibaan Afrịke, vilọsọvi mkpọk-nyak, vilọsọvi n̄ke, nne ukpep ido idung agwo. N̄wed ami abene awọd mme ikek nne nde mem idem usung nduongo ami. N̄wed ami atang mkpọ abanga se ido ukpeme nkan-nkuk ke Afrịke anwongo nne mme itai amọ, nne nte amọ ewam mbon nduongo ediọhọ nnanga ekpekakpa ibọrọ nduongo amọ. Ke n̄suuk ikọ, ukpep ami mkpọ abene awọd ate ke ekpena ekama usung nduongo vilọsọvi Afrịke enam nduongo ebanga ido ukpeme nkan-nkuk ke Afrịke man ibọrọ nduongo asanga akekem nne se adiiwam Afrịke. (shrink)

In “Topology of Balasaguni’s Kutadgu Bilig: Thinking the Between,” Onur Karamercan focuses on the philosophical dimension of Kutadgu Bilig, a poetic work of Yūsuf Balasaguni, an 11th century Central Asian thinker, poet, and statesman. Karamercan pays special attention to the meaning of betweenness and, in the first step of his argument, discusses the hermeneutic and topological implications of the between, distingushing the dynamic sense of betweenness from a static sense of in-betweenness. He then moves on to analyze Balasaguni’s notion (...) of language, which he interprets as an early critique of the instrumental account of language and, by examining several selected fragments from Kutadgu Bilig, illustrates Balasaguni’s designation of language as an inexhaustible phenomenon. In the process, he also points to the possible parallels between Balasaguni’s and Heidegger’s ideas of language. In the final section of the article, building on his argument, Karamercan thematizes the margins of Turkic languages and of Islamic philosophy, suggesting that they need to be reexamined. He problematizes the very meaning of Asia itself by decentering what he calls “its internal East–West antagonism” and puts forth instead a framework based on in-betweenness reinterpreted from a topological perspective, proposing it as an alternative view which might help us make sense of the hermeneutic neighborhoods of Asian philosophies. (shrink)

The concept of facticity denotes conditions of experience whose necessity is not logical yet whose contingency is not empirical. Although often associated with Heidegger, Fichte coins ‘facticity’ in his Berlin period to refer to the conclusion of Kant’s metaphysical deduction of the categories, which he argues leaves it a contingent matter that we have the conditions of experience that we do. Such rhapsodic or factical conditions, he argues, must follow necessarily, independent of empirical givenness, from the I through a process (...) of ‘genesis.’ I reconstruct Fichte’s argument by tracing the origin of his neologism, presenting his Jena critique of Kant’s rhapsodic appeal to the forms of judgment, and illustrating the Jena period’s continuity with the Berlin period’s genetic method, while noting a methodological shift whereby Fichte directs his critique against his own doctrine of intellectual intuition in order to eliminate its ‘factical terms.’. (shrink)

The fundamental error of the metaphysical tradition, according to Heidegger, is the subordination of general ontology to the ontology of a special, exemplary entity (God, the soul, etc.). But Being and Time itself treats one kind of entity as exemplary, namely Dasein. Does this mean that Heidegger fails to free himself from the kind of metaphysics that he sought to criticize? To show how he avoids this charge I propose to examine the parallels between the methodology of Being and Time (...) and the methodology Heidegger ascribes to Aristotle's Metaphysics. Heidegger takes the virtue of Aristotle's inquiry to reside in the way he resists the subordination of general to special ontology: Aristotle was guided by a "double concept" of metaphysics, pursued two irreducibly distinct methods of inquiry, and avoided the temptation to unite them. In proposing to similarly pursue a "double task" in Being and Time Heidegger seeks to apply this insight to his own work. Alongside the task of fundamental ontology, Heidegger spells out the shape of a second task, Destruktion, understood as a historical critique that traces ontological concepts back to their ontic roots. But Destruktion is not a mere addendum to fundamental ontology; the two tasks are meant to counterbalance one another and thereby prevent the collapse of the ontological difference between being and beings. Indeed, Heidegger proposes to apply Destruktion to the results of his own fundamental ontology. He hopes to thereby achieve a transformation of the philosophical attitude which underpins the metaphysical tradition. (shrink)