Formal Methods in the Philosophy of Science

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.     

重拾被遗忘的东方——兼评“东方哲学”与五卷本《东方哲学史》

在当代中国哲学界,东方哲学几乎属于被遗忘的领域:它从学科上被取消,从知识结构上被排除,从价值上被看轻,导致中国哲学界陷入一种中、西二元分立的简约化的格局之中。由中国社会科学院哲学研究所东方哲学研究室组织编写的五卷本《东方哲学史》的问世,对于改变这一状况起到了积极的作用。但是,东方哲学概念该如何理解?相较于西方民族,东方民族有着怎样的思考     

Introduction to the special issue on formal modeling of semantic concepts

We introduce the special issue on formal models of semantic concepts. After outlining the research questions that motivated the issue, we summarize the rich set of data provided by the Leuven Natural Concepts Database, and provide an overview of the seven research articles in the special issue. Each of these articles applies a formal modeling approach to one or more parts of the database, attempting to further our understanding of how people represent and use semantic concepts.     

Beyond congruence measures for the evaluation of personality factor structure replicability: An exploratory structural equation modeling approach

The present study aims to illustrate an encompassing approach to the evaluation of personality factor structure replicability based on novel exploratory structural equation modeling (ESEM) methods. This approach comprises formal tests of measurement invariance applied to the flexible ESEM framework and overcomes the limitations of congruence measures that have traditionally been used to assess factor replicability in personality research. On the basis of 1566 responses to the widely-used NEO Five-Factor-Inventory (NEO-FFI), we demonstrate this ESEM approach in the context of examining the invariance of the NEO-FFI factor structure across gender. The approach is shown to converge with traditional congruence measures and extend these measures for examining factorial structure consistency. In addition, more general replicative data supporting the validity of the NEO-FFI are reported. We discuss the ESEM approach as a viable alternative to the congruence approach and acknowledge some important limitations of the method.     

Two models of unawareness: comparing the object-based and the subjective-state-space approaches

This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs to anti-realism, but can meet those challenges and can perhaps convince some realists, at least those who are also naturalists.     

Deferentialism

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend—deferentialism, as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry.     

21% versus 79%: Explaining philosophy’s gender disparities with stereotyping and identification

This study tests the hypothesis that the perception of philosophy as a male-oriented discipline contributes to the pronounced gender disparity within the field. To assess the hypothesis, we determined the extent to which individuals view philosophy as masculine, and whether individual differences in this correspond with greater identification with philosophy. We also tested whether identification with philosophy correlated to interest in it. We discovered, first, that the more women view philosophy as masculine, the less they identify with it, and second, that the less women identify with philosophy, the less they want to major in it. Interestingly, this result does not hold for men—their viewing philosophy as masculine does not correspond to their identification with it, nor does it correlate with their likelihood of majoring in it. We also discovered that the typical student does not have a preconceived notion of philosophy as masculine; this suggests that they come to view philosophy as masculine the more they do it, which in turn supports the possibility that teaching the discipline differently may prevent students from conceiving of philosophy as masculine, thus allowing a path to reducing the gender disparity.     

Gist another panacea? Or just the illusion of inclusion

In this article, we call for a formal approach to modeling the development of reasoning. We discuss the need to operationalize the nature of encoding and processing. These problems are reviewed in the context of fuzzy-trace theory with particular emphasis on class-inclusion reasoning experiments. We argue that salience manipulations (perceptual or linguistic) give the illusion of inclusion by promoting subclass-subclass comparisons. We present an alternate, mathematical model of class-inclusion reasoning in which memory and reasoning parameters are estimated and integrated in a skills analysis of performance. We conclude that without similar formal modeling efforts, the nature of children's reasoning will remain elusive.     

Indian cognitivism and the phenomenology of conceptualization

We perform conceptual acts throughout our daily lives; we are always judging others, guessing their intentions, agreeing or opposing their views and so on. These conceptual acts have phenomenological as well as formal richness. This paper attempts to correct the imbalance between the phenomenal and formal approaches to conceptualization by claiming that we need to shift from the usual dichotomies of cognitive science and epistemology such as the formal/empirical and the rationalist/empiricist divides—to a view of conceptualization grounded in the Indian philosophical notion of “valid cognition”. Methodologically, our paper is an attempt at cross-cultural philosophy and cognitive science; ontologically, it is an attempt at marrying the phenomenal and the formal.     

Formal Ontology and Mathematics. A Case Study on the Identity of Proofs

We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) developed by the computer science community. In this article, (i) we describe this new approach and, (ii) to provide an example, we apply it to the problem of the identity of proofs. We also describe open issues and further applications of this approach (for example, the study of purity of methods). We lay some foundations to investigate rigorously and at large scale intellectual moves and attitudes that underpin the advancement of mathematics through cognitive means (carving out investigationally valuable concepts and techniques) and social means (like communication, collaboration, revision, and criticism of specific categories, inferential patterns, and levels of analysis). Our approach complements other types of analysis of proofs such as reconstruction in a deductive system and examination through a proof-assistant.

     

Spirituality’ as reconceptualisation of the self: Alan Turing and his pioneering ideas on artificial intelligence

This article investigates the underlying agenda of the philosophy of artificial intelligence (AI) – a discipline of computer science – and proposes a threefold model of ‘spirituality’ as reconceptualisation of the self, composed of one’s search, adaptation and transformation of self-knowledge, specifically concerning the rational humanity. By using the life and ideas of the father of AI and computer science, Alan Turing (1912–1954) as a case study, I will carefully examine his three stages of self-reconceptualisation and highlight the relevance of seeing spirituality as self-reconceptualisation for the current digital age.     

Verisimilitude and Belief Change for Conjunctive Theories

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results.     

The very idea of a social science

In The Idea of a Social Science Winch, argues that, sociology is more properly conceived as a branch of philosophy than of empirical science. Winch falls victim here to the Humean assimilation of the empirical to the generalizable. He notes that much of our talk about social practice is in terms of conventions, so that explanations of social action can be given without recourse to statistical or experimental findings. But such talk depends nonetheless on the accuracy and detail with which the situations in which actions occur are‐ recorded, and this is surely an empirical enterprise. It is the misleading conception of sociology as a discipline, characterized by common procedures, that leads Winch to espouse the assimilation of sociology to conceptual inquiry. We need to see instead that sociology embraces a group of questions and subjects so loosely connected that it would be mistaken to speak of, and idle to project, a procedure common to all of them.     

Truth Analysis of the Gettier Argument

Gettier (1963) presented the now famous Gettier problem as a challenge to epistemology. The methods Gettier used to construct his challenge, however, utilized certain principles of formal logic that are actually inappropriate for the natural language discourse of the Gettier cases. In that challenge to epistemology, Gettier also makes truth claims that would be considered controversial in analytic philosophy of language. The Gettier challenge has escaped scrutiny in these other relevant academic disciplines, however, because of its façade as an epistemological analysis. This article examines Gettier's methods with the analytical tools of logic and analytic philosophy of language.     

Digital Animation as a Method to Disseminate Research Findings to the Community Using a Community-Based Participatory Approach

Community-based participatory research (CBPR) has garnered increasing interest over the previous two decades as researchers have tackled increasingly complex health problems. In academia, professional presentations and articles are major ways that research is disseminated. However, dissemination of research findings to the people and communities who participated in the research is many times forgotten. In addition, little scholarly literature is focused on creative dissemination of research findings to the community using CBPR methods. We seek to fill this gap in the literature by providing an exemplar of research dissemination and partnership strategies that were used to complete this project. In this paper, we present a novel approach to the dissemination of research findings to our targeted communities through digital animation. We also provide the foundational thinking and specific steps that were taken to select this specific dissemination product development and distribution strategy.     

Truth,relativism and western conceptions of indian philosophy

We (relatively few) Western analytic philosophers who also work on classical Indian philosophy commonly encounter puzzlement or suspicion from our colleagues in Western philosophy because of our Indian interests. The ubiquity of these attitudes is itself revealing of Western conceptions of Indian philosophy, though their origins lie in cultural history often unknown to those who hold them. In the first part of this paper I relate a small but significant slice of that history before going on to distinguish and illustrate three different Western conceptions of Indian philosophy associated with three different approaches to India: the magisterial, the exoticist and the curatorial. I argue that none of these three approaches gives us an adequate conception of Indian philosophy: the magisterial approach is overly dismissive, the exoticist approach misrepresents the analytical achievements of Indian philosophy, and the curatorial approach fails to take seriously Indian philosophy's concern with truth. I advocate instead a different Western approach to Indian philosophy, an approach suggested by the Indian philosophers’ own discussions of the problem of truth.     

The Ideal of African Scholarship and its Implications for Introductory Philosophy: the Example of Placide Tempels

Abstract

Thinking of an academic discipline in terms of a ‘social practice’ (MacIntyre) helps in formulating what the ideal captured in the slogan ‘African scholarship’ can contribute to the discipline. For every practice is threatened by the attractiveness of goods external to the practice–in particular, competitiveness for its own sake–and to counter this virtues of character are needed. African traditional culture prioritizes a normative picture of the human person which could very well contribute here to upholding the values internal to scholarship. I argue, contrary to Matolino, that for these purposes Tempels’ notion of the transactional process of becoming more of what you are by virtue of the human insertion in nature, is a useful starting point. But the dominant way philosophy is framed today, the human person outside of ‘nature’, omitting the key notion of presence-to-self, disallows this dialogue between the dominant tradition and African thought culture. I show, by interrogating what I take to be an impoverished understanding of objectivity in the dominant philosophical approach, how the idea of personal, subjective, growth is crucial to introductory philosophy if the project of African scholarship is to find purchase. As an example I look at rival ways of understanding the value of justice, procedurally or, alternatively, substantively and hence foregrounding participation.¹     

Innovations in computational type theory using Nuprl

For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT)—a formal theory of computation closely related to Martin-Löf's intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover.

This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures.

We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howe's set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers.