This paper is intended to give for a general mathematical audience a survey of intriguing connections between analytic combinatorics and logic. We define the ordinals below ε0 in non-logical terms and we survey a selection of recent results about the analytic combinatorics of these ordinals. Using a versatile and flexible compression technique we give applications to phase transitions for independence results, Hilbert’s basis theorem, local number theory, Ramsey theory, Hydra games, and Goodstein sequences. We discuss briefly (...) universality and renormalization issues in this context. Finally, we indicate how regularity properties of ordinal count functions can be used to prove logical limit laws. (shrink)

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and (...) proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to (...) the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with k≥1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (Citation2020) as well as enriched with some previous results from Kostrzycka and Zaionc (Citation2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (Citation2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches. (shrink)

We consider logical expressions built on the single binary connector of implication and a finite number of literals . We prove that asymptotically, when the number of variables becomes large, all tautologies have the following simple structure: either a premise equal to the goal, or two premises which are opposite literals.

Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. of (...) the LMS 14 285–293]) and Harvey Friedman [S.G. Simpson, Non-provability of certain combinatorial properties of finite trees, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 87–117; R. Smith, The consistency strength of some finite forms of the Higman and Kruskal theorems, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 119–136] who produced the first mathematically interesting independence results in Ramsey theory and well-order and well-quasi-order theory .In this article we investigate Friedman-style principles of combinatorial well-foundedness for the ordinals below ε0. These principles state that there is a uniform bound on the length of decreasing sequences of ordinals which satisfy an elementary recursive growth rate condition with respect to their Gödel numbers.For these independence principles we classify their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability in the induced combinatorial well-foundedness principles.As Gödel numbering for ordinals we choose the one which is induced naturally from Gödel’s coding of finite sequences from his classical 1931 paper on his incompleteness results.This choice makes the investigation highly non-trivial but rewarding and we succeed in our objectives by using an intricate and surprising interplay between analytic combinatorics and the theory of descent recursive functions. For obtaining the required bounds on count functions for ordinals we use a classical 1961 Tauberian theorem of Parameswaran which apparently is far remote from Gödel’s theorem. (shrink)

In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multiset-construction, cycle-construction and labeled-tree-construction. Provability proofs use the asymptotic pigeonhole principle, unprovability proofs use Weiermann-style compression techniques and results from analytic combinatorics.

Drug design methods have made significant new advances over the last ten years, mainly in the areas of molecular modelling. In more recent times important developments in theory have led to a different type of modelling becoming possible, the so‐called de novo or automated design algorithms. In this new method the programs perform much of the chemist's thinking, in finding appropriately sized chemical groups to fit into a target site. However this is a combinatoric problem which has no general analytical (...) solution; it is ripe for optimization. Other advances, such as combinatorial chemical synthesis and screening, will dramatically influence the search for new lead structures for target sites, which at present are poorly understood. Already these methods are being applied to peptide libraries. Peptides do not make good drug compounds because of their poor bioavailability; further, their flexibility reduces their affinity. In some cases peptide backbones can be removed and replaced with rigid non‐peptide scaffolds. (shrink)

It is conventionally understood that computers play a rather limited role in theoretical mathematics. While computation is indispensable in applied mathematics and the theory of computing and algorithms is rich and thriving, one does not, even today, expect to find computers in theoretical mathematics settings beyond the theory of computing. Where computers are used, by those studying combinatorics , algebra, number theory, or dynamical systems, the computer most often assumes the role of an automated and speedy theoretician, performing manipulations (...) and checking cases in a way assumed to be possible for human theoreticians, if only they had the time, the memory, and the precision. Automated proofs have become standard tools in mathematical logic, and it is often expected that proofs be published in a computer-checkable format. It is not surprising, then, that most philosophical work on computers in theoretical mathematics has been on computers' roles as supplementary mathematicians. Donald MacKenzie's 2001 book Mechanizing Proof demonstrates the rich potential for social and historical studies to complement the substantial analytic debate in this area of philosophy. But what of computers in theoretical mathematics behaving as computers, and not as mere mechanized mathematicians? Very little role is commonly assumed for computers working as supplements to mathematicians, rather than as supplementary mathematicians themselves. Accordingly, very little philosophy has attempted to grapple with theoretical mathematics in which computers play an essential but essentially non-theoretical role. My presentation will draw on work I conducted as a researcher in harmonic analysis on fractals at Cornell University. I will analyze the explicit and implicit conceptual apparatus employed in my and my fellow researchers' use of computers in the theoretical study of second order differential equations, such as those for sound and heat flow, on various fractal analogues of the Sierpinski gasket. Such gaskets are easy to visualize in very crude approximation in a low number of dimensions. As one increases the complexity of the gasket or the refinement of one's analysis, visualization and precise computation become impossible, and soon computers are unable to produce even approximate data to model differential equations in these situations. We thus had to carefully choose analytic approaches and methods to make our theoretical mathematics amenable to computer simulation. In my case, studying the transformation of the gaskets as they are expanded into increasingly high dimensions, computer simulation eventually required that the problem be reimagined entirely in terms of interlinked systems of parameters. This computer-approximation-driven theoretical orientation shaped my mathematical intuitions toward the problem and guided my fellow researchers and me in both theoretical and computational directions. We discovered both that computer approximation could be incredibly powerful as an aid to intuition, and that it can be incredibly difficult to transfer computer-oriented mathematics back into the purely theoretical standards of our area of specialty. I will address the philosophical implications of computer-driven theoretical mathematics, asking how computer experiments can shape both the content and standards of theoretical sciences. (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

Using quantitative methods, we investigate the role of logic in analytic philosophy from 1941 to 2010. In particular, a corpus of five journals publishing analytic philosophy is assessed and evaluated against three main criteria: the presence of logic, its role and level of technical sophistication. The analysis reveals that logic is not present at all in nearly three-quarters of the corpus, the instrumental role of logic prevails over the non-instrumental ones, and the level of technical sophistication increases in (...) time, although it remains relatively low. These results are used to challenge the view, widespread among analytic philosophers and labeled here “prevailing view”, that logic is a widely used and highly sophisticated method to analyze philosophical problems. (shrink)

This book offers an unprecedented quantitative portrait of analytic philosophy focusing on two seemingly marginal features of philosophical texts: citations and acknowledgements in academic publications. Originating from a little network of philosophers based in Oxford, Cambridge, and Vienna, analytic philosophy has become during the Twentieth century a thriving philosophical community with thousands of members worldwide. Leveraging the most advanced techniques from bibliometrics, citations and acknowledgments are used in this book to shed light on both the epistemology and the (...) sociology of this philosophical field, illuminating the intellectual trajectory of analytic philosophy as well as the social characteristics of the analytic community. Special attention is dedicated to the last forty years, providing insights into a phase of analytic philosophy which is still understudied by historians of philosophy. In the eight chapters of the book, readers will find not only numerous quantitative investigations and technical explanations, but also a robust theoretical framework and epistemological reflections on the strengths and limitations of quantitative methods for the study of philosophy. With its strong interdisciplinary appeal, this book will engage a wide range of scholars, including historians of philosophy seeking new methodologies, analytic philosophers interested in a new look at their discipline, and scholars in digital humanities, bibliometrics, and quantitative studies of science, who will find many innovative techniques for investigating disciplinary fields. (shrink)

We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

This paper introduces the philosophy of Grace Andrus de Laguna in order to renew interest in it. I show that, in the 1910s and 1920s, she develops ideas and arguments that are also found playing key roles in the development of analytic philosophy decades later. Further, I describe her sympathetic, but acute, criticism of pragmatism and Heideggerian ontology, and situate her work in the tradition of American, speculative philosophy. Before 1920, we will see, de Laguna appeals to multiple realizability (...) to undermine reductionism in science, to support perspectival, scientific realism and, with help from a private language argument, to favour the view that mental states are classified by behavioural, teleological roles over what came to be called ‘type physicalism’. Her view of speech, mostly developed in the 1920s, tells us that its primary role is coordinating group behaviour rather than expressing thoughts. Belief is understood in terms of its causal role, including its causal relations to other kinds of mental states, when coordinating group behaviour. Thought is similarly understood. In developing her theory of mind, de Laguna rejects the pragmatist claims that belief can be reduced to dispositions to behaviour and that thought’s function is to address specific, rather than general, problems. She also favours meaning holism and rejects the analytic–synthetic distinction. In later work, de Laguna argues that individuals’ activity of self-maintenance brings universals, conceived of as irreducible potentialities, into being and makes them increasingly determinate. Further, she identifies the existence of all individuals with forms of self-maintenance and takes the existence of people to include maintenance of the cultural world. Such a unified treatment of existence, she holds, permits making its evolution intelligible. Heidegger’s view of being is rejected for not permitting this. All de Laguna’s work, we will see, fits a vision of philosophy as the systematic, imaginative and naturalistic examination of being as well as a source of criticism of science. (shrink)

We give a direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey.

There is a rather widespread consensus, among historians of philosophy, concerning the decline of Wittgenstein amid recent analytic philosophy. However, the exact import of such a decline,...

Analytic philosophy is roughly a hundred years old, and it is now the dominant force within Western philosophy. Interest in its historical development is increasing, but there has hitherto been no sustained attempt to elucidate what it currently amounts to, and how it differs from so-called 'continental' philosophy. In this rich and wide-ranging book, Hans Johann Glock argues that analytic philosophy is a loose movement held together both by ties of influence and by various 'family resemblances'. He considers (...) the pros and cons of various definitions of analytic philosophy, and tackles the methodological, historiographical and philosophical issues raised by such definitions. Finally, he explores the wider intellectual and cultural implications of the notorious divide between analytic and continental philosophy. His book is an invaluable guide for anyone seeking to understand analytic philosophy and how it is practised. (shrink)

Whether Trinitarianism is coherent depends not only on whether some account of the Trinity is coherent, but on which accounts of the Trinity count as "Trinitarian." After all, Arianism and Modalism are both accounts of the Trinity, but neither counts as Trinitarian (which is why defenses of Arianism or Modalism don’t count as defenses of Trinitarianism). This raises the question, if not just any account of the Trinity counts as Trinitarian, which do? Dale Tuggy is one of very few philosophers (...) to give explicit definitions of Trinitarian (versus Unitarian) theology. But they are no mere formalities. They are essential to his central criticisms of both historical and contemporary forms of Trinitarianism. In this paper, I offer my own definitions of Trinitarian and Unitarian theology, contrast them with Tuggy’s, and argue for the superiority of my definitions to Tuggy’s. If Trinitarianism and Unitarianism are what Tuggy says they are, the outlook for Trinitarianism is bleak indeed. If they are what I say they are, Tuggy’s central objection to Trinitarianism fails. To show what is at stake in these pairs of definitions, I examine a doctrine much neglected in Analytic Theology, but central to Nicene Trinitarianism—the Monarchy of the Father. (shrink)

This book offers a clear, analytic, and innovative interpretation of Heidegger's late work. This period of Heidegger's philosophy remains largely unexplored by analytic philosophers, who consider it filled with inconsistencies and paradoxical ideas, particularly concerning the notions of Being and nothingness. This book takes seriously the claim that the late Heidegger endorses dialetheism--namely the position according to which some contradictions are true--and shows that the idea that Being is both an entity and not an entity is neither incoherent (...) nor logically trivial. The author achieves this by presenting and defending the idea that reality has an inconsistent structure. In doing so, he takes one of the most discussed topics in current analytic metaphysics, grounding theory, into a completely unexplored area. Additionally, in order to make sense of Heidegger's concept of nothingness, the author introduces an original axiomatic mereological system that, having a paraconsistent logic as a base logic, can tolerate inconsistencies without falling into logical triviality. This is the first book to set forth a complete and detailed discussion of the late Heidegger in the framework of analytic metaphysics. It will be of interest to Heidegger scholars and analytic philosophers working on theories of grounding, mereology, dialetheism, and paraconsistent logic. (shrink)

In this paper, we consider the implications of Grace de Laguna and Joel Katzav's work for the charge of conservatism against the analytic tradition. We differentiate that conservatism into three kinds: starting place; path dependency; and modesty. We also think again about gender in philosophy, consider the positive account of speculative philosophy presented by de Laguna and Katzav in comparison to some other naturalist trajectories, and conclude with a brief Australian addendum that reflects on a similar period in our (...) own country which was also associated with the professional institutionalisation of analytic philosophy. (shrink)

Some time ago, the philosopher Luciano Floridi suggested that Western philosophy, and the mainstream contemporary approach to it traditionally called ‘analytic philosophy’, is in dire need of a reboot. The concern was that the discipline might be in a period of decadence. Analytic philosophy would be benefited by greater internationalization, wider and more transparent decision-making, and the reduction (as much as possible) of conflicts of interest as well as of its current habit of hiring and providing publication opportunities (...) on the basis of contacts, networking, and academic pedigree. If we are right, then we need a reconditioning of the institutional framework of analytic philosophy that adjusts it to the current global and interconnected world. (shrink)

Conceptual engineering is the method (or methods) via which we can assess and improve our concepts. Can conceptual engineering be usefully employed within analytic theology? Given that analytic theology and analytic philosophy effectively share the same philosophical toolkit then if conceptual engineering works well in philosophy then it ought to work well in analytic theology too. This will be our working hypothesis. To make good on this hypothesis, we first address two challenges. The first challenge makes (...) conceptual engineering look to be too inclusive; the second challenge makes it look to be too revolutionary (for analytic theology). To address these challenges, we propose a refined characterisation of conceptual engineering. We then turn to consider a number of case studies where analytic theology and conceptual engineering may fruitfully cooperate. These are: theological disagreements, inter-faith dialogue, meaning change, celibacy, AI, the name of God, and conceptual genealogy. (shrink)

In this paper I build a case for considering the pioneering behaviourist philosopher Grace de Laguna as one of the grandmothers of analytic philosophy. I argue against the ‘Great Men’ narrative of analytic philosophy as composed of Moore, Russell, Wittgenstein and their followers, and in favour of a more inclusive ‘movement’ narrative of analytic philosophy as a broad and varied movement with an anti-idealist and naturalistic orientation aimed at fitting around novel development in the sciences, including Einsteinian (...) physics and psychology. I compare de Laguna’s prescient early views to Whitehead’s; both share an anti-idealist but also anti-atomist solution to the problem of perception, and both oppose the bifurcation of nature, with de Laguna expressing these views before Whitehead did. I conclude that while both opposed the narrower project of logical atomism, both count as ancestors of the wider analytic movement. (shrink)

Analytic theology has sometimes been criticized as ahistorical. But what this means, and why it is problematic, have often been left unclear. This essay explicates and supports one way of making that charge while simultaneously showing this ahistoricity, although widespread within analytic theology, is not essential to it. Specifically, some analytic theologians treat problematic doctrines as metaphysical puzzles, constructing speculative accounts of phenomena such as the Trinity or Incarnation and taking the theoretical virtues of such accounts to (...) be sufficient in themselves to defend traditional doctrines with no need for additional, historical premises. But due to the different epistemic structures of metaphysical and theological puzzles, I argue that importing this methodology into philosophical theology results in invalid or question-begging arguments, and it is unclear how a virtue-centric methodology could be repaired without collapsing into a more historical methodology, which some of the best (but unfortunately not all) analytic theologians follow. (shrink)

This essay presupposes that Friedrich Nietzsche and Rudolf Carnap champion contrasting reactions to the fact that, throughout history, persons have been engaged in metaphysical disputes. Nietzsche embraces a libertarian reaction that is in agreement with his anti-democratic aristocratic political views, whereas Carnap endorses an egalitarian reaction aligned with his democratic and socialist political views. After characterizing these reactions, the essay argues for two claims. The first claim is that the stated contrasting reactions are to be considered, not only by the (...) few scholars who are interested both in Nietzsche’s and Carnap’s writings, but by a far larger group that includes those who have addressed the continental-analytic gap; those who are concerned with the development of contemporary philosophy; and/or those who are interested in the writings of Michel Foucault, Jacques Derrida, David Lewis and/or Peter van Inwagen. The second claim is that we have to entertain a synthesis of Nietzsche’s libertarian and Carnap’s egalitarian reaction in order to overcome the continental-analytic gap. (shrink)

An important collection of essays that rectifies a long-standing misconception in the history of the relation between Hegel and analytic philosophy.>.

The apparently circular arguments in Descartes’s Meditations should be read as analytic arguments, as Descartes himself suggested. This both explains and excuses the appearance of circularity. Analysis “digs out” what is already present in the meditator’s mind but not yet “expressly known”. Once this is achieved, the meditator may take the result of analysis as an epistemic starting point independent of the original argument. That is, analytic arguments may be reversed to yield demonstrative proofs that follow an already (...) worked-out order of ideas. The “Cartesian Circle,” for example, is circular only when Descartes’s original analytic argument is mistaken for the demonstration that it enables. This approach to Cartesian Circles is unlike the standard approach, which attempts to show that Descartes’s original arguments do work as demonstrations after all. (shrink)

The endorsement of epistemically suspect (i.e., paranormal, conspiracy, and pseudoscientific) beliefs is widespread and has negative consequences. Therefore, it is important to understand the reasoning processes – such as lower analytic thinking and susceptibility to cognitive biases – that might lead to the adoption of such beliefs. In two studies, I constructed and tested a novel questionnaire on epistemically suspect beliefs (Study 1, N = 263), and used it to examine probabilistic reasoning biases and belief bias in syllogistic reasoning (...) as predictors of the endorsement of those beliefs, while accounting for analytic thinking and worldview variables (Study 2, N = 397). Probabilistic reasoning biases, analytic thinking, religious faith, and political liberalism consistently predicted various epistemically suspect beliefs, whereas the effect of syllogistic belief bias was largely restricted to pseudoscientific beliefs. Further research will be needed to examine the role the biased evaluation of evidence plays in the endorsement of epistemically suspect beliefs. (shrink)

In the course of this article, I address the following question: why does analytic philosophy, which predominates throughout higher education in the United Kingdom, not feature prominently in UK madrasas (Islamic schools)? I provide two responses to this question. The first focuses on a possible intellectual conflict between the types of philosophy that are practiced in madrasas and in mainstream institutions of higher education. The second response focuses on the kind of philosophy that various organizations promote and practice in (...) communities of philosophic inquiry (CPI). These responses illustrate the conceptual and institutional reasons for madrasas’ reluctance toward analytic philosophy. Finally, I offer specific recommendations intended to help facilitate the introduction of analytic philosophy into madrasa curricula in the UK. (shrink)

There has been a growing interest within analytic philosophy in addressing political and social issues, which has been referred to as the “political turn” in the discipline. The aim of this paper is twofold. First, it discusses the very characterization of the political turn. In particular, it introduces the definition proposed by Bordonaba-Plou, Fernández-Castro, and Torices, suggests that we should not consider the turn a form of activism, and explores an additional benefit of the ideal/nonideal distinction for characterizing the (...) turn. Second, it addresses the concern of what attitude we should take in the face of the different sensitivities we might have with respect to what constitutes an injustice. Which philosophical works should count as part of the political turn? The paper explores three different attitudes toward this dilemma, and favors what it calls the revisionist attitude, which emphasizes the fact that our perception of injustice is subject to error. (shrink)

This is the second paper in the invited collection. Dieleman provides an overview of the “state-of-the-field” debate between Analytic Social Epistemology, represented by Alvin Goldman, and what Dieleman calls the Sociological Social Epistemology, represented by Steve Fuller. In response to this ongoing debate, this paper has two related and complementary objectives. The first is to show that the debate between analytic and sociological versions of social epistemology is overly simplistic and doesn’t take into account additional positions that are (...) available and, indeed, have been available since social epistemology was introduced in the mid to late 1980s. The second is to uncover and tell a story of how Lorraine Code’s Epistemic Responsibility is one such additional position. Looking to Code's Epistemic Responsibility reveals the artificiality of the debate between analytic and sociological social epistemologists. (shrink)

I revisit my paper, ‘Grace de Laguna’s 1909 Critique of Analytic Philosophy’ and respond to the commentary on it. I respond to James Chase and Jack Reynolds by further analysing the difference between speculative philosophy as de Laguna conceived of it and analytic philosophy, by clarifying how her critique of analytic philosophy remains relevant to some of its more speculative forms, and by explaining what justifies the criticism of established opinion that goes along with her rejection of (...) analytic philosophy’s epistemic conservatism. In response to Andreas Vrahimis, I contextualise my reading of de Laguna’s work in 1909. This clarifies her critique of pragmatism, distinguishes it from her critique of epistemically conservative philosophy, and shows that she was not only already aware of the full scope of the latter critique but is likely to have identified the then incipient analytic philosophy as its primary target. Also, contra Vrahimis, her argument is effective against Bertrand Russell’s later, epistemically conservative approach to philosophy. In response to Cheryl Misak, I point out that her argument that de Laguna is, despite herself, a pragmatist rests on a misunderstanding of the differences between pragmatism and idealism, and I show that de Laguna’s main early influences were Herbert Spencer and her teacher, James Edwin Creighton. I further argue that Misak’s rejection of de Laguna’s critique of pragmatism rests on a misrepresentation of the critique. (shrink)

This thesis articulates an analytic version of the ontology of idealism, according to which universal phenomenal consciousness is all there ultimately is, everything else in nature being reducible to patterns of excitation of this consciousness. The thesis’ key challenge is to explain how the seemingly distinct conscious inner lives of different subjects—such as you and me—can arise within this fundamentally unitary phenomenal field. Along the way, a variety of other challenges are addressed, such as: how we can reconcile idealism (...) with the fact that we all inhabit a common external world; why this world unfolds independently of our personal volition or imagination; why there are such tight correlations between measured patterns of brain activity and reports of experience; etc. The core idea of this thesis can be summarized thus: we, as well as all other living organisms, are dissociated alters of universal phenomenal consciousness, analogously to how a person with Dissociative Identity Disorder (DID) manifests multiple disjoint centers of subjectivity also called ‘alters.’ We, and all other living organisms, are surrounded by the transpersonal phenomenal activity of universal consciousness, which unfolds beyond the dissociative boundary of our respective alter. The inanimate world we perceive around us is the extrinsic appearance—i.e. the phenomenal image imprinted from across our dissociative boundary—of this activity. The living organisms we share the world with are the extrinsic appearances of other alters. (shrink)