Based on an original ethnographic study of a translational cancer research institute in the United States, we propose calibration as a process that makes interdisciplinary collaboration without consensus possible. Calibration refers to ongoing, day-to-day negotiation and alignment of personal identities, disciplinary commitments, and research group customs that occur during face-to-face group deliberations around everyday research concerns. Calibration provides a mechanism that explains how collaboration without consensus is possible. Crucially, it does not presuppose that interdisciplinary collaboration either indicates or causes the (...) blurring or softening of disciplinary boundaries. We argue that at the microsociological level it may be disciplinary robustness, rather than synthesis, that contributes to interdisciplinary innovation. (shrink)

Can an event’s blameworthiness distort whether people see it as intentional? In controversial recent studies, people judged a behavior’s negative side effect intentional even though the agent allegedly had no desire for it to occur. Such a judgment contradicts the standard assumption that desire is a necessary condition of intentionality, and it raises concerns about assessments of intentionality in legal settings. Six studies examined whether blameworthy events distort intentionality judgments. Studies 1 through 4 show that, counter to recent claims, intentionality (...) judgments are systematically guided by variations in the agent’s desire, for moral and nonmoral actions alike. Studies 5 and 6 show that a behavior’s negative side effects are rarely seen as intentional once people are allowed to choose from multiple descriptions of the behavior. Specifically, people distinguish between “knowingly” and “intentionally” bringing about a side effect, even for immoral actions. These studies suggest that intentionality judgments are unaffected by a behavior’s blameworthiness. (shrink)

Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...) by the groupoid model of (intensional) Martin–Löf type theory [14] due to Hofmann and Streicher [9]. In particular, we show that a form of Martin–Löf type theory can be soundly modelled in any model category. This result indicates moreover that any model category has an associated “internal language” which is itself a form of Martin-Löf type theory. This suggests applications both to type theory and to homotopy theory. Because Martin–Löf type theory is, in one form or another, the theoretical basis for many of the computer proof assistants currently in use, such as Coq and Agda (cf. [3] and [5]), this promise of applications is of a practical, as well as theoretical, nature. This paper provides a precise indication of this connection between homotopy theory and logic; a more detailed discussion of these and further results will be given in [20]. (shrink)

Examining the origin and development of my views of social epistemology, I contrast my position with the position held by analytic social epistemologists. Analytic social epistemology (ASE) has failed to make significant progress owing, in part, to a minimal understanding of actual knowledge practices, a minimised role for philosophers in ongoing inquiry, and a focus on maintaining the status quo of epistemology as a field. As a way forward, I propose questions and future areas of inquiry for a post-ASE to (...) address. (shrink)

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...) case 2.In the present work, we generalize the entire arrangement from propositional to first-order logic, using a representation result of Butz and Moerdijk. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed primarily in the form of a contravariant adjunction, is established by homming into a common dualizing object, now Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we give an elementary proof of Butz and Moerdijkʼs result in logical terms. (shrink)

This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

The purpose of this informal survey article is to introduce the reader to a new and surprising connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Per Martin-Löf into homotopy theory and higher-dimensional category theory.

This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of (...) ways, including topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright. (shrink)

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along (...) the way. (shrink)

‘Academic rentiership’ is an economistic way of thinking about the familiar tendency for academic knowledge to consolidate into forms of expertise that exercise authority over the entire society. The feature that ‘rentiership’ high-lights is control over what can be accepted as a plausible knowledge claim, which I call ‘modal power’. This amounts to how the flow of information is channelled in society, with academic training and peer-reviewed research being the main institutional drivers. This paper begins by contextualizing rentiership in the (...) deeper issues surrounding ‘cognitive economy ’that lie at the heart of the Western philosophical tradition. The psychological phenomenon of the ‘Gestaltshift’ is used to illustrate various ways in which the flow of information can be channelled to enable or disable certain possible ways of regarding the world. Against this background, such familiar concepts from academic practice as ‘quality control’ and ‘plagiarism’ acquire a new look. Quality control aims to maintain rentiership, whereas plagiarism aims to undermine it. The second half of the paper is largely concerned with the historical swings back and forth between rentiership and anti-rentiership in academia. Rentiership’s decline is associated with corruption of its quality control processes, which reveals academia’s reliance on equally corrupt power elites in society. In addition, the introduction of new communication media over which academia cannot exert proprietary control also serves to open up the sphere of plausible knowledge claims. The ongoing Internet revolution is likely to permanently alter the terms on which academic rentiership will be possible in the future. (shrink)

In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir Voevodsky’s univalent interpretation of it. This interpretation has given rise to the univalent foundations program, which is the topic of the current special year at the Institute for Advanced Study.

"Social epistemology" refers here to the work of analytic epistemologists and philosophers of science interested in providing an empirically adequate account of organized knowledge systems, with special emphasis on scientific inquiry. I critically survey the last ten years of this research. Unlike the pragmatist and Continental schools of philosophy, for which knowledge is "always already" social, progress in analytic social epistemology has been plagued by an oversharp distinction between individual and collective cognition; and a failure to query the ends of (...) science in addition to its means. Consequently, most analytic social epistemologists operate with a relatively weak sense of "normativity," one modelled more on taken-for-granted logical principles than legislated policy correctives. (shrink)

This article is the preface to the Russian translation of my Kuhn vs Popper. I use it as an opportunity to re-examine the difference between Kuhn and Popper on the nature of ‘revolutions’ in science. Kuhn is rightly seen as a ‘reluctant revolutionary’ and Popper a ‘permanent revolutionary’. In this respect, Kuhn sticks to the original medieval meaning of ‘revolution’ as restoration of a natural order, whereas Popper adopts the more modern meaning of ‘revolution’ that comes into fashion after the (...) French Revolution, which suggests a radical renewal. A key to understanding this difference in revolutionary mentalities lies in Kuhn’s and Popper’s respective treatment of the ‘Gestalt switch’ phenomenon. Kuhn sees the ambiguous Gestalt figure from the standpoint of the subject, and Popper from that of the experimenter. Behind this difference lies alternative interpretations of the significance of quantum mechanics for scientific epistemology, a preoccupation that Kuhn and Popper shared with the original Gestalt psychologists and is beginning engage the interest of social scientists. (shrink)

As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.

This article explores the proposition that the brain, normally seen as an organ of the human body, should be understood as a biologically based form of artificial intelligence, in the course of which the case is made for a new kind of ‘brain exceptionalism’. After noting that such a view was generally assumed by the founders of AI in the 1950s, the argument proceeds by drawing on the distinction between science—in this case neuroscience—adopting a ‘telescopic’ or a ‘microscopic’ orientation to (...) reality, depending on how it regards its characteristic investigative technologies. The paper concludes by recommending a ‘microscopic’ yet non-reductionist research agenda for neuroscience, in which the brain is seen as an underutilised organ whose energy efficiency is likely to outstrip that of the most powerful supercomputers for the foreseeable future. (shrink)

The SAGE Handbook of Complexity and Management will be the first substantive scholarly work to provide a map of the state of art research in the growing field ...

Robert Pirsig wrote of Steve Hagen's first book, Why the World Doesn't Seem to Make Sense, "For those who are certain that objectivity and intellect are the ground floor of all knowledge, this can be a valuable trip to the sub-basement." Now, in The Grand Delusion, Hagen drills deeper, into the most basic strengths, assumptions, and limitations of religion and belief, philosophy and inquiry, science, and technology. In doing so, he shines new light on the question Why is there (...) Something rather than Nothing?-and shines this light from an entirely unexpected (and largely unexplored) direction. Using a provocative mix of examples from physics, philosophy, religion, myth, neuroscience, and mathematics-and a clever, shade-throwing Socratic dialogue between Hagen and his foil, "ANYONE"-this book also offers a fresh perspective on other questions that science, philosophy, and religion have long grappled with. Such topics include: · What does it mean to exist? · What is mind? · What constitutes a measurement? · What exactly is motion? Layer by layer, Hagen examines the questions we ask, the way we ask them, the assumptions and beliefs we hold dear, and the ways in which we separate ourselves from the very answers we seek. In the process, he draws on sources that include Huang Po, Richard Feynman, Sir Arthur Eddington, Hui-Neng, Susan B. Anthony, Daniel Dennett, Joseph Campbell, Dogen, Emily Dickinson, Nagarjuna, Ikkyu, William I. McLaughlin, Sam Harris, and Henry David Thoreau. Ultimately, this book reveals how all of these fundamental questions-and many, many more-stem from a single error, a single unwarranted belief, a single Grand Delusion. The Grand Delusion helps readers move past this delusion into insight that can settle these age-old and seemingly intractable questions. (shrink)

Christian Quast has presented what he describes as a ‘role-functional’ account of expertise as a form of knowledge that purports to take into account prior discussions within recent analytic social epistemology and allied fields. I argue that his scrupulousness results in a confused version of the role-functional account, which I try to remedy by presenting a ‘clean’ account that clearly distinguishes such an account from what Quast calls a ‘competence-driven’ one. The key point of my account is that ‘competence’ pertains (...) to knowledge in closed systems and ‘expertise’ in open systems. I observe that the invocation of ‘reliability’ as an epistemic standard simply serves to confuse the difference between the competence-driven and role-functional accounts. (shrink)

The failed criterion of logical truth proposed by Carnap in the Logical Syntax of Language was based on the determinateness of all logical and mathematical statements. It is related to a conception which is independent of the specifics of the system of the Syntax, hints of which occur elsewhere in Carnap’s writings, and those of others. What is essential is the idea that the logical terms are invariant under reinterpretation of the empirical terms, and are therefore semantically determinate. A certain (...) objection to Carnap’s version of the invariance conception has been repeated several times in the literature. It is based on Gödel incompleteness, which is puzzling, since Carnap’s Syntax is otherwise quite careful to take account of Gödel. We show here that, in fact, the objection is invalid and is based on a confusion about determinacy. Sorting this out is worthwhile not only for the purpose of better understanding Carnap’s thinking in the Syntax, though. The invariance conception is also related to recent work in the philosophy of logic regarding “logicality”—the characterization of logical concepts—following a proposal of Tarski’s. It is even connected to some very recent developments in the foundations of mathematics. (shrink)

James McAllister’s 2003 article, “Algorithmic randomness in empirical data” claims that empirical data sets are algorithmically random, and hence incompressible. We show that this claim is mistaken. We present theoretical arguments and empirical evidence for compressibility, and discuss the matter in the framework of Minimum Message Length (MML) inference, which shows that the theory which best compresses the data is the one with highest posterior probability, and the best explanation of the data.

A Cantor series expansion for a real number x with respect to a basic sequence $Q=(q_1,q_2,\dots )$, where $q_i \geq 2$, is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $\boldsymbol {\Pi }^0_3$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio (...) normality, and distribution normality. These notions are equivalent for base b expansions, but not for more general Cantor series expansions. We show that for any basic sequence the set of distribution normal numbers is $\boldsymbol {\Pi }^0_3$ -complete, and if Q is $1$ -divergent then the sets of normal and ratio normal numbers are $\boldsymbol {\Pi }^0_3$ -complete. We further show that all five non-trivial differences of these sets are $D_2(\boldsymbol {\Pi }^0_3)$ -complete if $\lim _i q_i=\infty $ and Q is $1$ -divergent. This shows that except for the trivial containment that every normal number is ratio normal, these three notions are as independent as possible. (shrink)

Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements.

In this paper I make more explicit a position that I have being advocating for more than two decades, though its full force does not seem to have been felt. I write in defence of the *commodification* rather than the simple *commercialisation* of knowledge. The two italicised terms are often spoken about in the same breath—and, to be sure, they are related to each other. But they are not the same. Commercialisation refers to the subjection of social life to the (...) price mechanism, something that Adam Smith believed happened spontaneously, if it was not impeded by churches and states. And while Smith’s celebration of commercial culture makes him the philosophical father of capitalism, he would probably not approve of capitalism’s long-term tendency to turn aggregated versions of these spontaneous exchanges into objects that are themselves subject to exchange relations, which is commodification. Nevertheless, it is precisely in this sense of ‘commodification’ that I defend the university as a producer of knowledge as a public good, both in terms of teaching and research. I place the shi from commercialisation to commodification in a larger historical context first clearly identified by Ernst Cassirer – namely, a shi in metaphysical consciousness that accompanied the treatment of substances as the bearers of functions, which is associated with the introduction of algebra as a unifying principle of mathematical reasoning in the early modern era, initially through Descartes, which then became the basis of the modern physical world-view. (shrink)

A rich collection of critical essays, authored by philosophers and practicing artists, examining Deleuze and Guattari's engagement with a broad range of art forms.

The classical conception of academic freedom associated with Wilhelm von Humboldt and the rise of the modern university has a quite specific cultural foundation that centres on the controversial mental faculty of 'judgement'. This article traces the roots of 'judgement' back to the Protestant Reformation, through its heyday as the signature feature of German idealism, and to its gradual loss of salience as both a philosophical and a psychological concept. This trajectory has been accompanied by a general shrinking in the (...) scope of academic freedom from the promulgation of world-views to the offering of expert opinion. (shrink)

This paper focuses on the ethical and moral implications of findings from the authors? national survey of television news directors? policies, practices, and perceptions of good/bad news. In light of the potentially negative effects of excessive amounts of bad news on individuals and society, the authors ask whether television journalists have an ethical responsibility?beyond legal constraints and professional criteria?in the selection and presentation of bad news and good news. An earlier version of this paper, detailing the findings of the survey, (...) was presented to the Radio?TV Journalism Division of the Association for Education in Journalism and Mass Communication in August, 1986. (shrink)

We apply linear algebra to the study of the inconsistent figure known as the Crazy Crate. Disambiguation by means of occlusions leads to a class of sixteen such figures: consistent, complete, both and neither. Necessary and sufficient conditions for inconsistency are obtained.

Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby. In order to stay focused on the “big picture”, we merely sketch the overall form of each construction, referring to the (...) literature for details. Each of the three steps considered below is based on more recent logical research than the preceding one. The first step from sets to types is essentially the familiar idea of set theoretic semantics for a syntactic system, i.e. giving a model; we take a brief glance at this step from the current point of view, mainly just to fix ideas and notation. The second step from types to categories is known to categorical logicians as the construction of a “syntactic category”; we give some specifics for the benefit of the reader who is not familiar with it. The third step from categories to sets is based on quite recent work, but captures in a precise way an intuition from the early days of foundational studies. With these pieces in place, we can then draw some conclusions regarding the differences between the three schemes, and their relative merits. In particular, it is possible to state more precisely why the methods of category theory are more appropriate to philosophical structuralism. (shrink)

This article supports the idea that synthesis, rather than analysis, is the most powerful and promising route towards understanding the essence of brain function being understood at all. It discusses ‘understanding by doing’, outlines a methodology for the use of deep computer simulation and robotics in pursuing such a synthesis, and then briefly introduces the author’s ongoing, long-term attempt to build a neurologically plausible and hopefully at least subconscious being, whom he hopes will eventually answer to the name of Lucy.