The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy (...) type theory. It also gives the new system of foundations a distinctly structural character. (shrink)

An affirmative answer is given to the question quoted in the title.

THIS IS AN EARLY DRAFT OF MY PAPER "RESEARCH PROBLEMS" PUBLISHED IN BJPS IN 2021. PLEASE REFER TO THAT PAPER INSTEAD OF THIS ONE. -/- Philosophers increasingly study how scientists conduct actual scientific projects and the goals they pursue. But as of yet, there are few accounts of goals that can be used to identify different kinds, and specific instances, of goals pursued by scientists. I propose that there are at least four distinct kinds of goals pursued by scientists: ameliorating (...) problems, addressing questions, satisfying values, and achieving epistemic aims. I focus on the first two kinds, and I provide tools to help conceptualize, distinguish, and identify the problems and questions pursued by scientists. This paper illustrates the use of those tools with two examples. (shrink)

Conscientious objection was barely mentioned in debates about the ethics of healthcare provision before the 1970s.1 The conscientious objections that attracted public and academic attention were those of conscripts who objected to participation in military forces, and of parents who objected to the vaccination of their children. All of this was changed by the 1973 US Supreme Court decision Roe v. Wade, which established a constitutional right to abortion in the USA. Shortly after this decision, the American Medical Association's (AMA) (...) House of Delegates, the peak policy-making body within the AMA, adopted a resolution that sought to protect hospital employees from having to contribute to the provision of abortion if they felt that doing so was immoral. The resolution was adopted in response to a specific controversial court decision, but the language employed in it was broad in scope. House of Delegates Health Policy 5.995 contained a conscience clause stating that ‘Neither physician, hospital, …. (shrink)

An enquiry into what future labour markets might look like is, necessarily, an enquiry into what future labour market institutions might look like. Any such enquiry requires a conceptual apparatus capable of dealing with labour markets and institutions. The conceptual apparatus of orthodox labour economics is incapable of this. An alternative conceptual apparatus, the ‘socio-economics of labour markets’, augmented with critical realist metatheory, is capable of dealing with future labour markets. This claim is demonstrated via the example of future labour (...) markets based on Basic Income. (shrink)

Marc Lewis argues that addiction is not a disease, it is instead a dysfunctional outcome of what plastic brains ordinarily do, given the adaptive processes of learning and development within environments where people are seeking happiness, or relief, or escape. They come to obsessively desire substances or activities that they believe will deliver happiness and so on, but this comes to corrupt the normal process of development when it escalates beyond a point of functionality. Such ‘deep learning’ emerges from consumptive (...) habits, or ‘motivated repetition’, and although addiction is bad, it ferments out of the ordinary stuff underpinning any neural habit. Lewis gives us a convincing story about the process that leads from ordinary controlled consumption through to quite heavy addictive consumption, but I claim that in some extreme cases the eventual state of deep learning tips over into clinically significant impairment and disorder. Addiction is an elastic concept, and although it develops through mild and moderate forms, the impairment we see in severe cases needs to be acknowledged. This impairment, I argue, consists in the chronic automatic consumption present in late stage addiction. In this condition, the desiring self largely drops out the picture, as the addicted individual begins to mindlessly consume. This impairment is clinically significant because the machinery of motivated rationality has become corrupted. To bolster this claim I compare what is going on in these extreme cases with what goes on in people who dissociate in cases of depersonalization disorder. (shrink)

Standard epistemology takes it for granted that there is a special kind of value: epistemic value. This claim does not seem to sit well with act utilitarianism, however, since it holds that only welfare is of real value. I first develop a particularly utilitarian sense of “epistemic value”, according to which it is closely analogous to the nature of financial value. I then demonstrate the promise this approach has for two current puzzles in the intersection of epistemology and value theory: (...) first, the problem of why knowledge is better than mere true belief, and second, the relation between epistemic justification and responsibility. (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)

The combination of sex and horror may be disquieting to many, but the two are natural (if perhaps gruesome) bedfellows. In fact, sex and horror coincide with such regularity in contemporary horror fiction that the two concepts appear to be at least partially intertwined. The sex–horror relationship is sometimes connotative rather than overt; examples of this relationship range from the seduction overtones of 'Nosferatu' and the juxtaposition of nudity and horror promised by European exploitation filmmakers to the sadomasochistic iconography of (...) 'Hellraiser'. In other cases, sex and horror are balanced in a manner that thoroughly blurs the distinction between porn and horror. The sustained presence of sex-horror in film suggests that these two elements fit together and the combination is a source of pleasure (entertainment, fascination, intellectual stimulation and so forth) for many. Yet sex-horror is broadly perceived to be disturbing and these negative reactions indicate that sex-horror is a source of trepidation, moral disdain or disgust for some. Thus, it appears that sex-horror inspires directly competing responses. One might conclude that sex-horror itself is paradoxical; that it holds two directly oppositional meanings simultaneously. However, as I will illustrate in this chapter, these dual responses are not as contradictory as they might first appear to be. (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)

On the ten year anniversary of 2Girls1Cup, this article examines the complex balance of shock, pleasure and disgust elicited by this viral video.

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)

Despite the closure of virtually all original grindhouse cinemas, ‘grindhouse’ lives on as a conceptual term. This article contends that the prevailing conceptualization of ‘grindhouse’ is problematized by a widening gap between the original grindhouse context (‘past’) and the DVD/home-viewing context (present). Despite fans’ and filmmakers’ desire to preserve this part of exploitation cinema history, the world of the grindhouse is now little more than a blurry set of tall-tales and faded phenomenal experiences, which are subject to present-bias. The continuing (...) usefulness of grindhouse-qua-concept requires that one should pay heed to the contemporary contexts in which ‘grindhouse’ is evoked. (shrink)

Over the last century within the philosophy of mind, the intersubjective model of self has gained traction as a viable alternative to the oft-criticised Cartesian solipsistic paradigm. These two models are presented as incompatible inasmuch as Cartesians perceive other minds as “a problem” for the self, while intersubjectivists insist that sociality is foundational to selfhood. This essay uses the Paranormal Activity series (2007–2015) to explore this philosophical debate. It is argued that these films simultaneously evoke Cartesian premises (via found-footage camerawork), (...) and intersubjectivity (via an ongoing narrative structure that emphasises connections between the characters, and between each film). The philosophical debates illuminate premises on which the series’ story and horror depends. Moreover, Paranormal Activity also sheds light on the theoretical debate: the series brings those two paradigms together into a coherent whole, thereby suggesting that the two models are potentially compatible. By developing a combined model, scholars working in the philosophy of mind might better account for the different aspects of self-experience these paradigms focus on. (shrink)

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions . As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full (...) axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo-Fraenkel set theory. (shrink)

In this introduction we set out some salient themes that will help structure understanding of a complex set of intersecting issues discussed in this special issue on the work of Marc Lewis: conceptual foundations of the disease model, tolerating the disease model given socio-political environments, and A third wave: refining conceptualization of addiction in the light of Lewis’s model.

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.

Though famously Derek Parfit is known for his reductionism about persons, he does, in fact, also profess a form of realism about persons based on the way the language of persons and personal identity is used. We might say that Parfit is an ontological reductionist about persons but not a conceptual reductionist. In this discussion note I try to bring out a difficulty for this kind of hybrid view by showing that there are many ways – too many in fact (...) – in which we use the language of persons and personal identity that cannot be reconciled with the core of Parfitian ontological reductionism. If it is true that the kind of reconciliation Parfit and his followers assent to is untenable, then a stark choice is presented between reductionism and a repudiation of most, if not all vestiges of realism. A genuine reductionist ought to choose against the latter. (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)

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)

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)

On occasion, in multilateral negotiations, interested parties make unilateral demands. Certain agreements need unanimity. However, a lesser degree of consensus may be feasible. In this paper, an alternating demand bargaining game among n players is proposed, which envisages varying consensus requirements and commitment, both crucial in generating a unique and efficient outcome of the bargaining process.

What marks ours as the "post-epistemic era" is that it refuses to confer any special privilege on knowledge production as a social practice: whatever normative strictures apply to social practices in general, they apply specifically to epistemic practices as well. I trace how we have reached this state by distinguishing two conceptions of normativity in the history of epistemology: a top-down approach epitomized by Kant and Bentham, and a bottom-up approach associated with the Scottish Enlightenment. The advantage of the latter (...) is that it clearly distinguishes the emergence of norms from the conditions of their maintenance. I then show how more recent evolutionary epistemology has, in a pejorative way, "naturalized" socially constructed norms of cognitive competence, whereas the logical positivists — long the bane of "progressive" epistemologists — recognized the fully artificial character of epistemic norms and hence qualify as the first social epistemologists. (shrink)