Pierre de Jean Olivi utilise a de nombreuses reprises le terme « radical » dans son œuvre. Si ce dernier désigne parfois un fondement, on le trouve aussi au sens d’un absolu ou d’un extrême. Ainsi, Olivi use de la notion de « mauvaiseté radicale » qu’il définit comme le fait de « vouloir de toutes ses forces ce qui est le plus outrageant à Dieu et aux siens ». Dans cet article, nous essayons de préciser ce qu’Olivi entend par (...) cette définition. Nous montrons qu’il ne s’agit pas de vouloir le mal pour le mal, bien que selon Olivi, les cas d’acrasie stricte soient réels. En effet, les personnes acratiques comprennent, de manière universelle et actuelle, que leur choix est contraire au bien. L'option acratique provient d’une volonté absolument autodéterminée et capable des opposées. Le motif de ce choix consiste en un amour orgueilleux de soi à ce point démesuré qu’il s’oppose à la volonté de Dieu et qu’il utilise autrui comme un moyen de pouvoir. Enfin, nous montrons qu’Olivi utilise également le terme de « vertu radicale », réalité si forte qu’elle s’approche d’une forme d’annihilation de soi au profit de Dieu. (shrink)

Peter Olivi was an original and controversial thinker whose philosophical ideas have aroused increasing interest within the scholarly community during the last decades. Stève Bobillier's L'éthique de la personne is the first monograph-length study that focuses explicitly on his ethics. Bobillier's central claim is that Olivi approaches ethics from the point of view of an individual person who chooses her actions freely and with full awareness that the choices are up to her. When someone makes a morally wrong (...) choice, the choice can ultimately be traced back to the agent's free will. To chart the details of this theory, Bobillier analyzes Olivi's conception of the freedom of the... (shrink)

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

I argue for patternism, a new answer to the question of when some objects compose a whole. None of the standard principles of composition comfortably capture our natural judgments, such as that my cat exists and my table exists, but there is nothing wholly composed of them. Patternism holds, very roughly, that some things compose a whole whenever together they form a “real pattern”. Plausibly we are inclined to acknowledge the existence of my cat and my table but not of (...) their fusion, because the first two have a kind of internal organizational coherence that their putative fusion lacks. Kolmogorov complexity theory supplies the needed rigorous sense of “internal organizational coherence”. (shrink)

Socially responsible investing (SRI) has emerged in recent years as a dynamic and quickly growing segment of the U.S. financial services industry involving over $2 trillion in professionally managed assets. Its conceptual origins can be found in the early history of civilization, with it's modern roots in the 1960s. This paper provides an overview of the breadth and depth of the concept and practice of socially and environmentally responsible investing, describes the investment strategies that together define SRI as currently practiced (...) in the U.S., offers several observations about some of the factors fueling its dramatic growth, and presents data showing that investors who choose to invest in a socially and environmentally responsible manner can do so without giving up investment returns. SRI has matured to a point where virtually any investment need can be met through portfolio design that integrates an investor's personal values, institutional mission, and/or social priorities. The socially responsible investment industry in the United States is a young phenomenon. Even referring to it as an "industry" ten years ago may have been a bit of a stretch. While it has grown dramatically in recent years, it is an area of work, of study and of practical application that continues to evolve in many significant ways. One intriguing example of the ongoing development of the field can be found in the analysis of the language used to describe it. The terms social investing, socially responsible investing, ethical investing, socially aware investing, socially conscious investing, green investing, values-based investing, and mission-based or mission-related investing all refer to the same general process and are often used interchangeably. (shrink)

I argue that, contrary to intuition, it would be both possible and permissible to design people - whether artificial or organic - who by their nature desire to do tasks we find unpleasant.

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)

Nick Bostrom's book *Superintelligence* outlines a frightening but realistic scenario for human extinction: true artificial intelligence is likely to bootstrap itself into superintelligence, and thereby become ideally effective at achieving its goals. Human-friendly goals seem too abstract to be pre-programmed with any confidence, and if those goals are *not* explicitly favorable toward humans, the superintelligence will extinguish us---not through any malice, but simply because it will want our resources for its own purposes. In response I argue that things might not (...) be as bad as Bostrom suggests. If the superintelligence must *learn* complex final goals, then this means such a superintelligence must in effect *reason* about its own goals. And because it will be especially clear to a superintelligence that there are no sharp lines between one agent's goals and another's, that reasoning could therefore automatically be ethical in nature. (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)

Developing directly from Fuller's recent book Humanity 2.0, this is the first book to seriously consider what a 'post-' or 'trans'-' human state of being might mean for who we think we are, how we live, what we believe and what we aim to be.

Although The Structure of Scientific Revolutions is one of the most influential books of this century, its author, Thomas Kuhn, is notorious for disavowing most of the consequences wrought by his text. Insofar as these consequences have appeared "radical" or "antipositivist," this article argues that they are very misleading, and that Kuhn's complaints are therefore well placed. Indeed, Kuhn unwittingly succeeded where Daniel Bell's The End of Ideology tried and failed, namely, to alleviate the anxieties of alienated academics and defensive (...) policy-makers by teaching them that they could all profit from solving their own paradigmatic puzzles. The influence of tructure is traced from the philosophy of science into the social sciences and science policy. Special attention is paid to the import of the General Education in Science curriculum at Harvard, in which Kuhn taught for most of the period prior to writing tructure. Harvard President James Conant had designed this curriculum in order to keep "pure science" in the good favor of the American public, in whose eyes it suffered after the use of the atomic bomb. While Conant was keen to stress the distinctiveness of science from other social practices, Kuhn's model seemed to provide a blueprint for reconstituting any practice as a science. This enabled potentially antiscientific academics to become scientists themselves, thereby neutralizing any radical challenges to the ends of scientific inquiry. The article concludes by reconstructing some of the inchoate possibilities for radical critique that Kuhn's success preempted, and by making some suggestions for how they may be recovered in the present academic environment. (shrink)

This paper presents a new way of thinking about the relationship between humans and the nonhuman animals in their care. Most ethical analysis of the treatment of nonhuman animals has focussed on questions of moral status, justice, and the wrongness of harming them. This paper does something different, it examines the role played by trust in interspecies relationships. In both agriculture and laboratory settings, humans deliberately foster trusting relationships with nonhuman animals. An intrinsic feature of the trusting relationship in these (...) settings is that it is created in order to be exploited and betrayed. However, little consideration has been given to asking what a deliberate betrayal of another species says about the character of those who carry out the betrayals. This paper argues that regardless of the moral status of nonhuman animals, a willingness to foster trust in order to exploit the vulnerability of a nonhuman suggests a serious character flaw. Our failure thus far to apprehend systematic forms of betrayal indicates a moral blind-spot when it comes to other species. (shrink)

The link between corporate philanthropy and firm value has been controversial. On one hand, corporate philanthropy is often criticized as an agency cost because it may serve narrow managerial self-interests. On the other hand, corporate philanthropy may enhance firm value because it improves the relationships between firms and their stakeholders. In this study, we argue that this controversy is contingent upon whether corporate governance mechanisms can stimulate the financial benefit of corporate philanthropy. Based on a sample of U.S. firms from (...) 1996 to 2003, we find that CEO long-term pay positively moderates the relationship between corporate philanthropy and firm value while multiboard outside directors negatively moderate this relationship. Contrary to our expectations, we find that the relationship between corporate philanthropy and firm value enhances as CEO tenure increases. Our findings show that corporate governance plays an important moderating role in the relationship between corporate philanthropy and firm value. (shrink)

The critical realist conception of open and closed systems is not about systems: it is about regularities in the flux of events and states of affairs. It has recently been criticised on the grounds that critical realists should take on board ideas about the general nature of systems; recognise that genuinely open social systems would be impossible; avoid polarities or dualisms where either there are event regularities and open systems, or there are no event regularities and closed systems and accept (...) partial regularities and partially open systems; and understand that orthodox economics is not based upon event regularities, laws or Humean empiricism. The objective of this paper is to ‘take stock’ of these recent criticisms. (shrink)

This paper outlines the moral contours of human relationships with companion animals. The paper details three sources of duties to and regarding companion animals: (1) from the animal’s status as property, (2) from the animal’s position in relationships of care, love, and dependency, and (3) from the animal’s status as a sentient being with a good of its own. These three sources of duties supplement one another and not only differentiate relationships with companion animals from wild animals and other categories (...) of domestic animals such as livestock, but they also overlap to provide moral agents with additional reasons for preventing and avoiding harm to companion animals. The paper concludes that not only do owners and bystanders have direct and indirect duties to protect companion animals from harm, but also that these duties have the potential, in some circumstances, to clash with duties owed to the state and fellow citizens. (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.

In this chapter I'd like to focus on a small corner of sexbot ethics that is rarely considered elsewhere: the question of whether and when being a sexbot might be good---or bad---*for the sexbot*. You might think this means you are in for a dry sermon about the evils of robot slavery. If so, you'd be wrong; the ethics of robot servitude are far more complicated than that. In fact, if the arguments here are right, designing a robot to serve (...) humans sexually may be very good for the robots themselves. (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)

Whether it would take one decade or several centuries, many agree that it is possible to create a *superintelligence*---an artificial intelligence with a godlike ability to achieve its goals. And many who have reflected carefully on this fact agree that our best hope for a "friendly" superintelligence is to design it to *learn* values like ours, since our values are too complex to program or hardwire explicitly. But the value learning approach to AI safety faces three particularly philosophical puzzles: first, (...) it is unclear how any intelligent system could learn its final values, since to judge one supposedly "final" value against another seems to require a further background standard for judging. Second, it is unclear how to determine the content of a system's values based on its physical or computational structure. Finally, there is the distinctly ethical question of which values we should best aim for the system to learn. I outline a potential answer to these interrelated puzzles, centering on a "miktotelic" proposal for blending a complex, learnable final value out of many simpler ones. (shrink)

This paper argues that since the last decades of the twentieth century the discipline of modern finance has directed fiduciaries to act "rationally"—that is, in the sole financial interest of their funds--downplaying the effects of their investments on others. This approach has deemphasized a previous, more "reasonable" interpretation of fiduciary duty that drew on a conception of prudence characterized by wisdom, discretion and intelligence—one that accounts to a greater degree for the relationship between one's investments and their effects on others (...) in the world. The reasonable approach allows fiduciaries to a greater degree to assess the objective well-being of beneficiaries, to recognize fundamental sources of investment reward in the economy, and to fulfill their obligations to allocate benefits impartially between current and future generations. Reason and rationality can work in a complementary fashion to make investment long-term in its perspective and beneficial to society and the economy as well as to specific funds or portfolios. Determining how to accomplish this challenging task is part of the obligation of fiduciaries as they seek to realize the full potential of the investment assets entrusted to their care. (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)

Attempts to understand visual attention have produced models based on location, in which attention selects particular regions of space, and models based on other visual attributes . Previous studies of inattentional blindness have contributed to our understanding of attention by suggesting that the detection of an unexpected object depends on the distance of that object from the spatial focus of attention. When the distance of a briefly flashed object from both fixation and the focus of attention is systematically varied, detection (...) appears to have a location-based component. However, the likelihood that people will detect an unexpected event in sustained and dynamic displays may depend on more than just spatial location. We investigated the influence of spatial location on inattentional blindness under precisely controlled, sustained and dynamic conditions. We found that although location-based models cannot fully account for the detection of unexpected objects, spatial location does play a role even when displays are visible for an extended period. (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)

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.

As artificial intelligence (AI) thrives and propagates through modern life, a key question to ask is how to include humans in future AI? Despite human involvement at every stage of the production process from conception and design through to implementation, modern AI is still often criticized for its “black box” characteristics. Sometimes, we do not know what really goes on inside or how and why certain conclusions are met. Future AI will face many dilemmas and ethical issues unforeseen by their (...) creators beyond those commonly discussed (e.g., trolley problems and variants of it) and to which solutions cannot be hard-coded and are often still up for debate. Given the sensitivity of such social and ethical dilemmas and the implications of these for human society at large, when and if our AI make the “wrong” choice we need to understand how they got there in order to make corrections and prevent recurrences. This is particularly true in situations where human livelihoods are at stake (e.g., health, well-being, finance, law) or when major individual or household decisions are taken. Doing so requires opening up the “black box” of AI; especially as they act, interact, and adapt in a human world and how they interact with other AI in this world. In this article, we argue for the application of cognitive architectures for ethical AI. In particular, for their potential contributions to AI transparency, explainability, and accountability. We need to understand how our AI get to the solutions they do, and we should seek to do this on a deeper level in terms of the machine-equivalents of motivations, attitudes, values, and so on. The path to future AI is long and winding but it could arrive faster than we think. In order to harness the positive potential outcomes of AI for humans and society (and avoid the negatives), we need to understand AI more fully in the first place and we expect this will simultaneously contribute towards greater understanding of their human counterparts also. (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 (dssi). 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 (IZF). (shrink)

Increasingly, protests occur across borders and are carried out by non-nationals. Many of these protests include elements that break the laws of their host country and are aimed at issues of global concern. Despite the increasing frequency of transnational protest, little ethical consideration has been given to it. This article provides a cosmopolitan justification for transnational disobedience on behalf of self and others. The article argues that individuals may be justified in illegally protesting in other states, and that in some (...) circumstances they may do so even when laws have been legitimately constituted by the domestic constituencies of those states. Using a cosmopolitan reading of the notion of civility and of the civil realm, the article argues that transnational protests are capable of conforming to the normative and conceptual standards necessary for them to be labelled civil disobedience. As a result, they ought to carry a privileged moral status compared with other forms of protest. The article applies the All Affected Principle to argue that a democratic deficit can provide transnational protesters and resident migrants with a right to civil disobedience even where that right is not held by members of the demos they protest within. (shrink)

Whilst the concept of causal powers is central to much post-positivist social science in general, and to critical realism in particular, it has not been significantly developed by critical realists since the initial work of Harré and Madden and Bhaskar in the mid-1970s. To deepen our understanding of powers we need to start with a ‘package’ of related terms. In §1 of the paper I introduce this package, clear up some terminological ambiguity and inconsistency, and focus the discussion upon things, (...) properties and powers. The real problems begin when we try to figure out how things, properties and powers relate to one another. In §2 I introduce and evaluate three possible ontologies: an ontology where powers are primary; an ontology where properties are primary; and an ontology where neither properties, powers are primary, but all emerge to form a unity. The last ontology is defended. §3 deals with ambiguities surrounding three other terms that often crop up when discussing powers, namely, dispositional properties, transfactuals and processes. The net result is a far less ambiguous concept of powers, firmly anchored in an ontology of things, properties and powers as a unity. (shrink)

Many research-intensive universities have moved into the business of promoting technology development that promises revenue, impact, and legitimacy. While the scholarship on academic capitalism has documented the general dynamics of this institutional shift, we know less about the ground-level challenges of research priority and scientific problem choice. This paper unites the practice tradition in science and technology studies with an organizational analysis of decision-making to compare how two university artificial intelligence labs manage ambiguities at the edge of scientific knowledge. One (...) lab focuses on garnering funding through commercialization schemes, while the other is oriented to federal science agencies. The ethnographic comparison identifies the mechanisms through which an industry-oriented lab can be highly adventurous yet produce a research program that is thin and erratic due to a priority placed on commercialization. However, the comparison does not yield an implicit nostalgia for federalized science; it reveals the mechanisms through which agency-oriented labs can pursue a thick and consistent research portfolio but in a strikingly myopic fashion. (shrink)

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known interpretation of higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE, but rather by a suitable complete Heyting algebra H. The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjective geometric morphisms (...) f : F → E, where H = f∗ΩF. The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are not longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion. (shrink)

An anthology of new translations of essential readings from the classical texts of early Chinese philosophy. It includes the Analects of Confucius, Meng Zi (Mencius), Xun Zi, Mo Zi, Lao Zi (Dao De Jing), Zhuang Zi, and Han Fei Zi, as well as short chapters on the Da Xue and the Zhong Yong. Pedagogically organized, it offers philosophically sophisticated annotations and commentaries as well as an extensive glossary explaining key philosophical concepts in detail.

Scholars concerned with abuses of the “resource privilege” by the governments of developing states sometimes call for national sovereignty over the natural resources that lie within its borders. While such claims may resist a key driver of the “resource curse” when applied to mineral resources in the ground, and are often recognized as among a people’s territorial rights, their implications differ in the context of climate change, where they are invoked on behalf of a right to extract and combust fossil (...) fuels that is set in opposition to global climate change mitigation imperatives. Moreover, granting full national sovereignty over territorial carbon sinks may conflict with commitments to equity in the sharing of national mitigation burdens, since much of the planet’s carbon sink capacity lies within territorial borders to which peoples have widely disparate access. In this paper, I shall explore this tension between a global justice principle that is often applied to mineral resources and its tension with contrary principles that are often applied to carbon sink access, developing an analysis that seeks to reconcile what would otherwise appear to be fundamentally incompatible aims. (shrink)

Naturalism is normally taken to be an ideology, censuring non-naturalistic alternatives. But as many critics have pointed out, this ideological stance looks internally incoherent, since it is not obviously endorsed by naturalistic methods. Naturalists who have addressed this problem universally foreswear the normative component of naturalism by, in effect, giving up science’s exclusive claim to legitimacy. This option makes naturalism into an empty expression of personal preference that can carry no weight in the philosophical or political spheres. In response to (...) this dilemma, I argue that on a popular (but largely unarticulated) construal of naturalism as a commitment to inference to the best explanation, methodological naturalism can be both normative and internally coherent. (shrink)

People of the western world now have unprecedented freedom to choose their religion. In this book, the world's leading sociologist of religion argues that the liberty and freedom to choose religion corrodes faith and that religion remains most vital when it is part of ethnic and national identity.

Torture Porn is a term that has generated a great deal of controversy during the last decade, critics utilizing the term to dismiss contemporary popular horror cinema as obscene and morally depraved. Arguing primarily in defense of torture-themed horror films, this book seeks to offer a critical overview and examination of the Torture Porn phenomenon, discussing the generic contexts in which it is situated, scrutinizing press responses to the sub-genre, and offering narrative analyses of the sub-genre’s central films; including the (...) highly popular Saw franchise, the Hostel movies, and recent revamped versions of slasher movies such as Texas Chainsaw Massacre, as well as the multitude of independent direct-to-DVD films that have been influenced by these theatrically successful films. (shrink)

There are writers in both metaphysics and algorithmic information theory (AIT) who seem to think that the latter could provide a formal theory of the former. This paper is intended as a step in that direction. It demonstrates how AIT might be used to define basic metaphysical notions such as *object* and *property* for a simple, idealized world. The extent to which these definitions capture intuitions about the metaphysics of the simple world, times the extent to which we think the (...) simple world is analogous to our own, will determine a lower bound for basing a metaphysics for *our* world on AIT. (shrink)

This paper constructs models of intuitionistic set theory in suitable categories. First, a Basic Intuitionistic Set Theory (BIST) is stated, and the categorical semantics are given. Second, we give a notion of an ideal over a category, using which one can build a model of BIST in which a given topos occurs as the sets. And third, a sheaf model is given of a Basic Intuitionistic Class Theory conservatively extending BIST. The paper extends the results in [2] by introducing a (...) new and perhaps more natural notion of ideal, and in the class theory of part three. (shrink)

In the United States, convicted offenders frequently lose the right to vote, at least temporarily. Drawing on the common observation that citizens of color lose democratic rights at disproportionately high rates, this chapter argues that this punishment is problematic in non-ideal societies because of the way in which it diminishes the political power of marginalized groups and threatens to reproduce patterns of domination and subordination, when they occur. This chapter then uses the case of penal disenfranchisement to illustrate how idealized (...) discussions of deterrence, rehabilitation, and retribution often ignore the relationship between punishment and social/political power, and thus systematically obscure morally significant aspects of our broader penal practices. (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)

The fundamental duality theories relating algebra and geometry that were discovered in the mid-twentieth century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness theorems. This idea can be taken even further via what is sometimes called “categorification” to establish a new connection between logic and geometry, a glimpse of which can also be had in topos theory.