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)

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)

From Socrates and the Sophists to Kant, from Augustine to Aquinas and the Reformers, Colin Brown traces the turbulent, often tension-filled, always fascinating story of the thinkers, ideas and movements that have shaped our intellectual landscape. Is philosophy the "handmaiden of faith" or "the doctrine of demons"? Does it clarify the faith or undermine the very heart of Christian belief?Brown writes, "This book is about the changes in preconceptions, world views and paradigms that have affected the ways in which people (...) have thought about religion in general and Christianity in particular in the Western world.... It is a historical sketch, written to help students--and anyone else who might be interested--to get a better grasp of the love-hate relationship between philosophy and faith that has gone on for close to two thousand years."Students, pastors and thoughtful Christians will benefit from this rich resource. The first in a proposed three-volume work, Brown's easy-to-read, hard-to-put-down introduction to Christianity and Western thought focuses on developments from the ancient world to the Age of Enlightenment. (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)

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.

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)

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)

This article is meant to be an apologetic for spiritual formation to those within the evangelical tradition who find themselves concerned about its emphases. Eight common objections to spiritual formation are presented with the twofold aim of recognizing any needed corrective and defusing the objection. While more must be said in response to each of these objections, it is hoped that enough will be said here to relieve much of the anxiety surrounding spiritual formation.

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)

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.

This work is a response to a request from the phenomenology group at Edith Cowan University. The paper is based on seminar discussions, experiences and ideas that have been contextualized within phenomenological literature. The notion of phenomenology as intervention has become increasingly apparent owing to the value of its practical applications in the human and social sciences. The paper explores the theme with special reference to research and psychotherapeutic interventions. Indo-Pacific Journal of Phenomenology , Volume 1, Edition 2 September 2001.

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)

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.

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.

This dialogue concerns the nature of ethical responsibility in contemporary art practice, and its relation to questions of creativity; the role of writing in shaping the perception of transgenic art and related practices; and the problems that may be associated with trusting artists to act with integrity in the unchartered waters of their enthusiastic engagement with genetic technologies.

The complexity that we observe in nature can often be explained in terms of cooperative behavior. For example, the major transitions of evolution required the emergence of cooperation among the lower-level units of selection, which led to specialization through division-of-labor ultimately resulting in spontaneous order. There are two aspects to address explaining how such cooperation is sustained: how free-riders are prevented from free-riding on the benefits of cooperative tasks, and just as importantly, how those social benefits arise. We review these (...) problems from an economic perspective, and highlight how ideas from economics can help us to better understand how the benefits of social interactions arise, how they are sustained, and how they affect the underlying social dilemmas. (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)

The author compares the different interpretations by Castoriadis and Lefort of democratic autonomy. For both, autonomy involves questioning all pregiven meaning. Castoriadis, while rejecting any law of historical progress, regards the history of autonomy as the development of a movement which commenced in a limited political domain in ancient Greece and expanded in other domains in Western Europe from the 11th century on. In theory, it has eliminated pregiven meaning, but has remained stuck in a liberal oligarchy, bogged down by (...) a tide of insignificance. It remains to further the project of autonomy to the point where a truly autonomous society will be able to accept as such the “Abyss” (the “Chaos”) it experiences without hiding behind replicas such as those provided by religion. Lefort, on the other hand, while similarly accepting democracy’s desire for autonomy, believes the source of its principles are enigmatic and it will continue to remain open to the authentic human experience of radical transcendence even without God. He believes that the threat of relativism can be avoided as democracy is more just since it allows its members to be more open to this radical transcendence than other forms of society. (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.

Despite being a prevalent theme in popular cinema, revenge has received little dedicated attention within film studies. The majority of research concerning the concept of revenge is located within moral philosophy, but that body of literature has been overlooked by film studies scholars. Philosophers routinely draw on filmic examples to illustrate their discussions of revenge, but those interpretations are commonly hindered by their authors’ inexperience with film studies’ analytical methods. This article seeks to bridge those gaps. The 2010 remake of (...) I Spit on Your Grave is used as a case study to illustrate the benefits of an interdisciplinary engagement with revenge. Philosophical literature on the topic has routinely posited that revenge is either appealing or appalling, and that impasse has stifled conceptual understanding. The interdisciplinary approach employed here elucidates that revenge is simultaneously appealing and appalling; this dualistic nature is evident in I Spit on Your Grave since it is built into the narrative design. I conclude that an interdisciplinary approach to revenge has the potential to advance understanding of revenge-qua-concept both within films studies and philosophy. (shrink)