This paper argues that lexical and operator-based analyses of distributivity are not in conflict, but are both necessary components of any theory of distributivity that aims to account for all the relevant data. I use several contrasts between plural definites and group NPs to show that we need an operator-based analysis of distributivity; this kind of distributivity is available with plural definites but not with group subjects, which can be explained under the common assumption that group (...) NPs denote atoms rather than sums and hence do not allow quantification over their individual parts. At the same time, we need a lexical theory of distributivity to account for the various distributive interpretations that we do find with groups; a formalisation of such a theory is outlined in the final section of this paper. (shrink)

This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of (...) the boys owned three cars, though the same sentence withouttogether could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers likeeach and non-distributive or collective readings that arise withouttogether. (shrink)

We show that it is consistent that Martin's axiom holds, the continuum is large, and yet the dual distributivity number ℌ is κ1. This answers a question of Halbeisen.

We introduce a notion of complexity for interpretations, which is used to prove some new results about interpretations of sequential theories. In particular, we give a new, elementary proof of Pudlák's theorem that sequential theories are connected. We also demonstrate a counterexample to the infinitary distributive law $a \vee \bigwedge_{i \in I} b_i = \bigwedge_{i \in I} (a \vee b_i)$ in the lattice of chapters, in which the chapters a and b i are compact. (Counterexamples in which a is not (...) compact have been found previously.). (shrink)

In this article, we shall show the generalized notions of distributivity of Boolean algebras have essential relations with several axioms and properties of set theory, say the Axiom of Choice, the Axiom of Dependence Choice, the Prime Ideal Theorems, Martin's axioms, Lebesgue measurability and so on.

This paper presents a diagnostic for identifying distributive constructions and shows that it applies to pseudopartitives and for -adverbials. On this basis, a unified account is proposed for the parallels between the constructions involved. This account explains why for -adverbials reject telic predicates (*run to the store for five hours), why pseudopartitives reject count nouns (*five pounds of book ), and why both reject certain measure functions like temperature and speed (*30 of water, *drive for 5 mph). These restrictions all (...) follow from a general constraint on distributive constructions. Related concepts such as the D operator (Link, 1987), the subinterval property (Bennett and Partee, 1972), and divisive reference (Cheng, 1973) can be understood as formalizing special cases of this constraint. (shrink)

We examine 'weak-distributivity' as a rewriting rule $??$ defined on multiplicative proof-structures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proof-nets, but does nevertheless preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for $??$: starting from a set of simple generators (proof-nets which are a n-ary ⊗ of &-ized axioms), any mono-conclusion MLL proof-net can be reached by $??$ rewriting (up to ⊗ and (...) & associativity and commutativity). (shrink)

We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with h > N₁ is consistent. We work with a class of axiom A forcings with countable conditions such that q ≥ n p is determined by finitely many elements in the conditions p and q and that all strengthenings of a condition are subsets, and replace many names by actual sets. There are two types of technique: one for tree-like forcings and one for (...) forcings with creatures that are translated into trees. Both lead to new models of the club principle. (shrink)

In this talk, I first systematize the analogies and complete the picture in some corners. Then, I formally relate the three constructions, and I derive their properties from a single operator. Previous analyses were not designed to account for all three constructions at the same time. Accordingly, I not only assess how well they generalize beyond their intended purpose, but I also evaluate them in their own right. Even so, this analysis improves on previous accounts in several ways. Although I (...) will not focus on this in the talk, the analysis of distributive quantification is compatible with more general analyses of cumulative and collective quantification such as Landman (2000). (shrink)

The phenomenon of distributed knowledge is well-known in epistemic logic. In this paper, a similar phenomenon in ethics, somewhat neglected so far, is investigated, namely distributed morality. The article explains the nature of distributed morality, as a feature of moral agency, and explores the implications of its occurrence in advanced information societies. In the course of the analysis, the concept of infraethics is introduced, in order to refer to the ensemble of moral enablers, which, although morally neutral per se, can (...) significantly facilitate or hinder both positive and negative moral behaviours. (shrink)

According to the hypotheses of distributed and extended cognition, remembering does not always occur entirely inside the brain but is often distributed across heterogeneous systems combining neural, bodily, social, and technological resources. These ideas have been intensely debated in philosophy, but the philosophical debate has often remained at some distance from relevant empirical research, while empirical memory research, in particular, has been somewhat slow to incorporate distributed/extended ideas. This situation, however, appears to be changing, as we witness an increasing level (...) of interaction between the philosophy and the empirical research. In this editorial, we provide a high-level historical overview of the development of the debates around the hypotheses of distributed and extended cognition, as well as relevant theory and empirical research on memory, considering both the role of memory in theoretical debates around distributed/extended ideas and strands of memory research that resonate with those ideas; we emphasize recent trends towards increased interaction, including new empirical paradigms for investigating distributed memory systems. We then provide an overview of the special issue itself, drawing out a number of general implications from the contributions, and conclude by sketching promising directions for future research on distributed memory. (shrink)

Synthesizing the domains of investigation highlighted in current research in distributed cognition and related fields, this paper offers an initial taxonomy of the overlapping types of resources which typically contribute to distributed or extended cognitive systems. It then outlines a number of key dimensions on which to analyse both the resulting integrated systems and the components which coalesce into more or less tightly coupled interaction over the course of their formation and renegotiation.

There are various philosophical approaches and theories describing the intimate relation people have to artifacts. In this paper, I explore the relation between two such theories, namely distributed cognition and distributed morality theory. I point out a number of similarities and differences in these views regarding the ontological status they attribute to artifacts and the larger systems they are part of. Having evaluated and compared these views, I continue by focussing on the way cognitive artifacts are used in moral practice. (...) I specifically conceptualise how such artifacts (a) scaffold and extend moral reasoning and decision-making processes, (b) have a certain moral status which is contingent on their cognitive status, and (c) whether responsibility can be attributed to distributed systems. This paper is primarily written for those interested in the intersection of cognitive and moral theory as it relates to artifacts, but also for those independently interested in philosophical debates in extended and distributed cognition and ethics of (cognitive) technology. (shrink)

This paper explores the implications of extended and distributed cognition theory for our notions of personal identity. On an extended and distributed approach to cognition, external information is under certain conditions constitutive of memory. On a narrative approach to personal identity, autobiographical memory is constitutive of our diachronic self. In this paper, I bring these two approaches together and argue that external information can be constitutive of one’s autobiographical memory and thus also of one’s diachronic self. To develop this claim, (...) I draw on recent empirical work in human-computer interaction, looking at lifelogging technologies in both healthcare and everyday contexts. I argue that personal identity can neither be reduced to psychological structures instantiated by the brain nor by biological structures instantiated by the organism, but should be seen as an environmentally-distributed and relational construct. In other words, the complex web of cognitive relations we develop and maintain with other people and technological artifacts partly determines our self. This view has conceptual, methodological, and normative implications: we should broaden our concepts of the self as to include social and artifactual structures, focus on external memory systems in the (empirical) study of personal identity, and not interfere with people’s distributed minds and selves. (shrink)

Extended and distributed cognition theories argue that human cognitive systems sometimes include non-biological objects. On these views, the physical supervenience base of cognitive systems is thus not the biological brain or even the embodied organism, but an organism-plus-artifacts. In this paper, we provide a novel account of the implications of these views for learning, education, and assessment. We start by conceptualising how we learn to assemble extended cognitive systems by internalising cultural norms and practices. Having a better grip on how (...) extended cognitive systems are assembled, we focus on the question: If our cognition extends, how should we educate and assess such extended cognitive systems? We suggest various ways to minimize possible negative effects of extending one’s cognition and to efficiently find and organise (online) information by adopting a virtue epistemology approach. Educational and assessment implications are foregrounded, particularly in the case of Danish students’ use of the Internet during exams. (shrink)

Face perception, perhaps the most highly developed visual skill in humans, is mediated by a distributed neural system in humans that is comprised of multiple, bilateral regions. We propose a model for the organization of this system that emphasizes a distinction between the representation of invariant and changeable aspects of faces. The representation of invariant aspects of faces underlies the recognition of individuals, whereas the representation of changeable aspects of faces, such as eye gaze, expression, and lip movement, underlies the (...) perception of information that facilitates social communication. The model is also hierarchical insofar as it is divided into a core system and an extended system. The core system is comprised of occipitotemporal regions in extrastriate visual cortex that mediate the visual analysis of faces. In the core system, the representation of invariant aspects is mediated more by the face-responsive region in the fusiform gyrus, whereas the representation of changeable aspects is mediated more by the face-responsive region in the superior temporal sulcus. The extended system is comprised of regions from neural systems for other cognitive functions that can be recruited to act in concert with the regions in the core system to extract meaning from faces. (shrink)

One of the arguments against conducting human subject trials in the Third World adopts a distributive justice principle found in a commentary of the CIOM'S Eighth Guideline for international research on human subjects. Critics argue that non-participant members of the community in which the trials are conducted are exploited because sponsoring agencies do not ensure that the products developed have been made reasonably available to these individuals. I argue that the distributive principle's wording is too vague and ambiguous to be (...) used to criticize any trial. Furthermore, the mere fact that an experiment does not fulfill this particular distributive justice principle does not entail that it is unethical. (shrink)

This article describes a representation-based framework of distributed cognition. This framework considers distributed cognition as a cognitive system whose structures and processes are distributed between internal and external representations, across a group of individuals, and across space and time. The major issue for distributed research, under this framework, are the distribution, transformation, and propagation of information across the components of the distributed cognitive system and how they affect the performance of the system as a whole. To demonstrate the value of (...) this representation-based approach, the framework was used to describe and explain an important, challenging, and controversial issue — the concept of affordance. (shrink)

Should theories of distribution focus solely on subjective welfare or solely on objective resources? While both of these ‘currencies’ have well-known objections that make each of them implausible alone, I argue that neither currency should be jettisoned entirely. Instead, I construct a multi-currency distributive theory involving both welfare and resources. While I think that such a heterogeneous theory is able to mitigate objections to both pure resourcism and pure welfarism, it also creates a new concern, which I call the precedence (...) concern, in which a theorist must determine which currency takes precedence in a given situation. I argue that to answer the precedence concern, altering the currency should result in altering the site of distribution as well. As a result, moral value between individuals should be measured in terms of welfare while state justice should be measured in terms of resources. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix (...) models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)