Decision making is usually viewed as involving a period of thought, while the decision maker assesses options, their likely consequences, and his or her preferences, and selects the preferred option. The process ends in a terminating action. In this view errors of thought will inevitably show up as errors of action; costs of thinking are to be balanced against costs of decision errors. Fast and frugal heuristics research has shown that, in some environments, modest thought can lead to excellent action. (...) In this paper we extend this work to situations in which action is taken after little or no thought. We show that these `highly active' or `decision cycles' processes can lead to excellent results at the cost of almost no thought. The paper examines the settings in which this effectiveness is possible, and lists a number of environmental features that are required for decision cycles to work well. Several research directions for analytical, laboratory, and field-based research are identified. (shrink)

A number of national educational organizations and individual authors have called for the use of information technology to radically reform higher education. Several projections of how this reformation will unfold are presented here. Three different approaches to critically assessing these projections are considered in this article, two briefly and one in more detail. Brief consideration is given to an approach based on educational values and to an approach based on cost/benefit analysis. After some discussion of the strengths and weaknesses of (...) these approaches, a third approach deriving from a theory of technology control (Incrementalism) is elaborated in more detail and is found to offer helpful criticisms of the called for revolution in higher education. Some recommendations for how these new technologies can be developed in responsible ways are also offered. (shrink)

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

We introduce a suitable notion of eight-shaped curve in the product S × ℝ of a Suslin line S for the real line ℝ, and we prove that if S is dense in itself, then every collection of pairwise disjoint eight-shaped curves in S × ℝ is countable. This parallels a folklore result which holds for the real plane.

We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics. We will also provide a recipe to build philosophical interpretations for each of these logics, and show why the kind of permeability that characterized them is not such a bad feature.

A number of national educational organizations and individual authors have called for the use of information technology to radically reform higher education. Several projections of how this reformation will unfold are presented here. Three different approaches to critically assessing these projections are considered in this article, two briefly and one in more detail. Brief consideration is given to an approach based on educational values and to an approach based on cost/benefit analysis. After some discussion of the strengths and weaknesses of (...) these approaches, a third approach deriving from a theory of technology control (Incrementalism) is elaborated in more detail and is found to offer helpful criticisms of the called for revolution in higher education. Some recommendations for how these new technologies can be developed in responsible ways are also offered. (shrink)

Disjoint n-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this article, we show that if a countably categorical theory T admits an expansion with disjoint n-amalgamation for all n, then T is pseudofinite. All theories which admit an expansion with disjoint n-amalgamation for all n are simple, but the method can be extended, using filtrations of Fraïssé classes, to show that certain nonsimple theories are pseudofinite. As (...) case studies, we examine two generic theories of equivalence relations, Tfeq∗ and TCPZ, and show that both are pseudofinite. The theories Tfeq∗ and TCPZ are not simple, but they have NSOP1. This is established here for TCPZ for the first time. (shrink)

We show that it is consistent with ZFC + ¬CH that there is a maxima a most disjoint permutation family A ⊆ Symsuch that A is a proper subset of an eventually different family E ⊆ ℕℕ and |A| < |E|. We also ask severa questions in this area.

I will investigate the auditory illusion of continuity, which is the phenomenon of auditory occlusion in which we are able to hear a sound as continuous even though it has been masked by another sound. This phenomenon seems to have a perceptual nature when it occurs in the context of everyday sounds, while it seems to have a cognitive nature when it occurs in the context of speech sounds. This difference has the following consequences: (1) We need to have a (...) differentiated approach to the study of this phenomenon; (2) the perceptual explanation of the phenomenon involving everyday sounds indicates that everyday sounds can be auditorily perceived; and (3) the cognitive explanation of the phenomenon involving speech sounds suggests, instead, that semantic properties cannot be auditorily perceived. From (2) and (3) it follows that while we have a good argument for the rich view when focusing on everyday sounds, we seem to lack an analogous argument to support the rich view in the context of speech sounds. Thus, I will suggest a new argument for the view that we do not hear semantic properties, as language understanding seems to be primarily a cognitive ability. (shrink)

Disjointism is the view that co-located objects do not share any parts. A human-shaped statue is composed from a torso, head and limbs; the co-located lumpof clay is only composed from chunks of clay. This essay discusses the tenability of this relatively neglected view, focusing on two objections. The first objection is that disjointism implies co-located copies of microphysical particles. I argue that it doesn’t imply this and that there are more plausible disjointist views of tiny parts available. The second (...) objection is that disjointism is at a loss to explain how material objects can be co-located and why the weights of co-located objects don’t add up. The standard pluralist account appeals to the fact that co-located objects stand in mereological relations and this account is not available to the disjointist. I sketch an alternative account that appeals to a notion of ‘material identity’: the statue is taken to be the same matter as the lump of clay. The resort to a new theoretical primitive may seem to invite a quick rejection on grounds of unnecessary theoretical complexity but I argue that an abductive comparison with rival forms of pluralism shows that such a rejection is misguided. (shrink)

The transmission of a product or idea from one culture or point of origin to another and the maintenance of control outside the new locality has been referred to as the distribution and maintenance of “nothing.” This perspective has been used to describe the global marketplace and the influence of large multinational corporations on the politics and cultures of host countries. This paper uses this concept, but within a much smaller context. Using the sensitizing concept of a “disjoint constitution,” we (...) interviewed health inspectors and apple cider producers in Michigan to determine if the implementation of the Hazard Analysis and Critical Control Points (HACCP) program designed to ensure food safety was characterized by a power differential that would favor the inspectors. In addition, a larger survey of processors and an internet survey of apple cider consumers was conducted to supplement this data. It was found that HACCP had characteristics of both “nothing” and “something” and that better communication is needed between these groups to move it further along toward the something end of the continuum. (shrink)

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of Determinacy [Formula: see text][Formula: (...) see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

We present a survey of some results and problems concerning constructions which require a diagonalization of length continuum to be carried out, particularly constructions of almost disjoint families of various sorts. We emphasize the role of cardinal invariants of the continuum and their combinatorial characterizations in such constructions.

Obviation versus Blocking. Two approaches to the distribution of anaphors and pronominals have been explored in Binding Theory. The OBVIATION approach, originating in Lasnik 1976 and extensively developed in the GB tradition, posits autonomous disjoint reference principles which directly filter out illicit coindexations in certain structural domains. The BLOCKING approach treats disjoint reference derivatively, by making anaphors obligatory under coreference in the binding domain, and invoking a syntactic or pragmatic principle that forces disjoint reference pronominals in the “elsewhere” case.

Neural organization raises, in an especially clear way, a major problem confronting contemporary cognitive science. The problem (the “big issue” of my title) is: What is the relation between the strategies used to solve basic problems of perception and action and those used to solve more abstract or “cognitive” problems? Is there a smooth, incremental route from what Arbib et al. call “instinctual schemas” to higher-level kinds of cognitive prowess? I argue that, despite some suggestive comments, Arbib et al. do (...) not resolve this issue. (shrink)

We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.

We present a number of results involving almost disjoint sets and Martin's axiom. Included is an example, due to K. Kunen, of a c.c.c. partial order without property K whose product with every c.c.c. partial order is c.c.c.

We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.

For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to non-disjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to Andréka and Németi which is equivalent to the Barrett–Halvorson (...) generalization in the case of disjoint languages. We show that the Andréka–Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability, which is another definition for definitional equivalence, even for non-disjoint languages. Finally, we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories in non-disjoint languages. (shrink)

Keywords: almost disjoint families; small uncountable cardinals; iterations of ψ; Hausdorff; Urysohn.

For a set M, let |M| denote the cardinality of M. A family F is called strongly almost disjoint if there is an n∈ω such that |A∩B|<n for any two distinct elements A, B of F. It is shown in ZF (without the axiom of choice) that, for all infinite sets M and all strongly almost disjoint families F⊆P(M), |F|<|P(M)| and there are no finite-to-one functions from P(M) into F, where P(M) denotes the power set of M.

My interest lies in offering a phenomenological perspective on how noise is experienced, with particular attention to what may be common to different sorts of noise phenomena. As a counterpoint to the notion that noise is an empty or constructed notion, I argue for two desiderata of a phenomenological account of noise; accommodating a plurality of noise experiences, on the one hand, and clarifying their specific phenomenal character, on the other. I then pursue these desiderata by turning to an examination (...) of some contemporary views of perception that have implications for how the phenomenal character of perceptual noise in particular is to be understood; an epistemic misfire view and a sensory misfire view. After clarifying each and its appeal, I convey concerns about the one and the other. I propose a third alternative for further exploration - a perceptual disjoint view - and point to how it ought to explored. On the premise that there is something like a unity of consciousness or experience, I lay out the idea that there may then be many forms of 'disunities' of experience. From an analysis of the latter, I suggest, one may account for many different types of experiences of noise, though with a common ‘phenomenal’ thread running through them. (shrink)

For several decades, Ronald Dworkinhas been one of the most prominent voicesdefending the legality and justifiability ofrace-conscious programs aimed at undoing thecontinuing effects of prejudice. Writingwithin the framework of a liberal legalphilosophy, he has formulated powerfularguments against the view that color-blindpolicies are the only defensible ones. Nonetheless, I argue that a more completeliberal defense of race-conscious policieswould need to develop and modify Dworkin's lineof argument. Such a defense would go beyondhis policy-based arguments and incorporatearguments of principle. Race-conscious policiesdo not only (...) promote the general good; they arealso required in order to help realize theconstitutional right of equal citizenship. (shrink)

This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (_Synthese, 198_(S18), 4277–4302 2021 ) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.

Partitioner algebras are defined by Baumgartner and Weese 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of ω. We prove from PFA+ and that there exists a partitioner algebra which contains a subalgebra which is not representable as a partitioner algebra.

For simplicity, most of the literature introduces the concept of definitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the Andréka and Németi generalization as one of the many equivalent formulations for (...) languages with disjoint signatures. We show that the Andréka-Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures. (shrink)

In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers o and a.

The collection of branches (maximal linearly ordered sets of nodes) of the tree $^{ (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal--for example, any level of the tree is almost disjoint from all of the branches. How many sets must be added to the family of branches to make it maximal? This question leads to a series of definitions and results: a set of nodes is off-branch if it is almost disjoint (...) from every branch in the tree; an off-branch family is an almost disjoint family of off-branch sets; and o is the minimum cardinality of a maximal off-branch family. Results concerning o include: (in ZFC) a ≤ p, and (consistent with ZFC) o is not equal to any of the standard small cardinal invariants b,a,d, or c = 2 ω . Most of these consistency results use standard forcing notions--for example, $\mathfrak{b = a in the Cohen model. Many interesting open questions remain, though--for example, whether d ≤ o. (shrink)

In the following essay I set out the core argument expounded by Nicholas Rescher in regard of the link between reality and appearance, illustrating this argument based on chapter 6 of his Reality and its Appearance. Rescher’s argument overlaps with critical realist concerns based on his approach to metaphysical realism. I make the point that the argument exhibits the virtue of concision, but, as a result, suffers from under-elaboration in important areas; most particularly, an explicit engagement with standard philosophical problems (...) of appearance, such as Gettier, and, more generally, the fundamental issue of how appearance may or may not change in response to changes in the human condition. (shrink)

The nectar is in the journey, |3dotnld| ultimate goals may be illusory, nay, most likely are but a gossamer wing. Day by day, however, human life triumphs in its ineluctable capacity to hang in and make things better. Not perfect, simply better." John McDermott, Streams of Experience I investigate one manner in which classical American pragmatism might be utilized by theorists and practitioners interested in addressing urban environmental problems. Despite the widespread adoption of the sustainability moniker within the environmental movement, (...) evidence suggests that progress toward implementing urban environmental sustain ability proposals has been minimal. To address this inaction, I undertake an analysis of the philosophy of progress guiding efforts to transition urban environments toward sustainability. I argue that one of the reasons so little has been accomplished in terms of implementing existing urban environmental sustainability proposals is that a disproportionate emphasis has been placed on values that stem from economic-centered indicators of progress. I argue that the value of progress ought to be less about how much of a certain type of economic growth sustainability proposals ultimately can generate for urban environments and more about ensuring that continual incremental societal progress takes place. (shrink)