It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.

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.

The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.

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.

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but (...) that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

Descriptive set theory and computability theory are closely-related fields of logic; both are oriented around a notion of descriptive complexity. However, the two fields typically consider objects of very different sizes; computability theory is principally concerned with subsets of the naturals, while descriptive set theory is interested primarily in subsets of the reals. In this paper, we apply a generalization of computability theory, admissible recursion theory, to consider the relative complexity of notions that are of interest in descriptive set theory. (...) In particular, we examine the perfect set property, determinacy, the Baire property, and Lebesgue measurability. We demonstrate that there is a separation of descriptive complexity between the perfect set property and determinacy for analytic sets of reals; we also show that the Baire property and Lebesgue measurability are both equivalent in complexity to the property of simply being a Borel set, for $\boldsymbol {\Sigma ^{1}_{2}}$ sets of reals. (shrink)

The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas Blass.

We show that MAκ implies that each collection of Pc-points of size at most κ which has a Pc-point as an RK upper bound also has a Pc-point as an RK lower bound.

We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.

I argue that de se attitudes pose a special problem for philosophical theories of attitudes. Attitude contents are supposed to play a role in characterizing agreement and are also supposed to play a role in the explanation of action. De se attitudes reveal that no single type of object can play both roles.

We are drowning in information, while starving for wisdom.Are the smartest people also the wisest? Not necessarily. While traditional intellectual reasoning and procedural knowledge have helped build the communities we live in, there is a growing scientific understanding that we need emotionally balanced and better-fitting prosocial frameworks for coping with the uncertainties and complexities of life and addressing new challenges of the modern world. We are now poised on the edge of a new science of wisdom.The concept of wisdom, long (...) considered the “pinnacle of insight into the human condition”, has been that of an intangible, subjective, culturally specific entity—an unscientific... (shrink)

Introduction -- Evolution: how life and we came about -- Medicine: our health, illnesses and healing -- Order, disorder and chaos: complex phenomena around us -- Motion, space and time: where and when we are -- Cosmology: how did our universe come about -- Religion, science and scientists -- Science for life.

The objective of the present article is to support the idea that Machado de Assis’ work conforms well to what may be called a non-religious spirituality. For that, the article’s main focus is the analysis of the short story “O Segredo do Bonzo: Capítulo Inédito de Fernão Mendes Pinto”, published in 1882’s collection titled Papéis Avulsos, where the main principles of that spirituality, which is spread all over his work, are given in a nutshell. In a first moment, we analise (...) the intertextuality between Machado’s short story “O Segredo do Bonzo” and Portuguese Renaissance writer’s travelogue Peregrinação and the Machado’s nineteen century critique of the west’s main universalizing proposals: Christianity, scientificity and Enlightenment. In a second moment, we analise the philosophical implications of the primacy given to ‘opinion’ as an existential foundation and as a constitutive element of reality, in a context of close proximity with the soteriological traditions of ancient Greek skepticism, on the one hand, and Buddhism, on the other. A critic of religion, specially of Christian religion, Machado’s ‘accidental’ association with Buddhism is symptomatic of a very peculiar form of non-religious spirituality. (shrink)

This essay offers a proposal for how to understand the idea that there is a special connection between de se attitudes and the explanation of action.

Theories are conceptualized as predictors of phenomena using computable functions acting on prior world information. Formally, the concept of bounded prior world recursive function is defined and used as a candidate for a potential theory. An artificial world of fact is then constructed for which there exist two inconsistent best theories, in that they cannot be improved upon, and these theories are maximally inconsistent in that every best theory is a compromise. It is argued that in such a world the (...) scientific objective would be to find these maximally inconsistent theories. The construction is motivated as an attempt to illustrate the status of theory in the social sciences and in economics, in particular. (shrink)

In this book, first published by OUP USA in 1973, Professor Iyer elucidates the central concepts in the moral and political thought of Mahatma Gandhi, bringing out the subtlety, potency, and universal importance of his concepts of truth and non-violence, freedom and obligation, and his view of the relation between means and ends in politics.

Each of the three phrases-the revival of rhetoric, the new rhetoric, and the rhetorical turn-points to a rediscovery of rhetoric in contemporary thought. However, the scholarly work, motivation and commitments associated with each phrase invokes and puts into playa different notion of rhetoric. In this paper, I explore those differences with a view to showing how the "rhetorical turn," unlike the "revival of rhetoric" and the "new rhetoric," repositions rhetoric as a "metadiscipline." Thus, it signifies a radical shift in the (...) self-understanding of rhetoric. (shrink)

A case is made for supposing that the total probability accounted for in a decision analysis is less than unity. This is done by constructing a measure on the set of all codes for computable functions in such a way that the measure of every effectively accountable subset is bounded by a number <1. The consistency of these measures with the Savage axioms for rational preference is established. Implications for applied decision theory are outlined.

In this paper we describe the nature and problems of business and define one aspect of the business environment. We then propose a framework based on augmented soft systems methodology and object technology that captures both the soft and hard aspects of a business environment within the context of organisational culture. We also briefly discuss cognitive informatics and its relevance to understanding problems and solutions. Pólya's work, which is based around solving mathematical problems, is considered within the context of information (...) systems development. We propose a generic reusable business object model based on general systems theory. We also show how these approaches can be integrated to provide a strategy for understanding business problems and developing integrated solutions. (shrink)

This paper is about the relationship between two questions: the question of what the objects of assertion are and the question of how best to theorise about ‘shifty’ phenomena like modality and tense. I argue that the relationship between these two questions is less direct than is often supposed. I then explore the consequences of this for a number of debates in the philosophy of language.

This essay uses a puzzle about assertion and time to explore the pragmatics, semantics, and epistemology of future discourse. The puzzle concerns cases in which a subject is in a position to say, at an initial time t, that it will be that ϕ, but is not in a position to say, at a later time t′, that it is or was that ϕ, despite not losing or gaining any relevant evidence between t and t′. We consider a number of (...) approaches to the puzzle and defend the view that subjects in these cases lose knowledge simply by moving through time. (shrink)

This paper concerns two points of intersection between de se attitudes and the study of natural language: attitude ascription and communication. I first survey some recent work on the semantics of de se attitude ascriptions, with particular attention to ascriptions that are true only if the subject of the ascription has the appropriate de se attitude. I then examine – and attempt to solve – some problems concerning the role of de se attitudes in linguistic communication.

This essay introduces a puzzle about the interaction between quantifiers and epistemic modals. The puzzle motivates the idea that whether an object satisfies an epistemically modalized predicate depends on the mode of presentation of the domain of quantification. I compare two ways of implementing this idea, one using counterpart theory, the other using Aloni's 'conceptual covers' theory, and then provides some evidence in favor of the former.

Counterfactual attitudes like imagining, dreaming, and wishing create a problem for the standard formal semantic theory of de re attitude ascriptions. I show how the problem can be avoided if we represent an agent's attitudinal possibilities using "multi-centered worlds", possible worlds with multiple distinguished individuals, each of which represents an individual with whom the agent is acquainted. I then present a compositional semantics for de re ascriptions according to which singular terms are "assignment-sensitive" expressions and attitude verbs are "assignment shifters".

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of (...) attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions. (shrink)

Simple taste predications come with an `acquaintance requirement': they require the speaker to have had a certain kind of first-hand experience with the object of predication. For example, if I tell you that the crème caramel is delicious, you would ordinarily assume that I have actually tasted the crème caramel and am not simply relying on the testimony of others. The present essay argues in favor of a lightweight expressivist account of the acquaintance requirement. This account consists of a recursive (...) semantics and an account of assertion; it is compatible with a number of different accounts of truth and content, including contextualism, relativism, and purer forms of expressivism. The principal argument in favor of this account is that it correctly predicts a wide range of data concerning how the acquaintance requirement interacts with Boolean connectives, generalized quantifiers, epistemic modals, and attitude verbs. (shrink)

Yarkoni highlights patterns of overgeneralization in psychology research. In this comment, we note that such challenges also pertain to applied psychological and organizational research and practice. We use two examples – cross-cultural generalizability and implicit bias training – to illustrate common practices of overgeneralization from narrow research samples to broader operational populations. We conclude with recommendations for research and practice.

This essay surveys some of the literature on "imagining oneself to be another," and offers a theory of the content of such imaginings.

ABSTRACT The objective of this article is to contribute to the understanding of Nāgārjuna's 'two truths' doctrine as presented in the Mūlamadhyamakakārikā. For that purpose, we argue that 'two truths' doctrine the basic structural framework for the operational functionality of upāya of upāya, perhaps the most important epistemological/pedagogical notion of Mahāyāna Buddhism. RESUMO O objetivo deste artigo é contribuir para a compreensão da doutrina das "duas verdades", tal como presente no Mūlamadhyamakakārikā de Nāgārjuna. Argumentamos, para tanto, que a doutrina das (...) "duas verdades" constitui o fundamento estrutural básico para a funcionalidade operacional do upāya, que é, talvez, a noção epistemológico-pedagógica mais importante do budismo Mahāyāna. (shrink)

According to one tradition in the philosophy of language and mind, the content of a psychological attitude can be characterized by a set of possibilities. On the classic version of this account, advocated by Hintikka (1962) and Stalnaker (1984) among others, the possibilities in question are possible worlds, ways the universe might be. Lewis (1979, 1983a) proposed an alternative to this account, according to which the possibilities in question are possible individuals or centered worlds, ways an individual might be. The (...) motivation for the centered worlds theory has primarily to do with self-locating – or de se – attitudes. The focus of this paper is on the less-discussed question of how other-locating – or de re – attitudes ought to be treated within this framework. Most advocates of what we might call the modal approach to attitudes, Stalnaker and Lewis included, offer some kind of descriptivist solution to the well-known problems that other-locating attitudes raise. There are intramural differences between Stalnaker, Lewis, and other modal theorists (e.g. two-dimensionalists) on a number of issues: on the precise nature of the descriptivism involved, how attitude content relates to the asserted content of the sentences we utter, and on the proper semantic treatment of attitude reports. I pass over these differences to focus on a problem common to these various approaches: all face a problem when it comes to characterizing the contents of counterfactual attitudes like imagining, dreaming, and wishing. (shrink)