Nurses practising in mental health are faced with challenging decisions concerning confidentiality if a patient is deemed a potential risk to self or others, because releasing pertinent information pertaining to the patient may be necessary to circumvent harm. However, decisions to withhold or disclose confidential information that are inappropriately made may lead to adverse outcomes for stakeholders, including nurses and their patients. Nonetheless, there is a dearth of contemporary research literature to advise nurses in these circumstances. Cognitive Continuum Theory (...) presents a single‐system intuitive‐analytical approach to examining and understanding nurse cognition, analogous to the recommended single‐system approach to decision‐making in mental health known as structured clinical judgement. Both approaches incorporate cognitive poles of wholly intuition and analysis and a dynamic continuum characterised by a ‘common sense’ blending of intuitive and analytical cognition, whereby cues presented to a decision‐maker for judgement tasks are weighed and assessed for relevance. Furthermore, Cognitive Continuum Theory promotes the importance of determining pattern recognition and functional relations strategies, which can be used to understand the operationalisation of nurse cognition. (shrink)

The Continuum Companion to Continental Philosophy offers the definitive guide to contemporary continental thought.

The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based (...) on diagonal construction are caused by superficial understanding of what a name is. (shrink)

The Continuum Companion to Hume is a comprehensive and accessible guide to Hume's life and work includes 21 specially commissioned essays, written by a team of leading experts, covering every aspect of Hume's thought. The Companion presents details of Hume's life, historical and philosophical context, a comprehensive overview of all the key themes and topics apparent in his work, including his accounts of causal reasoning, scepticism, the soul and the self, action, reason, free will, miracles, natural religion, politics, human (...) nature, women, economics and history, and an account of his reception and enduring influence. This is an essential reference tool for anyone working in the fields of Hume Studies and Eighteenth-Century Philosophy. (shrink)

This is of course the relational, as opposed to the Newtonian absolutist, theory of space and time. The trouble is, as Clarke indicated several times during the correspondence, and as Russell pointed out in his early study of Leibniz: if continua such as space and time are relations, then it must be shown how a relation can behave as we recognize a continuum to do. How, for example, can a relation be divided or measured as we think space and (...) time can? Russell says. (shrink)

The five factor trait of conscientiousness is a supertrait, denoting on one hand a pattern of excessive labor, rigidity, orderliness and compulsivity, and on the other hand a pattern of strict rectitude, scrupulosity, dutifulness and morality. In both respects the obsessive-compulsive personality is conscientious; indeed, it has been labeled a disorder of extreme conscientiousness. Antisocial personality disorder, in the present paper, is described as occupying the opposite end of the conscientiousness continuum. The antisocial is impulsive rather than compulsive, illicit (...) rather than licit, and furtive rather than forthright.After clinically comparing the obsessive and antisocial personalities, the present paper invokes evolutionary theory to explain their resultant behavioral, ideological, political and demographic differences. (shrink)

Leibniz seems to have been the first to suggest a logical interpretation of probability, but there have always seemed formidable mathematical and interpretational barriers to implementing the idea. De Finetti revived it only, it seemed, to reject it in favour of a purely decision-theoretic approach. In this paper I argue that not only is it possible to view (Bayesian) probability as a continuum-valued logic, but that it has a very close formal kinship with classical propositional logic.

There are continuum problems in political economy. There are no objective non-debatable solutions to any of them. All answers to them are arbitrary. Responding to these challenges are, ideally, the responsibility of courts, juries, etc.

The Continuum Companion to Ethics offers a definitive guide to a key area of contemporary philosophy. The book covers all the fundamental questions asked by meta-ethics and normative ethical theory - areas that have continued to attract interest historically as well as topics that have emerged more recently as active areas of research. Fourteen specially commissioned essays from an international team of experts reveal where important work continues to be done in the field and, most valuably, the exciting new (...) directions the field is taking. The Companion explores issues pertaining to moral methodology, moral realism, ethical expressivism, constructivism and the error theory, morality and practical reason, moral psychology, morality and religion, consequentialism, Kantian ethics, virtue ethics, feminist ethics, moral particularism, experimental ethics, and biology, evolution, and ethics. Featuring a series of indispensable research tools, including important technical terms in ethics, a historical chronology, an extensive overview of contemporary meta-ethics and normative ethical theory, a detailed list of internet resources for research in ethics, and a thorough list of recommended works for further study, this is the essential reference tool for anyone working in contemporary philosophical ethics. (shrink)

CH is approached as a problem about the cardinality of the second number class Γ. For the purpose, the theory of constituents is extended to the countably infinite case where the nodes of a constituent tree are sequences of finite constituents. Certain branches (‘perfect’ ones) specify the structures of which a model of a countably infinite constituent consists. In the case of Γ, these branches keep on splitting indefinitely and hence have the cardinality of the continuum. Since Γ is (...) maximal, they are all satisfied in it. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly (...) pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz's sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz's Paris writings, in which he tackles such problems as whether the infinite division of matter (...) entails perfect points, whether matter and space can be regarded as true wholes, whether motion is truly continuous, and the nature of body and substance. Comprising the second section is Pacidius Philalethi, Leibniz's brilliant dialogue of late 1676 on the problem of the continuity of motion. In the selections of the final section, from his Hanover writings of 1677-1686, Leibniz abandons his earlier transcreationism and atomism in favor of the theory of corporeal substance, where the reality of body and motion is founded in substantial form or force.Leibniz's texts (one in French, the rest in Latin) are presented with facing-page English translations, together with an introduction, notes, appendixes containing related excerpts from earlier works by Leibniz and his predecessors, and a valuable glossary detailing important terms and their translations. (shrink)

Biogenic approaches investigate cognition from the standpoint of evolutionary function, asking what cognition does for a living system and then looking for common principles and exhibitions of cognitive strategies in a vast array of living systems—non-neural to neural. One worry which arises for the biogenic approach is that it is overly permissive in terms of what it construes as cognition. In this paper I critically engage with a recent instance of this way of criticising biogenic approaches in order to clarify (...) their theoretical commitments and prospects. In his critique of the biogenic approach, Fred Adams uses the presence of intentional states with conceptual content as a criterion to demarcate cognition-driven behaviour from mere sensory response. In this paper I agree with Adams that intentionality is the mark of the cognitive, but simultaneously reject his overly restrictive conception of intentionality. I argue that understanding intentionality simpliciter as the mark of the mental is compatible with endorsing the biogenic approach. I argue that because cognitive science is not exclusively interested in behaviour driven by intentional states with the kind of content Adams demands, the biogenic approach’s status as an approach to cognition is not called into question. I then go on to propose a novel view of intentionality whereby it is seen to exist along a continuum which increases in the degree of representational complexity: how far into the future representational content can be directed and drive anticipatory behaviour. Understanding intentionality as existing along a continuum allows biogenic approaches and anthropogenic approaches to investigate the same overarching capacity of cognition as expressed in its different forms positioned along the continuum of intentionality. Even if all organisms engage in some behaviour that is driven by weak intentional dynamics, this does not suggest that every behaviour of all organisms is so driven. As such, the worry that the biogenic approach is overly permissive can be avoided. (shrink)

While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.

We often speak of 'Eastern' and 'Western' philosophy, yet it is not always easy to distinguish the key factors that justify this distinction. This essay explores the two very different conceptions of the continuum that underlie these traditions of thought and knowledge. The views of Hermann Weyl are given and it is proposed they are correct. Attention is drawn to the mutually-exclusive visions of the continuum that separate the philosophies of East and West, for they offer us a (...) way of pinning down a definition of these vague geographical terms so as to give them, in at least one respect, a clear philosophical and scientific meaning. (shrink)

Life -- Influences -- Early critics -- Glossary -- Short synopses -- Spinoza scholarship.

What does world peace mean? Peace is more than the absence and prevention of war, whether international or civil, yet most of our ways of conceptualizing and measuring peace amount to just that definition. In this essay, as part of the roundtable “World Peace (And How We Can Achieve It),” I argue that any vision of world peace must grapple not only with war but with the continuums of violence and peace emphasized by feminists: running from the home and community (...) to the public spaces of international relations. Breaking free of the constraints of the last century's intellectual boundaries, I suggest that war and peace are not a dichotomy but rather are intimately related. Yet the dearth of feminist perspectives in global debates prevents us from seeing how violence and harm are exacerbated in households and through the global economy under conditions of both “war” and “peace.” To understand the possibilities for world peace, we must understand these varieties of violence and harm that threaten peace. And to sustain peace we must address the harmful gendered identities, ideologies, and social dynamics that support violence in every society. A narrow understanding of peace as merely the absence of organized violence does not engender the kind of nuanced and rich understanding of human history and human relations needed to bring an end to the structural and physical violence that remains pervasive worldwide. (shrink)

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.

Here we will go beyond the variety of violence to show its unity, common points and continuities. For although there are multiple forms of violence, they are interrelated: they define a continuum from trivial to extreme violence. Violence against oneself, things, living things such as plants and animals, other nations, the other, one’s fellow human beings, therefore the violence of society against its members, which returns to self-violence. Another continuum is its spiral development, with violence generating violence and (...) pushing it to grow. Violence can also be learned, we progress ever further in violence: in gangs, in armies, in society... Everyone is capable of violence, sometimes to a good advantage as in self-defence. Here it resides in necessity, that of survival, but in general it is impunity that allows and encourages it. In closed, totalitarian, universes: family, work, hospital, army, state... The proximity and distance between the perpetrator and the victim defines yet another continuity. We will discuss the various elements that contribute to its development. And paradoxically, to see that violence also serves to avoid violence. In this way, evacuating it, refusing it, is in fact feeding it, which makes today’s violence, which is an evolution of previous violence and which prepares and defines tomorrow’s violence. (shrink)

We give some results concerning various generalized continuum cardinals. The results answer some natural questions which have arisen in preparing a new edition of 5. To make the paper self-contained we define all of the cardinal functions that enter into the theorems here. There are many problems concerning these new functions, and we formulate some of the more important ones.

We examine the question of how many Boolean algebras, distinct up to isomorphism, that are quotients of the powerset of the naturals by Borel ideals, can be proved to exist in ZFC alone. The maximum possible value is easily seen to be the cardinality of the continuum $2^{\aleph_{0}}$ ; earlier work by Ilijas Farah had shown that this was the value in models of Martin's Maximum or some similar forcing axiom, but it was open whether there could be fewer (...) in models of the Continuum Hypothesis. We develop and apply a new technique for constructing many ideals whose quotients must be nonisomorphic in any model of ZFC. The technique depends on isolating a kind of ideal, called shallow, that can be distinguished from the ideal of all finite sets even after any isomorphic embedding, and then piecing together various copies of the ideal of all finite sets using distinct shallow ideals. In this way we are able to demonstrate that there are continuum-many distinct quotients by Borel ideals, indeed by analytic P-ideals, and in fact that there is in an appropriate sense a Borel embedding of the Vitali equivalence relation into the equivalence relation of isomorphism of quotients by analytic P-ideals. We also show that there is an uncountable definable wellordered collection of Borel ideals with distinct quotients. (shrink)

Includes contributions from an international team of leading Locke experts, covering all the key themes and topics, Locke's life, context, reception and ...

The claim that nonhuman animals lack foresight is common and intuitive. I propose an alternative whereby foresight is a gradual continuum in that it is present in animals to the extent that it is needed. A second aspect of this commentary points out that the requirements that the memory that mediates foresight be both specific yet flexible seem contradictory.

A one volume reference guide To The latest research in Philosophy of Science, written by an international team of leading scholars in the field.

The Continuum Companion to Philosophy of Language offers the definitive guide to contemporary philosophy of language. The book covers all the fundamental questions asked by the philosophy of language - areas that have continued to attract interest historically as well as topics that have emerged more recently as active areas of research. Ten specially commissioned essays from an international team of experts reveal where important work continues to be done in the area and, most valuably, the exciting new directions (...) the field is taking. The Companion explores issues pertaining to the nature of language, form semantics, theories of meaning, reference, intensional contexts, context-dependence, pragmatics, the normativity of language, analyticity, a priority and modality. Featuring a series of indispensable research tools, including an A to Z of key terms and concepts, a detailed list of resources and a fully annotated bibliography, this is the essential reference tool for anyone working in the philosophy of language. (shrink)

The first genuine and comprehensive English-language handbook to the study of Kant's philosophy, containing sections on Kant's key works, the philosophical and historical contexts of his philosophy, essays on the reception and influence of the Kantian philosophy, a lexical A-Z list of lemmata addressing central themes and concepts of Kant's thought and an extensive English-language bibliography of secondary literature.

There inevitably comes a time when even the best informed minds are tempted to yield to the lure of binarism: when we are no longer concerned with the details of a system, but rather with our vision of the relationship between man and the world. Without going any further it can already be said that the problem of existence is presented to us in terms of a man/world duality, as though we were unable to exceed our subjective vision of things (...) so as to assess their intrinsic reality.When linguists discovered that they could isolate discrete units called phonemes, they were tempted to oppose the discontinuity of these phonemes – reflecting the underlying discontinuity of the signifiers – to a continuum of prelinguistic experience, a continuum that is not arranged as discrete elements except with reference to any significant units of the language selected for the purpose of communicating this experience to others. At the outset we have nothing but a nebulous mass where only the application of a linguistic grid allows us to discern identifiable units. Even if, in the final analysis, it will prove necessary to doubt the universal validity of this vision of things, we must recognize its usefulness in concretizing a concept of linguistic facts – a concept that has for some time played a beneficent role in research. At least for some of us, this vision should reflect the manner in which the world is gradually organized in our minds each time a perceptible reality is isolated from its context at the instant it receives a name. Allow me to introduce an illustration from personal experience. It was the last day of July in 1914. In our little village in the Savoy the international tension – which would eventually end in general mobilization – was very perceptible; our classes were idle, and teachers and pupils had settled down in a field near the school. I was six. Sitting on the grass, my attention was attracted by a plant with large flat leaves. At that moment someone said the word plantain “plantain.” The plant had not been heretofore exactly unknown to me; it didn't strike me, at that moment, as a discovery; but it acquired a distinct existence only at that instant in the green carpet of the field when a signifier had definitively isolated it. It was most assuredly the gravity of the hour that engraved this incident in my memory. (shrink)

Neste trabalho, procuro explorar o significado filosófico da chamada hipótese do continuum de Darwin e a possibilidade de atribuir mente ou mentalidade a criaturas não-humanas: de um lado, temos o chamado problema de ‘distribuição dos fenômenos mentais’ na recente Etologia Cognitiva; e, de outro, o problema filosófico ‘outras mentes’. Assim, o trabalho procurar indicar uma possível ponte conceitual entre problemas em Filosofia da Mente e estudos em Etologia Cognitiva. Esta é, portanto, uma abordagem interdisciplinar entre filosofia e biologia tendo (...) em vista uma concepção ampla de mente ou mentalidade. (shrink)

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is (...) fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena. (shrink)

Including chapters written by leading scholars on a wide variety of topics, this is a comprehensive one-volume reference guide to the latest work in Pragmatism.

v. 1. A-C -- v. 2. D-J -- v. 3. K-Q -- v. 4. R-Z.

Mesoudi et al. overlook an illuminating parallel between cultural and biological evolution, namely, the existence in each realm of a continuum from intelligent, mindful evolution through to oblivious, mindless evolution. In addition, they underplay the independence of cultural fitness from biological fitness. The assumption that successful cultural traits enhance genetic fitness must be sidelined, as must the assumption that such traits will at least be considered worth having. (Published Online November 9 2006).

Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.