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)

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)

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)

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)

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)

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.

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

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)

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).

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.

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)

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.

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)

The Continuum Companion to Existentialism offers the definitive guide to a key area of modern European philosophy. The book covers the fundamental questions asked by existentialism, providing valuable guidance for students and researchers to some of the many important and enduring contributions of existentialist thinkers. Eighteen specially commissioned essays from an international team of experts explore existentialism’s relationship to philosophical method; ontology; politics; psychoanalysis; ethics; religion; literature; emotion; feminism and sexuality; cognitive science; authenticity and the self; its significance in Latin (...) American culture; and its contribution to the development of Poststructuralism. In addition, five short chapters summarise the status of canonical figures Kierkegaard, Nietzsche, Heidegger, Sartre and de Beauvoir, delineating the historical approach to their work, while pointing to new directions such research is now taking. Featuring a series of indispensable research tools (A to Z of terms, concepts and thinkers; timeline of existentialism; list of resources and an annotated guide to further reading), this Companion is an essential tool to help the new reader navigate through the heart of Existentialism and modern European philosophy. (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)

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)

A quotation from Russell concedes that the immensity of real numbers implied by the usual account of the continuum cannot mainly consist of ‘those whose digits procede according to some rule’. Russell concludes that the main body of real numbers ‘must be’ of the ‘lawless’ variety. The author scrutinises these so-called ‘lawless decimals’ and concludes that they are mythical. It follows that the totality of well-defined real numbers cannot be more than a countable whole. It is however clearly uncountable. An (...) explanation is offered using the ‘greater lexicographic sequence’. (shrink)

Barnett and Block (J Bus Ethics 18(2):179–194, 2011 ) argue that one cannot distinguish between deposits and loans due to the continuum problem of maturities and because future goods do not exist—both essential characteristics that distinguish deposit from loan contracts. In a similar way but leading to opposite conclusions (Cachanosky, forthcoming) maintains that both maturity mismatching and fractional reserve banking are ethically justified as these contracts are equivalent. We argue herein that the economic and legal differences between genuine deposit and (...) loan contracts are clear. This implies different legal obligations for these contracts, a necessary step in assessing the ethics of both fractional reserve banking and maturity mismatching. While the former is economically, legally, and perhaps most importantly ethically problematic, there are no such troubles with the latter. (shrink)

This chapter traces the historical and conceptual development of the idea of the continuum and the allied concept of real number. Particular attention is paid to the idea of infinitesimal, which played a key role in the development of the calculus during the seventeenth and eighteenth centuries, and which has undergone a revival in the later twentieth century.

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, (...) such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. (shrink)

Unitary field theories and “SUPER-GUT” theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian (1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, (4,5) and Heisenberg (6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against “all transformations” and which “depend on nothings” (Planck (9–11) ). A satisfactory unitary theory has to involve these constants like (...) the mathematical numbers. Today, Planck's conception of the three elementary constants ħ, c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory (12–16) of induction, such unitary theories are “universal explaining theories.” The fundamental constants involve the complementarity between the universal statements in unitary theory and the “basic statements” in the language of classical observables. (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)

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)

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.

For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f,g\in\omega^\omega}$$\end{document} let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\forall_{f,g}}$$\end{document} be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f,g}}$$\end{document} be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that (...) it is consistent that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\e psilon}$$\end{document} for continuum many pairwise different cardinals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa_\epsilon}$$\end{document} and suitable pairs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(f_\epsilon,g_\epsilon)}$$\end{document}. For the proof we introduce a new mixed-limit creature forcing construction. (shrink)

Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions.

I applaud Fenton and Wiers' attempt to find a demarcation point between cases of addiction that fall within the range of normal function and those that may count as disease. However, I argue that continua don't offer demarcation points, the mechanisms involved are not demonstrably different, and trying to pin down subjectivity doesn't help.

Deleuze’s philosophy is permeated with the problem of the continuum. The idea that the coexistence of durations is implied in the concept of duration itself allows Deleuze to offer a fresh perspective on multiplicity, which is distinct from Bergson’s approach, and which proposes new perspectives on the continuum. While Deleuze critiques Leibniz’s view on this concept by highlighting the non-uniform nature of the continuum, the infinitesimal still plays a significant role in his analysis. However, in his late reading of Leibniz, (...) Deleuze emphasises that folds, rather than infinitesimals, should be considered as the smallest components of the continuum’s labyrinth. This implies that there is a union of indiscernible cuts in the continuity, cuts that do not create gaps or breaks in the overall coherence, but rather a labyrinth. I will show how, in exploring this problem, Deleuze and Guattari draw inspiration from Kafka, in order to relate continuity to contiguity. This relation reveals an internal difference that defines the distinction between what is continuous and what is contiguous. This, in our view, marks a considerable shift between Deleuze’s early reading of Bergson and his late reading of Leibniz, and it allows Deleuze to further develop his idea of the continuum. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:240 Feminist Studies 45, no. 1. © 2019 by Mary Anna Evans Mary Anna Evans Personal Continuum The scent of gasoline is neither attractive nor repulsive. It falls somewhere on the continuum between. It is medicinal, but without the acrid bitterness of medicine. It draws children like a drug, but only when their parents aren’t hovering to warn of danger. Adults know about fire and poisoning and long-range carcinogenic (...) doom. Children only know that the odor around gas pumps smells naughty and fun, until their lips open and the flavor of petroleum turns their stomachs. Why do some things smell so much better than they taste? Gasoline, unlike honey, draws humans but not flies. Sarah was not thinking of fire, poisoning, or doom when she fitted the long metal nozzle into the mouth of her car’s fuel tank. She was trying not to think at all, though the customary thoughts slipped in. None of them were about gasoline. The pump’s air pollution control system was working well but not perfectly, so it took a moment for the odor to reach her nose. Her body roused and snarled at her. The baby. What are you thinking? If you breathe those fumes, what will they do to the baby? A moment passed while her body checked itself, remembering what it already knew. There was no baby. Where is the baby? Mary Anna Evans 241 The frantic voice didn’t echo between her ears. It had nothing to do with her brain at all. It was more than thought. It came from a place deeper than thought, and it wasn’t hers. Her body said things she didn’t want to say, and it needed things she didn’t need. Her body wanted things that were not good for her. Again, Where is the baby? And then, the darker question. What did you do? “Nothing,” she said aloud, since there was no one to hear. I didn’t do anything but bleed. I’m still bleeding. She resisted the instinct to clap her hands over her ears to shut out the voice that couldn’t be shut out. Her defiant hold on the nozzle kept her upright. She listened to the rhythmic throb of the pump. Refusing to turn her face from the gasoline’s stench, she opened her mouth and let the fumes seep in. * * * “Hello, sweetheart,” Frederick said as he came in the door. His peck on the cheek didn’t linger, so Sarah knew there would be no more expressions of affection that day. He had read in a self-help book that it was important for couples to use terms of endearment as a form of bonding. Physical displays of affection were important, too, or so said the self-affirmed relationship expert who wrote the book. In public, displays of affection affirmed the pair bond. In private, even a quick smooch forced men and women to secrete an attachment chemical called oxy-whatever. Oh, hell. She was a chemist. She knew what oxytocin was. She was just mystified by the notion of reading a book to find out how to get some. He turned away and went into the kitchen to fetch the marinating chicken. He always grilled when it was his night to cook. She had come to wonder whether modern men were drawn to cook with fire by an ageold hunter instinct, or whether they were attracted to an activity that put a well-insulated exterior wall between them and the women who remained inside to toss the salads. All across America, every warm summer night, lonely women toss salads and hope for romance. His head poked in the back door. “I bought slivered almonds and croutons.” 242 Mary Anna Evans Her “Thanks for remembering, sweetheart,” bounced off the closing door. Shit. She could have spared herself that soulless term of endearment. Leaving the lettuce in the refrigerator, she thrust her soapy hands under warm running water, because even thinking the word “shit” made the idea of handling raw food appalling. Her body, which had forgotten again that she’d lost the baby, approved of her caution. She guarded her thoughts against disturbing its... (shrink)

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,” 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 tosustainpeace 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)

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.

In the last few years, many countries have introduced laws combating the phenomenon colloquially known as ‘revenge porn’. While new laws criminalising this practice represent a positive step forwards, the legislative response has been piecemeal and typically focuses only on the practices of vengeful ex-partners. Drawing on Liz Kelly’s pioneering work, we suggest that ‘revenge porn’ should be understood as just one form of a range of gendered, sexualised forms of abuse which have common characteristics, forming what we are conceptualising (...) as the ‘continuum of image-based sexual abuse’. Further, we argue that image-based sexual abuse is on a continuum with other forms of sexual violence. We suggest that this twin approach may enable a more comprehensive legislative and policy response that, in turn, will better reflect the harms to victim-survivors and lead to more appropriate and effective educative and preventative strategies. (shrink)

The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although Kreisel's conclusion (...) is correct, his arguments are unsatisfactory. Later sections of the paper advance a different argument that the independence results do not show lack of truth values. (shrink)

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)

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.

Business and Society Review, Volume 127, Issue 1, Page 3-22, Spring 2022.

Business and Society Review, Volume 127, Issue 1, Page 3-22, Spring 2022.

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

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.

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)

The five factor trait of conscientiousnessis 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)

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)

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