Christopher Ormell; Is the Uncertainty of Mathematics the Real Source of Its Intellectual Charm?, Journal of Philosophy of Education, Volume 27, Issue 1, 30 May.

The Problem of the Paradoxes came to the fore in philosophy and mathematics with the discovery of Russell's Paradox in 1901. It is the "forgotten" intellectual-scientific problem of the Twentieth Century, because for more than sixty years a pretence was maintained, by a consensus of logicians, that the problem had been "solved".

In the first paper of this series the author outlined ‘the showdown phenomenon’: a live sequence of events of two distinct kinds, ‘red’ and ‘green’, which was experienced by the would-be predictor as absolutely and irreducibly unpredictable, because the predictor invariably got his or her predictions wrong. he argued that the showdown phenomenon is an epistemological landmark, because it establishes a clearly conceptualized, tangible, localized ‘limit of knowledge’.) At the end of the original paper the author remarked that if we (...) actually experienced suchabsolute, relentless unpredictability, we would infer the existence of another ‘out there’ doing this to us... In the current paper he returns to this ontological aspect of the new Cogito and fills out some of the thinking which lies behind it. (shrink)

The first paper of this series outlined ‘the showdown phenomenon’: a live sequence of events of two distinct kinds, ‘red’ and ‘green’, which was experienced by the would-be predictor as absolutely and irreducibly unpredictable, because the predictor invariably got his or her predictions wrong. We can clearly and distinctly imagine this happening: so a perverse-random experience of this sort is evidently ‘logically possible’. This raises the question of the relation of the new sequences to ordinary ‘random’ sequences. In this paper (...) an account is developed of the relationship of ‘perverse-randomness’ to ‘randomness’. Such an account may assist us in achieving a new, firmer conceptualization of ordinary probability, and hence in making sense of this notoriously elusive idea. (shrink)

Christopher Ormell; Is the Uncertainty of Mathematics the Real Source of Its Intellectual Charm?, Journal of Philosophy of Education, Volume 27, Issue 1, 30 May.

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)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means (...) excluding as inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

In an age where issues like climate change and the unintended consequences of technological innovation are high on the ethical and political agenda, questions about the nature and extent of our responsibilities to future generations have never been more important, yet simultaneously so difficult to answer. This book takes a unique approach to the problem by drawing on diverse traditions of thinking about care (including developmental psychology, phenomenology and feminist ethics) to explore the nature and meaning of our relationship with (...) the future. Demonstrating that many influential perspectives on intergenerational ethics, including positions advanced by John Rawls, Brian Barry, and Ulrich Beck are undermined by problems relating to uncertainty, it shows that an approach based on care ethics can confront the uncertain future successfully and give a viable account of the nature and scope of future-oriented responsibilities. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

Suppose we believe that God created the world. Then surely we want it to be the case that he intended, in some sense at least, to create THIS world. Moreover, most theists want to hold that God didn't just guess or hope that the world would take one course or another; rather, he KNEW precisely what was going to take place in the world he planned to create. In particular, of each person P, God knew that P was to exist. (...) Call this the "standard" conception. Most theists find the standard conception appealing. Unfortunately, the view seems to conflict with the equally appealing idea — call it "temporal actualism" — that there are no "future" individuals beyond those that already exist in the present moment. For, on this view, for any historical person P, prior to creation, there was no such person as P and hence nothing about P for God to know. Hence, in particular, God couldn't have known that P was to exist. This is of course not a new problem. But past solutions to it are highly problematic. In this paper, after canvassing previous approaches, I will propose a solution that seems to preserve both temporal actualism and a suitably robust form of the standard conception while avoiding the pitfalls of the past. (shrink)

Aristotle attaches particular significance to the homonymy of many central concepts in philosophy and science: that is, to the diversity of ways of being common to a single general concept. His preoccupation with homonymy influences his approach to almost every subject that he considers, and it clearly structures the philosophical methodology that he employs both when criticizing others and when advancing his own positive theories. Where there is homonymy there is multiplicity: Aristotle aims to find the order within this multiplicity, (...) and believes that doing so is crucial to scientific inquiry and philosophical progress.Christopher Shields investigates and evaluates Aristotle's approach to questions about homonymy, characterizing the metaphysical and semantic commitments necessary to establish the homonymy of a given concept. Then, in a series of case-studies, Shields examines in detail some of Aristotle's principal applications of homonymy--to the body, sameness and oneness, life, goodness, and being. Shields's aim is not only to give a fuller understanding of Aristotle's methodology and to illuminate his specific doctrines in a variety of areas, but to show that this methodology remains fruitful today. (shrink)

Christopher Hookway presents a series of studies of themes from the work of the great American philosopher and pragmatist, Charles S. Peirce (1839-1913). These themes center on the question of how we are to investigate the world rationally. Hookway shows how Peirce's ideas about this continue to play an important role in contemporary philosophy.

Moral error theories are often rejected by appeal to ‘companions in guilt’ arguments. The most popular form of companions in guilt argument takes epistemic reasons for belief as a ‘companion’ and proceeds by analogy. I show that this strategy fails. I claim that the companions in guilt theorist must understand epistemic reasons as evidential support relations if her argument is to be dialectically effective. I then present a dilemma. Either epistemic reasons are evidential support relations or they are not. If (...) they are not, then the companions in guilt argument fails. If they are, then a reduction of epistemic reasons to evidential support relations becomes available and, consequently, epistemic reasons cease to be a viable ‘companion’ for moral reasons. I recommend this structure of argument over existing strategies within the literature and defend my claims against recent objections from companions in guilt theorists. (shrink)

The paper provides a systematic overview of recent debates in epistemology and philosophy of science on the nature of understanding. We explain why philosophers have turned their attention to understanding and discuss conditions for “explanatory” understanding of why something is the case and for “objectual” understanding of a whole subject matter. The most debated conditions for these types of understanding roughly resemble the three traditional conditions for knowledge: truth, justification and belief. We discuss prominent views about how to construe these (...) conditions for understanding, whether understanding indeed requires conditions of all three types and whether additional conditions are needed. (shrink)

Miranda Fricker's important study of epistemic injustice is focussed primarily on testimonial injustice and hermeneutic injustice. It explores how agents' capacities to make assertions and provide testimony can be impaired in ways that can involve forms of distinctively epistemic injustice. My paper identifies a wider range of forms of epistemic injustice that do not all involve the ability to make assertions or offer testimony. The paper considers some examples of some other ways in which injustice can prevent someone from participating (...) in inquiry. (shrink)

Plato's Utopia Recast is an illuminating reappraisal of Plato's later works, which reveals radical changes in his ethical and political theory. Christopher Bobonich examines later dialogues, with a special emphasis upon the Laws, and argues that in these late works, Plato both rethinks and revises the basic ethical and poltical positions that he held in his better-known earlier works, such as the Republic. This book will change our understanding of Plato. His controversial moral and political theory, so influential in (...) Western thought, will henceforth be seen in a new light. (shrink)

DMet 10: Prime matter is the origin of all quantities. Hence it is the origin of every dimension of continuous quantity whatever. ...

According to commonsense psychology, one is conscious of everything that one pays attention to, but one does not pay attention to all the things that one is conscious of. Recent lines of research purport to show that commonsense is mistaken on both of these points: Mack and Rock (1998) tell us that attention is necessary for consciousness, while Kentridge and Heywood (2001) claim that consciousness is not necessary for attention. If these lines of research were successful they would have important (...) implications regarding the prospects of using attention research to inform us about consciousness. The present essay shows that these lines of research are not successful, and that the commonsense picture of the relationship between attention and consciousness can be. (shrink)

The psychological writing of Jung and the post-Jungians is all too often ignored as anachronistic, archaic and mystic. In Jung and the Postmodern, Christopher Hauke challenges this, arguing that Jungian psychology is more relevant now than ever before - not only can it be a response to modernity, but it can offer a critique of modernity and Enlightenment values which brings it in line with the postmodern critique of contemporary culture. After introducing Jungians to postmodern themes in Jameson, Baudrillard, (...) Jencks and Foucault, the author introduces postmodernists to Jung's cultural critique and post-Jungian discussions of representation, individuation, consciousness, and the alternatives to Enlightenment rationality. He also takes a totally fresh approach to topics such as hysteria and the body, Jung and Nietzsche, architecture and affect, Princess Diana and the 'death' of the subject, postmodern science and synchronicity, and to psychosis and alternative 'rationalities'. Jung and the Postmodern is vital reading for everyone interested in contemporary culture, not only Jungians and other psychotherapists who want to explore the social relevance of their discipline, but anyone who shares a assionate concern for where we are heading in postmodern times. (shrink)

What is involved in the consciousness of a conscious, "occurrent" propositional attitude, such as a thought, a sudden conjecture or a conscious decision? And what is the relation of such consciousness to attention? I hope the intrinsic interest of these questions provides sufficient motivation to allow me to start by addressing them. We will not have a full understanding either of consciousness in general, nor of attention in general, until we have answers to these questions. I think there are constitutive (...) features of these states which can be identified by broadly philosophical investigation, and in the early part of this paper I will try to do some of that identification. -/- Beyond the intrinsic interest of the topic, the nature of such conscious attitudes is highly pertinent to a philosophical account of psychological self-knowledge. So I will also say something about the significance of the constitutive features of these conscious attitudes for a philosophical account of how it can be that a thinker has a distinctive kind of knowledge of some of his mental states. The general challenge in this area is to find anything intermediate between the unexceptionable but uninformative, on the one hand, and the absolutely unbelievable on the other. (shrink)

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...) succeed. (shrink)

In apparent motion experiments, participants are presented with what is in fact a succession of two brief stationary stimuli at two different locations, but they report an impression of movement. Philosophers have recently debated whether apparent motion provides evidence in favour of a particular account of the nature of temporal experience. I argue that the existing discussion in this area is premised on a mistaken view of the phenomenology of apparent motion and, as a result, the space of possible philosophical (...) positions has not yet been fully explored. In particular, I argue that the existence of apparent motion is compatible with an account of the nature of temporal experience that involves a version of direct realism. In doing so, I also argue against two other claims often made about apparent motion, viz. that apparent motion is the psychological phenomenon that underlies motion experience in the cinema, and that apparent motion is subjectively indistinguishable from real motion. (shrink)

C P Ormell; Ideology and the Reform of School Mathematics, Journal of Philosophy of Education, Volume 3, Issue 1, 30 May 2006, Pages 37–54, https://doi.org/10.1.

What is required for an individual to entertain a singular thought about an object they have encountered before but that is currently no longer within their perceptual range? More specifically, does the individual have to think about the object as having been encountered in the past? I consider this question against the background of the assumption that non-human animals are cognitively ‘stuck in the present’. Does this mean that, for them, ‘out of sight is out of mind’, as, e.g., Schopenhauer (...) seems to have thought? I suggest an alternative answer, also drawing on some empirical work on animal cognition. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Ectogestation involves the gestation of a fetus in an ex utero environment. The possibility of this technology raises a significant question for the abortion debate: Does a woman’s right to end her pregnancy entail that she has a right to the death of the fetus when ectogestation is possible? Some have argued that it does not Mathison & Davis. Others claim that, while a woman alone does not possess an individual right to the death of the fetus, the genetic parents (...) have a collective right to its death Räsänen. In this paper, I argue that the possibility of ectogestation will radically transform the problem of abortion. The argument that I defend purports to show that, even if it is not a person, there is no right to the death of a fetus that could be safely removed from a human womb and gestated in an artificial womb, because there are competent people who are willing to care for and raise the fetus as it grows into a person. Thus, given the possibility of ectogestation, the moral status of the fetus plays no substantial role in determining whether there is a right to its death. (shrink)

In “Bayesianism, Infinite Decisions, and Binding”, Arntzenius et al. (Mind 113:251–283, 2004 ) present cases in which agents who cannot bind themselves are driven by standard decision theory to choose sequences of actions with disastrous consequences. They defend standard decision theory by arguing that if a decision rule leads agents to disaster only when they cannot bind themselves, this should not be taken to be a mark against the decision rule. I show that this claim has surprising implications for a (...) number of other debates in decision theory. I then assess the plausibility of this claim, and suggest that it should be rejected. (shrink)

We argue that while digital health technologies (e.g. artificial intelligence, smartphones, and virtual reality) present significant opportunities for improving the delivery of healthcare, key concepts that are used to evaluate and understand their impact can obscure significant ethical issues related to patient engagement and experience. Specifically, we focus on the concept of empowerment and ask whether it is adequate for addressing some significant ethical concerns that relate to digital health technologies for mental healthcare. We frame these concerns using five key (...) ethical principles for AI ethics (i.e. autonomy, beneficence, non-maleficence, justice, and explicability), which have their roots in the bioethical literature, in order to critically evaluate the role that digital health technologies will have in the future of digital healthcare. (shrink)

The paper argues that an account of understanding should take the form of a Carnapian explication and acknowledge that understanding comes in degrees. An explication of objectual understanding is defended, which helps to make sense of the cognitive achievements and goals of science. The explication combines a necessary condition with three evaluative dimensions: An epistemic agent understands a subject matter by means of a theory only if the agent commits herself sufficiently to the theory of the subject matter, and to (...) the degree that the agent grasps the theory (i.e., is able to make use of it), the theory answers to the facts and the agent’s commitment to the theory is justified. The threshold for outright attributions of understanding is determined contextually. The explication has descriptive as well as normative facets and allows for the possibility of understanding by means of non-explanatory (e.g., purely classificatory) theories. (shrink)

This introduction to the philosophy of the environment examines current debates on how we should think about the natural world and our place within it. The subject is examined from a determinedly analytic philosophical perspective, focusing on questions of value, but taking in attendant issues in epistemology and metaphysics as well. The book begins by considering the nature, extent and origin of the environmental problems with which we need to be concerned. Chapters go on to consider familiar strategies for dealing (...) with environmental problems, and then consider what sort of things are of direct moral concern, examining in turn at animals, non-sentient life-forms, natural but non-living things and deep ecology. The final part of the book investigates notions of value, natural beauty and the place of human beings in the scheme of things. (shrink)

In this detailed study, Christopher Norris defends the kinds of arguments advanced by the early realist, Hilary Putnam. Norris makes a point of placing Putnam's work in a wider philosophical context, and relating it to various current debates in epistemology and philosophy of science. Much like Putnam, Norris is willing to take full account of opposed viewpoints while maintaining a vigorously argued commitment to the values of debate and enquiry.