Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Ned Block argues that the higher-order (HO) approach to explaining consciousness is ‘defunct’ because a prominent objection (the ‘misrepresentation objection’) exposes the view as ‘incoherent’. What’s more, a response to this objection that I’ve offered elsewhere (Weisberg 2010) fails because it ‘amounts to abusing the notion of what-it’s-like-ness’ (xxx).1 In this response, I wish to plead guilty as charged. Indeed, I will continue herein to abuse Block’s notion of what-it’s-like-ness. After doing so, I will argue that the HO approach accounts (...) for the sense of what-it’s-like-ness that matters in a theory of consciousness. I will also argue that the only incoherence present in the HO theory is that generated by embracing Block’s controversial notion of what-it’s-like-ness, something no theorist of any stripe ought to do. Block is famous for (among other things) having introduced the notion of ‘phenomenal consciousness’ into contemporary philosophy of mind (Block 1995). This term is widely employed in the philosophical literature and it even appears in the empirical literature. But wide-speared usage has brought about divergent interpretations of the term. We can distinguish a ‘moderate’ and a ‘zealous’ reading of ‘phenomenal consciousness’. On the moderate reading, ‘phenomenal consciousness’ just means ‘experience’. Many people have embraced this sense of the term and use it to roughly pick out conscious experience involving sensory quality (states like conscious visual experiences or conscious pains, for example).2 On the zealous reading, however, phenomenal consciousness is held to be ‘distinct from any cognitive, intentional, or functional property’ (Block 1995: 234). That is, any explanation of phenomenal consciousness in exclusively cognitive, intentional, or functional terms will fail to capture, without remainder, what is really distinctive about phenomenal consciousness. Block, of course, is fully clear about embracing the zealous reading; indeed, his initial introduction of the notion is in those terms. The same ambiguity occurs with the much-used (and abused) idea of ‘what-it’s-like-ness’.. (shrink)

I present a new interpretation of Wittgenstein's later philosophy of logic and mathematics. This interpretation, like others, emphasizes Wittgenstein's attempt to reconcile platonistic and constructivistic approaches. But, unlike other interpretations, mine explains that attempt in terms of Wittgenstein's position about the relations between our concepts of necessity and provability. If what I say here is correct, then we can rescue Wittgenstein from the charge of naive relativism. For his relativism extends only to provability, and not to necessity.

Telling a patient that the outcome of his illness is not good, or even hopeless, requires sensitivity and the ability to communicate with him in the setting of a hospital which is an unnatural environment divorced from family and friends. It is a task which must be taught and learned by doctors and nurses.

This paper explores different interpretations of the word ‘deep’ as it is used by mathematicians, with a large number of examples illustrating various criteria for depth. Most of the examples are theorems with ‘historical depth’, in the sense that many generations of mathematicians contributed to their proof. Some also have ‘foundational depth’, in the sense that they support large mathematical theories. Finally, concepts from mathematical logic suggest that it may be possible to order certain theorems or problems according to ‘logical (...) depth’. (shrink)

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a (...) large extent, the story of philosophy of mathematics. (shrink)

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse (...) Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. (shrink)

The existential analysis -- The death of dasein -- The timeliness of dasein -- The derivation of time -- The time of being.

The achievements of the textile industry in Roman Britain are often underestimated as a result of the meagreness of our available evidence. The Edict on maximum prices issued by Diocletian in A.D. 301 shows that British capes commanded high prices on the markets of the Empire, and that in the late third century A.D. British rugs were the best in the world. In view of the competition from the traditional centres of rug manufacture in the East, this is an astonishing (...) achievement. (shrink)

The received translation and interpretation of many of the technical terms current in the textile industry of the Roman Empire are inaccurate, because lexicographers have either fought shy of being precise, or have thought that they recognized in the ancient world technical processes which originated at a much later date. The evidence is often equivocal or insufficient, but may still yield details that have been overlooked. The textile expression scutulatus, to take an example, deserves more attention than Blümner has devoted (...) to it. When it refers to the appearance of a garment, Lewis and Short, s.v. scutulatus, translate ‘diamond or lozenge-shaped, checkered’. It seems worth while to attempt a more precise translation, and, if possible, to estimate the significance in context of the goods so designated. (shrink)

Living out of silence, out of a fully functioning, lovingly attentive mind, and not just out of thought, out of a partially functioning mind, is requisite for depth or profundity in living or relating. A fully attentive, truly silent or meditative mind sees that there is real dualism of time and the timeless and that time and the timeless each has its own unique value. The timeless, or real silence, that which alone can make for depth in one's living and (...) relating, can be there only when, in one's awareness, time and all that is related to time, have come to an end. An examination of a wide variety of statements made by writers, both past and present, shows that these understandings are seldom there in contemporary writings, just as they were not there in writings that have come down to us from the past. 'Living beyond the One and the Many' invites readers to consider the possibility that what is presented in it can bring deep meaning to one's way of living in the world"--Publisher's description, back cover. (shrink)

If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.

The following three related contributions jointly serve to lift up elements of the thought of the anthropolo­gist Gregory Bateson that can be fruitfully compared with elements of Michael Polanyi’s thought. In a brief introduction, William Stillwell reviews Bateson’s life and developing interests. Stillwell also provides, in a creative dialog form akin to Bateson’s own dialogs, a short review article on Noel Charlton’s Understanding Gregory Bateson: Mind, Beauty and the Sacred Earth. The third piece is Jere Moorman’s short 1991 (...) essay (now out of print) discussing Polanyi’s ideas about tacit knowing and their connection with Bateson’s ideas about the double bind. (shrink)

Hilbert took to using ideal elements in the 1890's, in both algebraic number theory and geometry. His Zahlbericht of 1897 popularized the concept of the ideal introduced by Dedekind in 1871 (which in turn formalized the concept of "ideal number" introduced by Kummer in the 1840's). His geometric work likewise followed a long history of ideal elements, some that originated in geometry and others that originated elsewhere and were applied to geometry. Important examples were:Piero della Francesca's Ideal City.Points at infinity (...) in projective geometry, originating in the 1430s from the "vanishing points" in perspective drawing.Imaginary points in algebraic geometry, originating from the imaginary numbers used by .. (shrink)

How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence (...) on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field's power and progress. (shrink)

Jeffrey Collins’ new book aims to presents Locke’s views on religious toleration in the light of Thomas Hobbes’ political philosophy. At first blush, Hobbes seems an unusual choice as a point of co...

Ikujiro Nonaka, whose formative experience is Japanese, is an established scholar who has written about large business organizations. He sees knowledge at the heart of the organization and its products and aims to develop Michael Polanyi’s conception of tacit knowledge in a practical direction to enhance organizational “knowledge creation.” For Nonaka, what matters is the practice, the doing, the embodiment of knowledge. An organization can amplify and crystallize individuals’ tacit knowledge in a process that allows them to experience deeper understanding. (...) Nonaka holds that it is iimportant to explore the potential that knowledge holds. His spiral process describes disciplined practices that make tacit knowledge independent and available to restructure the organizational knowledge context. (shrink)

Doctors’ strikes are legally permissible in the UK, with the situation differing in other countries. But are they morally permissible? Doug McConnell and Darren Mann have systematically attempted to dismiss the arguments for the moral impermissibility of doctors’ strikes and creatively attempted to provide further moral justification for them. Unfortunately for striking doctors, they fail to achieve this. Meanwhile, junior doctors’ strikes have continued in the UK through 2023 and have now extended into 2024. In this response, which focuses on (...) the UK situation and specifically junior doctors’ strikes in the National Health Service (NHS) in England, I will demonstrate a central problem with their arguments—namely that they underplay the harms caused by prolonged doctors’ strikes by ignoring the harms to patients with cancer. This weakens their conclusion that strikes are morally permissible in terms of the conditions and thresholds they set. I then provide a psychological critique of their justification for strikes in terms of the interests of the public. It follows that invoking the controversial concept of supererogatory action is ungrounded but also absurd when you consider time-critical cancer care. If those representing striking doctors wish to maintain a modicum of moral respectability, they should mitigate for patients with cancer and negotiate reasonably and with urgency. (shrink)

Stereological techniques allow biologists to create quantitative, three-dimensional descriptions of biological structures from two- dimensional images of tissue viewed under the microscope. For example, they can accurately estimate the size of a particular organelle, the total length of a mass of capillaries, or the number of neurons or synapses in a particular region of the brain. This book provides a practical guide to designing and critically evaluating stereological studies of the nervous system and other tissues. It explains the basic concepts (...) behind design-based stereology and how to get started. Also included are detailed descriptions of how to prepare tissue appropriately, perform pilot studies and decide on the appropriate sampling strategy, and account for phenomena such as tissue shrinkage. Numerous examples of applications of stereological methods that are applicable to studies of the central system and a wide variety of other tissues are explained. The book is therefore essential reading for neurobiologists and cell biologists interested in generating accurate representations of cell and tissue architecture. (shrink)

Volume 20, Issue 8, August 2020, Page 27-29.

In the Critique of Judgment, Kant claims that genius is a talent for art, but not for science. Despite his restriction of genius to the domain of fine art, several recent interpreters have suggested that genius has a role to play in Kant’s account of cognition in general and scientific practice in particular. In this paper, I explore Kant’s reasons for excluding genius from science as well as the reasons that one might nevertheless be tempted to think that his account (...) allows room for the scientific genius. I then argue that Kant’s concerns are not only epistemic, but also moral, and together, they give us good reason for resisting the veneration of genius. (shrink)

Husserlian phenomenology, as the study of conscious experience, has often been accused of solipsism. Husserl’s method, it is argued, does not have the resources to provide an account of consciousness of other minds. This chapter will address this issue by providing a brief overview of the multiple angles from which Husserl approached the theme of intersubjectivity, with specific focus on the details of his account of the concrete interpersonal encounter – “empathy.” Husserl understood empathy as a direct, quasi-perceptual form of (...) intentionality through which the sense of the Other is constituted. Furthermore, his account of empathy is holistically integrated with his overall theory of intersubjectivity, including his discussions of the objectivity of nature, and the social, historical, and communal aspects of subjectivity. Husserl’s theory of empathy continues to cast a long shadow, influencing both the analytic and continental approaches to the problem of other minds, as well as contemporary account of social cognition in the cognitive sciences. (shrink)