By suitably adapting an argument of Hirschfeld , we show that there is a single Δ1 formula that defeats “bounded collection” for any model of II2 Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MSC: 03F30, 03C62.

There are at least a few plausible grounds for our use of the term Beta in our title, notwithstanding that there is a key departure, in our framework, from classical Beta Existential Graphs. The situation, in brief, is as follows.The reader accustomed to Peirce’s graphical development of quantificational logic may, if desired, continue to think of formulas being written on a “sheet of assertion.” We retain the “cut” notation for negation and continue to represent conjunction simply by juxtaposition of diagrams. (...) However, on the side of departure, we dispense with the sometimes problematic “lines of identity” of classical Beta and instead represent a quantification by a.. (shrink)

In his long and illuminating paper [1] Joe Barback defined and showed to be non-vacuous a class of infinite regressive isols he has termed “complete y torre” isols. These particular isols a enjoy a property that Barback has since labelled combinatoriality. In [2], he provides a list of properties characterizing the combinatoria isols. In Section 2 of our paper, we extend this list of characterizations to include the fact that an infinite regressive isol X is combinatorial if and only if (...) its associated Dekker semiring D satisfies all those Π2 sentences of the anguage LN for isol theory that are true in the set ω of natural numbers. of the various function and relation symbols of LN via the “lifting ” to D of their Σ1 definitions in ω coincide with their interpretations via isolic extension.) We also note in Section 2 that Π2-correctness, for semirings D, cannot be improved to Π 3-correctness, no matter how many additional properties we succeed in attaching to a combinatoria isol; there is a fixed equation image sentence that blocks such extension. In Section 3, we provide a proof of the existence of combinatorial isols that does not involve verification of the extremely strong properties that characterize Barback's CT isols. (shrink)

Let Λ denote the semiring of isols. We characterize existential completeness for Nerode subsemirings of Λ, by means of a purely isol-theoretic “Σ1 separation property”. Our characterization is purely isol-theoretic in that it is formulated entirely in terms of the extensions to Λ of the Σ1 subsets of the natural numbers. Advantage is taken of a special kind of isol first conjectured to exist by Ellentuck and first proven to exist by Barback . In addition, we strengthen the negative part (...) of [13] by showing that existential completeness is not secured, for a given Nerode semiring, by either a certain “functional closure” property for the extensions of partial recursive functions or the property of “pulling in” some portion of each partial recursive fiber; these latter results are perhaps a little surprising. (shrink)

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many do, some (...) do not. (shrink)

I argue that the Aristotelian definition of motion,“the act of what exists potentially insofar as it exists potentially,” and the mover causality principle,“whatever is moved is moved by another,” are compatible with Newton’s First Law of Motion, which treats inertialmotion as a state equivalent to rest and which requires no sustaining mover for such motion. Both traditions treat motion as such as requiring an initial, generating mover but not necessarily a sustaining motor. Through examining examples of motion as treated by (...) Newtonian physics, and through arguing that potential energy is Aristotelian potentiality, I argue that the First Law is understandable according to the Aristotelian definition as an incomplete act with a twofold ordination of the same potentiality. I then propose that, through the notion of spacetime, Special and General Relativity instantiate motion as a unity of differentiated prior and posterior parts that do not coexist in reality. (shrink)

This paper argues that inertia is an inherent principle and that inertia and Newton’s First Law are in this way natural in the Aristotelian sense. Indeed, many difficulties concerning inertia and the First Law of Motion may be resolved by understanding them through an Aristotelian conception of nature. The paper proceeds by examining the characteristic activities of inertia, the Aristotelian idea of nature, various accounts of inertia as force and as inert, and the manner in which an Aristotelian conception of (...) nature improves on these accounts. It concludes that the unsuccessful attempts by physicists to find an extrinsic origin of inertia, though they may eventually lead to new discoveries, support the view that inertia is an inherent principle of nature. Newton himself understood the principle of inertia through an eclectic but largely nonAristotelian conception of nature and matter and by the problematic notion of a vis inertiae. However, Newton’s general philosophy of nature should be distinguished from the more specific content of the First Law and of inertia itself. A general Aristotelian conception of nature can resolve many of Newton’s difficulties. Thus, inertia and the First Law of Motion are reasonably regarded as natural in the general Aristotelian sense. (shrink)

Given a Δ1 ultrapower ℱ/[MATHEMATICAL SCRIPT CAPITAL U], let ℒU denote the set of all Π2-correct substructures of ℱ/[MATHEMATICAL SCRIPT CAPITAL U]; i.e., ℒU is the collection of all those subsets of |ℱ/[MATHEMATICAL SCRIPT CAPITAL U]| that are closed under computable functions. Defining in the obvious way the lattice ℒ) with domain ℒU, we obtain some preliminary results about lattice embeddings into – or realization as – an ℒ. The basis for these results, as far as we take the matter, (...) consists of the well-known class of minimal ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, which function as atoms, and the class of minimalfree ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, to whose nonemptiness a substantial section of the paper is devoted. It is shown that an infinite, convergent monotone sequence together with its limit point is embeddable in an ℒ, and that the initial segment lattices {0, 1,…, n } are not just embeddable in , but in fact realizable as, lattices ℒ. Finally, the diamond is embeddable; and if it is not realizable, then either the 1 - 3 - 1 lattice or the pentagon is at least embeddable. (shrink)

This paper summarizes (in German) recent tendencies in the philosophy of the life sciences.

I : PETRARCH'S BRITAIN 1: Piero Boitani: Petrarch and the barbari Britanni II: PETRARCH AND THE SELF 2: Jennifer Petrie: Petrarch solitarius 3: Zygmunt G. Baranski: The Ethics of Ignorance: Petrarch's Epicurus and Averroes and the Structures of the De Sui Ipsius et Aliorum Ignorantia 4: Jonathan Usher: Petrarch's Second Death III: PETRARCH IN DIALOGUE 5: Francesca Galligan: Poets and Heroes in Petrarch's Africa: Classical and Medieval Sources 6: Enrico Santangelo: Petrarch reading Dante: the Ascent of Mont Ventoux 7: John (...) Took: Petrarch and Cino da Pistoia: A Moment in the Pre-history of the Canzoniere IV: PETRARCHISM AND ANTIPETRARCHISM IN ITALY 8: Abigail Brundin: Petrarch and the Italian Reformation 9: Hilary Gatti: Petrarch, Sidney, Bruno 10: Diego Zancani: Renaissance Misogyny and the Rejection of Petrarch 11: Letizia Panizza: Impersonations of Laura in Sixteenth and Seventeenth Century Italy V: PETRARCHISM: ENGLISH AND SCOTTISH CONNECTIONS 12: Michael Wyatt: Other Petrarchs in Early Modern England 13: Stephen Clucas: Thomas Watson's Hekatompathia and European Petrarchism 14: John Roe: The Comedy of Astrophil: Petrarchan Motifs in Sidney's Astrophil and Stella 15: Syrithe Pugh: Sidney, Spenser and Political Petrarchism 16: R. D. S. Jack: Petrarch and the Scottish Renaissance Sonnet VI: PETRARCH AND THE MODERNS: ITALY AND BRITAIN 17: Pamela Williams: Leopardi and Petrarch 18: Ela Tandello: Between Tradition and Transgression: Amelia Rosselli's Petrarch 19: Martin McLaughlin: Nineteenth-century British Biographies of Petrarch 20: Peter Hainsworth: Translating Petrarch. (shrink)

In volume 1 of this three-volume work, Paul Ricoeur examined the relations between time and narrative in historical writing. Now, in volume 2, he examines these relations in fiction and theories of literature. Ricoeur treats the question of just how far the Aristotelian concept of "plot" in narrative fiction can be expanded and whether there is a point at which narrative fiction as a literary form not only blurs at the edges but ceases to exist at all. Though some semiotic (...) theorists have proposed all fiction can be reduced to an atemporal structure, Ricoeur argues that fiction depends on the reader's understanding of narrative traditions, which do evolve but necessarily include a temporal dimension. He looks at how time is actually expressed in narrative fiction, particularly through use of tenses, point of view, and voice. He applies this approach to three books that are, in a sense, tales about time: Virgina Woolf's _Mrs. Dalloway;_ Thomas Mann's _Magic Mountain;_ and Marcel Proust's _Remembrance of Things Past_. "Ricoeur writes the best kind of philosophy—critical, economical, and clear."—Eugen Weber, _New York Times Book Review _ "A major work of literary theory and criticism under the aegis of philosophical hermenutics. I believe that... it will come to have an impact greater than that of Gadamer's Truth and Method—a work it both supplements and transcends in its contribution to our understanding of the meaning of texts and their relationship to the world."—Robert Detweiler, _Religion and Literature_ "One cannot fail to be impressed by Ricoeur's encyclopedic knowledge of the subject under consideration.... To students of rhetoric, the importance of Time and Narrative... is all too evident to require extensive elaboration."—Dilip Parameshwar Gaonkar, _Quarterly Journal of Speech_. (shrink)

Does the viability of the discovery program depend on showing either (1) that methods of generating new problem solutions, per se, have special probative weight (the per se thesis); or, (2) that the original conception of an idea is logically continuous with its justification (anti-divorce thesis)? Many writers have identified these as the key issues of the discovery debate. McLaughlin, Pera, and others recently have defended the discovery program by attacking the divorce thesis, while Laudan has attacked the discovery (...) program by rejecting the per se thesis. This disagreement over the central issue has led to communication breakdown. I contend that both friends and foes of discovery mistake the central issues. Recognizing a form of divorce helps rather than hurts the discovery program. However, the per se thesis is not essential to the program (nor is the related debate over novel prediction); hence, the status of the per se thesis is a side issue. With these clarifications in hand, we can proceed to the next stage of the discovery debate--the development (or revival) of a generative conception of justification which goes beyond consequentialism to forge a strong linkage of generation (or rather, generatability) with justification. (shrink)

The study of the mind has always been one of the main preoccupations of philosophers, and has been a booming area of research in recent decades, with remarkable advances in psychology and neuroscience. Oxford University Press now presents the most authoritative and comprehensive guide ever published to the philosophy of mind. An outstanding international team of contributors offer 45 specially written critical surveys of a wide range of topics relating to the mind. The first two sections cover the place of (...) the mind in the natural world: its ontological status, how it fits into the causal fabric of the universe, and the nature of consciousness. The third section focuses on the much-debated subjects of content and intentionality. The fourth section examines a variety of mental capacities, including memory, imagination, and emotion. The fifth section looks at epistemic issues, in particular regarding knowledge of one's own and other minds. The volume concludes with a section on self, personhood, and agency. The Oxford Handbook of Philosophy of Mind will be an invaluable resource for advanced students and scholars of philosophy, and also for researchers in neighboring disciplines seeking a high-level survey of the state of the art in this flourishing field. (shrink)

This important text introduces students to both feminism and other social and political theories via an examination of the inter-relationship between different feminist positions and key contemporary debates. The book takes each debate in turn, outlines the main themes, discusses different feminist responses and evaluates the implications for real-life political and social issues. This user-friendly structure effectively redraws the map of contemporary feminist thought, offering a fresh and succinct summary of an extensive range of material and graphically demonstrating the ongoing (...) relevance and value of a feminist perspective. (shrink)

_How to Think Critically_ begins with the premise that we are all, every day, engaged in critical thinking. But just as we may develop bad habits in daily life if we don’t scrutinize our practices, so are we apt to develop bad habits in critical thinking if we are careless in our reasoning. Readers are presented with a traditional step-by-step method for analysis that can be applied to all argument forms. Hundreds of exercises (with solutions) are included, as are several (...) random statement generators that can be used to create thousands of additional examples. Truth tables, Venn diagrams, and other essential concepts are introduced not merely as objects for academic study but also as tools for better thinking and living. At a time when the value of critical thinking is recognized to be greater than ever, this book is an important resource both inside and outside the classroom. (shrink)

Issues of reliability are claiming center-stage in the epistemology of machine learning. This paper unifies different branches in the literature and points to promising research directions, whilst also providing an accessible introduction to key concepts in statistics and machine learning – as far as they are concerned with reliability.

Thomas Reid, the Scottish natural and moral philosopher, was one of the founding members of the Aberdeen Philosophical Society and a significant figure in the Scottish Enlightenment. Reid believed that common sense should form the foundation of all philosophical inquiry. He criticised the sceptical philosophy propagated by his fellow Scot David Hume and the Anglo-Irish bishop George Berkeley, who asserted that the external world did not exist outside the human mind. Reid was also critical of the theory of ideas (...) propagated by Locke and Descartes, arguing that it was incompatible with physical and experiential facts. For Reid, our senses demonstrate that the external world must exist, and this work is organised in chapters examining each of the senses in turn. The book, based on his lectures, was first published in 1764 when Reid was a regent professor at King's College, Aberdeen, and was reissued in 1818. (shrink)

The application of machine-learning technologies to medical practice promises to enhance the capabilities of healthcare professionals in the assessment, diagnosis, and treatment, of medical conditions. However, there is growing concern that algorithmic bias may perpetuate or exacerbate existing health inequalities. Hence, it matters that we make precise the different respects in which algorithmic bias can arise in medicine, and also make clear the normative relevance of these different kinds of algorithmic bias for broader questions about justice and fairness in healthcare. (...) In this paper, we provide the building blocks for an account of algorithmic bias and its normative relevance in medicine. (shrink)

The question of when and how the basic concepts that characterize modern science arose in Western Europe has long been central to the history of science. This book examines the transition from Renaissance engineering and philosophy of nature to classical mechanics oriented on the central concept of velocity. For this new edition, the authors include a new discussion of the doctrine of proportions, an analysis of the role of traditional statics in the construction of Descartes' impact rules, and go deeper (...) into the debate between Descartes and Hobbes on the explanation of refraction. They also provide significant new material on the early development of Galileo's work on mechanics and the law of fall. (shrink)

This chapter contains sections titled: Religion Spirituality Education.

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

Death.--The absurd.--Moral luck.--Sexual perversion.--War and massacre.--Ruthlessness in public life.--The policy of preference.--Equality.--The fragmentation of value.--Ethics without biology.--Brain bisection and the unity of consciousness.--What is it like to be a bat?--Panpsychism.--Subjective and objective.

In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other.