Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...) argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

. History of the concept of economic efficiency . INTRODUCTION James Buchanan won the Nobel Prize by proving that the process by which elected officials ...

A general survey of Frege's views on truth, the paper explores the problems in response to which Frege's distinctive view that sentences refer to truth-values develops. It also discusses his view that truth-values are objects and the so-called regress argument for the indefinability of truth. Finally, we consider, very briefly, the question whether Frege was a deflationist.

This paper explores two ways in which evaluations of an agent's character as virtuous or vicious are properly influenced by what the agent finds salient or attention-grabbing. First, we argue that ignoring salient needs reveals a greater deficit of benevolent motivation in the agent, and hence renders the agent more blameworthy. We use this fact to help explain our ordinary intuition that failing to give to famine relief is in some sense less bad than failing to help a child who (...) is drowning right before your eyes, in a way that's compatible with the contention that there's no principled reason to see the one life-saving act as any more or less choiceworthy than the other. Second, we argue that alleged ‘virtues of ignorance’ are better understood as ‘virtues of salience’. Rather than placing demands on what we believe, these virtues place demands on what we find salient. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

ABSTRACT:Moral realism entails that there are metaphysically necessary moral principles of the form ‘all actions of nonmoral kind Z are morally good’; being discoverable a priori, these must be logically necessary. This article seeks to justify this apparently puzzling consequence. A sentence expresses a logically necessary proposition iff its negation entails a contradiction. The method of reflective equilibrium assumes that the simplest account of the apparently correct use of sentences of some type in paradigm examples is probably logically necessary. An (...) account is simple insofar as it uses few predicates designating properties easily recognizable in many different kinds of paradigm examples. I illustrate how reflective equilibrium uses these criteria to discover logically necessary nonmoral propositions such as ‘if S remembers doing X, S believes that he did X’ and ‘if it is scarlet, it is red’. I then illustrate how exactly the same procedures can lead us from paradigm examples of apparently true sentences asserting that actions of some kind are good to discovering moral principles. I advance the contingent hypothesis that most contemporary humans, although they initially disagree about moral issues, have derived from different paradigm examples the same concept of moral goodness, which will ensure that the use of reflective equilibrium will lead to eventual agreement about moral issues. That strongly suggests that the moral principles eventually reached by reflective equilibrium are logically necessary ones. (shrink)

Sociomaterial theories, including actor–network theory (ANT), materialist feminism and posthumanism, are sometimes argued to not be addressing or unable to address sufficiently the political and are therefore dismissed as irrelevant to educational research. Through an extended discussion of writers across the social sciences, this article seeks to counter such a view. Drawing specifically on the work of Latour on the nature of critique and on examples of political analysis from writers such as Barad, Bennett, Braidotti, Marres and Whatmore, we suggest (...) that sociomaterialist approaches to the more-than-human open up extended understandings and productive alternative practices of politics. While recognising that this is a work in progress and not without difficulties and challenges, we argue that there is much to be gained for educational researchers from engaging with such approaches. (shrink)

In _Charles Peirce and Modern Science_, T.L. Short encourages us to read Peirce’s oeuvre in the spirit of philosophical experimentalism. The result is a rewarding and refreshing book that clarifies longstanding controversies and stakes out novel positions in the debates. In these comments, I subject Short’s statements regarding the validity of induction to critical scrutiny. I argue that while much of what he states is correct, he errs in holding that induction is invalid in the short run of an individual’s (...) life. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions will include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How should we understand Julia Staffel's distinction between transitional attitudes and terminal attitudes (Staffel 2021a,b)? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict (Friedman 2020)? And how should we understand the epistemic error that occurs when someone is resistant to evidence (Simion 2023)? (shrink)

Conscientious refusal involves decisions by healthcare workers, on grounds of their conscience, to refuse to provide legal, professionally permissible and safe health interventions to patients. Conscientious provision involves decisions by healthcare workers, also on grounds of conscience, to provide safe and beneficial healthcare to patients that is prohibited by law or policy. Some bioethicists believe that the moral issues governing both are identical, and that if one permits conscientious refusals, one should also permit conscientious provisions. This article argues that this (...) assumption of symmetry is incorrect. To demonstrate this, it does the following: first, it establishes why it matters that we understand the difference between them; second, it describes three recent cases of conscientious provision in Canadian healthcare to help characterize its nature and scope; third, it situates these cases in a socio-economically nuanced analysis of the role of the conscientious provider under conditions or privilege and oppression; finally, it applies insights from the cases and the intersectional analysis to common criticisms of conscientious refusal to reinforce the fundamental asymmetries between conscientious refusal and conscientious provision. (shrink)

Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...) practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz’s philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance. (shrink)

Very few scholars discuss the moral basis of the right of persons accused of crimes to be supplied with attorneys if they cannot afford them. More discussion of the topic is needed, in particular because political theorists who prefer a minimal state deny that indigent persons have such a moral right. This article addresses their contentions by developing three arguments for supplying poor persons accused of crimes with defense attorneys. First, doing so will prevent state officials from becoming emboldened in (...) their dealings with the poor, such that they might come to pose a threat to the non-poor. Second, poor persons who believe that the state does not treat them fairly will have reduced incentives to abide by the law, which will, in turn, increase the cost of the minimal state. Third, the better off should show solidarity with the poor in demanding that the minimal state honor all citizens’ rights to life, liberty, and property. Crucial to these arguments is the claim that a right of indigent defense is unlike other welfare rights in that securing it protects other basic moral rights that minimal statists acknowledge. (shrink)

I argue that uniquely human forms of ‘Theory of Mind’ (or ‘ToM’) are a product of cultural evolution. Specifically, propositional attitude psychology is a linguistically constructed folk model of the human mind, invented by our ancestors for a range of tasks and refined over successive generations of users. The construction of these folk models gave humans new tools for thinking and reasoning about mental states—and so imbued us with abilities not shared by non-linguistic species. I also argue that uniquely human (...) forms of ToM are not required for language development, such that an account of the cultural origins of ToM does not jeopardise the explanation of language development. Finally, I sketch a historical model of the cultural evolution of mental state talk. (shrink)

In this paper I will address a few of the many questions that fall under the general heading of “the ethics of belief.” In section I I will discuss the adequacy of what has come to be known as the “deontological conception of epistemic justification” in the light of our apparent lack of voluntary control over what we believe. In section II I’ll defend an evidentialist view about what we ought to believe. And in section III I will briefly discuss (...) apparent conflicts between epistemic considerations and moral or other considerations. (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)

This is the first volume compiling English translations of Leibniz's journal articles on natural philosophy, presenting a selection of 26 articles, only three of which have appeared before in English translation. It also includes in full Leibniz's public controversies with De Catelan, Papin, and Hartsoeker. The articles include work in optics, on the fracture strength of materials, and on motion in a resisting medium, and Leibniz's pioneering applications of his calculus to these issues by construing them as mini-max and inverse (...) tangent problems. Other topics covered by the articles include: criticisms of the Cartesian estimate of motive force and Leibniz's proposal of a different way of estimating force to replace it; a proposed theory of celestial motions and gravitation, and derivation of the inverse square law; challenge problems concerning the isochronous curve and the catenary; a sample of work on gaming theory; and Leibniz's critique of atomism. (shrink)

In his new introduction, "Note on a Missing Text," Richard Wolin uses the absence from this edition of an interview with Jacques Derrida as a springboard for ...

This title was first published in 2000. Drawing on exclusive interviews with Karl Popper, this book provides the first comprehensive examination of the educational implications of his philosophy. Critically exploring key elements of Popper's work, his theory of knowledge, psychology of learning and politics, Richard Bailey also extrapolates an approach to teaching and learning in schools and the wider community.

Charles Sanders Peirce is regarded as the founding father of pragmatism and a key figure in the development of American philosophy, yet his practical philosophy remains under-acknowledged and misinterpreted. In this book, Richard Atkins argues that Peirce did in fact have developed and systematic views on ethics, on religion, and on how to live, and that these views are both plausible and relevant. Drawing on a controversial lecture that Peirce delivered in 1898 and related works, he examines Peirce's theories (...) of sentiment and instinct, his defence of the rational acceptability of religious belief, his analysis of self-controlled action, and his pragmatic account of practical ethics, showing how he developed his views and how they interact with those of his great contemporary William James. This study will be essential for scholars of Peirce and for those interested in American philosophy, pragmatism, the philosophy of religion, the philosophy of action, and ethics. (shrink)

Few philosophers have been as widely misunderstood as Nietzsche. His detractors and followers alike have often fundamentally misinterpreted him, distorting his views and intentions and criticizing or celebrating him for reasons removed from the views he actually held. Now available in paper, Nietzsche assesses his place in European thought, concentrating upon his writings in the last decade of his productive life. Nietzsche emerges in this comprehensive study as a philosopher of considerable sophistication who diverged sharply from traditional and ordinary ways (...) of thinking, but whose criticism, departures, and alternative views and strategies deserve to be given the most serious attention by philosophers. (shrink)

In this article, we develop and defend an account of the normative significance of nonhuman animal agency. In particular, we examine how animals’ agency interests impact upon the moral permissibility of our interactions with them. First, we defend the claim that nonhuman animals sometimes have rights to self-determination. However, unlike typical adult humans, nonhuman animals cannot exercise this right through the giving or withholding of consent. This combination of claims generates a puzzle about the permissibility of our interactions with nonhuman (...) animals. If animals sometimes have rights to self-determination, but lack the capacity to consent, then when, if ever, is it permissible for us to touch them, hold them, bathe them, or confine them? In the second half of the article, we develop a solution to this puzzle. We argue that while we cannot obtain animals’ consent, they can engage in authoritative communications of will through acts of “assent” and “dissent.”. (shrink)

An assortment of different points of view on conspiracy thinking and conspiracy theories, pro and con.

_What does it mean when a radical understanding of National Socialism is inextricably embedded in the work of the twentieth century’s most important philosopher?_ Martin Heidegger’s sympathies for the conservative revolution and National Socialism have long been well known. As the rector of the University of Freiburg in the early 1930s, he worked hard to reshape the university in accordance with National Socialist policies. He also engaged in an all-out struggle to become the movement’s philosophical preceptor, “to lead the leader.” (...) Yet for years, Heidegger’s defenders have tried to separate his political beliefs from his philosophical doctrines. They argued, in effect, that he was good at philosophy but bad at politics. But with the 2014 publication of Heidegger’s _Black Notebooks_, it has become clear that he embraced a far more radical vision of the conservative revolution than previously suspected. His dissatisfaction with National Socialism, it turns out, was mainly that it did not go far enough. The notebooks show that far from being separated from Nazism, Heidegger’s philosophy was suffused with it. In this book Richard Wolin explores what the notebooks mean for our understanding of arguably the most important philosopher of the twentieth century, and of his ideas—and why his legacy remains radically compromised. (shrink)

Drawing upon hitherto-unused sources and written in a lively, accessible style, this book represents a shift in the historiography of British education. At the center of the investigation is Joseph Payne, born in humble circumstances in 1808, who in 1873 was appointed to the first professorship in Britain, established by a chartered body of schoolteachers. By that date Payne had acquired a considerable reputation-as the founder of two of the most successful of Victorian private schools; a classroom practitioner of rare (...) skill; the author of bestselling textbooks; a scholar, despite no formal education; and as a leading member of such bodies as the College of Preceptors, the Scholastic Registration Association, the Girls' Public Day School Trust, the Women's Education Union, and the Social Science Association. (shrink)

Psychopathological delusions have a number of features that are curiously difficult to explain. Delusions are resistant to counterevidence and impervious to counterargument. Delusions are theoretically, affectively, and behaviorally circumscribed: delusional individuals often do not act on their delusions and often do not update beliefs on the basis of their delusions. Delusional individuals are occasionally able to distinguish their delusions from other beliefs, sometimes speaking of their “delusional reality.” To explain these features, I offer a model according to which, contrary to (...) appearances, delusions are not beliefs at all. Delusions are acceptances that are generated by pathologically powerful cognitive feelings. This model has implications for the way that we should think about non-pathological doxastic states and emotions. (shrink)