In the early years of the twentieth century, Gottlob Frege and David Hilbert, two titans of mathematical logic, engaged in a controversy regarding the correct understanding of the role of axioms in mathematical theories, and the correct way to demonstrate consistency and independence results for such axioms. The controversy touches on a number of difficult questions in logic and the philosophy of logic, and marks an important turning-point in the development of modern logic. This entry gives an overview of that (...) controversy and of its philosophical underpinnings. (shrink)

In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.

This essay addresses the question of the effect of Russell's paradox on Frege's distinctive brand of arithmetical realism. It is argued that the effect is not just to undermine Frege's specific account of numbers as extensions (courses of value) but more importantly to undermine his general means of explaining the object-directedness of arithmetical discourse. It is argued that contemporary neo-Fregean attempts to revive that explanation do not successfully avoid the central problem brought to light by the paradox. Along the way, (...) it is argued that the need to fend off an eliminative construal of arithmetic can help explain the so-called Caesar problem in the Grundlagen, and that the "syntactic priority thesis" is insufficient to establish the claim that numbers are objects. (shrink)

Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...) to which his understanding of logic differs importantly from that of the model-theoretic tradition that grows out of Hilbert's work. (shrink)

This paper examines the connection between model-theoretic truth and necessary truth. It is argued that though the model-theoretic truths of some standard languages are demonstrably ''''necessary'''' (in a precise sense), the widespread view of model-theoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.

Hourya Benis-Sinaceur, Marco Panza, and Gabriel Sandu. Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. Logic, Epistemology, and the Unity of Science; 37. Springer, 2015. ISBN: 978-3-319-17108-1 ; 978-3-319-36782-8, 978-3-319-17109-8.. Pp. xxi + 125.

This paper defends the view that Frege’s reduction of arithmetic to logic would, if successful, have shown that arithmetical knowledge is analytic in essentially Kant’s sense. It is argued, as against Paul Benacerraf, that Frege’s apparent acceptance of multiple reductions is compatible with this epistemological thesis. The importance of this defense is that (a) it clarifies the role of proof, definition, and analysis in Frege’s logicist works; and (b) it demonstrates that the Fregean style of reduction is a valuable tool (...) for those who would investigate the nature of arithmetical knowledge. (shrink)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

Frege claims that mathematical theories are collections of thoughts, and that scientific continuity turns on thought-identity. This essay explores the difficulties posed for this conception of mathematics by the conceptual development canonically involved in mathematical progress. The central difficulties are that mathematical development often involves sufficient conceptual progress that mature versions of theories do not involve easily-recognizable synonyms of their earlier versions, and that the introduction of new elements in the domains of mathematical theories would seem to conflict with Frege’s (...) view that the original theories involved determinate reference. It is argued here that the difficulties apparently posed to Frege’s central views stem from an overly-simple view of Frege’s understanding of mathematical objects and of reference. The positive view recommended is one on which Frege’s view of mathematical theories is largely consistent with, and helps make sense of, the phenomenon of theoretical unity across conceptual development. (shrink)

This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...) and the prospects for a logical grounding of arithmetic in the wake of the paradox. (shrink)

All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

Whenever one asserts a claim of any kind, one engages in a commitment not just to that claim itself, but to a variety of other claims that follow in its wake, claims that, as we tend to say, follow logically from the original claim. To say that Smith and Jones are both great basketball players is to say something from which it follows that Smith is a great basketball player, that someone is a great basketball player, that there is something (...) at which Smith is great, and so on. (shrink)

This thesis is an examination of Frege's logicism, and of a number of objections which are widely viewed as refutations of the logicist thesis. In the view offered here, logicism is designed to provide answers to two questions: that of the nature of arithmetical truth, and that of the source of arithmetical knowledge. ;The first objection dealt with here is the view that logicism is not an epistemologically significant thesis, due to the fact that the epistemological status of logic itself (...) is not well understood. I argue to the contrary that on Frege's conception of logic, logicism is of clear epistemological importance. ;The second objection examined is the claim that Godel's first incompleteness theorem falsifies logicism. I argue that the incompleteness theorem has no impact on logicism unless the logicist is compelled to hold that logic is recursively enumerable. I argue, further, that there is no reason to impose this requirement on logicism. ;The third objection concerns Russell's paradox. I argue that the paradox is devastating to Frege's conception of numbers, but not to his logicist project. I suggest that the appropriate course for a post-Fregean logicist to follow is one which divorces itself from Frege's platonism. ;The conclusion of this thesis is that logicism has of late been too easily dismissed. Though several critical aspects of Frege's logicism must be altered in light of recent results, the central Fregean thesis is still an important and promising view about the nature of arithmetic and arithmetical knowledge. (shrink)

All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is ‘semantically laden’ and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in (...) general and Frege's philosophy in particular. (shrink)

This is a unique book. It is excellently written, crammed with information, wise and a pleasure to read.' ---Daniel C. Dennett, Tufts University.

Philosopher, theologian, educational theorist, feminist and political pamphleteer, Mary Astell was an important figure in the history of ideas of the early modern period. Among the first systematic critics of John Locke's entire corpus, she is best known for the famous question which prefaces her Reflections on Marriage: 'If all men are born free, how is it that all women are born slaves?' She is claimed by modern Republican theorists and feminists alike but, as a Royalist High Church Tory, the (...) peculiar constellation of her views sits uneasily with modern commentators. Patricia Springborg's study addresses these apparent paradoxes, recovering the historical and philosophical contexts to her thought. She shows that Astell was not alone in her views; rather, she was part of a cohort of early modern women philosophers who were important for the reception of Descartes and who grappled with the existential problems of a new age. (shrink)

The author provides an original reflection on the notion of selfhood as intersubjective, taking the form of phenomenological reflections on the building blocks of the perennial philosophy, recasting Aristotelian-Thomistic metaphysics from the perspective of a phenomenology.

This essay contrasts Damaris Masham and Catharine Trotter Cockburn’s respective moral philosophies. It argues that their views are both remarkably innovative, yet strikingly similar. By focusing on Masham and Cockburn’s accounts of agency and virtue, it is demonstrated that both thinkers take human nature as a sort of guide to moral behavior – i.e., it shows that the moral agent operates under the perception of moral principles as arising from human nature. While both thinkers are known to have been directly (...) influenced by John Locke, it is also argued that both of their moral philosophies bear significant dissimilarities to Lockean morality. (shrink)

Metaphysics is not often spoken of as a venue for dialogue about anything, let alone culture or religion, which are more readily associated with phenomenology or hermeneutics in contemporary thinking. This collection of essays, however, by the late Boston College philosopher Oliva Blanchette, maintains the absolute necessity of metaphysics as a prerequisite for examining any particular 'realm of being,' in all areas of human inquiry, from the particular sciences to historical cultures and religions. Blanchette proposes metaphysics as a (...) fundamental and necessary level of intelligence presupposed in any exercise of judgment, discourse, or dialogue, among rational beings. At the same time, he defends the idea that dialogue is the first and most fundamental form in which such reasoning takes place in human experience, on a radically intersubjective level through language. (shrink)

The history of the recovery movement began with a pushback against treatment, and the philosophies that it was founded upon still have relevant applications to contemporary social work practice. Financial aspects of service provision for people with serious mental illnesses have enabled other actors in the medical model of psychosis treatment to benefit, while disempowering and dehumanizing the consumers of those services. Since then, other movements like Psychopolitics and the Mad Movement have helped empower psychosis survivors to advocate for their (...) right to self-determination amid the epistemological pressure to identify as disabled. Social workers would like to believe that the field has moved beyond the philosophies that perpetuated institutionalization of people with serious mental illnesses. Contemporary examples, however, reveal how social services in the US maintain the status quo of sanism for psychosis survivors. (shrink)

The papers from the 2000 symposium of the Royal Society of Canada explore the crucial relationship between science and ethics.

Imagining Dewey' features productive (re)interpretations of 21st century experience using the lens of John Dewey's 'Art as Experience', through the doubled task of putting an array of international philosophers, educators, and artists-researchers in transactional dialogue and on equal footing in an academic text. This book is a pragmatic attempt to encourage application of aesthetic learning and living, ekphrasic interpretation, critical art and agonist pluralism.0There are two foci: (a) Deweyan philosophy and educational themes with (b) analysis and examples of how educators, (...) artists, and researchers envision and enact artful meaning making. This structure meets the needs of university and high school audiences, who are accustomed to learning about challenging ideas through multimedia and aesthetic experience.00Contributors are: James M. Albrecht, Adam I. Attwood, John Baldacchino, Carolyn L. Berenato, M. Cristina Di Gregori, Holly Fairbank, Jim Garrison, Amanda Gulla, Bethany Henning, Jessica Heybach, David L. Hildebrand, Ellyn Lyle, Livio Mattarollo, Christy McConnell Moroye, Maria-Isabel Moreno-Montoro, Maria Martinez Morales, Stephen M. Noonan, Louise G. Phillips, Scott L. Pratt, Joaquin Roldan, Leopoldo Rueda, Tadd Ruetenik, Leisa Sasso, Bruce Uhrmacher, David Vessey, Ricardo Marin Viadel, Sean Wiebe, Li Xu and Martha Patricia Espiritu Zavalza. (shrink)

Human Specialization in Design and Technology explores emerging trends in learning and training-standardization, customization, personalization-with a unique focus on human needs and conditions. Analyzing evidence from current academic research as well as the popular press, this concise volume defines and examines the trajectory of instructional design and technologies toward more human-centered and specialized products, services, processes, environments, and systems. Examples from education, healthcare, business, and other sectors offer real-world demonstrations for scholars and graduate students of educational technology, instructional design, ICT, (...) and business development. (shrink)

Introduction to the Institutional Logics Perspective -- Precursors to the Institutional Logics Perspective -- Defining the Inter-institutional System -- The Emergence, Stability and Change of the Inter-institutional System -- Micro-Foundations of Institutional Logics -- The Dynamics of Organizational Practices and Identities -- The Emergence and Evolution of Field-Level Logics -- Implications for Future Research.

Biopolitics and Utopia explores the intersection of biopolitics and utopian thought. As an interdisciplinary work, it addresses many salient biopolitical issues (state and medical interventions in the body, fears over scientific progress, resistance to state biopower, and ethical concerns), while also engaging in the utopian drive behind biopolitical efforts. The book is structured into four main sections: Actions, Speculations, Reactions, and Reflections. The chapters in Actions examine the practices of direct, medical intervention to 'normalize' citizens' bodies. The next section, Speculations, (...) approaches the intersection of utopia and biopolitics through a literary lens, reviewing science fiction texts as expressions of cultural and social fears about scientific progress. Reactions outlines potential acts of resistance in the face of biopower. Finally, Reflections offers a more philosophical essay, which engages the reader in the potential for creating an ethics for scientific standards. (shrink)

In commerce, many moral failures are due to narrow mindsets that preclude taking into account the moral dimensions of a decision or action. In turn, sometimes these mindsets are caused by failing to question managerial decisions from a moral point of view, because of a perceived authority of management. In the 1960s, Stanley Milgram conducted controversial experiments to investigate just how far obedience to an authority figure could subvert his subjects' moral beliefs. In this thought-provoking work, the authors examine the (...) prevalence of narrow mental models and the phenomenon of obedience to an authority to analyse and understand the challenges which business professionals encounter in making ethical decisions. Obstacles to Ethical Decision-Making proposes processes - including collaborative input and critique - by which individuals may reduce or overcome these challenges. It provides decision-makers at all levels in an organisation with the means to place ethical considerations at the heart of managerial decision-making. (shrink)

One way to discuss personal identity is by distinguishing between specific and numerical types of similar things. Some of the ways in which the individuality of each clone comes out are found in the alterations they make to their alphanumeric designations, uniforms, and living environments. In his important article “Freedom of the Will and the Concept of a Person,” Harry G. Frankfurt explains that what makes humans unique according to his concept of personhood is their “capacity for reflective self‐evaluation.” The (...) activation of the Fett clones' inhibitor chips with Order 66 represents the intention of the Empire to deprive all the chipped clones of their freedom of action and will. As Frankfurt states, “Suppose, however, that he enjoys both freedom of action and freedom of the will. Then he is not only free to do what he wants to do; he is also free to want what he wants to want.”. (shrink)

Zachariah's description of a wonderful fornicating life for Sam and Dean captures some truth but it also misses the importance women play in shaping the Winchesters' moral decisions. In general, important women in the lives of Sam and Dean fall into three broad categories: mothers, lovers, and monsters. Sam and Dean are all too familiar with this philosophy of utilitarianism. Many times they have sacrificed relationships with women for the sake of their mission. Throughout Supernatural the objectification of the Winchesters (...) is contrasted with a happy domestic life. Sam and Dean are mistaken in thinking that their only value resides in the roles they play in the larger battles of good and evil; if they looked deeper they would see that they both would prefer a loving relationship with a woman. (shrink)