One of the more distinctive features of Bob Hale and Crispin Wright’s neologicism about arithmetic is their invocation of Frege’s Constraint – roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. In particular, they maintain that, if adopted, Frege’s Constraint adjudicates in favor of their preferred foundation – Hume’s Principle – and against alternatives, such as the Dedekind-Peano axioms. In what follows we establish two main (...) claims. First, we show that, if sound, Hale and Wright’s arguments for Frege’s Constraint at most establish a version on which the relevant application of the naturals is transitive counting – roughly, the counting procedure by which numerals are used to answer “how many”-questions. Second, we show that this version of Frege’s Constraint fails to adjudicate in favor of Hume’s Principle. If this is the version of Frege’s Constraint that a foundation for arithmetic must respect, then Hume’s Principle no more – and no less – meets the requirement than the Dedekind-Peano axioms do. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and (...) on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

In their book Relativism, Maria Baghramian and Annalisa Coliva (B&C; 2020) offer a panoramic view of various forms of relativism and their history. They mak.

We now know of a number of ways of developing real analysis on a basis of abstraction principles and second-order logic. One, outlined by Shapiro in his contribution to this volume, mimics Dedekind in identifying the reals with cuts in the series of rationals under their natural order. The result is an essentially structuralist conception of the reals. An earlier approach, developed by Hale in his "Reals byion" program differs by placing additional emphasis upon what I here term Frege's (...) class='Hi'>Constraint, that a satisfactory foundation for any branch of mathematics should somehow so explain its basic concepts that their applications are immediate. This paper is concerned with the meaning of and motivation for this constraint. Structuralism has to represent the application of a mathematical theory as always posterior to the understanding of it, turning upon the appreciation of structural affinities between the structure it concerns and a domain to which it is to be applied. There is, therefore, a case that Frege's Constraint has bite whenever there is a standing body of informal mathematical knowledge grounded in direct reflection upon sample, or schematic, applications of the concepts of the theory in question. It is argued that this condition is satisfied by simple arithmetic and geometry, but that in view of the gap between its basic concepts (of continuity and of the nature of the distinctions among the individual reals) and their empirical applications, it is doubtful that Frege's Constraint should be imposed on a neo-Fregean construction of analysis. (shrink)

Foundational projects disagree on whether pure and applied mathematics should be explained together. Proponents of unified accounts like neologicists defend Frege’s Constraint (FC), a principle demanding that an explanation of applicability be provided by mathematical definitions. I reconsider the philosophical import of FC, arguing that usual conceptions are biased by ontological assumptions. I explore more reasonable weaker variants — Moderate and Modest FC — arguing against common opinion that ante rem structuralism (and other) views can meet them. I (...) dispel doubts that such constraints are ‘toothless’, showing they both assuage Frege’s original concerns and accommodate neo-logicist intents by dismissing ‘arrogant’ definitions. (shrink)

Hilary Putnam and John McDowell have each argued against representational realist theories of perception and in favor of direct realist (or “common-sense realist”) alternatives. I claim that in both cases they beg the question against their representational realist opponents. Moreover, in neither case has any alternative been offered to the representational realist position where the solution to perceptual or demonstrative versions of Frege’s problem is concerned. In this paper I present a transcendental argument that some of our perceptions of (...) external objects must be direct in the sense that we perceive them and there is nothing else we perceive in virtue of which we do so. I also present a reply to standard objections to the claim that transcendental arguments can be used to support conclusions about the world and not simply about our own use of concepts. Finally, I present a theory in terms of which the relevant Frege problems can be solved without appeal to any of the sorts of representations in terms of which representational realism is defined. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK JACKET.

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

[Translation of Frege's 'Gedankengefüge' (1923)].

Translation of Frege's 'Über die Begriffsschrift des Herrn Peano und meine eigene' (1896). Translated by V.H. Dudman.

[Translation of Frege's 'Über das Trägheitsgesetz].

The first complete English translation of a groundbreaking work. An ambitious account of the relation of mathematics to logic. Includes a foreword by Crispin Wright, translators' Introduction, and an appendix on Frege's logic by Roy T. Cook. The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was (...) to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook. Readership: Scholars and advanced students in philosophy of logic, philosophy of mathematics, and early analytic philosophy. (shrink)

This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography.

(Translation of Frege's Grundgesetze II, §§ 86-137).

Translation of Frege's 'Über den Zweck der Begriffsschrift' (1882).

(Translation of Frege's "Le nombre entier", 1895).

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

Frege's essay "Der Gedanke.Eine logische Untersuchung" was first published in the Beitrage zur Philosophie des Deutschen Idealismus for 1918-1919 and is one of three related logical studies published as a complete work by Gunther Patzig entitled Logische Untersuchungen in Gottingen, 1966 .

Blackburn has outlined a formal account for moral expressivism, and we argued that the moral Frege-Geach problem can be solved formally by appending two rules for the boo-operator which are missing from his account. We then extended Blackburn’s formal account to generate a similar solution to the problem in modal context and showed that the validity of the modal argument can be preserved too in modal expressivism. However, the higher-order element endorsed by Blackburn does not seem necessary for solving the (...) Frege-Geach problem. Nor is his extension from moral expressivism to modal expressivism tenable, since the latter violates its own ontological constraint. A general moral is drawn on the basis on three observations made in evaluating Blackburn’s expressivism. (shrink)

It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + 3 (...) are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)

Sustainability problems often seem intractable. One reason for this is due to difficulties coordinating actors’ efforts to address socially responsible outcomes. Drawing on theories of bounded ethicality and incorporating work on communicating shared values in coordinating action this paper outlines the lack coordination as a matching issue, one complicated by underlying heterogeneity in actors’ moral values and thus motivation to address socially responsible outcomes. Three factors contribute to this matching problem. First, we argue it is not actors’ simple cognitive awareness, (...) but their moral awareness of social issues that explains why certain actors move to address problems while others do not. In other words, actors may recognize sustainability problems, but are not motivated to solve them as they are not understood as moral problems. Second, we posit that progress requires alignment in issues that some actors find worth addressing whereas others do not, thus explaining how heterogeneity in moral perceptions interrupt coordination towards socially important goals. Finally, we propose that progress is undermined if actors myopically focus on level-specific outcomes in ways that elucidates why institutional responses often fail to address individual outcomes and vice versa. We use the existing literature on the socially important issue of food waste to examine our theoretical contribution and develop a typology that explains conditions that inhibit coordination. Thus, our work proposes a psycho-structural view on matching and coordination toward sustainable outcomes, highlighting how psychological and structural constraints prevent effective coordination in addressing sustainability goals. (shrink)

In this short monograph, John Horty explores the difficulties presented for Gottlob Frege's semantic theory, as well as its modern descendents, by the treatment of defined expressions. The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the treatment of simple stipulative definitions led Frege to important difficulties. Horty is able to suggest ways out of these difficulties that are both philosophically and logically plausible and Fregean in (...) spirit. This discussion is then connected to a number of more familiar topics, such as indexicality and the discussion of concepts in recent theories of mind and language. In the latter part of the book, after introducing a simple semantic model of senses as procedures, Horty considers the problems that definitions present for Frege's idea that the sense of an expression should mirror its grammatical structure. The requirement can be satisfied, he argues, only if defined expressions--and incomplete expressions as well--are assigned senses of their own, rather than treated contextually. He then explores one way in which these senses might be reified within the procedural model, drawing on ideas from work in the semantics of computer programming languages. With its combination of technical semantics and history of philosophy, Horty's book tackles some of the hardest questions in the philosophy of language. It should interest philosophers, logicians, and linguists. (shrink)

The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the ...

Frege argued that though it is logically possible for an illogical community to exist, It is not possible that it should be right. Neither the assertion of false statements nor the acceptance of invalid arguments suffices to render a community illogical. The kinds of behavior which would suffice prove, On examination, To be very rare, But to justify frege's rather obscure remarks on illogicality and the universality of logical laws. The laws of logic are to be understood as constraints on (...) the kinds of rules governing linguistic exchanges needed if the language is to accommodate attempts to prove. (edited). (shrink)

Concerns a problem posed, but not solved, by Frege in part III of his Grundgesetze. As a preliminary to defining ‘real number’, Frege attempts to analyse the notion of a quantitative domain. He was unaware of the previous attempt of Otto Holder to do this; it is remarked how much weaker Frege's assumptions were in deriving theorems than Holder's. Frege deals with groups on which there is a right‐invariant semilinear ordering, although he does not use this terminology. He is uncertain (...) whether it can be deduced that the ordering is also left‐invariant, and proves as much as possible without invoking the assumption that it is. The independence proof, due to Dr Peter Neumann, establishes that it could not be deduced. (shrink)

STEPHEN TOULMIN George Santayana used to insist that those who are ignorant of the history of thought are doomed to re-enact it. To this we can add a corollary: that those who are ignorant of the context of ideas are doom ed to misunderstand them. In a few self-contained fields such as pure mathematics, concepts and conceptual systems can perhaps be de tached from their historico-cultural situations; so that (for instance) a self-taught Ramanujan, living alone in India, mastered number theory (...) to a point at which he could make major contributions to European mathematics. But elsewhere the situation is different - and, in philosophy, inevitably so. For philosophical ideas and problems confront us like geological specimens in situ; and, in the act of prising them free from their historical and cultural locations, we can too easily forget about the matrix in which they took shape, and end by impossing on them a sculptural form of our own making. Something of this kind has happened in the case of Ludwig Wittgen stein. For his philosophical work has commonly been seen as an episode in the development, either of mathematicallogic, or oftwentieth-century British philosophy. His associations with Frege and Russell, Moore and Waismann, have over-shadowed everything else in his cultural origins and intellectual concerns. (shrink)

This article concerns the morality of establishing regulated kidney markets in an effort to reduce the chronic shortage of kidneys for transplant. The article tries to rebut the view, recently defended by James Taylor, that if we hold autonomy to be intrinsically valuable, then we should be in favor of such markets. The article then argues that, under current conditions, the buying and selling of organs in regulated markets would sometimes violate two Kantian principles that are seen as moral constraints. (...) One principle forbids expressing disrespect for the dignity of humanity; the other forbids treating others merely as means. In light of the moral danger posed by regulated markets, the article advocates an alternative way of diminishing the current organ shortage, namely opt-out systems of cadaveric organ donation. (shrink)

In this paper I briefly summarize Pellegrino’s phenomenological analysis of the ethics of the physician–patient relationship. In delineating the essential elements of the healing relationship, Pellegrino demonstrates the necessity for health care professionals to understand the patient’s lived experience of illness. In considering the phenomenon of illness, I identify certain essential characteristics of illness-as-lived that provide a basis for developing a rigorous understanding of the patient’s experience. I note recent developments in the systematic delivery of health care that make it (...) difficult for health care professionals to realize Pellegrino’s ethical model of the role of healer. Such developments limit both the physician’s freedom to act on behalf of the patient without the constraint of third parties and the physician’s freedom to act in light of his or her own ethical or religious convictions. Given these difficulties, I note MacIntyre’s call for the development of moral communities, as an alternative to the prevailing culture, and share a first-hand example illustrating how intentional Christian community provides an alternative nurturing context that permits the full development of the healing relationship. (shrink)

Two topics are presently discussed. first, the distinction frege draws between two kinds of laws, natural and normative. secondly, we show how a remark made by frege with respect to different notions of truth is related to the analysis of meaning by family resemblances, as stressed later by wittgenstein. the historical dimension of family formation is discussed and references to 18th and 19th-century philosophers holding similar views are made. (edited).

Although social scientists have identified diverse behavioral patterns among children from dissimilarly structured families, marketing scholars have progressed little in relating family structure to consumption-related decisions. In particular, the roles played by members of single-mother families—which may include live-in grandparents, mother’s unmarried partner, and step-father with or without step-sibling(s)—may affect children’s influence on consumption-related decisions. For example, to offset a parental authority dynamic introduced by a new stepfather, the work-related constraints imposed on a breadwinning mother, or the imposition of adult-level (...) household responsibilities on children, single-mother families may attend more to their children’s product preferences. -/- Without a profile that includes socio-economic, behavioral, and psychological aspects, efficient and socially responsible marketing to single-mother households is compromised. Relative to dual-parent families, single-mother families tend to have fewer resources and less buying power, children who consume more materialistic and compulsively, and children who more strongly influence decision making for both own-use and family-use products. Timely research would ensure that these and other tendencies now differentiate single-mother from dual-parent families in ways that marketers should address. Hence, our threefold goal is (1) to consolidate and highlight gaps in existing theory applied to studying children’s influence on consumption-related decision making in single-mother families, and (2) to propose a hybrid framework that merges two theories conducive to such research, and (3) to identify promising research propositions for future research. (shrink)

This paper considers the potentially wrongful discriminatory nature of certain of our dating preferences. It argues that the wrongfulness of such preferences lies primarily in the simple lookism they involve. While it is ultimately permissible for us to date people partly because of how they look, I argue that we have a duty to ‘look behind’ people’s appearance, which I take to mean that we ought not, on the basis of their appearance, to regard them as absolutely out of the (...) question for us to engage with in a romantic setting. Further, constraints similar to those suggested by a duty to look behind people’s appearance gain support from another duty we have, namely, a duty to counteract, also in our daily lives, the fact that people are undeservedly disadvantaged in various ways. (shrink)

Stakeholder theory is widely recognized as a management theory, yet very little research has considered its implications for individual managerial decision-making. In the two studies reported here, we used stakeholder theory to examine managerial decisions about balancing stakeholder interests. Results of Study 1 suggest that indivisible resources and unequal levels of stakeholder saliency constrain managers’ efforts to balance stakeholder interests. Resource divisibility also influenced whether managers used a within-decision or an across-decision approach to balance stakeholder interests. In Study 2 we (...) examined instrumental and normative implications of these two approaches. We conclude by considering the contributions of this research. (shrink)

Effective robots and autonomous systems must be trustworthy. This chapter examines models of trustworthiness from a philosophical and empirical perspective to inform the design and adoption of autonomous systems. Trustworthiness is a property of trusted agents or organisations that engenders trust in other agent or organisations. Trust is a complex phenomena defined differently depending on the discipline. This chapter aims to bring different approaches under a single framework for investigation with three sorts of questions: Who or what is trustworthy?–metaphysics. How (...) do we know who or what is trustworthy?–epistemology. What factors influence what or who should we trust?–normativity. A two-component model of trust is used that incorporates competence (skills, reliability and experience) and integrity (motives, honesty and character). It is supposed that human levels of competence yield the highest trust whereas trust is reduced at sub-human and super-human levels. The threshold for trustworthiness of an agent or organisation in a particular context is a function of their relationship with the truster and potential impacts of decisions. Building trustworthy autonomous systems requires obeying the norms of logic, rationality and ethics under pragmatic constraints–even though there is disagreement on these principles by experts. Autonomous systems may need sophisticated social identities including empathy and reputational concerns to build human-like trust relationships. Ultimately transdisciplinary research drawing on metaphysical, epistemological and normative human and machine theories of trust are needed to design trustworthy autonomous systems for adoption. (shrink)