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.

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)

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 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)

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.

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)

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)

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)

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.

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)

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.

Overview -- Locke's internal sense and Kant's changing views -- Personal identity amd its problems -- Rationalist metaphysics of mind -- Consciousness, self-consciousness, and cognition -- Strands of Argument in the Duisburg Nachlass -- A transcendental deduction for a priori concepts -- Synthesis : why and how? -- Arguing for apperception -- The power of apperception -- "I-think" as the destroyer of rational psychology -- Is Kant's theory consistent? -- The normativity objection -- Is Kant's thinker (as such) a free (...) and responsible agent? -- Kant our contemporary. (shrink)

Abstract:During recent years, the principle and practice of employment-at-will have been under attack. While progress has been made in eroding the practice, the principle still governs the philosophical assumptions underlying employment practices in the United States, and, indeed, EAW has been promulgated as one of the ways to address economic ills in other countries. This paper will briefly review the major critiques of EAW. Given the failure of these arguments to erode the underpinnings of EAW, we shall suggest new avenues (...) for approaching employment issues to achieve the desirable goal of employee dignity and respect. (shrink)

The ways in which knowledge relates to power have been much discussed in radical education theory. New emphasis on the role of gender and the growing debate about subjectivity have deepened the discussion, while making it more complex. In Getting Smart , Patti Lather makes use of her unique integration of feminism and postmodernism into critical education theory to address some of the most vital questions facing education researchers and teachers.

The effect of contextual information on the resolution of ambiguity was investigated in a group of individuals awaiting dental treatment and a group of control individuals. Participants heard threat/neutral, neutral/neutral and positive/neutral homophones while being simultaneously presented with a context word that was consistent with one of the two meanings of the homophone. Participants then made a lexical decision task on a target word that was one of the two alternate spellings of the homophone. We found that the dental group (...) was more sensitive to context for all types of homophones, and there was no evidence for mood congruency. It also appeared that there might have been an element of mood regulation in the dental group, as they were slower to respond to the emotional targets overall. Our results show that sensitivity to context in state anxiety is a robust phenomenon and one that generalises to naturally occurring anxious moods. (shrink)

This is a study of Blondel's philosophy of the supernatural as it appeared only in the dissertation on Action of 1893. First, it reviews how Blondel brought philosophy to focus concretely on human action and what he focuses on in this action as the principle for its dialectical unfolding. Second, it shows how this focus brings him to a radical critique of superstition and any idea of natural religion, since even the latter is viewed as a kind of superstition. Third, (...) it examines how he proceeds to the affirmation of God as the necessary being of action and how this affirmation places the human being in a position of having to choose between saying yes or no to God at the core of his action. Fourth, it shows how Blondel argues from this existential exigency that the thought of the supernatural necessarily arises with regard to the question of human destiny and that such a thought, if it actualized in human action through a gratuitous initiative on the part of God, necessarily entails a revelation, a mediation, and a religious practice on the part of man. In conclusion it reflects on how this science of practice remains a philosophy, as distinct from theology, even though it has to do with religious practice in the most supernatural sense. /// O presente artigo constitui urn estudo sobre o problema do sobrenatural, tal como Blondel comeca por o tratar em sua tese de doutoramento sobre a Ácção, publicada em 1893. Em primeiro lugar, passa-se em revista não só o modo concreto como Blondel fez do problema da acção assunto para a filosofia, mas também se procura discernir aquilo que, segundo ele, na acção mesma constitui o princípio do seu desdobramento dialéctico. Em segundo lugar, mostra-se como a partir deste ponto de focagem Blondel procede a uma critica radical da superstição bem como de toda e qualquer ideia de religião natural, por ele igualmente vista como uma espécie de superstição. Em terceiro lugar, examina-se o modo como Blondel avança em direcção a uma afirmação de Deus como o ser necessário da acção e como esta mesma afirmação coloca o ser humano numa posicjio de, no fulcro do seu agir, ter de optar entre o dizer sim ou não a Deus. Em quarto lugar, mostra-se o modo como Blondel, partindo desta exigência existencial, argumenta no sentido de que o pensamento do sobrenatural necessariamente se dá em conexão com a questão do destino humano e de como tal pensamento, actualizado na acção humana graças a uma iniciativa gratuita da parte de Deus, necessariamente implica a ideia de revelação, mediação, e prática religiosa da parte do homem. Finalmente, em conclusão, reflecte-se sobre o modo como esta ciência da prática permanece filosofia, distinta da teologia, mesmo quando, enquanto tal, ela tern a ver com uma prática religiosa no sentido mais sobrenatural do termo /// Ceci est une étude de la philosophie du surnaturel de Blondel telle qu'elle parut uniquement dans la thèse sur L'Action de 1893. Premièrement, elle revoit comment Blondel a amené la philosophie à réfléchir concrétement sur l'action humaine et ce sur quoi cette réflexion s'appuie comme principe du déploiement dialectique de cette action. Deuxièmement, elle montre comment ce déploiement amène Blondel à une critique radicale de la superstition et de toute idée de religion naturelle, puisque cette dernière est vue comme une sorte de superstition. Troisièmement, elle examine comment Blondel avance vers une affirmation de Dieu comme Fetre necessaire de l'action et comment cette affirmation amène l'être humain à devoir choisir entre dire oui ou non face à Dieu au plus profond de son action. Quatrièmement, elle montre comment Blondel, à partir de cette exigence existentielle, arrive à poser que la pensée du surnaturel surgit nécessairement par rapport à la question du destin de l'être humain et comment une telle pensée, si elle devient réalite dans l'action humaine par une initiative gratuite du côté de Dieu. entraine du côté de l'homme la nécessité d'une révélation, une médiation et une pratique religieuse. En conclusion, l'étude se demande comment cette science de la pratique reste une philosophie, distincte de toute théologie, même si elle traite de la pratique religieuse dans son sens le plus surnaturel. (shrink)