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  1. Frege and the Origins of Model Theory in Nineteenth Century Geometry.Günther Eder - forthcoming - Synthese:1-29.
    The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic idea, the idea of reinterpreting non-logical terms, gradually came to play a substantial role: the introduction of elements at infinity in projective geometry; the study of transfer principles, especially (...)
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  2. A Phenomenology of Race in Frege's Logic.Joshua M. Hall - forthcoming - Humanities Bulletin.
    This article derives from a project attempting to show that Western formal logic, from Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. In the present article, I will first discuss, in light of Frege’s honorary role as founder of the philosophy of mathematics, Reuben Hersh’s What is Mathematics, Really? Second, I will explore how the infamous section of Frege’s 1924 diary (specifically the entries from March 10 to April 9) supports (...)
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  3. Did Frege Solve One of Zeno’s Paradoxes?Gregory Lavers - 2020 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume. Springer Verlag. pp. 99--107.
    Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends a novel (...)
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  4. Why Did Frege Reject the Theory of Types?Wim Vanrie - 2020 - British Journal for the History of Philosophy:1-20.
    I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to neglect. (...)
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  5. Simplex Sigillum Veri: Peano, Frege, and Peirce on the Primitives of Logic.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):80-95.
    We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...)
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  6. Logic, Judgment, and Inference: What Frege Should Have Said About Illogical Thought.Daniele Mezzadri - 2018 - Journal of the History of Philosophy 56 (4):727-746.
    This paper aims to contribute to the scholarly debate about Frege's discussion of the possibility of illogical thought in the introduction to The Basic Laws of Arithmetic. There, Frege imagines beings "whose laws of thought flatly contradicted ours, so that their application often led to opposite results,"1 namely, beings who straightforwardly and systematically judge and infer illogically: they thus represent a radical example of illogical thought. The literature on this aspect of Frege's views on the relation between logic and thought (...)
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  7. Frege on Thinking and Thoughts: Pieranna Garavaso and Nicla Vassallo: Frege on Thinking and its Epistemic Significance. Lanham: Lexington Books, 2015, Viii+128 Pp, US $83 HB. [REVIEW]Thorsten Sander - 2018 - Metascience 27 (1):127-129.
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  8. Badiou and Frege: A Continental Critique of Logical Form.Joseph M. Spencer - 2018 - Open Philosophy 1 (1):94-114.
    Various critiques of important analytic thinkers made by Alain Badiou in the late 1960s have been largely overlooked by continental philosophers and entirely overlooked by analytic philosophers. This paper looks in detail at Badiou’s 1969 essay ‟Mark and Lack,” providing an exposition and clarification of his direct and sustained critique of Gottlob Frege’s supposed ideological philosophical commitments. Badiou’s intellectual context is analyzed in some detail, not only explaining his theoretical debt to his then-master Louis Althusser, but also clarifying his understandings (...)
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  9. Quantifiers. Hintikka and Frege on Quantification Concepts.Neftalí Villanueva & María Frápolli - 2018 - In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer. pp. 279-298.
    Hintikka’s semantic approach to meaning, a development of Wittgenstein’s view of meaning as use, is the general theme of this chapter. We will focus on the analysis of quantified sentences and on the scope of the principle of compositionality and compare Hintikka’s take on these issues with that of Frege. The aim of this paper is to show that Hintikka’s analysis of quantified expressions as choice functions, in spite of its obvious dissimilarities with respect to the higher-order approach, is actually (...)
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  10. Frege's Case for the Logicality of His Basic Laws.Yates Alexander - 2017 - Dissertation, St. Andrews University
    Frege wanted to show that arithmetical truths are logical by proving them from purely logical basic laws. But how do we know that these basic laws are logical? Frege uses generality and undeniability to make a prima facie case for logicality—if a truth is general and undeniable, then it’s likely logical. I argue that Frege could, did, and had to make a deeper case for why we’re right in recognizing his basic laws as logical. Implicit in his work is a (...)
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  11. La lingua characteristica: el proyecto lógico de Gottlob Frege.Angela Rocio Bejarano - 2017 - Agora 36 (1).
    Para Frege las relaciones lógicas se dan entre contenidos judicables, entre pensamientos. Aquellas relaciones son inferenciales. Los pensamientos se definen a través de sus relaciones inferenciales con otros. De acuerdo con esto es discutible afirmar, como lo hizo Schröder, que el proyecto lógico de Frege es como el proyecto lógico de Boole. También es cuestionable afirmar, como lo hizo Dummett, que la relación inferencial no es siempre central en el proyecto fregeano. En este texto defenderé una lectura del proyecto lógico (...)
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  12. Frege on Thinking and Its Epistemic Significance. [REVIEW]Carlo Cellucci - 2017 - History and Philosophy of Logic 38 (1):92-95.
  13. Zelfpredicatie: Middeleeuwse en hedendaagse perspectieven.Jan Heylen & Can Laurens Löwe - 2017 - Tijdschrift Voor Filosofie 79 (2):239-258.
    The focus of the article is the self-predication principle, according to which the/a such-and-such is such-and-such. We consider contemporary approaches (Frege, Russell, Meinong) to the self-predication principle, as well as fourteenth-century approaches (Burley, Ockham, Buridan). In crucial ways, the Ockham-Buridan view prefigures Russell’s view, and Burley’s view shows a striking resemblance to Meinong’s view. In short the Russell-Ockham-Buridan view holds: no existence, no truth. The Burley-Meinong view holds, in short: intelligibility suffices for truth. Both views approach self-predication in a uniform (...)
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  14. Logic, Thinking and Language in Frege.Daniele Mezzadri - 2017 - Paradigmi. Rivista di Critica Filosofica 3 (3):165-180.
    In this paper I take the opportunity of the recent publication of Pieranna Garavaso’s and Nicla Vassallo’s Frege on Thinking and Its Epistemic Significance (with whose main tenets this paper is in constant dialogue) to provide an overview of some important components of Frege’s conception of logic. Section 1 discusses Frege’s view that the task of logic is to provide justification for what we think, and in sections 2 and 3 this idea is shown to play a central role in (...)
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  15. On Structural Features of the Implication Fragment of Frege’s Grundgesetze.Andrew Tedder - 2017 - Journal of Philosophical Logic 46 (4):443-456.
    We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.
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  16. P. Garavaso and N. Vassallo, Frege on Thinking and its Epistemic Significance. [REVIEW]Clinton Tolley - 2017 - Notre Dame Philosophical Reviews 2017.
  17. PEIRCE, FREGE, RUSSELL E O SURGIMENTO DA PREDICAÇÃO LÓGICA CONTEMPORÂNEA.Rafael dos Reis Ferreira - 2016 - Kinesis 8 (17):115-135.
    Apresentamos neste artigo explicitações histórico-conceituais sobre o surgimento da predicação lógica contemporânea. Quando se trata de predicação, remete-se de imediato à obra de Aristóteles, mas, com as transformações trazidas pela Lógica Contemporânea, o estudo da predicação deixa o plano do estudo lógico-gramatical para o estudo do plano da análise lógicomatemática. Veremos, nesse sentido, a importância dos trabalhos de Peirce, Frege e Russell para o surgimento da predicação lógica contemporânea. Embora Peirce tenha sido o precursor da introdução do conceito de função (...)
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  18. Identity in Frege’s Shadow.Jaakko Hintikka - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag.
    Frege overlooked the role of quantifiers as expressing, by their formal dependence on each other, the actual dependences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. The dependence relations are codified in the Skolem functions that correspond to existential-force quantifiers. Their existence is the natural truth condition. Such functions are not adequately handled in first-order predicate logic. In any adequate logic, a fixed mode of identification is (...)
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  19. Frege, Logic, and Logicism.John-Michael Kuczynski - 2016 - Amazon Digital Services LLC.
    Gottlob Frege (1848-1925) invented the discipline of mathematical logic. In this short work, it is clearly stated what Frege did and did not accomplish.
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  20. Frege on Thinking and its Epistemic Significance Garavaso Pieranna and Nicla Vassallo Lanham, Maryland: Lexington Books, 2014; 128 Pp.; $ 75.00. [REVIEW]Daniele Mezzadri - 2016 - Dialogue 57 (3):675-677.
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  21. What Is the Frege/Russell Analysis of Quantification?Scott Soames - 2014 - In Analytic Philosophy in America: And Other Historical and Contemporary Essays. Princeton University Press. pp. 191-199.
  22. PM's Circumflex, Syntax and Philosophy of Types.Kevin C. Klement - 2013 - In Bernard Linsky & Nicholas Griffin (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan. pp. 218-246.
    Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...)
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  23. Fregean Quantification Theory.Saul A. Kripke - 2013 - Journal of Philosophical Logic (5):1-3.
    Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.
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  24. Frege's Notations: What They Are and How They Mean.Gregory Landini - 2012 - Palgrave-Macmillan.
  25. Quantification: Transcending Beyond Frege’s Boundaries: A Case Study in Transcendental-Metaphysical Logic.Aleksy Molczanow - 2012 - Brill.
    Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely ...
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  26. Peirce entre Frege e Boole: sobre a busca de diálogos possíveis com Wittgenstein.Rafael Duarte Oliveira Venancio - 2012 - Estudos Semioticos (USP) 8 (2):99-108.
    O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantes peirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspirador da visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra Calculus Ratiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamos esse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift, 1879) e a (...)
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  27. The Universal Set and Diagonalization in Frege Structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.
    In this paper we summarize some results about sets in Frege structures. The resulting set theory is discussed with respect to its historical and philosophical significance. This includes the treatment of diagonalization in the presence of a universal set.
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  28. Frege's Elucidatory Holism.Clinton Tolley - 2011 - Inquiry: An Interdisciplinary Journal of Philosophy 54 (3):226-251.
    Abstract I argue against the two most influential readings of Frege's methodology in the philosophy of logic. Dummett's ?semanticist? reading sees Frege as taking notions associated with semantical content?and in particular, the semantical notion of truth?as primitive and as intelligible independently of their connection to the activity of judgment, inference, and assertion. Against this, the ?pragmaticist? reading proposed by Brandom and Ricketts sees Frege as beginning instead from the independent and intuitive grasp that we allegedly have on the latter activity (...)
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  29. Frege on Indirect Proof.Ivan Welty - 2011 - History and Philosophy of Logic 32 (3):283-290.
    Frege's account of indirect proof has been thought to be problematic. This thought seems to rest on the supposition that some notion of logical consequence ? which Frege did not have ? is indispensable for a satisfactory account of indirect proof. It is not so. Frege's account is no less workable than the account predominant today. Indeed, Frege's account may be best understood as a restatement of the latter, although from a higher order point of view. I argue that this (...)
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  30. Der Begriff der Logischen Form in der Analytischen Philosophie. Russell in Auseinandersetzung MIT Frege, Meinong Und Wittgenstein – By Elena Tatievskaya. [REVIEW]Jan Woleński - 2011 - Theoria 77 (1):87-89.
  31. Between Frege and Peirce: Josiah Royce's Structural Logicism.J. Brent Crouch - 2010 - Transactions of the Charles S. Peirce Society 46 (2):155-177.
    In the opening sentence of his Methods of Logic, W. V. O. Quine writes, “Logic is an old subject, and since 1879 it has been a great one.”1 Quine is referring to the year in which Gottlob Frege presented his Begriffschrift, or “concept-script,” one of the first published accounts of a logical system or calculus with quantification and a function-argument analysis of propositions. There can be no doubt as to the importance of these introductions, and, indeed, Frege’s orientation and advances, (...)
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  32. Dov M. Gabbay and John Woods, Eds., Handbook of the History of Logic, Volume 3: The Rise of Modern Logic From Leibniz to Frege. [REVIEW]Irving H. Anellis - 2009 - Transactions of the Charles S. Peirce Society 45 (3):456-463.
  33. Modal Logic From Kant to Possible Worlds Semantics.Tapio Korte, Ari Maunu & Tuomo Aho - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner in which necessity and truth imply possibility in even the weakest systems of modern modal logic. The chapter then discusses theories of judgment-form after Kant, the theory of quantification, Frege's Begriffsschrift, C. I. Lewis and the beginnings of modern modal logic, the proof-theoretic approach to modal logic, possible world (...)
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  34. The Rise of Modern Logic: From Leibniz to Frege. [REVIEW]Joan Roselló Moya - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (1):115-119.
  35. Positive Frege and its Scott‐Style Semantics.Thierry Libert - 2008 - Mathematical Logic Quarterly 54 (4):410-434.
    We show that the untyped λ -calculus can be extended with Frege's interpretation of propositional notions, provided we restrict β -conversion to positive expressions. The system of illative λ -calculus so obtained admits a natural Scott-style semantics.
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  36. Frege's Logic - by Danielle Macbeth. [REVIEW]Thomas J. Brommage - 2007 - Philosophical Books 48 (3):262-265.
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  37. Understanding the Goodness of Inference: Modality and Relevance in Frege's System of Logic.Danielle Macbeth - 2007 - Soochow Journal of Philosophical Studies 16:133 - 151.
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  38. Logic in Philosophy.Johan van Benthem - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: pp. 65-99.
    1 Logic in philosophy The century that was Logic has played an important role in modern philosophy, especially, in alliances with philosophical schools such as the Vienna Circle, neopositivism, or formal language variants of analytical philosophy. The original impact was via the work of Frege, Russell, and other pioneers, backed up by the prestige of research into the foundations of mathematics, which was fast bringing to light those amazing insights that still impress us to-day. The Golden Age of the 1930s (...)
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  39. Die Reinheit der Reinen Logik: Kant Und Frege.Michael Wolff - 2007 - In Jürgen Stolzenberg (ed.), Kant in der Gegenwart. Berlin: Walter de Gruyter. pp. 53-70.
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  40. Macbeth Danielle. Frege's Logic. Harvard University Press, Cambridge, Massachusetts, 2005, Xii+ 206 Pp. [REVIEW]Norma B. Goethe - 2006 - Bulletin of Symbolic Logic 12 (3):496-498.
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  41. Comments on Prof. Kazuyuki Nomoto's Paper.Per Martin-Löf - 2006 - Annals of the Japan Association for Philosophy of Science 14 (2):98-99.
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  42. Frege's Hidden Assumption.Hartley Slater - 2006 - Critica 38 (113):27-37.
    This paper is concerned with locating the specific assumption that led Frege into Russell's Paradox. His understanding of reflexive pronouns was weak, for one thing, but also, by assimilating concepts to functions he was misled into thinking one could invariably replace a two-place relation with a one-place property. /// Este trabajo se ocupa de localizar el supuesto específico que llevó a Frege a la Paradoja de Russell. Por una parte, su comprensión de los pronombres reflexivos era débil pero, por otra, (...)
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  43. Hegel to Frege: Concepts and Conceptual Content in Nineteenth-Century Logic.Stephan Käufer - 2005 - History of Philosophy Quarterly 22 (3):259 - 280.
  44. Der Begriff der logischen Form in der analytischen Philosophie. Russell in Auseinandersetzung mit Frege, Meinong und Wittgenstein.Elena Tatievskaya - 2005 - Frankfurt a.M.: Ontos Verlag.
  45. Semantic Descent.Joan Weiner - 2005 - Mind 114 (454):321-354.
    Does Frege have a metatheory for his logic? There is an obvious and uncontroversial sense in which he does. Frege introduces and discusses his new logic in natural language; he argues, in response to criticisms of Begriffsschrift, that his logic is superior to Boole's by discussing formal features of both systems. In so far as the enterprise of using natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has (...)
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  46. Putting Form Before Function: Logical Grammar in Frege, Russell, and Wittgenstein.Kevin C. Klement - 2004 - Philosophers' Imprint 4:1-47.
    The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...)
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  47. On Frege's Logical Diagrams.Iulian D. Toader - 2004 - In Diagrammatic Representation and Inference. Springer: Lecture Notes in Computer Science, vol. 2980,. pp. 22-25.
    This paper argues that a particular point raised by Schröder – that Frege's logical notation fails to be modelled on arithmetical notation – is based on a misunderstanding, for the modelling was meant as conceptual, rather than notational.
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  48. Frege's Horizontal and the Liar-Paradox.Dirk Greimann - 2003 - Manuscrito 26 (2):359-387.
    According to Peter Aczel, the inconsistency of Frege’s system in Grundgesetze is due, not to the introduction of sets, as is usually thought, but to the introduction of the Horizontal. His argument is that the principles governing sets are intuitively correct and therefore consistent, while the scheme introducing the Horizontal amounts to an internal definition of truth conflicting with Tarski’s classic result on the undefinability of truth in the object language. The aim of this paper is to show that the (...)
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  49. Broadened Logic.Avrum Stroll - 2003 - Topoi 22 (1):93-104.
    The early formal logicians (Frege, Russell, Peano et al.) were worried about differentiating logic from psychology. As a result, they interpreted logic in the most abstract way possible: as a theory about inference patterns whose terms lacked descriptive content. Such a theory was also acontextual. What they did not realize was that psychological concepts like expecting someone, doubting, pain etc. each had their own logic, a logic that had two features: it was contextually oriented and its concepts had a restricted (...)
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  50. Frege and Wittgenstein on a Logically Perfect Language.M. Zouhar - 2003 - Filozofia 58 (6):363-382.
    A logically perfect language must meet following requirements: it must not contain „empty“ expressions designating nothing and it must not involve phrases that are synonymous, homonymous etc. According to Frege, the meaning of a compound expression is a function of meanings of its components, i.e. the meaning of an expression consisting of a functional phrase and a name is the value of the function for the argument. However, for some arguments a function need not give values and, hence, some compound (...)
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