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The Logic of Relatives

The Monist 7 (2):161-217 (1897)

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  1. Language mediated mentalization: A proposed model.Yair Neuman - 2019 - Semiotica 2019 (227):261-272.
    Mentalization describes the process through which we understand the mental states of oneself and others. In this paper, I present a computational semiotic model of mentalization and illustrate it through a worked-out example. The model draws on classical semiotic ideas, such as abductive inference and hypostatic abstraction, but pours them into new ideas and tools from natural language processing, machine learning, and neural networks, to form a novel model of language-mediated-mentalization.
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  • (1 other version)The Sign of Consequence.Francesco Bellucci - 2016 - The Digital Encyclopedia of Peirce Studies 1:1-5.
    The “sign of consequence” is a notation for propositional logic that Peirce invented in 1886 and used at least until 1894. It substituted the “copula of inclusion” which he had been using since 1870.
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  • A Torch and a Compass.Riccardo Lameri - 2024 - European Journal of Pragmatism and American Philosophy 16 (1).
    Any attempt to understand the meaning of Charles Sanders Peirce’s philosophy must necessarily involve the study of his maxim of pragmatism, first formulated in 1878. The maxim is the basis for Peirce’s pragmatism, and its development is a fundamental thread that allows the overall meaning of his system to be grasped. Furthermore, the maxim cannot be separated from the entire body of Peirce’s speculations. In his 2020 paper, Jon Alan Schmidt compiled a rich chronological list of passages that show how (...)
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  • The development of mathematical logic from Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  • From word to sentence: A pregroup analysis of the object pronoun who ( M ). [REVIEW]J. Lambek - 2007 - Journal of Logic, Language and Information 16 (3):303-323.
    We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).
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  • Peirce’s Dragon-Head Logic (R 501, 1901).Minghui Ma & Ahti-Veikko Pietarinen - 2022 - Archive for History of Exact Sciences 76 (3):261-317.
    Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...)
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  • The logical relation of consequence.Basil Evangelidis - 2020 - Humanities Bulletin 3 (2):77-90.
    The present endeavour aims at the clarification of the concept of the logical consequence. Initially we investigate the question: How was the concept of logical consequence discovered by the medieval philosophers? Which ancient philosophical foundations were necessary for the discovery of the logical relation of consequence and which explicit medieval contributions, such as the notion of the formality (formal validity), led to its discovery. Secondly we discuss which developments of modern philosophy effected the turn from the medieval concept of logical (...)
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  • Peircean studies in Russia: A historical and cross-cultural perspective.Natalia Lukianova & Elena Fell - 2021 - Empedocles European Journal for the Philosophy of Communication 12 (1):19-33.
    This article aims to contribute to the Peircean studies by providing an account of the reception of Peirce’s philosophy in Russian academia. Peirce was introduced to Russian scholarship at the beginning of the twentieth century, but Russian scholars’ work on Peirce remains unnoticed for the most part in the international academic world. Presenting an outline of their research fills a certain gap in the Peircean studies demonstrating how Peirce was received in imperial Russia, the USSR and post-Soviet Russian academia. This (...)
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  • What is Wrong with Machine Art? Autonomy, Spirituality, Consciousness, and Human Survival.Ioannis Trisokkas - 2020 - Humanities Bulletin 3 (2):9-26.
    There is a well-documented Pre-Reflective Hostility against Machine Art (PRHMA), exemplified by the sentiments of fear and anxiety. How can it be explained? The present paper attempts to find the answer to this question by surveying a considerable amount of research on machine art. It is found that explanations of PRHMA based on the (alleged) fact that machine art lacks an element that is (allegedly) found in human art (for example, autonomy) do not work. Such explanations cannot account for the (...)
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  • Lingua characterica and calculus ratiocinator: The Leibnizian background of the Frege-Schröder polemic.Joan Bertran-San Millán - 2021 - Review of Symbolic Logic 14 (2):411-446.
    After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...)
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  • Charles S. Peirce, Evolutionary Pragmatism and the History of Science.Joseph W. Dauben - 1996 - Centaurus 38 (1):22-82.
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  • 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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  • Peirce and Schröder on the auflösungsproblem.Davide Bondoni - 2009 - Logic and Logical Philosophy 18 (1):15-31.
    The aim of this article is Schröder’s treatment of the so called solution problem [Auflösungsproblem]. First, I will introduce Schröder’s ideas; then I will discuss them taking into account Peirce’s considerations in The Logic of Relatives ([13, pp. 161–217] now republished in [9, pp. 288–345]).
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  • The origin of relation algebras in the development and axiomatization of the calculus of relations.Roger D. Maddux - 1991 - Studia Logica 50 (3-4):421 - 455.
    The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and the (...)
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  • Contingency without unreason: Speculation after meillassoux.Joshua Ramey - 2014 - Angelaki 19 (1):31-46.
    In this essay I critique the identification of contingency with sheer arbitrary possibility in Quentin Meillassoux's After Finitude: An Essay on the Necessity of Contingency. After offering logical and metaphysical reasons for why such an identification is a limitation on the speculative potential of reason, I draw upon Charles S. Peirce, Gilles Deleuze, and Giambattista Vico to articulate the outlines of a view of contingency which can underwrite a different speculative position to one that is grounded upon an absolute of (...)
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  • Existential graphs as an instrument of logical analysis: Part I. alpha.Francesco Bellucci & Ahti-Veikko Pietarinen - 2016 - Review of Symbolic Logic 9 (2):209-237.
    Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...)
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  • Introduction: History and Philosophy of Logical Notation.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):1-2.
    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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  • A Cauchy-Dirac Delta Function.Mikhail G. Katz & David Tall - 2013 - Foundations of Science 18 (1):107-123.
    The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.
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  • Stevin Numbers and Reality.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (2):109-123.
    We explore the potential of Simon Stevin’s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.
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  • Pragmaticism.Charles S. Peirce - 2024 - De Gruyter.
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  • The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic.Gianfranco Basti - 2022 - Philosophies 7 (6):121.
    This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both (...)
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  • Signs and phylogeny: A semiotic approach to systematics.Lars Vogt - 2004 - Semiotica 2004 (149):125-159.
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  • Exploring the beta quadrant.Ahti-Veikko Pietarinen - 2015 - Synthese 192 (4):941-970.
    The theory of existential graphs, which Peirce ultimately divided into four quadrants , is a rich method of analysis in the philosophy of logic. Its $$\upbeta $$ β -part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of natural-language expressions such as complex donkey-type anaphora, quantificational patterns describing new mathematical concepts, and cognitive information processing. In the $$\upbeta $$ β -quadrant, he came close to inventing independence-friendly logic, the idea of which he (...)
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  • Essay review.Alison Walsh - 1998 - History and Philosophy of Logic 19 (2):107-114.
    Nathan Houser, Don D. Roberts and James Van Evra (eds), Studies in the Logic of Charles Sanders Peirce, In:Bloomington and Indianapolis, Indiana University Press, 1997, xiii + 653 pp. £41.95. ISBN 0-253-33020-3.
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  • Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus.Dirk Schlimm & David Waszek - 2021 - Synthese 199 (5-6):11913-11943.
    By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known approach—which we believe sheds light on the concepts of ‘calculus’ and ‘mechanization’ and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege’s Begriffsschrift, on the other hand, (...)
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  • Kontinuum und Konstitution der Wirklichkeit.Julia Zink - unknown
    The work has two parts. The first part is about Peirce and his ideas about the continuum. There are considered the connection of his theory of continuity with his loic and his philosophy. In the second part Peirce's ideas are compared with models of todays logic and mathematics. There is considerd constructive mathematics, the logic of perception from Bell, Blau's Logic of reflection and a model of Myrvold. Then there is developed a new model.
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  • Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like.Ahti-Veikko Pietarinen - 2011 - History and Philosophy of Logic 32 (3):265-281.
    This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ‘moving pictures of thought’. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...)
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  • Toward a Clarity of the Extreme Value Theorem.Karin U. Katz, Mikhail G. Katz & Taras Kudryk - 2014 - Logica Universalis 8 (2):193-214.
    We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.
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  • Thinking About Contradictions: The Imaginary Logic of Nikolai Aleksandrovich Vasil’Ev.Venanzio Raspa - 2017 - Cham, Switzerland: Springer Verlag.
    This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of (...)
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  • Reprint of: Assertion and denial: A contribution from logical notations.Ahti-Veikko Pietarinen & Francesco Bellucci - 2017 - Journal of Applied Logic 25:S3-S24.
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  • Just Following the Rules: Collapse / Incoherence Problems in Ethics, Epistemology, and Argumentation Theory.Patrick Bondy - 2020 - In J. Anthony Blair & Christopher W. Tindale (eds.), Rigour and Reason: Essays in Honour of Hans Vilhelm Hansen. University of Windsor. pp. 172-202.
    This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into one (...)
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  • Should Pregroup Grammars be Adorned with Additional Operations?Joachim Lambek - 2007 - Studia Logica 87 (2-3):343-358.
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  • Relevance logic and the calculus of relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  • Beyond Transcendentalism and Naturalization: A Categorial Framework for the Semiotic Phenomenology.Martina Properzi - 2019 - International Journal of Philosophy 7 (3):122.
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  • Hermann Weyl motivations philosophiques d'un choixMaverik.Demetrio Ria - 2005 - Revue de Synthèse 126 (2):463-479.
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