Results for 'Philsophical Notation'

995 found
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  1. Colin oakes/interpretations of intuitionist logic in non-normal modal logics 47–60 Aviad heifetz/iterative and fixed point common belief 61–79 dw mertz/the logic of instance ontology 81–111. [REVIEW]Richard Bradley, Roya Sorensen, Mirror Notation & Philip Kremer - 1999 - Journal of Philosophical Logic 28:661-662.
  2.  17
    Notational systems are distinct cognitive systems with different material prehistories.Karenleigh A. Overmann - 2023 - Behavioral and Brain Sciences 46:e250.
    Notations are cognitive systems involving distinctive psychological functions, behaviors, and material forms. Seen through this lens, two main types – semasiography and visible language – are fundamentally differentiated by their material prehistories, emphasis on iconography, and the centrality of language's combinatorial faculty. These fundamental differences suggest that key qualities (iconicity, expressiveness, concision) are difficult to conjoin in a single system.
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  3.  8
    Musical Notation.Michael Dickson - 2024 - Ergo: An Open Access Journal of Philosophy 11.
    The main goal of this essay is to propose and make plausible a framework for developing a philosophical account of musical notation. The proposed framework countenances four elements of notation: symbols (abstract objects that collectively constitute the backbone of a ‘system’ of notation), their characteristic ‘forms’ (for example, shapes, understood abstractly), the concrete instances, or ‘engravings’, of those forms, and the meanings of the symbols. It is argued that these elements are distinct. Along the way, several preliminary (...)
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  4.  5
    Philsophical implications in curriculum development.B. I. Cornelius-Ukpebi & R. A. Ndifon - 2008 - Sophia: An African Journal of Philosophy 10 (1).
  5.  11
    Notational usage modulates attention networks in binumerates.Atesh Koul, Vaibhav Tyagi & Nandini C. Singh - 2014 - Frontiers in Human Neuroscience 8:77089.
    Multicultural environments require learning multiple number notations wherein some are encountered more frequently than others. This leads to differences in exposure and consequently differences in usage between notations. We find that differential notational usage imposes a significant neurocognitive load on number processing. Despite simultaneous acquisition, forty-two adult binumerate populations, familiar with two positional writing systems namely Hindu Nagari digits and Hindu Arabic digits, reported significantly lower preference and usage for Nagari as compared to Arabic. Twenty-four participants showed significantly increased reaction (...)
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  6.  46
    Notational Variants and Cognition: The Case of Dependency Grammar.Ryan M. Nefdt & Giosué Baggio - forthcoming - Erkenntnis:1-31.
    In recent years, dependency grammars have established themselves as valuable tools in theoretical and computational linguistics. To many linguists, dependency grammars and the more standard constituency-based formalisms are notational variants. We argue that, beyond considerations of formal equivalence, cognition may also serve as a background for a genuine comparison between these different views of syntax. In this paper, we review and evaluate some of the most common arguments and evidence employed to advocate for the cognitive or neural reality of dependency (...)
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  7. Ontological Pluralism and Notational Variance.Bruno Whittle - 2021 - Oxford Studies in Metaphysics 12:58-72.
    Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...)
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  8.  43
    Negotiating notation: Chemical symbols and british society, 1831–1835.Timothy L. Alborn - 1989 - Annals of Science 46 (5):437-460.
    One of the central debates among British chemists during the 1830s concerned the use of symbols to represent elements and compounds. Chemists such as Edward Turner, who desired to use symbolic notation mainly for practical reasons, eventually succeeded in fending off metaphysical objections to their approach. These objections were voiced both by the philosopher William Whewell, who wished to subordinate the chemists' practical aims to the rigid standard of algebra, and by John Dalton, whose hidebound opposition to abbreviated (...) symbolized the suspicion with which older British chemists perceived continental innovations. It is argued that the success of chemists like Turner in this debate reflects their larger success in the 1830s in achieving disciplinary autonomy and in beginning to align themselves more closely with prevailing chemical practice across the Channel. (shrink)
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  9.  16
    Notational/poetics: Noting, Gleaning, Itinerary.Maureen N. McLane - 2024 - Critical Inquiry 50 (2):277-304.
    This article establishes itself first in a kind of slough, a lack of inspiration, and transvalues this via Fred Wah’s poem “Ikebana” and Roland Barthes’s celebration of haiku as a form that “lacks inspiration.” Following Barthes on “the minimal act of writing that is Notation,” this article explores and theorizes the status of the notational in and for poetics. The article registers and sustains the ambiguity in notatio, notationis and suggests that the notational points to a conceptual dialectic between (...)
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  10.  36
    Ordinal notation systems corresponding to Friedman’s linearized well-partial-orders with gap-condition.Michael Rathjen, Jeroen Van der Meeren & Andreas Weiermann - 2017 - Archive for Mathematical Logic 56 (5-6):607-638.
    In this article we investigate whether the following conjecture is true or not: does the addition-free theta functions form a canonical notation system for the linear versions of Friedman’s well-partial-orders with the so-called gap-condition over a finite set of n labels. Rather surprisingly, we can show this is the case for two labels, but not for more than two labels. To this end, we determine the order type of the notation systems for addition-free theta functions in terms of (...)
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  11.  17
    Is Standard Music Notation Able to Picture Aristotle’s Time?Niko Strobach - 2024 - History of Philosophy & Logical Analysis 26 (2):303-320.
    It is argued that standard music notation pictures Aristotle’s time (time, as Aristotle conceived of it) in a number of important respects, which concern its micro-structure. It is then argued that this allows us to see some features of Aristotle’s time more clearly. Most importantly, Aristotelian instants can be pictured by bar-lines. This allows us to see as how radically devoid of any content Aristotelian instants should be interpreted. Thus, attention to music notation may show why Aristotle was (...)
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  12.  43
    Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 7 (1):20.
    Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of _which number_ is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of _notation_. The purpose of this article is to explore the relationship between (...)
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  13. A Diagrammatic Notation for Visualizing Epistemic Entities and Relations.Kye Palider, Ameer Sarwar, Hakob Barseghyan, Paul Patton, Julia Da Silva, Torin Doppelt, Nichole Levesley, Jessica Rapson, Jamie Shaw, Yifang Zhang & Amna Zulfiqar - 2021 - Scientonomy 4:87–139.
    This paper presents a diagrammatic notation for visualizing epistemic entities and relations. The notation was created during the Visualizing Worldviews project funded by the University of Toronto’s Jackman Humanities Institute and has been further developed by the scholars participating in the university’s Research Opportunity Program. Since any systematic diagrammatic notation should be based on a solid ontology of the respective domain, we first outline the current state of the scientonomic ontology. We then proceed to providing diagrammatic tools (...)
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  14.  12
    Notation.Christoph Baumberger - 2012 - Glossar der Bildphilosophie.
    Die Theorie der Notation wurde von Nelson Goodman ([Goodman 1968]: Kap. 4) im Zusam­menhang mit der Frage nach den Iden­titäts­krite­rien für Kunstwer­ke ent­wickelt. Eine Nota­tion ist ein Zeichen­system, das ein syntak­tisches oder seman­tisches Krite­rium dafür ermög­licht, welche Gegen­stände oder Ereig­nisse Einzel­fälle eines bestimm­ten Werks sind. Ein solches Krite­rium ist dann notwen­dig, wenn Werke mehre­re Einzel­fälle zulas­sen, deren Iden­tität nicht durch ihre Entste­hungsge­schichte bestimmt ist. Da dies in para­digma­tischer Weise in der Musik der Fall ist, führe ich den Begriff der (...)
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  15.  99
    On Frege’s Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs.Dirk Schlimm - 2018 - History and Philosophy of Logic 39 (1):53-79.
    Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of (...)
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  16.  89
    Architectural notation and computer aided design.Saul Fisher - 2000 - Journal of Aesthetics and Art Criticism 58 (3):273-289.
    In his Languages of Art, Nelson Goodman proposes a theory of artistic notation that includes foundational requirements for any system of symbols we might use to specify and communicate the features of an artwork, in architecture or any other art form. Goodmans' theory usefully explains how notation can reveal linguistic-like phenomena of various art forms. But not all art forms can enjoy benefits of a full-blown notational system, in Goodman's view, and he suggests that architecture's symbol systems fall (...)
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  17.  91
    Notational Variance and Its Variants.Rohan French - 2019 - Topoi 38 (2):321-331.
    What does it take for two logics to be mere notational variants? The present paper proposes a variety of different ways of cashing out notational variance, in particular isolating a constraint on any reasonable account of notational variance which makes plausible that the only kinds of translations which can witness notational variance are what are sometimes called definitional translations.
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  18.  4
    Normalizing notations in the Ershov hierarchy.Cheng Peng - 2021 - Mathematical Logic Quarterly 67 (4):506-513.
    The Turing degrees of infinite levels of the Ershov hierarchy were studied by Liu and Peng [8]. In this paper, we continue the study of Turing degrees of infinite levels and lift the study of density property to the levels beyond ω2. In doing so, we rely on notations with some nice properties. We introduce the concept of normalizing notations and generate normalizing notations for higher levels. The generalizations of the weak density theorem and the nondensity theorem are proved for (...)
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  19.  23
    On Notation for Ordinal Numbers.S. C. Kleene - 1939 - Journal of Symbolic Logic 4 (2):93-94.
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  20.  34
    Iconicity in mathematical notation: commutativity and symmetry.Theresa Wege, Sophie Batchelor, Matthew Inglis, Honali Mistry & Dirk Schlimm - 2020 - Journal of Numerical Cognition 3 (6):378-392.
    Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects—those which visually resemble in some way the concepts they represent—offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey (...)
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  21.  82
    Notational Variants and Invariance in Linguistics.Kent Johnson - 2015 - Mind and Language 30 (2):162-186.
    This article argues that the much-maligned ‘notational variants’ of a given formal linguistic theory play a role similar to alternative numerical measurement scales. Thus, they can be used to identify the invariant components of the grammar; i.e., those features that do not depend on the choice of empirically equivalent representation. Treating these elements as the ‘meaningful’ structure of language has numerous consequences for the philosophy of science and linguistics. I offer several such examples of how linguistic theorizing can profit from (...)
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  22.  14
    Bibliopolitics: The History of Notation and the Birth of the Citational Academic Subject.Matthew Sharpe & Kirk Turner - 2018 - Foucault Studies 25:146.
    The paper builds upon a growing body of critical research on the proliferating use of bibliometrics as a means to evaluate academic research, but brings to it a specifically Foucauldian, genealogical approach. The paper has three parts. Part 1 situates bibliometrics as a new technology of neoliberal, biopolitical governmentality, alongside the host of other ‘metrics’ that have emerged in the last two decades. Part 2 analyses bibliometrics’ antecedents in prior notational practices in the Western heritage, highlighting how forms of noting (...)
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  23.  41
    Linear notation for existential graphs.Eric Hammer - 2011 - Semiotica 2011 (186):129-140.
    A linear notation for Charles S. Peirce's alpha and beta diagrammatic systems of existential graphs is presented. These two systems are equivalent to propositional and first-order logic. Some differences between the linear and graphical notation are analyzed, revealing some of the strengths and weaknesses of Peirce's system.
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  24.  42
    Stabilizer Notation for Spekkens' Toy Theory.Matthew F. Pusey - 2012 - Foundations of Physics 42 (5):688-708.
    Spekkens has introduced a toy theory (Spekkens in Phys. Rev. A 75(3):032110, 2007) in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the (...)
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  25. Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7).
    Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship (...)
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  26.  12
    Deixis and Desire: Transitional Notation and Semiotic Philosophy of Education.Derek Pigrum - 2014 - Journal of Philosophy of Education 48 (4):574-590.
    The philosophical underpinnings of this article are the Peircian notion of the triadic nature of the sign as iconic, linguistic and indexical, and the use of the sign as a ‘Zeug’ or thing as a means of pointing to or deixis in the context of creative activity in the classroom. This involves Lyotard's conception of desire as the generation of a space where the pupil can be affected by what the world donates. Both deixis and desire take on added value (...)
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  27.  30
    Notational Differences.Francesco Bellucci & Ahti-Veikko Pietarinen - 2020 - Acta Analytica 35 (2):289-314.
    Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...)
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  28.  14
    A notation system for ordinal using ψ‐functions on inaccessible mahlo numbers.Helmut Pfeiffer & H. Pfeiffer - 1992 - Mathematical Logic Quarterly 38 (1):431-456.
    G. Jäger gave in Arch. Math. Logik Grundlagenforsch. 24 , 49-62, a recursive notation system on a basis of a hierarchy Iαß of α-inaccessible regular ordinals using collapsing functions following W. Buchholz in Ann. Pure Appl. Logic 32 , 195-207. Jäger's system stops, when ordinals α with Iα0 = α enter. This border is now overcome by introducing additional a hierarchy Jαß of weakly inaccessible Mahlo numbers, which is defined similarly to the Jäger hierarchy. An ordinal μ is called (...)
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  29.  40
    Acceptable notation.Stewart Shapiro - 1982 - Notre Dame Journal of Formal Logic 23 (1):14-20.
  30.  25
    The Role of Notations in Mathematics.Carlo Cellucci - 2020 - Philosophia 48 (4):1397-1412.
    The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic (...)
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  31.  35
    Finite notations for infinite terms.Helmut Schwichtenberg - 1998 - Annals of Pure and Applied Logic 94 (1-3):201-222.
    Buchholz presented a method to build notation systems for infinite sequent-style derivations, analogous to well-known systems of notation for ordinals. The essential feature is that from a notation one can read off by a primitive recursive function its n th predecessor and, e.g. the last rule applied. Here we extend the method to the more general setting of infinite terms, in order to make it applicable in other proof-theoretic contexts as well as in recursion theory. As examples, (...)
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  32. Notation systems for infinitary derivations.Wilfried Buchholz - 1991 - Archive for Mathematical Logic 30 (5-6):277-296.
  33.  29
    Ordinal notations and well-orderings in bounded arithmetic.Arnold Beckmann, Chris Pollett & Samuel R. Buss - 2003 - Annals of Pure and Applied Logic 120 (1-3):197-223.
    This paper investigates provability and non-provability of well-foundedness of ordinal notations in weak theories of bounded arithmetic. We define a notion of well-foundedness on bounded domains. We show that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below 0 and Γ0. As a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below 0 and Γ0 without increasing the class PLS.
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  34.  21
    Ordinal notations and well-orderings in bounded arithmetic (vol 120, pg 197, 2003).Arnold Beckmann, Samuel R. Buss & Chris Pollett - 2003 - Annals of Pure and Applied Logic 123 (1-3):291-291.
    This paper investigates provability and non-provability of well-foundedness of ordinal notations in weak theories of bounded arithmetic. We define a notion of well-foundedness on bounded domains. We show that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below 0 and Γ0. As a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below 0 and Γ0 without increasing the class PLS.
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  35.  47
    Notation and expression of emotion in operatic laughter.Robert R. Provine - 2008 - Behavioral and Brain Sciences 31 (5):591-592.
    The emotional expression of laughter in opera scores and performance was evaluated by converting notation to temporal data and contrasting it with the conversational laughter it emulates. The potency of scored and sung laughter was assayed by its ability to trigger contagion in audiences.
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  36.  86
    Notations for Living Mathematical Documents.Michael Kohlhase - unknown
    Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading time, (...)
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  37.  26
    Sound and Notation: Comparative Study on Musical Ontology.So Jeong Park - 2017 - Dao: A Journal of Comparative Philosophy 16 (3):417-430.
    Music is said to consist of melody, rhythm, and harmony. Sound is assumed to be something that automatically follows once musical structure is determined. Sound, which is what actually impinges on our eardrums, has been so long forgotten in the history of musical theory. It is ironic that we do not talk about the music which we hear every day but rather are exclusively concerned about the abstracted structure behind it. This is a legacy of ancient Greek ideas about music, (...)
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  38.  8
    Notations of Affect. An Architecture of Memory.Bernhard Stumpfhaus & Klaus Herding - 2004 - In Bernhard Stumpfhaus & Klaus Herding (eds.), Pathos, Affekt, Gefühl: Die Emotionen in den Künsten. Walter de Gruyter.
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  39. Naturalism, notation, and the metaphysics of mathematics.Madeline M. Muntersbjorn - 1999 - Philosophia Mathematica 7 (2):178-199.
    The instability inherent in the historical inventory of mathematical objects challenges philosophers. Naturalism suggests we can construct enduring answers to ontological questions through an investigation of the processes whereby mathematical objects come into existence. Patterns of historical development suggest that mathematical objects undergo an intelligible process of reification in tandem with notational innovation. Investigating changes in mathematical languages is a necessary first step towards a viable ontology. For this reason, scholars should not modernize historical texts without caution, as the use (...)
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  40.  61
    Atomic notation and atomistic hypotheses translated by Paul Needham.Paul Needham - 2000 - Foundations of Chemistry 2 (2):127-180.
    This article was first published as “Notation atomique et hypothèses atomistiques”, Revue des questions scientifiques, 31 (1892), 391– 457. It is the second of a series of articles Duhem was to publish in the Catholic journal Revue des questions scientifiques, in which he presents his understanding of what can justifiably be said about the structure of chemical substances as captured by chemical formulas. The argument unfolds following a broadly historical development of events throughout the course of the century which (...)
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  41.  47
    Wittgenstein's ab-Notation: An Iconic Proof Procedure.Timm Lampert - 2017 - History and Philosophy of Logic 38 (3):239-262.
    This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how (...)
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  42. On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
  43.  6
    (Gesichts)züge, Notation and Graphicness of Signs. Deconstruction in Wittgenstein’s Tractatus.Michał Piekarski - 2022 - Studia Philosophiae Christianae 58 (2):145-160.
    In this paper, I attempt to address some of the themes of Ludwig Wittgenstein’s Tractatus logico-philosophicus with the aim of their deconstructionist interpretation. My analysis is based on David Gunkel’s book Deconstruction (MIT Press 2021). Based on some of its findings, I show how the Tractatus allows deconstruction and its practice to be thought. I show that the graphic structure of signs is crucial for the young Wittgenstein’s analysis and that it justifies the metaphysical findings in favor of which he (...)
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  44.  42
    Peano on Symbolization, Design Principles for Notations, and the Dot Notation.Dirk Schlimm - 2021 - Philosophia Scientiae 25:95-126.
    Peano was one of the driving forces behind the development of the current mathematical formalism. In this paper, we study his particular approach to notational design and present some original features of his notations. To explain the motivations underlying Peano's approach, we first present his view of logic as a method of analysis and his desire for a rigorous and concise symbolism to represent mathematical ideas. On the basis of both his practice and his explicit reflections on notations, we discuss (...)
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  45.  28
    Frege's Notations: What They Are and How They Mean.Gregory Landini - 2011 - London and Basingstoke: Palgrave-Macmillan.
    Gregory Landini offers a detailed historical account of Frege's notations and the philosophical views that led Frege from Begriffssscrhrift to his mature work Grundgesetze, addressing controversial issues that surround the notations.
  46. Filosofiske notater.Arne Næss - 1963 - [Oslo]: Universitetsforlaget.
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  47.  46
    Conceptual Notation, and Related Articles. Translated [From the German] and Edited with a Biography and Introduction by Terrell Ward Bynum.Gottlob Frege - 1972 - Oxford, England: Oxford University Press UK. Edited by Terrell Ward Bynum.
    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.
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  48. Ordinal notations based on a weakly Mahlo cardinal.Michael Rathjen - 1990 - Archive for Mathematical Logic 29 (4):249-263.
  49. Movement notation systems as conceptual frameworks: The Laban system.Suzanne Youngerman - 1984 - In Maxine Sheets-Johnstone (ed.), Illuminating Dance: Philosophical Explorations. Wiley-Blackwell. pp. 101--123.
  50.  36
    A notation system for ordinal using ψ-functions on inaccessible mahlo numbers.Helmut Pfeiffer & H. Pfeiffer - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):431-456.
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