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  1. Artificial Intelligence and Cognition. Proceedings of the First International Workshop AIC 2013.Antonio Lieto & Marco Cruciani (eds.) - 2013 - CEUR Workshop Proceedings.
  • Meaning and Demonstration.Matthew Stone & Una Stojnic - 2015 - Review of Philosophy and Psychology 6 (1):69-97.
    In demonstration, speakers use real-world activity both for its practical effects and to help make their points. The demonstrations of origami mathematics, for example, reconfigure pieces of paper by folding, while simultaneously allowing their author to signal geometric inferences. Demonstration challenges us to explain how practical actions can get such precise significance and how this meaning compares with that of other representations. In this paper, we propose an explanation inspired by David Lewis’s characterizations of coordination and scorekeeping in conversation. In (...)
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  • Diagrams.Sun-Joo Shin - 2008 - Stanford Encyclopedia of Philosophy.
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  • Handbook of Logical Thought in India.Sundar Sarukkai & Mihir Chakraborty (eds.) - 2018 - New Delhi, India: Springer.
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  • Visualizando Signos.Priscila Farias & Joao Queiroz - 2017 - Sao Paulo: Blucher.
    Os signos e as classes dos signos estão entre os tópicos mais importantes do sistema filosófico de Charles S. Peirce. As 10, 28, e 66 classes de signos são classificações desenvolvidas especialmente a partir de 1903 e representam um grande refinamento da divisão fundamental de signos – ícone, índice, símbolo. Nossa abordagem aqui define uma estratégia de visualização das classificações dos signos, com especial atenção para as 10 e 66 classes de signos. O livro está dividido em duas partes: (i) (...)
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  • Introduction: Varieties of Iconicity.Valeria Giardino & Gabriel Greenberg - 2015 - Review of Philosophy and Psychology 6 (1):1-25.
    This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...)
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  • Reasoning with Knowledge of Things.Matt Duncan - forthcoming - Philosophical Psychology:1-22.
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  • A Holey Perspective on Venn Diagrams.Anna N. Bartel, Kevin J. Lande, Joris Roos & Karen B. Schloss - 2021 - Cognitive Science 46 (1):e13073.
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  • Introduction: Diagrammatical Reasoning and Peircean Logic Representations.João Queiroz & Frederik Stjernfelt - 2011 - Semiotica 2011 (186):1-4.
  • What Is the Use of Diagrams in Theoretical Modeling?Anouk Barberousse - 2013 - Science in Context 26 (2):345-362.
    ArgumentThe use of diagrams is pervasive in theoretical physics. Together with mathematical formulae and natural language, diagrams play a major role in theoretical modeling. They enrich the expressive power of physicists and help them to explore new theoretical ideas. Diagrams are not only heuristic or pedagogical tools, but they are also tools that enable developing the content of models into novel implications.
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  • Representational Analyticity.Jack C. Lyons - 2005 - Mind and Language 20 (4):392–422.
    The traditional understanding of analyticity in terms of concept containment is revisited, but with a concept explicitly understood as a certain kind of mental representation and containment being read correspondingly literally. The resulting conception of analyticity avoids much of the vagueness associated with attempts to explicate analyticity in terms of synonymy by moving the locus of discussion from the philosophy of language to the philosophy of mind. The account provided here illustrates some interesting features of representations and explains, at least (...)
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  • Euler’s Visual Logic.Eric M. Hammer & Sun-Joo Shin - 1998 - History and Philosophy of Logic 19 (1):1-29.
    The evolution of Euler diagrams is examined from Euler's original system through the modifications made by Venn and Peirce. It is shown that these modifications were motivated by an attempt to increase the expressivity of the diagrams, but that a side effect of these modifications was a loss of the visual clarity of Euler's original system. Euler's original system is reconstructed from a modern, logical point of view. Formal semantics and rules of inference are provided for this reconstruction of Euler's (...)
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  • It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic.R. Lanier Anderson - 2004 - Philosophy and Phenomenological Research 69 (3):501–540.
    Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...)
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  • Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - forthcoming - Philosophers' Imprint.
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
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  • What the Heck is Logic? Logics-as-Formalizations, a Nihilistic Approach.Aadil Kurji - 2020 - Dissertation,
    Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...)
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  • Thinking with Maps.Elisabeth Camp - 2007 - Philosophical Perspectives 21 (1):145–182.
    Most of us create and use a panoply of non-sentential representations throughout our ordinary lives: we regularly use maps to navigate, charts to keep track of complex patterns of data, and diagrams to visualize logical and causal relations among states of affairs. But philosophers typically pay little attention to such representations, focusing almost exclusively on language instead. In particular, when theorizing about the mind, many philosophers assume that there is a very tight mapping between language and thought. Some analyze utterances (...)
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  • Diagrams in Mathematics.Carlo Cellucci - 2019 - Foundations of Science 24 (3):583-604.
    In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...)
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  • Semantics of Pictorial Space.Gabriel Greenberg - 2021 - Review of Philosophy and Psychology 1 (4):847-887.
    A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes from recent (...)
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  • Diagrams of the Past: How Timelines Can Aid the Growth of Historical Knowledge.Marc Champagne - 2016 - Cognitive Semiotics 9 (1):11-44.
    Historians occasionally use timelines, but many seem to regard such signs merely as ways of visually summarizing results that are presumably better expressed in prose. Challenging this language-centered view, I suggest that timelines might assist the generation of novel historical insights. To show this, I begin by looking at studies confirming the cognitive benefits of diagrams like timelines. I then try to survey the remarkable diversity of timelines by analyzing actual examples. Finally, having conveyed this (mostly untapped) potential, I argue (...)
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  • Knowledge of Things.Matt Duncan - 2020 - Synthese 197 (8):3559-3592.
    As I walk into a restaurant to meet up with a friend, I look around and see all sorts of things in my immediate environment—tables, chairs, people, colors, shapes, etc. As a result, I know of these things. But what is the nature of this knowledge? Nowadays, the standard practice among philosophers is to treat all knowledge, aside maybe from “know-how”, as propositional. But in this paper I will argue that this is a mistake. I’ll argue that some knowledge is (...)
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  • Speedith: A Reasoner for Spider Diagrams.Matej Urbas, Mateja Jamnik & Gem Stapleton - 2015 - Journal of Logic, Language and Information 24 (4):487-540.
    In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams. Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. Speedith’s inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. This allows (...)
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  • Abduction: Between Subjectivity and Objectivity.João Queiroz & Floyd Merrell - 2005 - Semiotica 2005 (153 - 1/4):1-8.
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  • Proofs and Pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
    Everyone appreciates a clever mathematical picture, but the prevailing attitude is one of scepticism: diagrams, illustrations, and pictures prove nothing; they are psychologically important and heuristically useful, but only a traditional verbal/symbolic proof provides genuine evidence for a purported theorem. Like some other recent writers (Barwise and Etchemendy [1991]; Shin [1994]; and Giaquinto [1994]) I take a different view and argue, from historical considerations and some striking examples, for a positive evidential role for pictures in mathematics.
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  • Rhematische Graphen: Über Peirce'Theorien der diagrammatischen Nachbildung von Propositionen.Constantin von Pückler - 2000 - Philosophia Scientiae 4 (2):67-131.
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  • Cognitive Stories and the Image of Mathematics.Wagner Roy - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):305-323.
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  • Query Graphs with Cuts: Mathematical Foundations.Frithjof Dau - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 32--50.
  • Grafos existenciais de CS Peirce: uma introdução ao sistema alfa.Lafayette de Moraes & João Queiroz - 2001 - Cognitio 2:112-133.
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  • Introdução ao Sistema Beta dos Grafos Existenciais de CS Peirce.Lafayette de Moraes & João Queiroz - 2004 - Cognitio 5 (1):28-43.
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  • Diagrams for Navya-Nyāya.Jim Burton - 2020 - Journal of Indian Philosophy 48 (2):229-254.
    Although a number of authors have used diagrams extensively in their studies of Navya-Nyāya, they have done so to explain and illustrate concepts, not with the goal of reasoning with the diagrams themselves. Adherents of diagrammatic reasoning have made claims for its potential by pointing to key structural correspondences between diagrams and logical concepts, arguably lacking in sentential representations, and describing these relations using concepts such as “well matchedness” and “iconicity”. A canonical example of this iconicity is the use of (...)
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  • What Makes an Effective Representation of Information: A Formal Account of Observational Advantages.Gem Stapleton, Mateja Jamnik & Atsushi Shimojima - 2017 - Journal of Logic, Language and Information 26 (2):143-177.
    In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the (...)
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  • Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
    Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...)
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  • The Skill of Translating Thought Into Action: Framing The Problem.Wayne Christensen - 2020 - Review of Philosophy and Psychology (3):1-27.
    The nature of the cognition-motor interface has been brought to prominence by Butterfill & Sinigaglia, who argue that the representations employed by the cognitive and motor systems should not be able to interact with each other. Here I argue that recent empirical evidence concerning the interface contradicts several of the assumptions incorporated in Butterfill & Sinigaglia’s account, and I seek to develop a theoretical picture that will allow us to explain the structure of the interface presented by this evidence. The (...)
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  • Main Problems of Diagrammatic Reasoning. Part I: The Generalization Problem. [REVIEW]Zenon Kulpa - 2009 - Foundations of Science 14 (1-2):75-96.
    The paper attempts to analyze in some detail the main problems encountered in reasoning using diagrams, which may cause errors in reasoning, produce doubts concerning the reliability of diagrams, and impressions that diagrammatic reasoning lacks the rigour necessary for mathematical reasoning. The paper first argues that such impressions come from long neglect which led to a lack of well-developed, properly tested and reliable reasoning methods, as contrasted with the amount of work generations of mathematicians expended on refining the methods of (...)
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  • Venn Diagram with Names of Individuals and Their Absence: A Non-Classical Diagram Logic.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - 2018 - Logica Universalis 12 (1-2):141-206.
    Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.
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  • The Semiotics of Spider Diagrams.James Burton & John Howse - 2017 - Logica Universalis 11 (2):177-204.
    Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality. Rather than being primarily intended for logicians, spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce (...)
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  • Syllogisms in Rudimentary Linear Logic, Diagrammatically.Ruggero Pagnan - 2013 - Journal of Logic, Language and Information 22 (1):71-113.
    We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...)
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  • Mathematics Through the Glasses of Hjelmslevs Semiotics.Solomon Marcus - 2003 - Semiotica 2003 (145).
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  • Material Representations in Mathematical Research Practice.Mikkel W. Johansen & Morten Misfeldt - 2020 - Synthese 197 (9):3721-3741.
    Mathematicians’ use of external representations, such as symbols and diagrams, constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and (...)
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  • The Mystery of Deduction and Diagrammatic Aspects of Representation.Sun-Joo Shin - 2015 - Review of Philosophy and Psychology 6 (1):49-67.
    Deduction is decisive but nonetheless mysterious, as I argue in the introduction. I identify the mystery of deduction as surprise-effect and demonstration-difficulty. The first section delves into how the mystery of deduction is connected with the representation of information and lays the groundwork for our further discussions of various kinds of representation. The second and third sections, respectively, present a case study for the comparison between symbolic and diagrammatic representation systems in terms of how two aspects of the mystery of (...)
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  • A Diagrammatic Calculus of Syllogisms.Ruggero Pagnan - 2012 - Journal of Logic, Language and Information 21 (3):347-364.
    A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
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  • Redescubriendo la lógica diagramática de Leibniz.J. Martín Castro Manzano - 2017 - Tópicos: Revista de Filosofía 52:89-116.
    En este artículo recuperamos la lógica diagramática lineal de Leibniz para la silogística y descubrimos sus propiedades lógicas y computacionales a través de una aproximación formal en términos metalógicos, lo cual es algo que, hasta donde sabemos, aún falta por hacerse. Así, en esta contribución buscamos, respectivamente, dos metas, una histórica y una lógica: i) prestar más atención a los aspectos algorítmicos del sistema diagramático lineal de Leibniz para la silogística, de los cuales creemos que han sido desdeñados por un (...)
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  • Singular Propositions, Negation and the Square of Opposition.Lopamudra Choudhury & Mihir Kumar Chakraborty - 2016 - Logica Universalis 10 (2-3):215-231.
    This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions, their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the context of open universe.
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  • $$Hbox {Venn}{I{O1}}$$ Venn I o 1 : A Diagram System for Universe Without Boundary.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - 2019 - Logica Universalis 13 (3):289-346.
    A new diagram system \ where properties are fundamental and an object exists only w.r.t a property is presented. This work modifies both in syntax and semantics the system \ proposed by Choudhury and Chakraborty to picturise and address issues connected with open universe. Semantics for the current system is given. Soundness and completeness w.r.t the semantics are established.
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