Results for 'logical diagrams'

962 found
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  1. Logic Diagrams as Argument Maps in Eristic Dialectics.Jens Lemanski - 2023 - Argumentation 37 (1):69-89.
    This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in (...)
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  2. What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Basel: Birkhaüser. pp. 1-18.
    Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind (...)
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  3. Transcendental Philosophy and Logic Diagrams.Jens Lemanski - forthcoming - Philosophical Investigations:1-27.
    Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. This (...)
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  4. Scriptural logic: Diagrams for a postcritical metaphysics.Peter Ochs - 1995 - Modern Theology 11 (1):65-92.
    You ask if metaphysics is possible after modernity, or after Barth and Wittgenstein and Derrida and the critique of foundationalism? May I invite you, by way of response, to listen in on a conversation? It is a dialogue between what I will call a postcritical philosopher ("P") and a postcritical scriptural theologian —— I'll label the latter a "textualist" ("T"). What I mean by "postcritical" would be displayed as the pattern of inquiry traced by this dialogue. I take the term (...)
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  5. Means or end? On the Valuation of Logic Diagrams.Jens Lemanski - 2016 - Logic-Philosophical Studies 14:98-122.
    From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that since (...)
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  6. Argument Diagramming in Logic, Artificial Intelligence, and Law.Chris Reed, Douglas Walton & Fabrizio Macagno - 2007 - The Knowledge Engineering Review 22 (1):87-109.
    In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated - informal logic, argumentation theory, evidence law and legal reasoning – but also more recent work in applying and developing it in computer science and artificial intelligence. Beginning with a simple example of an everyday argument, we present an analysis of it visualised as an argument diagram constructed using a software tool. In the context of (...)
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  7. Enhancing the Diagramming Method in Informal Logic.Dale Jacquette - 2011 - Argument: Biannual Philosophical Journal 1 (2):327-360.
    The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially pedagogically in teaching (...)
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  8. Kant’s Crucial Contribution to Euler Diagrams.Jens Lemanski - 2024 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 55 (1):59–78.
    Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England (...)
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  9. On the Origin of Venn Diagrams.Amirouche Moktefi & Jens Lemanski - 2022 - Axiomathes 32 (3):887-900.
    In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this (...)
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  10. Reism, Concretism and Schopenhauer Diagrams.Jens Lemanski & Michał Dobrzański - 2020 - Studia Humana 9 (3/4):104-119.
    Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two (...)
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  11. Combing Graphs and Eulerian Diagrams in Eristic.Jens Lemanski & Reetu Bhattacharjee - 2022 - In Valeria Giardino, Sven Linker, Tony Burns, Francesco Bellucci, J. M. Boucheix & Diego Viana (eds.), Diagrammatic Representation and Inference. 13th International Conference, Diagrams 2022, Rome, Italy, September 14–16, 2022, Proceedings. Springer. pp. 97–113.
    In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type (...)
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  12. ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that (...)
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  13. An Aid to Venn Diagrams.Robert Allen - 1997 - American Philosophical Association Newsletter on Teaching Philosophy 96 (Spring 1997):104-105.
    The following technique has proven effective in helping beginning logic students locate the sections of a three-circled Venn Diagram in which they are to represent a categorical sentence. Very often theses students are unable to identify the parts of the diagram they are to shade or bar.
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  14. Syllogisms Diagrammed: OOA to OOO.Mark Andrews - manuscript
    This document diagrams the forms OOA, OOE, OOI, and OOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a system (...)
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  15. Diagrams and alien ways of thinking.Marc Champagne - 2019 - Studies in History and Philosophy of Science Part A 75 (C):12-22.
    The recent wave of data on exoplanets lends support to METI ventures (Messaging to Extra-Terrestrial Intelligence), insofar as the more exoplanets we find, the more likely it is that “exominds” await our messages. Yet, despite these astronomical advances, there are presently no well-confirmed tests against which to check the design of interstellar messages. In the meantime, the best we can do is distance ourselves from terracentric assumptions. There is no reason, for example, to assume that all inferential abilities are language-like. (...)
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  16. “The Diagram is More Important Than is Ordinarily Believed”: A Picture of Lonergan’s Cognitional Structure.Ryan Miller - 2021 - The Lonergan Review 12:51-78.
    In his article “Insight: Genesis and Ongoing Context,” Fred Crowe calls out Lonergan’s line “the diagram is more important than…is ordinarily believed” as the “philosophical understatement of the century.” Sixteen pages later he identifies elaborating an invariant cognitional theory to underlie generalized emergent probability and thus “the immanent order of the universe of proportionate being,” as “our challenge,” “but given the difficulty” he does not “see any prospect for an immediate answer.” Could this have something to do with the lack (...)
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  17. Periods in the Use of Euler-type Diagrams.Jens Lemanski - 2017 - Acta Baltica Historiae Et Philosophiae Scientiarum 5 (1):50-69.
    Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase (...)
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  18. Interlacing the singularity, the diagram and the metaphor. Translated by Simon B. Duffy.Gilles Châtelet - 2006 - In Simon Duffy (ed.), Virtual Mathematics: the logic of difference. Clinamen.
    If the allusive stratagems can claim to define a new type of systematicity, it is because they give access to a space where the singularity, the diagram and the metaphor may interlace, to penetrate further into the physico-mathematic intuition and the discipline of the gestures which precede and accompany ‘formalisation’. This interlacing is an operation where each component backs up the others: without the diagram, the metaphor would only be a short-lived fulguration because it would be unable to operate: without (...)
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  19. Depicting Negation in Diagrammatic Logic: Legacy and Prospects.Fabien Schang & Amirouche Moktefi - 2008 - Diagrammatic Representation and Inference: Proceedings of the 5th International Conference Diagrams 2008 5223:236-241.
    Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: a review of the main concepts involved in the definition of logical negation; an explanation of the epistemological obstacles against the introduction of non-classical negations within diagrammatic logic.
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  20. On the Formal Cause of Diagrams: Mimesis and Phenomenology.Noah Greenstein - 2024 - In Jens Lemanski, Mikkel Willum Johansen, Emmanuel Manalo, Petrucio Viana, Reetu Bhattacharjee & Richard Burns (eds.), Diagrammatic Representation and Inference 14th International Conference, Diagrams 2024, Münster, Germany, September 27 – October 1, 2024, Proceedings. Cham: Springer. pp. 472-475.
    We investigate the formal cause of diagrams, initially realizing that diagrams have no obvious form. It is argued their form is to mimic expert perspectives. This perspective provides a organizational structure that represents the relations important in understanding the worldly situation. We then shift to a study of how we are to understand an expert perspective. Using the distinction between intuitive and formal logic, logica utens versus logica docens, we identify games of habituation: games of focus and distraction. (...)
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  21. Logic: A Modern Guide.Colin Beckley - 2016 - Milton Keynes: Think Logically Books.
    This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be understood with examples (...)
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  22. A Holey Perspective on Venn Diagrams.Anna N. Bartel, Kevin J. Lande, Joris Roos & Karen B. Schloss - 2021 - Cognitive Science 46 (1):e13073.
    When interpreting the meanings of visual features in information visualizations, observers have expectations about how visual features map onto concepts (inferred mappings.) In this study, we examined whether aspects of inferred mappings that have been previously identified for colormap data visualizations generalize to a different type of visualization, Venn diagrams. Venn diagrams offer an interesting test case because empirical evidence about the nature of inferred mappings for colormaps suggests that established conventions for Venn diagrams are counterintuitive. Venn (...)
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  23. Logikdiagramme und Logikmaschinen aus der Zittauer Schule um Christian Weise.Jens Lemanski - 2019 - Neues Lausitzische Magazin 141 (1):39-57.
    A particularly promising trail on the search for forgotten logic diagrams leads to Upper Lusatia in the 17th century, more precisely to Christian Weise and his students. Samuel Grosser, who later became rector in Görlitz, and Johann Christian Lange, who later became professor of logic at the University of Gießen, are the most prominent to have published remarkable logic diagrams. Even more remarkable, however, is the fact that Lange's interest in these diagrams ultimately gave rise to the (...)
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  24. Using Argument Diagramming to Teach Critical Thinking in a First-Year Writing Course.Maralee Harrell & Danielle Wetzel - 2015 - In Ron Barnett & Bob Ennis Martin Davies (ed.), Palgrave Handbook of Critical Thinking in Higher Education. pp. 213-232.
    The importance of teaching critical thinking skills at the college level cannot be overemphasized. Teaching a subcategory of these skills—argument analysis—we believe is especially important for first-year students with their college careers, as well as their lives, ahead of them. The struggle, however, is how to effectively teach argument analysis skills that will serve students in a broad range of disciplines.
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  25. Syntactic characterizations of first-order structures in mathematical fuzzy logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  26. Individuals, Existence, and Existential Commitment in Visual Reasoning.Jens Lemanski - 2024 - Open Philosophy 7 (1):1-25.
    This article examines the evolution of the concept of existence in modern visual representation and reasoning, highlighting important milestones. In the late eighteenth century, during the so-called golden age of visual reasoning, nominalism reigned supreme and there was limited scope for existential import or individuals in logic diagrams. By the late nineteenth century, a form of realism had taken hold, whose existential commitments continue to dominate many areas in logic and visual reasoning to this day. Physical, metaphysical, epistemological, and (...)
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  27. Multiple Generality in Scholastic Logic.Boaz Faraday Schuman - 2022 - Oxford Studies in Medieval Philosophy 10:215-282.
    Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of (...)
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  28. Introduction: Diagrammatical reasoning and Peircean logic representations.João Queiroz & Frederik Stjernfelt - 2011 - Semiotica 2011 (186):1-4.
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  29. A Darkly Bright Republic: Milton's Poetic Logic.Joshua M. Hall - 2018 - South African Journal of Philosophy 37 (2):158-170.
    My first section considers Walter J. Ong’s influential analyses of the logical method of Peter Ramus, on whose system Milton based his Art of Logic. The upshot of Ong’s work is that philosophical logic has become a kind monarch over all other discourses, the allegedly timeless and universal method of mapping and diagramming all concepts. To show how Milton nevertheless resists this tyrannical result in his non-Logic writings, my second section offers new readings of Milton’s poems Il Penseroso and (...)
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  30. The Metaphysics and Logic of Psychology: Peirce's Reading of James's Principles.Mathias Girel - 2003 - Transactions of the Charles S. Peirce Society 39 (2):163-203.
    The present paper deals thus with some fundamental agreements and disagreements between Peirce and James, on crucial issues such as perception and consciousness. When Peirce first read the Principles, he was sketching his theory of the categories, testing its applications in many fields of knowledge, and many investigations were launched, concerning indexicals, diagrams, growth and development. James's utterances led Peirce to make his own views clearer on a wide range of topics that go to the heart of the foundations (...)
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  31. Sound Reasoning : Prospects and Challenges of Current Acoustic Logics.Marc Champagne - 2015 - Logica Universalis 9 (3):331-343.
    Building on the notational principles of C. S. Peirce’s graphical logic, Pietarinen has tried to develop a propositional logic unfolding in the medium of sound. Apart from its intrinsic interest, this project serves as a concrete test of logic’s range. However, I argue that Pietarinen’s inaugural proposal, while promising, has an important shortcoming, since it cannot portray double-negation without thereby portraying a contradiction.
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  32. Beyond the ‘Last Phenomenology’: Rhythmic Modulations in Gilles Deleuze’s The Logic of Sensation.Iain Campbell - 2023 - Deleuze and Guattari Studies 17 (3):301-325.
    This article reconstructs Gilles Deleuze’s engagement with phenomenology, and with the phenomenological problematic of sensation, in his Francis Bacon: The Logic of Sensation. Considering Deleuze’s adoption, from the phenomenology of art, of notions of sensation and rhythm, it examines how Deleuze complexifies these phenomenological notions by aligning them with his profoundly non-phenomenological notion of the body without organs, as well as with the concepts of modulation and the diagram. In mapping Deleuze’s complexification of rhythm and his development of a logic (...)
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  33. Realistics Premises of Epistemic Argumentation for Dynamic Epistemic Logics.Edward Bryniarski, Zbigniew Bonikowski, Jacek Waldmajer & Urszula Wybraniec-Skardowska - 2011 - Studies in Logic, Grammar and Rhetoric 23 (36):173-187.
    In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, the (...)
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  34. On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.John Venn - 1880 - Philosophical Magazine 9 (59):1-18.
    Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even of those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called "Eulerian circles," has met with any general acceptance. A variety of others indeed have been proposed by ingenious and celebrated logicians, several of which (...)
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  35. Characteristica Universalis.Barry Smith - 1991 - In Kevin Mulligan (ed.), Language, Truth and Ontology. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 48--77.
    Recent work in formal philosophy has concentrated over-whelmingly on the logical problems pertaining to epistemic shortfall - which is to say on the various ways in which partial and sometimes incorrect information may be stored and processed. A directly depicting language, in contrast, would reflect a condition of epistemic perfection. It would enable us to construct representations not of our knowledge but of the structures of reality itself, in much the way that chemical diagrams allow the representation (at (...)
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  36. Seneca’s and Porphyry’s Trees in Modern Interpretation.Jens Lemanski - 2023 - In Jens Lemanski & Ingolf Max (eds.), Historia Logicae and its Modern Interpretation. London: College Publications. pp. 61-87.
    This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through the perspective of (...)
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  37. Signs as a Theme in the Philosophy of Mathematical Practice.David Waszek - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer.
    Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential (...)
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  38. Las reglas de Irving Copi y Carl Cohen son una condición necesaria y suficiente de la validez en los silogismos categóricos de forma estándar.Franklin Galindo & Kris Martins - 2005 - Episteme 25 (1):123-148.
    Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...)
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  39. La représentation visuelle des classes d’objets.Amirouche Moktefi - 2013 - Visible 10:153-164.
    It is customary to draw a circle to represent a collection of objects. This makes it easy to represent logical relations between classes thanks to topological relations between spaces. The aim of this paper is to discuss the process by which spaces represent visually classes.
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  40. Why Images Cannot be Arguments, But Moving Ones Might.Marc Champagne & Ahti-Veikko Pietarinen - 2020 - Argumentation 34 (2):207-236.
    Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its conclusion, then that conclusion must be demarcated from the premise or otherwise the argument will beg the question. If (...)
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  41. Greimas embodied: How kinesthetic opposition grounds the semiotic square.Jamin Pelkey - 2017 - Semiotica 2017 (214):277-305.
    According to Greimas, the semiotic square is far more than a heuristic for semantic and literary analysis. It represents the generative “deep structure” of human culture and cognition which “define the fundamental mode of existence of an individual or of a society, and subsequently the conditions of existence of semiotic objects” (Greimas & Rastier 1968: 48). The potential truth of this hypothesis, much less the conditions and implications of taking it seriously (as a truth claim), have received little attention in (...)
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  42. From Ideal Worlds to Ideality.Craig Warmke - 2023 - Journal of the American Philosophical Association 9 (1):114-134.
    In common treatments of deontic logic, the obligatory is what is true in all deontically ideal possible worlds. In this article, I offer a new semantics for Standard Deontic Logic with Leibnizian intensions rather than possible worlds. Even though the new semantics furnishes models that resemble Venn diagrams, the semantics captures the strong soundness and completeness of Standard Deontic Logic. Since, unlike possible worlds, many Leibnizian intensions are not maximally consistent entities, we can amend the semantics to invalidate the (...)
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  43.  68
    Proofs of valid categorical syllogisms in one diagrammatic and two symbolic axiomatic systems.Antonielly Garcia Rodrigues & Eduardo Mario Dias - manuscript
    Gottfried Leibniz embarked on a research program to prove all the Aristotelic categorical syllogisms by diagrammatic and algebraic methods. He succeeded in proving them by means of Euler diagrams, but didn’t produce a manuscript with their algebraic proofs. We demonstrate how key excerpts scattered across various Leibniz’s drafts on logic contained sufficient ingredients to prove them by an algebraic method –which we call the Leibniz-Cayley (LC) system– without having to make use of the more expressive and complex machinery of (...)
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  44. Using Computer-Assisted Argument Mapping to Teach Reasoning to Students.Martin Davies, Ashley Barnett & Tim van Gelder - 2021 - In J. Anthony Blair (ed.), The Critical Thinking Anthology. pp. 115-152.
    Argument mapping is a way of diagramming the logical structure of an argument to explicitly and concisely represent reasoning. The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. This paper overviews the innovation and provides a procedural approach for new teaches wanting to use argument mapping in the classroom. A brief history of argument mapping is provided at the end of this paper.
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  45. The Interpretation of Classically Quantified Sentences: A set-theoretic approach.Guy Politzer, Jean-Baptiste Van der Henst, Claire Delle Luche & Ira A. Noveck - 2006 - Cognitive Science 30 (4):691-723.
    We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...)
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  46.  75
    Diagramas Interativos para as Classificações dos Signos de Charles S. Peirce.Priscila Farias & João Queiroz - 2003 - Cognitio 4 (2):33-45.
    This article presents the first results of a research on visual models for the classifications of semiotic processes. The main issue discussed is how a graphic design methodology, associated with computer graphics resources, may contribute to the construction of interactive models, that can be used as tools for the investigation of C. S. Peirce theory of signs. Two models are presented: the first is an interactive 3-D model of Peirce's 3-trichotomic classification; the second is a computer program that builds (...) for any n-trichotomic classification of signs, and facilitates the analysis and comparison of different hypothesis regarding their structures. (shrink)
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  47. Some notes on the Aristotelian doctrine of opposition and the propositional calculus.Gerardo Ó Matía Cubillo - 2023 - Disputatio. Philosophical Research Bulletin 12 (26):53-70.
    We develop some of Williamson’s ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using ‘conditioned truth tables’, we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.
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  48. (1 other version)Teaching the PARC System of Natural Deduction.Daryl Close - 2015 - American Association of Philosophy Teachers Studies in Pedagogy 1:201-218.
    PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be used (...)
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    Brouwer's Intuition of Twoity and Constructions in Separable Mathematics.Bruno Bentzen - 2023 - History and Philosophy of Logic 45 (3):341-361.
    My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the constructions (...)
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  50. The Iconic-Symbolic Spectrum.Gabriel Greenberg - 2023 - Philosophical Review 132 (4):579-627.
    It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of (...)
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