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 (...) a dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

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 (...) theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer. (shrink)

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 role diagrams play as means of discovery and understanding. Alternatively, this paper purports to show that the view that the method of mathematics is the analytic method is capable of dealing with diagrams qua diagrams, and of accounting for such role. (shrink)

This book investigates a number of central problems in the philosophy of Charles Peirce grouped around the realism of his semiotics: the issue of how sign systems are developed and used in the investigation of reality. Thus, it deals with the precise character of Peirce's realism; with Peirce's special notion of propositions as signs which, at the same time, denote and describe the same object. It deals with diagrams as signs which depict more or less abstract states-of-affairs, facilitating reasoning (...) about them; with assertions as public claims about the truth of propositions. It deals with iconicity in logic, the issue of self-control in reasoning, dependences between phenomena in their realist descriptions. A number of chapters deal with applied semiotics: with biosemiotic sign use among pre-human organisms: the multimedia combination of pictorial and linguistic information in human semiotic genres like cartoons, posters, poetry, monuments. All in all, the book makes a strong case for the actual relevance of Peirce's realist semiotics. (shrink)

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 (...) a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyze and work with argumentation in law, philosophy and artificial intelligence. (shrink)

Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.

We contend that diagrams are tools not only for communication but also for supporting the reasoning of biologists. In the mechanistic research that is characteristic of biology, diagrams delineate the phenomenon to be explained, display explanatory relations, and show the organized parts and operations of the mechanism proposed as responsible for the phenomenon. Both phenomenon diagrams and explanatory relations diagrams, employing graphs or other formats, facilitate applying visual processing to the detection of relevant patterns. Mechanism (...) class='Hi'>diagrams guide reasoning about how the parts and operations work together to produce the phenomenon and what experiments need to be done to improve on the existing account. We examine how these functions are served by diagrams in circadian rhythm research. (shrink)

In a multi-study naturalistic quasi-experiment involving 269 students in a semester-long introductory philosophy course, we investigated the effect of teaching argument diagramming on students’ scores on argument analysis tasks. An argument diagram is a visual representation of the content and structure of an argument. In each study, all of the students completed pre- and posttests containing argument analysis tasks. During the semester, the treatment group was taught AD, while the control group was not. The results were that among the different (...) pretest achievement levels, the scores of low-achieving students who were taught AD increased significantly more than the scores of low-achieving students who were not taught AD, while the scores of the intermediate- and high-achieving students did not differ significantly between the treatment and control groups. The implication of these studies is that learning AD significantly improves low-achieving students’ ability to analyze arguments. (shrink)

From his earliest student days through the writing of his last book, Charles Darwin drew diagrams. In developing his evolutionary ideas, his preferred form of diagram was the tree. An examination of several of Darwin’s trees—from sketches in a private notebook from the late 1830s through the diagram published in the Origin—opens a window onto the role of diagramming in Darwin’s scientific practice. In his diagrams, Darwin simultaneously represented both observable patterns in nature and conjectural narratives of evolutionary (...) history. He then brought these natural patterns and narratives into dialogue, allowing him to explore whether the narratives could explain the patterns. But Darwin’s diagrams did not reveal their meaning directly to passive readers; they required readers to engage dynamically with them in order to understand the connections they disclosed between patterns and narratives. Moreover, the narratives Darwin depicted in his diagrams did not represent past sequences of events that he claimed had actually occurred; the narratives were conjectural, schematic, and probabilistic. Instead of depicting actual histories in all their particularity, Darwin depicted narratives in his diagrams in order to make general claims about how nature works. The conjunction of these features of Darwin’s diagrams is central to how they do their epistemic work. (shrink)

The way in which one understands information and concepts, and the way a student works to develop this, is an individual aspect of learning that cannot be universally defined as (at least manifested) the same for everyone. ‘Understanding’ is a broad term, and the way one achieves understanding is dependent on the way that material is presented. In this article, we argue that the philosophy of science can be important to nursing education—in particular, by showing that the way we imbue (...) understanding might depend on the meaning of ‘understanding’. Diagrams and concept maps are meant to guide newly formed knowledge and connections to develop proper thinking (e.g., the order in which nursing students must prioritize data) that a student requires in the field. We argue that whether or not an image/diagram/concept map confers understanding will depend on both what the object is and what we mean by ‘understanding’. (shrink)

This article presents diagrams developed from the insights of three middle school children with limited mobility about their experiences navigating social and spatial relations in their home, school and neighbourhoods. The paper explores the concept of assemblage as well as operationalising the Deleuzian idea of the diagram. The diagrams we produce are developed in connection with dominant idealisations of neighbourhood and home range that function in North America to choreograph children's progression from infancy through adolescence. We undertake this (...) diagramming in order to immediately and affectively illustrate the limits and possibilities of the challenges these young people face. (shrink)

Biologists depend on visual representations, and their use of diagrams has drawn the attention of philosophers, historians, and sociologists interested in understanding how these images are involved in biological reasoning. These studies, however, proceed from identification of diagrams on the basis of their spare visual appearance, and do not draw on a foundational theory of the nature of diagrams as representations. This approach has limited the extent to which we under- stand how these diagrams are involved (...) in biological reasoning. In this paper, I characterize three different kinds of figures among those previously identified as diagrams. The features that make these figures distinctive as representational types, furthermore, illuminate the ways in which they are involved in biological reasoning. (shrink)

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one (...) has come to expect in modern logic. Finally, challenges and opportunities for further work are indicated. (shrink)

This paper explores the question of what makes diagrammatic representations effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to successfully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic logic (...) and introduce an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllogistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences. (shrink)

Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential (...) equation is and in describing the global behavior of such a solution. (shrink)

In his Berlin Lectures of the 1820s, the German philosopher Arthur Schopenhauer (1788–1860) used spatial logic diagrams for philosophy of language. These logic diagrams were applied to many areas of semantics and pragmatics, such as theories of concept formation, concept development, translation theory, clarification of conceptual disputes, etc. In this paper we first introduce the basic principles of Schopenhauer’s philosophy of language and his diagrammatic method. Since Schopenhauer often gives little information about how the individual diagrams are (...) to be understood, we then make the attempt to reconstruct, specify and further develop one diagram type for the field of conceptual analysis. (shrink)

Using as case studies two early diagrams that represent mechanisms of the cell division cycle, we aim to extend prior philosophical analyses of the roles of diagrams in scientific reasoning, and specifically their role in biological reasoning. The diagrams we discuss are, in practice, integral and indispensible elements of reasoning from experimental data about the cell division cycle to mathematical models of the cycle’s molecular mechanisms. In accordance with prior analyses, the diagrams provide functional explanations of (...) the cell cycle and facilitate the construction of mathematical models of the cell cycle. But, extending beyond those analyses, we show how diagrams facilitate the construction of mathematical models, and we argue that the diagrams permit nomological explanations of the cell cycle. We further argue that what makes diagrams integral and indispensible for explanation and model construction is their nature as locality aids: they group together information that is to be used together in a way that sentential representations do not. (shrink)

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations (...) of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician. (shrink)

In his Berlin Lectures of the 1820s, the German philosopher Arthur Schopenhauer (1788–1860) used spatial logic diagrams for philosophy of language. These logic diagrams were applied to many areas of semantics and pragmatics, such as theories of concept formation, concept development, translation theory, clarification of conceptual disputes, etc. In this paper we first introduce the basic principles of Schopenhauer’s philosophy of language and his diagrammatic method. Since Schopenhauer often gives little information about how the individual diagrams are (...) to be understood, we then make the attempt to reconstruct, specify and further develop one diagram type for the field of conceptual analysis. (shrink)

In his 1903 Syllabus, Charles S. Peirce makes a distinction between icons and iconic signs, or hypoicons, and briefly introduces a division of the latter into images, diagrams, and metaphors. Peirce scholars have tried to make better sense of those concepts by understanding iconic signs in the context of the ten classes of signs described in the same Syllabus. We will argue, however, that the three kinds of hypoicons can better be understood in the context of Peirce's sixty-six classes (...) of signs. We analyze examples of hypoicons taken from the field of information design, describing them in the framework of the sixty-six classes, and discuss the consequences of those descriptions to the debate about the order of determination of the 10 trichotomies that form those classes. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, (...) Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

This article puts forward the notion of “evolving diagram” as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter “diagrams*”) in the context of “sketch theory,” a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* (...) theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of (...) most importance for a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...) the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

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 that neglecting timelines might mean neglecting significant aspects of reality that are revealed only by those signs. My overall message is that once we accept that relations are as important for the mind as what they relate, we have to pay closer attention to any semiotic device that enables or facilitates the discernment of new relations. (shrink)

Not simply set out in accompaniment of the Greek geometrical text, the diagram also is coaxed into existence manually (using straightedge and compasses) by commands in the text. The marks that a diligent reader thus sequentially produces typically sum, however, to a figure more complex than the provided one and also not (as it is) artful for being synoptically instructive. To provide a figure artfully is to balance multiple desiderata, interlocking the timelessness of insight with the temporality of construction. Our (...) account of the diagram complements those of Manders and Macbeth by more strongly emphasizing practical synthesis. (shrink)

There is substantial evidence from many domains that visual representations aid various forms of cognition. We aimed to determine whether visual representations of argument structure enhanced the acquisition and development of critical thinking skills within the context of an introductory philosophy course. We found a significant effect of the use of argument diagrams, and this effect was stable even when multiple plausible correlates were controlled for. These results suggest that natural⎯and relatively minor⎯modifications to standard critical thinking courses could provide (...) substantial increases in student learning and performance. (shrink)

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 (...) played a crucial role in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, (...) Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

In this paper, I explore general features of the “architecture” (relations of white space, diagram, and text on the page) of medieval manuscripts and early printed editions of Euclidean geometry. My focus is primarily on diagrams in the Arabic transmission, although I use some examples from both Byzantine Greek and medieval Latin manuscripts as a foil to throw light on distinctive features of the Arabic transmission. My investigations suggest that the “architecture” often takes shape against the backdrop of an (...) educational landscape. The constraints of the economic marketplace and cultural aesthetic ideals also appear to play a role in determining the “architecture” of both manuscripts and early printed editions. (shrink)

In his well-known paper on Euclid’s geometry, Ken Manders sketches an argument against conceiving the diagrams of the Elements in ‘semantic’ terms, that is, against treating them as representations—resting his case on Euclid’s striking use of ‘impossible’ diagrams in some proofs by contradiction. This paper spells out, clarifies and assesses Manders’s argument, showing that it only succeeds against a particular semantic view of diagrams and can be evaded by adopting others, but arguing that Manders nevertheless makes a (...) compelling case that semantic analyses ought to be relegated to a secondary role for the study of mathematical practices. (shrink)

This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a (...) role in concept formation as well as representations of proofs. In addition we note that 'visualization' is used in two different ways. In the first sense 'visualization' denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense 'visualization' denotes a diagram or representation of something. (shrink)

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.

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 (...) one of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

Bayesian networks (BN) and argumentation diagrams (AD) are two predominant approaches to legal evidential reasoning, that are often treated as alternatives to one another. This paper argues that they are, instead, complimentary and proposes the beginnings of a method to employ them in such a manner. The Bayesian approach tends to be used as a means to analyse the findings of forensic scientists. As such, it constitutes a means to perform evidential reasoning. The design of Bayesian networks that accurately (...) and comprehensively represent the relationships between investigative hypotheses and evidence remains difficult and sometimes contentious, however. Argumentation diagrams are representations of reasoning, and are used as a means to scrutinise reasoning (among other applications). In evidential reasoning, they tend to be used to represent and scrutinise the way humans reason about evidence. This paper examines how argumentation diagrams can be used to scrutinise Bayesian evidential reasoning by developing a method to extract argument diagrams from BN. (shrink)

Arguments with what are called "independent" or "convergent" premises are typically diagrammed by using an arrow between each premise and the conclusion. This makes diagramming objections to the reasoning difficult. It also obscures differences in argument structure. I suggest that a single arrow should be used for such arguments and that this is so even in the extreme form of independent premises when the argument is entirely unstructured. I then discuss the diagramming of objections.

Throughout the history of the philosophy of science, theories have been linked to formulas as a privileged representational format. In this paper, following, I defend a semantic-representational conception of theories, where theories are identified with sets of scientific re-presentations by virtue of their epistemic potential and independently of their format. To show the potential of this proposal, I analyze as a case study the use of phase diagrams in statistical mechanics to convey in a semantically consistent and syntactically correct (...) way theoretical principles such as Liouville’s theorem. I conclude by defending this philosophical position as a tool to show the enormous representational richness underlying scientific practices. (shrink)

In this paper, we intend to discuss how, according to Peirce’s semiotics, gestures can be conceptualized and described as diagrams. We are not concerned with answering when, why or how gestures emerged as semiotic motor activities. As a prerequisite for the very formulation of these problems, we are rather interested in discussing the theoretical conditions which should be fulflled for gestures to be characterized as iconic processes - and more specifcally as diagrammatic processes. The frst step is to summarize (...) a systematic analysis of the variety of iconic signs, elaborated by Peirce, followed by his typology of hypoicons in order to describe the hypoiconic class of diagrams. After that, we present some tentative answers to the question of how to describe gestures as diagrammatic signs. (shrink)

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play (...) in organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

This article offers an analysis of the cognitive role of diagrammatic movements in the theater. Based on the recognition of a theatrical work’s inherent ability to provide new insights concerning reality, the article concentrates on the way by which actors’ movements on stage create spatial diagrams that can provide new insights into the spectators’ world. The suggested model of theater’s epistemology results from a combination of Charles S. Peirce’s doctrine of diagrammatic reasoning and David Lewis’s theoretical account of the (...) truth value of counterfactual conditionals. I argue that in several theatrical works – in particular those whose central image is dominated by movements – the relation of what Lewis names “comparative overall similarity” between the fictional and the actual world is based on diagrammatic homology. The cognitive process involved in deciphering them is, hence, based on diagrammatic reasoning. The main emphasis of the analysis is on the previously unnoticed but important cognitive role of observation in the theater: the idea that observation takes an active role in the reasoning process that enables the spectators to form new knowledge about their actual world. Samuel Beckett’s plays Quad and Come and Go serve here as case studies. (shrink)

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

Abstract The artwork of Joseph Beuys was provocative in his time. Although he was very successful on the international art scene and on the art market, the larger The public is still bewildered by his Fat Chair or his installations and his performances. The article shows the evolution of his artwork from classical materials (stone, steel) to soft materials (animals, products of animals) and further to his concept of “social sculpture” and to programmatic diagrams (with words and graphics). A (...) special point of interest is the transition towards language (phonic and conceptual), the philosophy of art exposed in his drawings, and diagrams and the relation between art and science in his artwork. (shrink)

In this paper we introduce a recursive notation system $O(\mu)$ of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each $\alpha<\Omega$ in $O(\mu)$ KPM proves that the initial segment of $O(\mu)$ determined by $\alpha$ is a well ordering. Proof theoretic study for such theories will be reported in [9].

There are two important ways in which, when dealing with documents, we go beyond the boundaries of linear text. First, by incorporating diagrams into documents, and second, by creating complexes of intermeshed documents which may be extended in space and evolve and grow through time. The thesis of this paper is that such aggregations of documents are today indispensable to practically all complex human achievements from law and finance to orchestral performance and organized warfare. Documents provide for what we (...) can think of as a division of intellectual, instructional, and deontic labour, allowing plans, orders, and obligations to be enmeshed together in a way that often involves the use of diagrammatic elements, as for example in a musical score. (shrink)

Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle (...) diagrams. The comparison of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary. (shrink)

In this paper we introduce a recursive notation system O(Π 3 ) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π 3 -reflection. We show that for each $\alpha in O(Π 3 ) a set theory KP Π 3 for Π 3 -reflection proves that the initial segment of O(Π 3 ) determined by α is a well ordering. Proof theoretic study for such theories (...) will be reported in [4]. (shrink)

On 4 January 1971, Ti-Grace Atkinson delivered a talk entitled ‘Strategy and Tactics: A Presentation of Political Lesbianism’. The talk was later published in her collected essays, Amazon Odyssey. The essay contains thirty-five diagrams: ten ‘Strategy Charts’, three ‘Tactical Charts’ and twenty-two ‘Tactical-Strategy Charts’, which map a strategy of the ‘Oppressor’ (men) and the tactics that the ‘Oppressed’ (women) might develop to lead to a revolution – lesbians, significantly, are the ‘Buffer Zone’ between these two classes. In the only (...) reference I have managed to find to these diagrams, they are referred to as ‘crazy’. This article re-visits these diagrams, exploring the role of the diagram in how Atkinson attempts to map patriarchal relations and also imagine a feminist revolution. Taking Atkinson’s diagrams as a starting point, the article then uses them to begin to narrate a genealogy of the diagram in feminist theory, exploring a diagrammatic imaginary that is an often-used but rarely discussed tactic in feminist writing. Finally, the article opens out to consider how this history of feminist diagrams might be a precursor to more contemporary feminist data visualisations. (shrink)