Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. (...) Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning. (shrink)

Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations and linguistic features. Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: highlighting relevant relations in a micrograph ; sketching the plan for an experiment; and expressing expected visually salient (...) information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as heuristic tools in proof construction ; notational devices; and full-blown proof procedures. Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception. (shrink)

Today the economic diagram is employed universally in teaching and research by professional economists. Yet the history of its construction shows that much that has been regarded as distinctive of twentieth-century visual culture was prefigured in the nineteenth. This paper will place the construction of the first economic diagrams by Alfred Marshall in the context both of contemporary visual technologies developed in other moral sciences, and of his wider theory of industrial production. The paper will argue that an (...) understanding of the background to the historical graphs, constructed by the Cambridge political economist from the late 1860s onwards, will necessitate a revision of the narrative of modern visual reasoning, as recently advanced by Lev Manovich. (shrink)

Spatial and diagrammatic reasoning is a significant part not only of logical abilities, but also of logical studies. The authors of this paper consider some novel trends in studying this type of reasoning. They show that there are the following two main trends in spatial logic: (i) logical studies of the distribution of various objects in space (logic of geometry, logic of colors, etc.); (ii) logical studies of the space algorithms applied by nature itself (logic of swarms, logic (...) of fungi colonies, etc.). (shrink)

This monograph treats the important topic of the epistemology of diagrams in Euclidean geometry. Norman argues that diagrams play a genuine justificatory role in traditional Euclidean arguments, and he aims to account for these roles from a modified Kantian perspective. Norman considers himself a semi-Kantian in the following broad sense: he believes that Kant was right that ostensive constructions are necessary in order to follow traditional Euclidean proofs, but he wants to avoid appealing to Kantian a priori intuition as the (...) epistemological background for these constructions.Norman's main argument is limited to the thesis that certain Euclidean arguments—in particular, that of Proposition 1.32, the internal-angle-sum theorem—require inferences from diagrams. Interestingly, Norman is not committed to the view that these arguments are proofs. This becomes clear only quite late in the book, when he distinguishes argument from proofs, remarking that the argument he has been focusing on is not rigorous, and so is not a proof. Norman does not, however, explicitly classify all Euclidean arguments as non-proofs. His view is that diagrammatic reasoning can in principle feature in rigorous proofs, but he is not committed to the thesis that any particular argument, Euclidean or otherwise, provides an example of this. Rather than proofs in particular, Norman is more interested in the general issue of justification in mathematics.The argument has three components. First, Norman argues against competing accounts of Euclidean arguments such as empiricism, and ‘Leibnizianism’—the view that diagrams play only a heuristic role. Second, he provides a more direct, or positive, argument that the way we actually follow the standard argument for 1.32 does appeal to the diagram. This is an appeal to the phenomenology of following the argument. Third, he articulates and defends his semi-Kantian position against some objections.The book has a very careful and …. (shrink)

: Faraday is often described as an experimentalist, but his work is a dialectical interplay of concrete objects, visual images, abstract, theoretically-informed visual models and metaphysical precepts. From phenomena described in terms of patterns formed by lines of force he created a general explanation of space-filling systems of force which obey both empirical laws and principles of conservation and economy. I argue that Faraday's articulation of situated experience via visual models into a theory capable of verbal expression (...) owed much to his strategy of moving—via conjectural visual models—between the phenomenology of particulars (often displayed as patterns) and the general features of dynamical phenomena which he depicted as structures. (shrink)

It is argued that seeing that P is a mode of knowing that P that is to be explained in terms of the exercise of visual-perceptual recognitional abilities. The nature of those abilities is described. The justification for believing that P, when one sees that P, is provided by the fact that one sees that P. Access to this fact is explained in terms of an ability to recognize of seen objects that one is seeing them. Reasons for resistance (...) to such an account are considered. The distinction between merely reasonable belief and well-founded belief is emphasised. (shrink)

This paper discusses abductive reasoning---that is, reasoning in which explanatory hypotheses are formed and evaluated. First, it criticizes two recent formal logical models of abduction. An adequate formalization would have to take into account the following aspects of abduction: explanation is not deduction; hypotheses are layered; abduction is sometimes creative; hypotheses may be revolutionary; completeness is elusive; simplicity is complex; and abductive reasoning may be visual and non-sentential. Second, in order to illustrate visual aspects of (...) hypothesis formation, the paper describes recent work on visual inference in archaeology. Third, in connection with the evaluation of explanatory hypotheses, the paper describes recent results on the computation of coherence. (shrink)

This monograph treats the important topic of the epistemology of diagrams in Euclidean geometry. Norman argues that diagrams play a genuine justificatory role in traditional Euclidean arguments, and he aims to account for these roles from a modified Kantian perspective. Norman considers himself a semi-Kantian in the following broad sense: he believes that Kant was right that ostensive constructions are necessary in order to follow traditional Euclidean proofs, but he wants to avoid appealing to Kantian a priori intuition as the (...) epistemological background for these constructions.Norman's main argument is limited to the thesis that certain Euclidean arguments—in particular, that of Proposition 1.32, the internal-angle-sum theorem—require inferences from diagrams. Interestingly, Norman is not committed to the view that these arguments are proofs. This becomes clear only quite late in the book, when he distinguishes argument from proofs, remarking that the argument he has been focusing on is not rigorous, and so is not a proof . Norman does not, however, explicitly classify all Euclidean arguments as non-proofs. His view is that diagrammatic reasoning can in principle feature in rigorous proofs, but he is not committed to the thesis that any particular argument, Euclidean or otherwise, provides an example of this. Rather than proofs in particular, Norman is more interested in the general issue of justification in mathematics.The argument has three components. First, Norman argues against competing accounts of Euclidean arguments such as empiricism, and ‘Leibnizianism’—the view that diagrams play only a heuristic role. Second, he provides a more direct, or positive, argument that the way we actually follow the standard argument for 1.32 does appeal to the diagram. This is an appeal to the phenomenology of following the argument. Third, he articulates and defends his semi-Kantian position against some objections.The book has a very careful and …. (shrink)

Biographical studies have shown that visual mental imagery plays a significant role in the conduct of scientific research, particularly in the generation of hypotheses. But the nature of visual mental imagery and its participation in abductive inference is not systematically understood. This paper discusses examples of visual abductive reasoning by archaeologists, analyzing them according to the visual information and the process of inference employed. This work supports the conclusion that visual abduction is useful to (...) scientists under certain conditions and that it is amenable to detailed study. (shrink)

In today’s science, the output of measurement processes are often visual representations of the data detected. Moreover, we find such visual data as parts of scientific reasoning in different contexts. In this article, we will take a look at two of them. On the one hand, visual representations are used as a kind of surrogate for the real object to ask questions about it – we will call this the exploratory use of visual data. On (...) the other hand, visualisations are often used to communicate research results to scientific peers or to laymen. Instances of the latter case we will subsequently call the explanatory use of visual data. However, in both contexts the question arises what might justify these epistemic practices. Believing without reasons is epistemically irresponsible, it leads to gullibility. Thus, we will try to answer the question whether there are any reasons to support our epistemic practices concerning scientific visualisations in the above-mentioned senses and whether these are good reasons to rely on. (shrink)

An important debate in the reasoning literature concerns the extent to which inference processes are domain-free or domain-specific. Typically, evidence in support of the domain-specific position comprises the facilitation observed when abstract reasoning tasks are set in realistic context. Three experiments are reported here in which the sources of facilitation were investigated for contextualised versions of Raven's Progressive Matrices (Richardson, 1991) and non-verbal analogies from the AH4 test (Richardson & Webster, 1996). Experiment 1 confirmed that the facilitation observed (...) for the contextualised matrices was in part due to extraneous aspects of commentaries originally intended to activate domainspecific processes. Experiments 2 and 3 indicated that the remainder of the facilitation for the matrices, and all of the facilitation for the analogies, could be explained by visual salience: Converting the item elements into realistic objects had enabled them and their transitions to be identified more easily. Hence, performance at simplified abstract items was as good as, or better than, at contextualised items. It is concluded that facilitation effects cannot be interpreted as showing that domain-specific processes constitute a self-contained system separate from domain-free processes. In turn, this means that domain-free processes cannot be dismissed as being unimportant for reasoning. (shrink)

Three experiments examined the effects of interactive visualizations and spatial abilities on a task requiring participants to infer and draw cross sections of a three‐dimensional (3D) object. The experiments manipulated whether participants could interactively control a virtual 3D visualization of the object while performing the task, and compared participants who were allowed interactive control of the visualization to those who were not allowed control. In Experiment 1, interactivity produced better performance than passive viewing, but the advantage of interactivity disappeared in (...) Experiment 2 when visual input for the two conditions in a yoked design was equalized. In Experiments 2 and 3, differences in how interactive participants manipulated the visualization were large and related to performance. In Experiment 3, non‐interactive participants who watched optimal movements of the display performed as well as interactive participants who manipulated the visualization effectively and better than interactive participants who manipulated the visualization ineffectively. Spatial ability made an independent contribution to performance on the spatial reasoning task, but did not predict patterns of interactive behavior. These experiments indicate that providing participants with active control of a computer visualization does not necessarily enhance task performance, whereas seeing the most task‐relevant information does, and this is true regardless of whether the task‐relevant information is obtained actively or passively. (shrink)

This thesis challenges a general prejudice against visualization in the history of logic and mathematics, by providing a semantic analysis of two graphical representation systems--a traditional Venn diagram representation system and an extension of it. While Venn diagrams have been used to solve problems in set theory and to test the validity of syllogisms in logic, they have not been considered valid proofs but heuristic tools for finding valid formal proofs. ;I present Venn diagrams which have been used in logic (...) as a formal system of representation equipped with its own syntax and semantics. I also show that Venn-I, with the rules of transformation that I specify, is sound and complete. The soundness of Venn-I refutes a worry that mathematicians and logicians have about graphical representation: Fallacies often have arisen from the misuse of diagrams in mathematical proofs, especially in geometry. However, the validity of the transformation rules assures us that the correct application of these rules will not lead to fallacies. ;I extend Venn-I so that this new system has a general way to convey disjunctive information. A new formation rule is introduced and new transformation rules are added. I call this extended system Venn-II. The semantics of Venn-II is formalized as an extension of the semantics of Venn-I. The soundness and completeness of Venn-II are also proven. I then show that Venn-II and a monadic first-order language are equivalent in their expressiveness. ;The analysis of Venn-I and Venn-II leads to interesting issues which have their analogues in other deductive systems. I conclude the thesis with a discussion of some fundamental differences between graphical systems and linguistic systems. (shrink)

It is a commonplace of discussion about the impact of visual media, whether visual images in print, televisual images or the images of the internet, to claim that it functions irrationally. This paper argues against that claim. First, the assumptions about the connection between rationality and linear, written, unemotional prose are unjustified. Secondly, using analytic techniques analogous to those used in identifying argumentation in verbal text, is possible to discern arguments in visual text, in particular in image (...) based advertisements. (shrink)

This article argues that the foundational separation between psychoanalysis and experimental psychology was challenged in important ways by psychoanalytic infant researchers. Through a close examination of American psychoanalyst René Spitz, it extends John Forrester’s conception of reasoning in cases outside classic psychoanalytic practices. Specifically, the article interrogates the foundations of reasoning in cases—the individual, language, and the doctor–patient relationship—to show how these are reimagined in relation to the structures of American developmental psychology. The article argues that the staunch (...) separation of experimental psychology and psychoanalysis, reiterated by philosophers and historians of psychology, is flimsy at best—and, conversely, that the maintenance of these boundaries enabled the production of a cinematic case study. Spitz created films that used little language and took place outside the consulting room with institutionalized infants. Yet key aspects of the psychoanalytic case, as put forth by John Forrester, were depicted visually. These visual displays of transference, failure, and interpersonal emotions highlight the foundations of what Forrester means by reasoning in cases. The article concludes that Spitz failed at creating classic psychoanalytic evidence, but in so doing stretched the epistemology of the case. (shrink)

Language is more than a source of information for accessing higher-order conceptual knowledge. Indeed, language may determine how people perceive and interpret visual stimuli. Visual processing in linguistic contexts, for instance, mirrors language processing and happens incrementally, rather than through variously-oriented fixations over a particular scene. The consequences of this atypical visual processing are yet to be determined. Here, we investigated the integration of visual and linguistic input during a reasoning task. Participants listened to sentences (...) containing conjunctions or disjunctions and looked at visual scenes containing two pictures that either matched or mismatched the nouns. Degree of match between nouns and pictures and between their expected and actual spatial positions affected fixations as well as judgments. We conclude that language induces incremental processing of visual scenes, which in turn becomes susceptible to reasoning errors during the language-meaning verification process. (shrink)

Data literacy – the ability to analyze, interpret, evaluate, and use data and data visualizations – has become increasingly important for understanding and communicating information in the discipline of history. In the United States, curricular standards and standardized assessments already reflect this importance, but educators lack a clear picture of how students use data visualizations when reasoning about the past. How do students use data visualizations when reasoning about a historical question? To what degree does using data visualizations (...) enhance students’ historical reasoning? What challenges do students face when attempting to use data visualizations? This study addresses these questions, investigating how fifth-grade, eighth-grade, and high school students use data visualizations from typical school textbooks. Twenty-seven students were interviewed, surveyed, and asked to think aloud about a historical question while using a textbook entry that included a data visualization. Results from qualitative and quantitative analyses highlight the potential for data visualizations to enhance historical reasoning. However, results also indicate that students are unlikely to read data visualizations on their own, underscoring the importance of providing targeted data literacy instruction. (shrink)

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)

Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise cognitively inaccessible. Despite their important functional roles in scientific practices, philosophers of science have more or less neglected visual representations in their analyses of epistemic methods and tools of (...) class='Hi'>reasoning in science. This book is meant to fill this gap. It presents a detailed investigation into central conceptual issues and into the epistemology of visual representations in science. (shrink)

In this book, Michael Madary examines visual experience, drawing on both phenomenological and empirical methods of investigation. He finds that these two approaches—careful, philosophical description of experience and the science of vision—independently converge on the same result: Visual perception is an ongoing process of anticipation and fulfillment. Madary first makes the case for the descriptive premise, arguing that the phenomenology of vision is best described as on ongoing process of anticipation and fulfillment. He discusses visual experience as (...) being perspectival, temporal, and indeterminate; considers the possibility of surprise when appearances do not change as we expect; and considers the content of visual anticipation. Madary then makes the case for the empirical premise, showing that there are strong empirical reasons to model vision using the general form of anticipation and fulfillment. He presents a range of evidence from perceptual psychology and neuroscience, and reinterprets evidence for the two-visual-systems hypothesis. Finally, he considers the relationship between visual perception and social cognition. An appendix discusses Husserlian phenomenology as it relates to the argument of the book. Madary argues that the fact that there is a convergence of historically distinct methodologies itself is an argument that supports his findings. With Visual Phenomenology, he creates an exchange between the humanities and the sciences that takes both methods of investigation seriously. (shrink)

In this era of increased polarization of opinion and contentious disagreement, CRITICAL REASONING presents a cooperative approach to critical thinking and formation of beliefs. CRITICAL REASONING emphasizes the importance of developing and applying analytical skills in real life contexts. This book is unique in providing multiple, diverse examples of everyday arguments, both textual and visual, including hard to find long argument passages from real-life sources. The book provides clear, step-by-step procedures to help you decide for yourself what (...) to believe--to be a consumer of information in our contemporary "world of experts.". (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)

Visual aids can improve comprehension of risks associated with medical treatments, screenings, and lifestyles. Do visual aids also help decision makers accurately assess their risk comprehension? That is, do visual aids help them become well calibrated? To address these questions, we investigated the benefits of visual aids displaying numerical information and measured accuracy of self-assessment of diagnostic inferences (i.e., metacognitive judgment calibration) controlling for individual differences in numeracy. Participants included 108 patients who made diagnostic inferences about (...) three medical tests on the basis of information about the sensitivity and false-positive rate of the tests and disease prevalence. Half of the patients received the information in numbers without a visual aid, while the other half received numbers along with a grid representing the numerical information. In the numerical condition, many patients --especially those with low numeracy-- misinterpreted the predictive value of the tests and profoundly overestimated the accuracy of their inferences. Metacognitive judgment calibration mediated the relationship between numeracy and accuracy of diagnostic inferences. In contrast, in the visual aid condition, patients at all levels of numeracy showed high-levels of inferential accuracy and metacognitive judgment calibration. Results indicate that accurate metacognitive assessment may explain the beneficial effects of visual aids and numeracy --a result that accords with theory suggesting that metacognition is an essential part of risk literacy. We conclude that well-designed risk communications can inform patients about health-relevant numerical information while helping them assess the quality of their own risk comprehension. (shrink)

This paper argues that a theory of situated vision, suited for the dual purposes of object recognition and the control of action, will have to provide something more than a system that constructs a conceptual representation from visual stimuli: it will also need to provide a special kind of direct (preconceptual, unmediated) connection between elements of a visual representation and certain elements in the world. Like natural language demonstratives (such as `this' or `that') this direct connection allows entities (...) to be referred to without being categorized or conceptualized. Several reasons are given for why we need such a preconcep- tual mechanism which individuates and keeps track of several individual objects in the world. One is that early vision must pick out and compute the relation among several individual objects while ignoring their properties. Another is that incrementally computing and updating representations of a dynamic scene requires keeping track of token individuals despite changes in their properties or locations. It is then noted that a mechanism meeting these requirements has already been proposed in order to account for a number of disparate empiri- cal phenomena, including subitizing, search-subset selection and multiple object tracking (Pylyshyn et al., Canadian Journal of Experimental Psychology 48(2) (1994) 260). This mechanism, called a visual index or FINST, is brie. (shrink)

(Open Access article, freely available to download from publisher's site.) Our visual experiences of objects as located in external space, and as having definite three-dimensional shapes, are closely linked to our implicit expectations about what things will look like from alternative viewpoints. What sorts of contents do these expectations involve? One standard answer is that they relate to what things will look like to us upon changing our positions. And what sorts of mental representations do the expectations call upon? (...) A standard answer is that they involve our powers of visual imagery; this answer requires us to allow for the possibility of unconscious visual imagery, however. The current paper presents an alternative model of the contents of our implicit visual expectations, one that regards them as wholly nonreflexive. It also argues that, once we ascribe the relevant contents to the expectations, there is no longer any reason for holding that they involve our powers of visual imagery. (shrink)

Recent work in "embodied, embedded" cognitive science links mental contents to large-scale distributed effects: dynamic patterns implicating elements of (what are traditionally seen as) sensing, reasoning and acting. Central to this approach is an idea of biological cognition as profoundly "action-oriented" - geared not to the creation of rich, passive inner models of the world, but to the cheap and efficient production of real-world action in real-world context. A case in point is Hurley's (1998) account of the profound role (...) of motor output in fixing the contents of conscious visual awareness - an account that also emphasizes distributed vehicles and long-range dynamical loops. Such stories can seem dramatically opposed to accounts, such as Milner and Goodale (1995), that stress relatively local mechanisms and that posit firm divisions between processes of visual awareness and of visuomotor action. But such accounts, I argue, can be deeply complimentary and together illustrate an important lesson. The lesson is that cognition may be embodied and action-oriented in two distinct - but complimentary - ways. There is a way of being embodied and action-oriented that implies being closely geared to the fine-grained control of low level effectors (hands, arms, legs and so on). And there is a way of being embodied and action-oriented that implies being closely geared to gross motor intentions, current goals, and schematic motor plans. Human cognition, I suggest, is embodied and action-oriented in both these ways. But the neural systems involved, and the size and scope of the key dynamic loops, may be quite different in each case. (shrink)

Susanna Siegel argues that visual contents are rich: visual experiences represent a variety of properties, over and above mere colors and shapes, including, notably, kind properties, e.g., the property of being a pine tree. To argue her case, she makes use of the method of phenomenal contrasts, which involves choosing among different explanatory hypotheses to account for phenomenal contrasts between relevant experiences. I will argue that there is reason to question whether the method of phenomenal contrasts is suitable (...) for establishing that kind properties are represented in visual experiences, insofar as the method draws upon first-person intuitions eclectically. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " (...) Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

Charles S. Peirce’s second trichotomy, which introduces the concepts of iconicity, indexicality, and symbolicity, is probably the only piece of his semiotic that is familiar to visual artists and designers. Although the concepts have found their way into the academy, their utility in the field has been reduced for a couple of reasons. First, as with all of Peirce’s philosophy, his second trichotomy is a concept that is subtle, fluid, and difficult to fully grasp in a sound bite. Second, (...) there has simply been no bridge concept that would form a working connection between that philosophy in its logical guise and the studio practice in the visual arts. The purpose of this article is to remedy that situation by investigating the subtle ways the second trichotomy functions within the visual sphere, and to then suggest a model that can serve to bridge the divide between pure theory and practice. The article makes four main points: first, using examples from visual identity and the graphic arts, it demonstrates how the modes of icon, index, and symbol tend to be blended; second, examples from fine art are used to illustrate how the concept of abstraction, as used in the art world, can only be partially accounted for within the second trichotomy, but can be modeled by supplying a syntactical supplement; third, it expands on and elaborates a previously sketched model, the visual gamut, which makes it possible to classify visual entities according to their position within a map of semantic and syntactic space; finally, it concludes by suggesting ways this enhanced version of the visual gamut model might be used in the analysis of, or creation of, art and design, presenting suggestions for further study. (shrink)

Visual analogy is believed to be important in human problem solving. Yet, there are few computational models of visual analogy. In this paper, we present a preliminary computational model of visual analogy in problem solving. The model is instantiated in a computer program, called Galatea, which uses a language for representing and transferring visual information called Privlan. We describe how the computational model can account for a small slice of a cognitive-historical analysis of Maxwell’s reasoning (...) about electromagnetism. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " (...) Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

Since its inception as a topic of inquiry, mirror-self-recognition has usually been explained by two models: one, initiated by Guillaume, proposes that mirror-self-recognition depends upon kinesthetic-visual matching, and the other, initiated by Gallup, that self-recognition depends upon a self-concept. These two models are examined historically and conceptually. This examination suggests that the kinesthetic-visual matching model is conceptually coherent and makes reasonable and accurate predictions; and that the self-concept model is conceptually incoherent and makes inaccurate predictions from premises which (...) are themselves inaccurate. From a theoretical standpoint, the kinesthetic-visual matching model is the better explanation of self-recognition. (shrink)

People often struggle with Bayesian reasoning. However, research showed that people’s performance (and rationality) can be supported by the way of representing the statistical information. First, research showed that using natural frequencies instead of probabilities as format of statistical information increases people’s performance in Bayesian situations thoroughly. Second, research also yielded that people’s performance increases through using visualization. We build our paper on existing research in this field. The main aim is to analyse people’s strategies in Bayesian situations that (...) are still erroneous although statistical information is represented by natural frequencies and visualizations. In particular, we compare two pairs of visualization with similar numerical information (tree diagram vs. unit square and double-tree diagram vs. 2x2-table) concerning their impact on people’s erroneous strategies in Bayesian situations. For this aim, we conducted an experiment with 540 university students. The students were randomly assigned to four conditions that are defined by the four different visualizations of statistical information. The students were asked to indicate a fraction as response in four Bayesian situations. We documented the numerator and the denominator of the students’ responses representing a basic set and a subset in a Bayesian situation. Our results show that people’s erroneous strategies are highly dependent on the visualization. A central finding is that the visualization’s characteristic of making the nested-sets structure of a Bayesian situation transparent has a facilitating effect on people’s Bayesian reasoning. For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation. Accordingly, compared to a unit square, a tree diagram partly hinders people to find the correct denominator in a Bayesian situation, and, in particular, triggers to select a wrong numerator. By analyzing people’s erroneous strategies in Bayesian situations, we contribute to investigating approaches to facilitate Bayesian reasoning and to further develop the teaching of Bayesian reasoning. (shrink)

Semantic networks were developed in cognitive science and artificial intelligence studies as graphical knowledge representation and inference tools emulating human thought processes. Formal analysis of the representation and inference capabilities of the networks modeled them as subsets of standard first-order logic (FOL), restricted in the operations allowed in order to ensure the tractability that seemed to characterize human reasoning capabilities. The graphical network representations were modeled as providing a visual language for the logic. Sub-sets of FOL targeted on (...) knowledge representation came to be called description logics, and research on these logics has focused on issues of tractability of subsets with differing representation capabilities, and on the implementation of practical inference systems achieving the best possible performance. Semantic network research has kept pace with these developments, providing visual languages for knowledge entry, editing, and presenting the results of inference, that translate unambiguously to the underlying description logics. This paper discusses the design issues for such semantic network formalisms, and illustrates them through detailed examples of significant generic knowledge structures analyzed in the literature, including determinables, contrast sets, genus/differentiae, taxonomies, faceted taxonomies, cluster concepts, family resemblances, graded concepts, frames, definitions, rules, rules with exceptions, essence and state assertions, opposites and contraries, relevance, and so on. Such examples provide important test material for any visual language formalism for logic. (shrink)

Seeing happens effortlessly and yet is endlessly complex. Among the most fascinating aspects of visual perception is its stability and constancy. As we shift our gaze or move about the world, the light projected onto the retinas is constantly changing. Yet the surrounding objects appear stable in their properties. Psychologists have long been interested in the constancies. They have asked questions such as: How good is constancy? Is constancy a fact about how things look, or is it a product (...) of our beliefs and judgments about how things look? How can the contents of visual experience be studied experimentally? Philosophers have long been interested in characterizing visual experience and have become widely interested in the constancies more recently. As psychologists and philosophers have interacted, new questions have arisen: If experience is not as of retinal stimulation (proximal mode), but does not always exhibit constancy (or at least not in all respects), how shall we describe this intermediate state? Also, should we regard any departure from constancy as a failure of the visual system, or might it be a reasonable or adaptive response? In what circumstances is seeing highly conditioned by cognitive factors such as background assumptions, and in what circumstances not? Our volume focuses on size constancy and color constancy. It considers methodologies for studying conscious visual perception, efforts to describe visual experience in relation to constancy, what it means that constancy is not always perfect, and the conceptual resources needed for explaining visual experience. (shrink)

This thesis falls into two parts, a characterizing part, and an explanatory part. In the first part, I outline some of the core aspects of our ordinary understanding of visual perception, and how we regard it as a means of knowing. What explains the fact that I know that the lemon before me is yellow is my visual perception: I know that the lemon is yellow because I can see it. Some explanations of how one knows specify that (...) in virtue of which one genuinely knows, as opposed to merely believes, some content. Such explanations are epistemically satisfactory explanations. We think that visual perceptual explanations of knowledge can be epistemically satisfactory. I argue that that is what it is to regard visual perception as being among our means of knowing. In the second part, I explore how we might explain the fact that visual perception is a means of knowing (assuming that it is a fact). I ask what makes it the case that visual perception is a means of knowing (in the way we ordinarily think that it is)? I suggest that part of the answer to this question is that visual perception, given the nature it has, has a reason giving role. And that is just to say that the nature of visual perception is such that visually perceiving can ensure the satisfaction of some important condition on knowledge (namely, that if one knows that something is the case one must have a good reason to believe that it is the case). In concluding I suggest that giving this sort of explanation doesn't require a specific theory of perception. (shrink)

Some philosophers—for example, Husserl, Alva Noë and Susanna Siegel—have claimed that the contents of visual sensations standardly include references to the later visual episodes that one would have under certain conditions. The current paper claims that there are no good reasons for accepting that view. Instead, it is argued that the conscious phenomena which have been cited as manifesting the presence within visual contents of references to ways that things would look in the course of later (...) class='Hi'>visual sensations are better explained in another manner: in terms of references within the contents of ordinary visual sensations to ways that things actually then look from various perspectives. (shrink)

I argue that a basic similarity analysis of analogical reasoning handles many apparent cases of visual analogy. I consider how the visual and verbal elements interact in analogical cases. Finally, I offer two analyses of visual elements. One analysis is evidential. The visual elements are evidence for their ver-bal counterparts. One is non-evidential: the visual elements link to verbal elements without providing evi-dence for those elements. The result is to make more room for the (...) logical analysis of visual argumentation. (shrink)

Visual comparison is a key process in everyday learning and reasoning. Recent research has discovered the spatial alignment principle, based on the broader framework of structure‐mapping theory in comparison. According to the spatial alignment principle, visual comparison is more efficient when the figures being compared are arranged in direct placement—that is, juxtaposed with parallel structural axes. In this placement, (1) the intended relational correspondences are readily apparent, and (2) the influence of potential competing correspondences is minimized. There (...) is evidence for the spatial alignment principle in adults’ visual comparison (Matlen et al., 2020). Here, we test whether it holds for children. Six‐ and eight‐year‐old children performed a same‐different task over visual pairs. The results indicated that direct placement led to faster and more accurate comparison, both for concrete same‐different matches (matches of both objects and relations) and for purely relational matches—evidence that the same structural alignment process holds for visual comparison in 6‐ and 8‐year‐olds as in adults. These findings have implications for learning and education. (shrink)