Name der Zeitschrift: Das Mittelalter Jahrgang: 22 Heft: 2 Seiten: 314-331.

We all intuitively know what a diagram is, and still it is surprisingly difficult to describe it as a semiotic function or type. In this article, we present four groups of hypotheses in view of a clarification. We hypothesize: (1) That diagrams are signs of a distinct type, unknown to classical semiotics; (2) That the elementary graphs of a diagram are all derived fromlines and pointsintopologicalmental spaces. The mind applies these diagrammatic spaces to referential spaces in many ways, (...) but basically through conceptual integration (blending). The mind blends topology and reference, which makes the topology unnoticeable; (3) That elementary diagrammatic graphs constitute a natural, phenomenological, spatiotemporal, figurative and dynamic but informal geometry in the embodied, thinking mind; (4) That diagrammatic signs are the active components of the abstract mental figuration in working memory that accompany perception and deliver the schematizing ideas which invest and connect our categories and construe proper descriptive, narrative, patterns of inferentialthoughtand programs of sensorimotor and social action. (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)

This article aims to examine the relationship between image and narrative by means of Peirce’s first trichotomy of qualisign-sinsign-legisign or, for the purposes of the current argument, image-diagram-metaphor. It is argued that narrative, as an extended metaphor, can be examined in three modes: in the image; schematically, in the imagination; and allegorically or in a thought experiment, through hypothetic interpretation. The article outlines two kinds of diagrammatic reasoning emphasized by Peirce: corollarial deduction in which the image is ‘literally seen’ (...) and the reasoning steps are manifest in its conclusion; and theorematic deduction where the conclusion in a diagram is subject to a hypothesis which transforms the image into something new. Demonstrating the breadth of diagrammatic reasoning with reference to the 2018 film, The Shape of Water, the article seeks to explore how allegory and diagram are mutually cooperative, based on three ontological modes: the expressive, the cognitive, and the symbolic. Its primary focus, then, is not so much on the story events of the narrative, as the way that they are visualized and characterized as the fairy story unfolds. It is suggested that the interpreting activity involved in allegory and diagram ties interpretation to metacognition, ultimately (re)recognizing the image in The Shape of Water in an attempt to ascertain the meaning of love. (shrink)

This paper outlines a method to assess the effectiveness of diagrams, from semiotic foundations. In doing so, we explore the Peircian notion of signification, as applied to diagrammatic representations. We review a history of diagrams, with particular emphasis on schematics used for representing systems, and uncover the neglect of semiotic analysis of diagrammatic representations. Through application of category theory to the Peircian triadic model, we propose a set of quantitative quality measures for diagrams, and a framework for their assessment, based (...) on the properties of their encoding, pragmatic and perceptual morphisms. These measures include diagram complexity, utility, aesthetics and expert assessment of semiotic content, together with qualitative feedback. We consider the diagrams as an aid to cognitive processes, rather than a purely communication media. This utility-focused perspective on diagram quality dimensions allows for fresh insights into the creation of effective diagrams. (shrink)

The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first (...) part, we tested whether the processing of metric vs topological relations yielded the same hemispheric specialization as the processing of coordinate vs categorical relations. In the second part, we investigated the specific performance patterns for the processing of five pairs of exact/co-exact relations, where stimuli for the co-exact relations were divided into three categories depending on their distance from the exact case. Regarding the processing of metric vs topological relations, hemispheric differences were found for only a few of the stimuli used, which may indicate that other processing mechanisms might be at play. Regarding the processing of exact vs co-exact relations, results show that the level of agreement among participants in judging co-exact relations decreases with the distance from the exact case, and this for the five pairs of exact/co-exact relations tested. The philosophical implications of these empirical findings for the epistemological analysis of Euclid's diagram-based geometric practice are spelled out and discussed. (shrink)

Establishing interdisciplinary academic departments has been a common response to the challenge of addressing complex problems. However, the assumptions that guide the formation of such departments are rarely questioned. Additionally, the designers and managers of interdisciplinary academic departments in any field of endeavour struggle to set an organisational climate appropriate to the diversity of their members. This article presents a preliminary analysis of collaborative dynamics within two interdisciplinary university departments in Australia focused on sustainability. Social network diagrams and metrics of (...) coauthorship and cosupervision are analysed qualitatively. A "vicarious interdisciplinarity" was identified among key academics working narrowly in order to earn the resources that allow them to support others working interdisciplinarily. Those supported in this way appear to benefit from the esteem and nonredundant collaborative connections their mentors provide via this strategy, but they experience uncertainty about their own career opportunities in similar settings. This article thus unearths a conundrum of succession for interdisciplinary academic environments, and suggests that simple colocation of diverse academic stars is an inadequate strategy to achieve effective intradepartmental collaboration. (shrink)

This article presents Derrida as a philosopher of history by reinterpreting his De la Grammatologie. In particular, it provides a schematic reconstruction of Part II of that book from the perspective of the problem of history. My account extends work on historicity in Derrida by privileging the themes of ‘history’ and ‘diagram’ in the Rousseau part. I thereby establish a Derridean concept of history which aims at accounting for the continuities and discontinuities of the past. This is in (...) contrast to some criticism that Derrida leaves behind, or inadequately accounts for history. Derrida describes a necessarily contorted condition of relating any historical event or development to itself or to another. This historicity informs other well-known aspects of Derrida's work, like the ‘quasi-transcendental’ terms he developed. I conclude that ‘history’ is a critical element in any understanding of deconstruction, and that deconstruction entails new kinds of history, but that some axioms of current historical thought require reformation. (shrink)

Brandom's method of analyzing pragmatic relations among different practices and vocabularies through meaning-use diagrams is used to specify how Laruelle's nonphilosophical suspension of the Principle of Sufficient Philosophy may be distinguished from the philosophical auto-critiques of such thinkers as Badiou and Derrida. A superposition of diagrams modeling philosophical sufficiency on the one hand and supplementation through the Other on the other provides a schematic representation of the core duality of what Laruelle calls The-Philosophy. In contrast to this self-implicating and (...) self-reproducing structure, Laruelle's axiomatic method is shown to enable a unilateral usage of the practices and vocabularies of philosophy as mere material that is no longer subject to the presuppositions or ineluctable restitution of philosophy as such. (shrink)

We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in [0, 1], we introduce two kinds of diagrams at each level: the closed diagram, which encapsulates weak inequalities of the form $$\phi ^\mathcal {M}\le r$$, and the open diagram, which encapsulates strict inequalities of the form $$\phi ^\mathcal (...) {M}< r$$. We show that the closed and open $$\Sigma _N$$ diagrams are $$\Pi ^0_{N+1}$$ and $$\Sigma ^0_N$$ respectively, and that the closed and open $$\Pi _N$$ diagrams are $$\Pi ^0_N$$ and $$\Sigma ^0_{N + 1}$$ respectively. We then introduce effective infinitary formulas of continuous logic and extend our results to the hyperarithmetical hierarchy. Finally, we demonstrate that our results are optimal. (shrink)

The paper raises the question of the function of visual representations in medieval cosmographical texts. It proposes to view diverse functions of figures in relation to changing discursive environments, including differing philosophical positions and changing social and intellectual contexts. It further suggests a distinction between figures that were elaborated within the highly specialized disciplines of mathematics and philosophy of nature in Greek Antiquity and figures that were instrumental in transmitting accepted world models, thus avoiding the opposition between scientific and unscientific (...) types of verbal and pictorial documents. Simplifying changes, when figures are abstracted form their geometrical context and accompany doxographical, descriptive accounts, are characterized in terms of schematization. Concomitantly, mathematical and philosophical demonstrations tend to give way to proofs of a predominantly rhetorical nature: images are verbally construed and, in order to enhance these, actual visual figures— mostly linear, diagrammatic constructs—are added. With regard to the Middle Ages, the paper distinguishes two principal periods: the period from the seventh to the eleventh century and the period of the so-called twelfth-century Renaissance. First, the verbal and pictorial cosmological corpus of Roman origin gave rise to explanations and variations but not to consequential theoretical developments and cosmological diagrams tended to fuse with summarizing tables at this time. Then, during the twelfth century, mathematical and philosophical documents of a specialized kind that were translated from the Arabic and also from the Greek became available in the Latin West. In mathematics, specialized types of study remained, however, sparse. Continuous elaborations of the assimilated material set in later only, within the thirteenth-century university context. Nevertheless, twelfth-century authors of cosmographical accounts became increasingly aware that their expositions and visual figures were ultimately derived from geometrical models of the universe. More diversified types of demonstration and corresponding visual figures were being used, as exemplified by William of Conches’ Dragmaticon philosophiae. (shrink)

Separatism, representationalism, and phenomenal intentionalism are the primary views on the relationship between the phenomenality and intentionality of experience. I defend a novel position that is incompatible with separatism, can enrich representationalism and phenomenal intentionalism, but can also be accepted independently of those views. I call itphenomenal schematics: The phenomenal characters of our experiences have structures that place a priori, formal, and sometimes semantic constraints on our experience's possible intentional contents. Phenomenal structures are like the grammar of a language (or (...) the compositional rules governing maps, models, and diagrams). Unlike words, however, phenomenal characters possess their “grammatical properties” essentially. (shrink)

In 1971, Günter Blobel and David Sabatini proposed a novel and quite speculative schematic model to describe how proteins might reach the proper cellular location. According to their proposal, proteins destined to be secreted from the cell contain a “signal” to direct their release. Despite the fact that Blobel and Sabatini presented their signal hypothesis as a “beautiful idea” not grounded in experimental evidence, they received criticism from other scientists who opposed such speculation. Following the publication of the 1971 (...) model, Blobel persisted in conducting experiments and revising the model to incorporate new data. In fact, over the period of 1975–1984, Blobel and colleagues published five subsequent schematic models of the signal hypothesis, each revised based on new laboratory evidence. I propose that the original 1971 model can be viewed as an epistemic creation. Additionally, analysis of the subsequent schematic diagrams over the period of 1975–1984 allows one to track Blobel’s changing conception of an epistemic object over time. Furthermore, the entire series of schematic diagrams presented by Blobel from 1971 to 1984 allow one to visualize the initial conception and subsequent reworking of a scientific theory. In 1999, Blobel was awarded the Nobel Prize in Physiology or Medicine for his work on the signal hypothesis, which was ultimately supported by experimental evidence gathered after the speculative model was published. (shrink)

The paper analyses the formal features of the characters of Oresteia in Greek tragedy. The protagonists and the minor characters are compared, for which the rhythmical liveliness and variability of the personages’ utterances, the length and number of utterances, and the number of dialogue verses in the metrical repertoire of the corresponding personage are taken into account. The analysis revealed that the data of Sophocles and Euripides are more close to each other both in the respect of general “liveliness” and (...) the “liveliness” of characters’ utterances. Certain differences in the metrics and rhythmics of the main and minor characters’ verses become most obvious when we compare Electra’s part with minor characters (e. g., in Electra’s part there is always the biggest proportion of lyrical parts, more unstandard settlements, more verses with splits than any other character). The index of liveliness of Electra’s part is almost the same in all the authors. Although the same tendencies in Orestes are more schematical, the metrics and rhythmics of his utterances are rather similar to those of Electra. Thus, in respect of the proportion of lyrical verses, he always comes second after Electra; he also has quite many split verses. The parts of minor characters are usually made up entirely of iambic trimesters, the rhythmical variety of their speeches is higher than average, but there are no splits in their parts (except for Aegisthus). However, there are characters which parts have unstandard rhythm, e.g., the pedagogue in Sophocles or Chrysothemis, who is a contrast to Electra by her nature as well as her rhythmics. The contrast with other minor characters is even bigger. Clytaemnestra’s part is both rhythmically and metrically intermediate: inAeschylus her utterances consist entirely of iambic trimeters, but in Sophocles and Euripides she pronounces also a couple of lyrical verses. There are alsosome splits in her verses which usually do not occur in minor persons. (shrink)

Producing a properly philosophical theory of capitalism as an open axiomatic system requires adding intensive multiplicities to the mathematical account of set theory, which allows only extensive multiplicities. Doing so enables us to understand pricing as a process of transforming intensive quantities into metric quantities, and thereby develop a diagram of the dynamics of axiomatisation and of the market as the two-sided and asymmetrical recording surface of the capitalist socius whose slope represents the infinite debt owed to finance (...) capital. The capitalist market axiomatises four kinds of flows – flows of liquid capital and abstract labour, of course, but also flows of raw materials and energy and of human populations. At the same time that axiomatisation conjugates these flows in denumerable sets to extract surplus-value, it connects flows in minor, non-denumerable sets that escape axiomatisation and may become revolutionary. Such minor connections would constitute the fabric of a post-capitalist axiomatics. (shrink)

This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or (...) imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, the information thus displayed is not metrical and it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions. (shrink)

Descartes considered the methods of reasoning put forth in the Discourse to be correct because, among other justifications, he had examples of scientific theories in which the techniques were successful: the Optics, Meteorology, and Geometry. The chief value of this edition is to have the Discourse back in its proper setting, as well as the more obvious one of having available three works of importance in the history of the exact sciences in one compact and readable edition. The Optics is (...) especially useful for the study of Descartes' theory of sight and perception. There are a large number of diagrams and figures which are quite helpful in making some rather schematic presentations more complete.—P. J. M. (shrink)

We propose a new relational direction in higher education that acknowledges external and internal images as integrated in thinking and learning. We expand educational theory and practice that commonly rely on discrete conceptual developments that exclude images. Our argument epistemologically relies on certain semiotic views that consider the role of iconic signs and iconicity (meaning making by the virtue of similarity) as significant in relation to knowledge and learning. The analogical and imaginative work required to discover similarity between external pictures (...) and any educational concept is a form of iconic mind work that opens a space for transformational thinking and creative solutions. The novelty of our argument lies in the schematic philosophy of mind by C.S. Peirce, and specifically, an adaptation of Peirce’s triadic sign diagram for learning, exemplified via an ‘inquiry graphic’ sign and reflective method. This outlook seeks connections in diversity, arguing for an education that acknowledges and teaches intrinsic human relatedness to other humans, beings and things in the environment, thus challenging any notions of anthropocentrism and superiority. It calls for a reaction in international higher education to acknowledge the iconicity of concepts and thinking and embrace integrated image-concept signs for deep and critical teaching-learning, towards a modest educational contribution to counteracting social and environmental crises. (shrink)

We present a new model of skilled performance in geometry proof problem solving called the Diagram Configuration model (DC). While previous models plan proofs in a step‐by‐step fashion, we observed that experts plan at a more abstract level: They focus on the key steps and skip the less important ones. DC models this abstract planning behavior by parsing geometry problem diagrams into perceptual chunks, called diagram configurations, which cue relevant schematic knowledge. We provide verbal protocol evidence that (...) DC's schemas correspond with the step‐skipping inferences experts make in their initial planning. We compare DC with other models of geometry expertise and then, in the final section, we discuss more general implications of our research. DC's reasoning has important similarities with Larkin's (1988) display‐based reasoning approach and Johnson‐Laird's (1983) mental model approach. DC's perceptually based schemas are a step towards a unified explanation of (1) experts' superior problem‐solving effectiveness, (2) experts' superior problem‐state memory, and (3) experts' ability, in certain domains, to solve relatively simple problems by pure forward inferencing. We also argue that the particular and efficient knowledge organization of DC challenges current theories of skill acquisition as it presents an end‐state of learning that is difficult to explain within such theories. Finally, we discuss the implications of DC for geometry instruction. (shrink)

In this paper, I discuss the concept of complexity. I show that the principle of natural selection as acting on complexity gives a solution to the problem of reconciling the seemingly contradictory notion of generally increasing complexity and the observation that most species don’t follow such a trend. I suggest the process of evolution to be illustrated by means of a schematic diagram of complexity versus time, interpreted as a form of the Tree of Life. The suggested model (...) implies that complexity is cumulatively increasing, giving evolution a direction, an arrow of time, thus also implying that the latest emerging species will be the one with the highest level of complexity. Since the human species is the last species evolved in the evolutionary process seen at large, this means that we are the species with the highest complexity. The model implies that the human species constitutes an integral part of organic evolution, yet rendering us the exclusive status as the species of the highest complexity. (shrink)

Diagrams make it possible to present scientific facts in more abstract and generalized form. While some detail is lost, simplified and accessible knowledge is gained. E. B. Wilson's work in cytology provides a case study of changing uses of diagrams and accompanying abstraction. In his early work, Wilson presented his data in photographs, which he saw as coming closest to “fact.” As he gained confidence in his interpretations, and as he sought to provide a generalized textbook account of cell development, (...) he relied on increasingly abstract diagrams. In addition, he came to see that highly abstract and even schematic drawings could provide more than pictures directly from life. (shrink)

This commentary starts with a simplified Cartesian vector space of the tristimulus theory of color. This vector space is then further simplified so that bitstrings are used to represent the vector space. The Commission Internationale de l'Eclairage (CIE) diagram is shown to follow directly and simply from this vector space. The Berlin & Kay results are shown to agree quite well with the vector space and the two-dimensional version of it, especially if the dimensions are normalized to take into (...) account the sensitivity of the eye to the different wavelengths comprising color. There is asymmetry with respect to the colors and a similar asymmetry in vocalic phonemes; these effects can be explained in terms of physiology. The (in)famous problem of the color channels is given a unified treatment at various levels. An eight-valued color algebra is created, with addition and multiplication corresponding to additive and subtractive blending of colors. Finally, it is shown that the discrete Hamming metric for colors has a natural toroidal topology. (shrink)

What is meant under the genuine title of Aristotle’s ta Analytika is rarely properly understood. Presumably, his analytics was inspired by the method of geometric analysis. For Aristotle, this was a regressive or heuristic procedure, departing from a proposed conclusion and asking which premises could be found in order to syllogize, demonstrate or explain it. The terms that form categorical and modal propositions play a fundamental role in analytics. Aristotle introduces letters in lieu of the triples of terms constitut­ing the (...) propositions and the three syllogistic figures that schematize them. His formulation of the three syllogistic figures refers to a syntacti­cal and predicative order and position of the triples of terms, arranged in some diagrammed schemata, which, regrettably, are missing from the extant text of the Prior Analytics. Considering planar and graphic arrangements, both vertical and horizontal orders as well as the posi­tion of the three terms involved, we propose a reconstruction, at least to some extent, of these probable lettered diagrams. In such reconstructed diagrams, we can appropriately capture the definition of syllogism as a predicative connexion of terms, and easier survey a synoptic account of all valid predicative relations and transpositions, and also reduce the imperfect syllogisms into the moods of the first figure. Aristotle’s syllogistic is an analytical calculation of terms, understood as predicates and subjects within the categorical propositions, and more precisely of three terms schematized in three figures in predicative links such that, by means of a middle, follows from necessity a conclusion of the extreme terms. The necessity of the consequence is not based on the implication or inference of the propositions, but on a predictive transi­tivity through the middle term within the syllogistic figures. Syllogism must draw its conclusion through the way its terms are predicated of one another. Aristotle in his Prior Analytics developed also a complex account of modal syllogisms within necessity and possibility of belonging. This account involves also such an analyti­cal reduction to the syllogistic figures. In this analytical perspective, we try to throw some light on his modal syllogisms, although this difficult and nowadays thoroughly discussed topic would require a much wider treatment. (shrink)

The concept of approximate truth plays a prominent role in most versions of scientific realism. However, adequately conceptualizing ?approximate truth? has proved challenging. This article argues that the goal of articulating the concept of approximate truth can be advanced by first investigating the processes by which science accords theories the status of accepted or rejected. Accordingly, this article uses a path diagram model as a visual heuristic for the purpose of showing the processes in science that are involved in (...) determining a theory's status. This ?inductive realist? model of theory status then serves as a starting point for explicating an inductive realist view of approximate truth that, it is argued, can explain instances of the success of science, but does not (1) require science's theories to be strictly true in any world or (2) require a metric for measuring how close an approximately true theory is to some strictly true theory. To show the advantages of the inductive realist approach to approximate truth, an example of a major success story of science, the successful eradication of smallpox, is reviewed and then explained. (shrink)

A distorted representation of one's own body is a diagnostic criterion and core psychopathology of both anorexia nervosa (AN) and bulimia nervosa (BN). Despite recent technical advances in research, it is still unknown whether this body image disturbance is characterized by body dissatisfaction and a low ideal weight and/or includes a distorted perception or processing of body size. In this article, we provide an update and meta-analysis of 42 articles summarizing measures and results for body size estimation (BSE) from 926 (...) individuals with AN, 536 individuals with BN and 1920 controls. We replicate findings that individuals with AN and BN overestimate their body size as compared to controls (ES= 0.63). Our meta-regression shows that metric methods (BSE by direct or indirect spatial measures) yield larger effect sizes than depictive methods (BSE by evaluating distorted pictures), and that effect sizes are larger for patients with BN than for patients with AN. To interpret these results, we suggest a revised theoretical framework for BSE that accounts for differences between depictive and metric BSE methods regarding the underlying body representations (conceptual vs. perceptual, implicit vs. explicit). We also discuss clinical implications and argue for the importance of multimethod approaches to investigate body image disturbance. (shrink)

Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up–down, vertical/left–right) and the marks on it (e.g., (...) dots, lines, arrows, boxes, blobs, likenesses, symbols) to convey meanings. The visual expressions of these meanings (e.g., individual, category, order, relation, correspondence, continuum, hierarchy) have analogs in language, gesture, and especially in the patterns that are created when people design the world around them, arranging things into piles and rows and hierarchies and arrays, spatial-abstraction-action interconnections termed spractions. The designed world is a diagram. (shrink)

The problem of distinguishing within the same investigation between the scientific and the philosophical orders of constructive thinking has increased with the complex speculation of current theory and urgently demands systematic clarification, against the dangers of ambiguity and abuse of evidence. M. Maritain has proposed a detailed conceptual classification, which expands Aristotle’s division of the planes of abstraction: his pioneer effort is still under discussion even in Scholastic circles. In particular his proposed distinction of mathematics and its allied empirio-schematic (...) and empirio-metrical sciences from the philosophy of nature, which he brought nearer to, and yet really distinguished from the empiriological sciences has been recently criticised by the Laval and Forest Hill schools in North America. Now Father Connolly outlines this debate and bravely offers a tentative ‘compromise theory’. Restricting philosophy to metaphysics proper, he proposes that “some of the empiriological sciences belong to the philosophy of nature—and to this extent the theory agrees with the anti-Maritain position; secondly, some of the empiriological sciences fall outside its orbit and, along with Mathematics, constitute a distinct field of human knowledge—and to this extent the theory agrees with the Maritain position”. (shrink)

The temple schematics in the Dead Sea Scrolls (DSS), that is, New Jerusalem and Temple Scroll, has often been comparatively examined with the sanctuary structures in the Hebrew Bible (HB) (Ezk 40–48 and Num 2). Typically, in scholarship, the irreconcilable differences between all accounts (regarding the size, shape, name-gate ordering, etc.) is underscored, thus rendering a literary conundrum. This article argues that New Jerusalem and Temple Scroll drew from both Ezekiel 40–48 and Numbers 2 in different ways, purporting the sect(s)’s (...) theologies and ideologies which accords, further, with the life setting of the Qumran communities; the influence of Numbers in the DSS is underscored. These aspects include (1) the eastern orientation of sacred structures and the compound at Khirbet Qumran, (2) the precise locale of the communities at the Dead Sea vis-à-vis Ezekiel 47 and (3) the desert encampment configuration together with its militaristic overtones in Numbers, which corresponds to the DSS sect(s)’s apocalyptic expectations as indicated in the War Scroll. Consequently, the Qumran sect(s) truly saw itself as an alternative priesthood of the forthcoming restored temple of God, even as in the interim they functioned as an alternative sanctuary (4QFlor; 4QMMT; 1QS). The import of Numbers upon the DSS sect(s)’s temple ideologies and priestly theologies is, therefore, equivalent to that of Ezekiel. Contribution: This article traces theological themes of temple and priestly ideologies between and among the Qumran literature and Hebrew Scriptures; both the respective library or canon and methodological approach are core to the historical thought’s aim and scope of HTS Teologiese Studies/Theological Studies. (shrink)

본 연구는 칸트의 『도식론』을 ‘언어론’의 관점에서 일관되게 판독함으로써 칸트 인식론의 언어적 측면을 『도식론』에 한정하여 심층적으로 고찰하고자 한다. ‘칸트철학이 언어론으로 불릴 수 있는가’ 하는 의문에 대한 긍정적인 답의 한 시도라고 볼 수 있다. 사고와 언어는 불가분적 관계에 있기 때문에 인간이 어떻게 대상에 대한 개념을 만드는가에 대한 연구는 반드시 인간의 인식이 어떻게 이루어지는가에 대한 해명을 필요로 한다. 그래서 사고의 체계에 대한 물음은 곧 우리가 세계를 어떻게 인식하여 말로 표현하는가를 묻는 것과 다르지 않다. 그리고 이러한 물음은 우리의 정신과 두뇌 속에 언어사용을 가능하게 하는 (...) 원리들이 내재해 있다는 것을 자연스럽게 가정하도록 이끈다. 만일 우리가 지식의 체계와 언어구성의 체계가 구별되지 않는다는 것을 의심하지 않고 받아들인다면, 우리는 언어능력에 고정되어 있는 원리들을 생리적으로 부여된 인간 유기체의 일부분으로 받아들여야 한다. 칸트의 『도식론』은 개념 형성에 대한 해명이기 때문에 논자는 칸트 인식론이 ‘언어론’으로 읽힐 수 있다고 생각하고, 그것을 정당화 하고자 한다. (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)

This paper is a follow up of the author’s programme of characterizing Ramsey classes of structures by a combination of model theory and combinatorics. This relates the classification programme for countable homogeneous structures to the proof techniques of the structural Ramsey theory. Here we consider the classes of topological and metric spaces which recently were studied in the context of extremally amenable groups and of the Urysohn space. We show that Ramsey classes are essentially classes of finite objects only. (...) While for Ramsey classes of topological spaces we achieve a full characterization, for metric spaces this seems to be at present an intractable problem. (shrink)

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 diagrams, then (...) give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues. (shrink)

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 paper proposes that (...) transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn. (shrink)

Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on (...) paths between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. Suggest reactive arrows to simplify the algorithms for the winning paths. We give a conceptual analysis of inheritance diagrams, and compare our analysis to the “small” and “big sets” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism of a particularly simple type. We show that the small and big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. We will also interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information. It is easily seen that inheritance diagrams can also be analysed in terms of reactive diagrams - as can all argumentation systems. AMS Classification: 68T27, 68T30. (shrink)

We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not (...) recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q +. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function. (shrink)

This article motivates and develops a reductive account of the structure of certain physical quantities in terms of their mereology. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. The resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and explain.

Speakers often construct their utterances based on the immediately co-present utterances of dialogue partners. They array their linguistic resources parallel to their partners¿ and activate resonance. Based on the theories of dialogic syntax and cognitive linguistics, this study undertakes to explain how speakers activate resonance and how parallelism contributes to constructing linguistic forms as well as to shaping the ongoing flow of conversation. Three phases of resonance activation are illustrated in relation to cognitive processes: (a) parallelism constituted with extension of (...) multiple categories in synthesis; (b) parallelism meeting or failing the previous speaker¿s intention due to schematization; and (c) parallelism achieved as a consequence of priming through schematization and extension. It is concluded that linguistic forms develop in the ongoing flow of socially coordinated cognition, where patterns emerge through activation of mapping relations between linguistic elements. This process is anchored in speakers¿ concepts of grammatical equivalences, ability of categorization, and grasp of linguistic conventions. (shrink)

Corroborative evidence has a dual function in argument. Primarily, it functions to provide direct evidence supporting the main conclusion. But it also has a secondary, bolstering function which increases the probative value of some other piece of evidence in the argument. This paper argues that the bolstering effect of corroborative evidence is legitimate, and can be explained as counter–rebuttal achieved through inference to the best explanation. A model (argument diagram) of corroborative evidence, representing its structure and operation as a (...) schematic pattern of defeasible argument is also supplied. In addition to explaining the operation and theoretical foundation of corroborative evidence, the model facilitates the correct analysis and guides the evaluation (assessment and critique) of corroborative evidence as it occurs in argument. (shrink)

We argue that the diagram is the equivalent of the Kantian schema, i.e. the translation into time and space of a meaning, and therefore of a concept, which would otherwise be empty. Understood as a schematic structure materialized in a support, the diagram is the explicitation of the meaning of the concept understood as a guide to action. We show why the class of judgements made by diagrammatic intuition is equivalent to that of the "steps" - the (...) expression is Peirce's – used to produce a theorem. Such an analysis allows us to argue in favour of the thesis that the schematism at work in the organic production of form is fundamentally diagrammatic in nature, which is why we speak of a diagrammatic schematism of morphogenesis. (shrink)

This commentary is intended to illuminate Gold's & Stoljar 's main contentions by exploiting a favorite comparison, namely, that between biology and electronics. Roughly, and leaving out Darwinian theory and the like, biology is physics and chemistry plus natural history just as electronics is physics plus wiring diagrams. Natural history contains generalizations, not laws. Psychology and cognitive science typically give more abstract explanations, as do “block diagrams” in electronics, and are less dispensable.

Spatial relations are central to geometrical thinking. With respect to the classical elementary geometry of Euclid’s Elements, a distinction between co-exact, or qualitative, and exact, or metric, spatial relations has recently been advanced as fundamental. We tested the universality of intuitions of these relations in a group of Senegalese and Dutch participants. Participants performed an odd-one-out task with stimuli that in all but one case display a particular spatial relation between geometric objects. As the exact/co-exact distinction is closely related (...) to Kosslyn’s categorical/coordinate distinction, a set of stimuli for testing all four types was used. Results suggest that intuitions of all spatial relations tested are universal. Yet, culture has an important effect on performance: Dutch participants outperformed Senegalese participants and stimulus layouts affect the categorical and coordinate processing in different ways for the two groups. Differences in level of education within the Senegalese participants did not affect performance. (shrink)