This paper endeavors to look into the physiognomical syllogism as occurring in Avicenna’s different summae and to tentatively discuss possible reasons for its select occurrence in some of them and not others, as well as possible implications of this selectiveness. These occurrences are in principle reducible to two different textual versions. Further, it will be argued that the inclusion of this syllogism might be connected with a certain nearness of the respective works to Aristotle, due to an assumed personal disfavoring (...) of this syllogism by Avicenna. However, there is also some evidence for Avicenna’s usage of the ps.-Aristotelian Physiognomics. (shrink)

This volume offers the first critical edition and English translation of the Book of Physics of Barhebraeus' magnum opus, Butyrum Sapientiae . It also analyzes Barhebraeus' sources, and the unique and personal way in which he rearranged them.

This paper shall look briefly into the treatment of some topics related to scepticism in general in works by Barhebraeus, the famous Syrian Orthodox polymath and theologian (1226–1286). He addresses scepticism both directly by a discussion of sensory and intellectual fallacies or sceptical scenarios as well as indirectly by the definition of knowledge and the role of intuitive knowledge regarding primary notions and logical principles, which have an impact on establishing secure knowledge. Despite writing in Syriac, his dealing with the (...) matter is heavily indebted to Arabic sources, primarily contemporary post‐Avicennan authors, and here especially Fakhr al‐Dīn al‐Rāzī (1149–1209) and Naṣīr al‐Dīn al‐Tūṣī (1201–1274) but also Avicenna (980–1037) himself, although Barhebraeus adds a decisively Christian note in some instances. The Syriac tradition, therefore, should not be neglected when dealing with medieval scepticism. (shrink)

This paper endeavors to look into the physiognomical syllogism as occurring in Avicenna’s different summae and to tentatively discuss possible reasons for its select occurrence in some of them and not others, as well as possible implications of this selectiveness. These occurrences are in principle reducible to two different textual versions. Further, it will be argued that the inclusion of this syllogism might be connected with a certain nearness of the respective works to Aristotle, due to an assumed personal disfavoring (...) of this syllogism by Avicenna. However, there is also some evidence for Avicenna’s usage of the ps.-Aristotelian Physiognomics. (shrink)

Although fictional characters have long dominated the reception of literature, films, television programs, comics, and other media products, only recently have they begun to attract their due attention in literary and media theory. The book systematically surveys todays diverse and at times conflicting theoretical perspectives on fictional character, spanning research on topics such as the differences between fictional characters and real persons, the ontological status of characters, the strategies of their representation and characterization, the psychology of their reception, as well (...) as their specific forms and constellations in - and across - different media, from the book to the internet.". (shrink)

The book explores ancient interpretations and usages of the famous Delphic maxim “know yourself”. The primary emphasis is on Jewish, Christian and Greco-Roman sources from the first four centuries CE. The individual contributions examine both direct quotations of the maxim as well as more distant echoes. Most of the sources included in the book have never previously been studied in any detail with a view to their use and interpretation of the Delphic maxim. Thus, the book contributes significantly to the (...) origin and different interpretations of the maxim in antiquity as well as to its reception history in ancient philosophical and theological discourses. The chapters of the book are linked to each other by numerous cross-references which makes it possible to compare the different views of the maxim with each other. It also helps readers to notice relationships and trajectories within the material. The explorations of the relevant sources are also set in the context of ongoing debates about the shape and nature of ancient conceptions of self and self-knowledge. The book thus demonstrates the wide variety of philosophical and theological approaches in that the injunction to know oneself could be viewed and how these interpretations provide windows into ancient discourses about self and self-knowledge. (shrink)

Inspired by theories of prosocial behavior, we tested the effect of relationship status and incentives on intended voluntary blame-taking in two experiments. Participants imagined a close family member, a close friend, or an acquaintance and read a scenario that described this person committing a minor traffic offense. The person offered either a monetary, social, or no incentive for taking the blame. Participants indicated their willingness to take the blame and reasons for and against blame-taking. Overall, a sizable proportion of participants (...) indicated to be willing to take the blame. Blame-taking rates were higher for family members than close friends or acquaintances in both experiments, as expected. Unexpectedly, there was no difference between a close friend and an acquaintance in Experiment 2. Social incentives did not have an effect on voluntary blame-taking in either experiment. Neither did we find an interaction between relationship status and incentives. The results highlight the importance of kin relationships in the context of voluntary blame-taking. (shrink)

The tsunami effect of the COVID-19 pandemic is affecting many aspects of scientific activities. Multidisciplinary experimental studies with international collaborators are hindered by the closing of the national borders, logistic issues due to lockdown, quarantine restrictions, and social distancing requirements. The full impact of this crisis on science is not clear yet, but the above-mentioned issues have most certainly restrained academic research activities. Sharing innovative solutions between researchers is in high demand in this situation. The aim of this paper is (...) to share our successful practice of using web-based communication and remote control software for real-time long-distance control of brain stimulation. This solution may guide and encourage researchers to cope with restrictions and has the potential to help expanding international collaborations by lowering travel time and costs. (shrink)

Recording and manipulating neuronal ensemble activity is a key requirement in advanced neuromodulatory and behavior studies. Devices capable of both recording and manipulating neuronal activity brain-computer interfaces should ideally operate un-tethered and allow chronic longitudinal manipulations in the freely moving animal. In this study, we designed a new intracortical BCI feasible of telemetric recording and stimulating local gray and white matter of visual neural circuit after irradiation exposure. To increase the translational reliance, we put forward a Göttingen minipig model. The (...) animal was stereotactically irradiated at the level of the visual cortex upon defining the target by a fused cerebral MRI and CT scan. A fully implantable neural telemetry system consisting of a 64 channel intracortical multielectrode array, a telemetry capsule, and an inductive rechargeable battery was then implanted into the visual cortex to record and manipulate local field potentials, and multi-unit activity. We achieved a 3-month stability of the functionality of the un-tethered BCI in terms of telemetric radio-communication, inductive battery charging, and device biocompatibility for 3 months. Finally, we could reliably record the local signature of sub- and suprathreshold neuronal activity in the visual cortex with high bandwidth without complications. The ability to wireless induction charging combined with the entirely implantable design, the rather high recording bandwidth, and the ability to record and stimulate simultaneously put forward a wireless BCI capable of long-term un-tethered real-time communication for causal preclinical circuit-based closed-loop interventions. (shrink)

Regular musical activity as a complex multimodal lifestyle activity is proposed to be protective against age-related cognitive decline and Alzheimer’s disease. This cross-sectional study investigated the association and interplay between musical instrument playing during life, multi-domain cognitive abilities and brain morphology in older adults from the DZNE-Longitudinal Cognitive Impairment and Dementia Study study. Participants reporting having played a musical instrument across three life periods were compared to controls without a history of musical instrument playing, well-matched for reserve proxies of education, (...) intelligence, socioeconomic status and physical activity. Participants with musical activity outperformed controls in global cognition, working memory, executive functions, language, and visuospatial abilities, with no effects seen for learning and memory. The musically active group had greater gray matter volume in the somatosensory area, but did not differ from controls in higher-order frontal, temporal, or hippocampal volumes. However, the association between gray matter volume in distributed frontal-to-temporal regions and cognitive abilities was enhanced in participants with musical activity compared to controls. We show that playing a musical instrument during life relates to better late-life cognitive abilities and greater brain capacities in OA. Musical activity may serve as a multimodal enrichment strategy that could help preserve cognitive and brain health in late life. Longitudinal and interventional studies are needed to support this notion. (shrink)

Includes articles by: Ulrich Arnswald, Jens Kertscher, Matthias Kross, Thomas Macho, Walter Mesch, Dieter Mersch, Regine Munz, Hans Julius Schneider, Hans-Peter Schutt, Ilse Somavilla, Samuel C. Wheeler III, Anja Weiberg, Rüdiger Zill.

Meaningful work is an important ideal, but it seems hard to give an adequate account of meaningful work. In this article, I conduct a revisionary conceptual analysis of ‘meaningful work’, i.e. a conceptual analysis that aims at finding a better and more useful way to use this term. I argue for a distinction between cases where work itself is meaningful and cases where other sources of meaning are found at work. The term ‘meaningful work’ is most useful for the former (...) cases. I then argue for the reasons account of what makes work itself meaningful: work is meaningful if (and to the extent that) there are good reasons to do it. I compare this to established accounts of meaningful work, such as subjective meaningfulness, self-realization, alienation, the unity of conception and execution, autonomy, social contribution, and Veltman’s four-dimensional account. None of these capture the distinct concern that the concept ‘meaningful work’ should capture, or they do so less well than the reasons account. This also shows that work can be meaningful regardless of whether it is good in other respects, such as in inherent interest or opportunities for self-realization. (shrink)

There has recently been a revived interest in temporal justice among political philosophers. For example, lone mothers have, on average, 30 h less free time per week than people in couples without children. Recent work has focussed on free time as a distinct distributive good, but this paper argues that it would be a mistake for a theory of temporal justice to focus only on shares of free time. First, I argue that the concept of free time does not succeed (...) in tracking discretionary control over time. All of time is a resource, and the particular moral relevance of free time must be established otherwise. Second, hours of time differ in use value, and we cannot fully track our concerns about the allocation of time, whether free or necessary, without taking this into account. We care about free time but also about ‘quality time’. To explain this observation, I develop an account of the value of time as a resource. The value of time periods differs with the prospects for which a time period can be used, that is, what we can do and be with it. What we are allocating when we are allocating time is not just hours; it is hours of time with a certain value. Finally, I argue that a concern for the value of time is compatible with a resourcist theory of temporal justice. (shrink)

Advanced AI systems are rapidly making their way into medical research and practice, and, arguably, it is only a matter of time before they will surpass human practitioners in terms of accuracy, reliability, and knowledge. If this is true, practitioners will have a prima facie epistemic and professional obligation to align their medical verdicts with those of advanced AI systems. However, in light of their complexity, these AI systems will often function as black boxes: the details of their contents, calculations, (...) and procedures cannot be meaningfully understood by human practitioners. When AI systems reach this level of complexity, we can also speak of black-box medicine. In this paper, we want to argue that black-box medicine conflicts with core ideals of patient-centered medicine. In particular, we claim, black-box medicine is not conducive for supporting informed decision-making based on shared information, shared deliberation, and shared mind between practitioner and patient. (shrink)

Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights (...) into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation. (shrink)

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two (...) uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation. (shrink)

Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by "impossible worlds". We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the (...) same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both). (shrink)

Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices that contradict the original (...) intention of modern eristic. Eristic is not an art of being right or winning an argument, but an art of protecting oneself from the one who deliberately violates norms of discourse ethics to gain argumentative acceptance. For this reason, eristic must be seen as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Especially in the age of alternative facts and post-factual politics, this makes eristic a valuable discipline. (shrink)

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came (...) from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. (shrink)

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian strategy. But (...) in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (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)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. (...) -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...) Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (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)

The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.

Algorithms are used across a wide range of societal sectors such as banking, administration, and healthcare to make predictions that impact on our lives. While the predictions can be incredibly accurate about our present and future behavior, there is an important question about how these algorithms in fact represent human identity. In this paper, we explore this question and argue that machine learning algorithms represent human identity in terms of what we shall call the statistical individual. This statisticalized representation of (...) individuals, we shall argue, differs significantly from our ordinary conception of human identity, which is tightly intertwined with considerations about biological, psychological, and narrative continuity—as witnessed by our most well-established philosophical views on personal identity. Indeed, algorithmic representations of individuals give no special attention to biological, psychological, and narrative continuity and instead rely on predictive properties that significantly exceed and diverge from those that we would ordinarily take to be relevant for questions about how we are. (shrink)

Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase of regression the entire knowledge (...) about the systematic application and the history of euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with lange. The third period of expansion started around 1760 with the works of Ploucquet, euler and lambert. Finally, it is shown that euler-type diagrams became popular in the debate about intuition which took place in the 1790s between leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800. (shrink)

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

During the past decades, research collaboration between researchers from different disciplines has become more frequent. However, there is a need to look into the generic modalities and challenges. The article explores a series of potential obstructions to cross-disciplinary collaboration of methodological and epistemological nature. Furthermore, a number of contextual, inhibiting factors are outlined. As means of overcoming the obstacles, the importance of mutual knowledge, allocation of adequate time and conducive research management is emphasised. New teams may benefit from tutoring by (...) facilitators, who can help to make problem areas explicit and negotiate solutions. Owing to the training background of the author, most of the examples are drawn from the interface between biomedicine/natural science and applied medical anthropology. However, the issues raised basically apply to all sorts of cross-disciplinary research collaboration in various combinations. (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)

It is little known that Schopenhauer (1788–1860) made thorough use of Euler diagrams in his works. One specific diagram depicts a high number of concepts in relation to Good and Evil. It is, hence, uncharacteristic as logicians of that time seldom used diagrams for more than three terms (the number demanded by syllogisms). The objective of this paper is to make sense of this diagram by explaining its function and inquiring whether it could be viewed as an early serious attempt (...) to construct complex diagrams. (shrink)

In this paper we explore the potential bearing of the extended mind thesis—the thesis that the mind extends into the world—on epistemology. We do three things. First, we argue that the combination of the extended mind thesis and reliabilism about knowledge entails that ordinary subjects can easily come to enjoy various forms of restricted omniscience. Second, we discuss the conceptual foundations of the extended mind and knowledge debate. We suggest that the theses of extended mind and extended knowledge lead to (...) a bifurcation with respect to the concepts of belief and knowledge. We suggest that this conceptual bifurcation supports a form of pluralism about these concepts. Third, we discuss whether something similar can be said at the metaphysical level. (shrink)

Are people with superior intelligence also superior in interpreting the emotions of others? Some studies find that an underlying g-factor links all mental processes leading to an expectation of a positive answer to the question, while other studies find that there is a cost to giftedness. No previous study have tested social cognition among highly gifted, or the Mensa society specifically. The study measures emotion recognition in 63 members of the Norwegian Mensa and 100 community controls. The Mensa group had (...) a higher total score on the EmoBio test and was specifically better at differentiating the anger emotion, otherwise hypthesized to be mediated by subcortical processes. There was no difference in heterogeneity between the groups, contrary to the expectation of an autistic subgroup in Mensa. The study indicate that the positive manifold extends also to social cognition, and runs counter to the concept of a cost to giftedness. (shrink)

Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...) that the ontology of CL enables numerically exact assertions and inferences. (shrink)

This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through the perspective of modern graph (...) theory. Although traditional trees can be interpreted in a modern way, their terms and definitions defy modern standardisation. These distinctions are not only useful for differentiating between Seneca's and Porphyry's trees, but also for comprehending the evolution of this philosophical tradition. Thus the paper highlights the continued significance of these tree diagrams in analysing concepts and categories in philosophy and structuring objects and information in modern fields such as artificial intelligence, computer science, bioinformatics, graph theory, and many more. (shrink)

The question of naturalness in logic is widely discussed in today’s research literature. On the one hand, naturalness in the systems of natural deduction is intensively discussed on the basis of Aristotelian syllogistics. On the other hand, research on “natural logic” is concerned with the implicitly existing logical laws of natural language, and is therefore also interested in the naturalness of syllogistics. In both research areas, the question arises what naturalness exactly means, in logic as well as in language. We (...) show, however, that this question is not entirely new: In his Berlin Lectures of the 1820s, Arthur Schopenhauer already discussed in depths what is natural and unnatural in logic. In particular, he anticipates two criteria for the naturalness of deduction that meet current trends in research: (1) Naturalness is what corresponds to the actual practice of argumentation in everyday language or scientific proof; (2) Naturalness of deduction is particularly evident in the form of Euler-type diagrams. (shrink)

The paper examines Schopenhauer's logic lectures and the eristic dialectics of the manuscript remains in particular. The content of the logic lectures is briefly presented, then the characteristics are highlighted and finally Schopenhauer’s Euler diagrams are examined. The section on eristic dialectics summarizes the history of the text and its origin and reflects the content and order of the document.

The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses (...) mainly on the adaptation of the square of opposition in CL and offers an algebraic notation, which corresponds to the diagrammatic representation. (shrink)

In this paper, we interpret a 19th century diagram, which is meant to visualise G.W.F. Hegel’s entire method of the `Science of Logic' on the basis of bitwise operations. For the interpretation of the diagram we use a binary numeral system, and discuss whether the anti-Hegelian argument associated with it is valid or not. The reinterpretation is intended to make more precise rules of construction, a stricter binary code and a review of strengths and weaknesses of the critique.