What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of (...) language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role (...) in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.

In this paper, we present and defend an analysis of harm that we call the Negative Influence on Well-Being Account (NIWA). We argue that NIWA has a number of significant advantages compared to its two main rivals, the Counterfactual Comparative Account (CCA) and the Causal Account (CA), and that it also helps explain why those views go wrong. In addition, we defend NIWA against a class of likely objections, and consider its implications for several questions about harm and its role (...) in normative theorizing. (shrink)

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that they are founded on only (...) one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today. (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a (...) dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

This article discusses the problem of global democracy, and why democratic legitimacy seems so difficult to attain at the global level. I start by arguing that the difficulties we experience when we try to widen the scope of democratic governance beyond the boundaries of individual states have nothing to do with the characteristics of global society, but result from the underlying assumption that a political community has to be bounded and based on consent in order for democratic legitimacy to be (...) possible. I then explore how this view came into being, arguing that the perennial paradoxes of democratic legitimacy are little but results of earlier and successful attempts to make the concept of political community coextensive with that of the nation. Finally, I argue that once we let go of the idea that political communities have to be bounded and based on consent in order to qualify as democratic ones, the paradox of democratic legitimacy will look like a category mistake rather than an inescapable obstacle to global democracy. Keywords : cosmopolitanism, democratic paradox, legitimacy, global governance (Published online: 7 November 2008) Citation: Ethics & Global Politics. Vol. 1, No. 4, 2008, pp. 159-174. DOI: 10.3402/egp.v1i4.1858. (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)

The counterfactual comparative account of harm has counterintuitive implications in cases involving overdetermination and preemption. A popular strategy for dealing with these problems appeals to plural harm—several events being jointly harmful. Björn Petersson criticizes this strategy on the grounds that it conflicts with a strong intuition that helps to motivate the counterfactual comparative account, namely, that harming someone essentially involves making a difference for the worse for her. In this paper, I argue that Petersson’s argument is unconvincing.

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)

In many social contexts, social influence seems to be inescapable: the behavior of others influences us to modify ours, and vice-versa. However, social psychology is full of examples of phenomena where individuals experience a discrepancy between their public behavior and their private opinion. This raises two central questions. First, how does an individual reason about the behavior of others and their private opinions in situations of social influence? And second, what are the laws of the resulting information dynamics? In this (...) paper, we address these questions by introducing a formal framework for representing reasoning about an individual’s private opinions and public behavior under the dynamics of social influence in social networks. Moreover, we dig deeper into the involved information dynamics by modeling how individuals can learn about each other based on this reasoning. This compels us to introduce a new formal notion of reflective social influence. Finally, we initialize the work on proof theory and automated reasoning for our framework by introducing a sound and complete tableaux system for a fragment of our logic. Furthermore, this constitutes the first tableau system for the “Facebook logic” of J. Seligman, F. Liu, and P. Girard. (shrink)

Suppose your evil sibling travels back in time, intending to lethally poison your grandfather during his infancy. Determined to save grandpa, you grab two antidotes and follow your sibling through the wormhole. Under normal circumstances, each antidote has a 50% chance of curing a poisoning. Upon finding young grandpa, poisoned, you administer the first antidote. Alas, it has no effect. The second antidote is your last hope. You administer it---and success: the paleness vanishes from grandpa's face, he is healed. As (...) you administered the first antidote, what was the chance that it would be effective? -/- This essay offers a systematic account of this case, and others like it. The central question is this: Given a certain time travel structure, what are the chances? In particular, I'll develop a theory about the connection between these chances and the chances in ordinary, time-travel-free contexts. Central to the account is a Markov condition involving the boundaries of spacetime regions. (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)

Offers historical and philosophical arguments for treating the humanities as sciences.

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)

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)

Logicians have often suggested that the use of Euler-type diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Euler-type diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Euler-type diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Euler-type diagrams can (...) be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712. (shrink)

This article defends three claims. First, that collection and division in the Phaedrus are described as procedures that underlie human speaking and thinking in general, as well as philosophical inquiry, and are not identified with either. Second, that what sets the dialectical use of these procedures apart from their ordinary use are philosophical suppositions independent of the procedures of collection and division themselves; for that reason, collection and division cannot be identified with dialectic as such. Third, that the second part (...) of the Phaedrus is concerned with the broader question how noble or beautiful speaking, in general, may be said to depend on dialectic as much as it is concerned with the question how rhetoric, as a kind of expertise, is related to dialectic. (shrink)

According to the “deprivation approach,” a person’s death is bad for her to the extent that it deprives her of goods. This approach faces the Lucretian problem that prenatal non-existence deprives us of goods just as much as death does, but does not seem bad at all. The two most prominent responses to this challenge—one of which is provided by Frederik Kaufman (inspired by Thomas Nagel) and the other by Anthony Brueckner and John Martin Fischer—claim that prenatal non-existence is relevantly (...) different from death. This paper criticizes these responses. (shrink)

We propose a new dynamic hybrid logic to reason about social networks and their dynamics building on the work of “Logic in the Community” by Seligman, Liu and Girard. Our framework distinguishes between the purely private sphere of agents, namely their mental states, and the public sphere of their observable behavior, i.e., what they seem to believe. We then show how such a distinction allows our framework to model many social phenomena, by presenting the case of pluralistic ignorance as an (...) example and discussing some of its dynamic properties. (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.

In this article I discuss the question of whether a person’s existence can be better (or worse) for him than his non-existence. Recently, Nils Holtug and Melinda A. Roberts have defended an affirmative answer. These defenses, I shall argue, do not succeed. In different ways, Holtug and Roberts have got the metaphysics and axiology wrong. However, I also argue that a person’s existence can after all be better (or worse) for him than his non-existence, though for reasons other than those (...) provided by Holtug and Roberts. (shrink)

A prominent objection to the counterfactual comparative account of harm is that it classifies as harmful some events that are, intuitively, mere failures to benefit. In an attempt to solve this problem, Duncan Purves has recently proposed a novel version of the counterfactual comparative account, which relies on a distinction between making upshots happen and allowing upshots to happen. In this response, we argue that Purves’s account is unsuccessful. It fails in cases where an action makes the subject occupy a (...) high well-being level though one of the available alternatives would have made it even higher. In fact, it fails even in some cases where each of the available alternatives to the action that was actually performed would have made the subject’s well-being level lower. (shrink)

One of the most controversial areas of animal research is the use of nonhuman primates for fundamental research. At the centre of the controversy is the question of whether the benefits of research outweigh the harms. We argue that the evaluation of harms and benefits is highly problematic. We describe some common procedures in neurological research using nonhuman primates and the difficulties in evaluating the harm involved. Even if the harm could be quantified, it is unlikely that it could be (...) meaningfully aggregated over different procedures, let alone different animals. A similar problem arises for evaluating benefits. It is not clear how benefits could be quantified, and even if they could be, values for different aspects of expected benefits cannot be simply added up. Sorting harms and benefits in three or four categories cannot avoid the charge of arbitrariness and runs the risk of imposing its structure on the moral decision. The metaphor of weighing or balancing harms and benefits is inappropriate for the moral decision about whether to use nonhuman primates for research. Arguing that the harms and benefits in this context are incommensurable, we suggest describing the moral consideration of harms and benefits as a coherent trade-off. Such a decision does not require commensurability. It must be well-informed about the suffering involved and the potential benefits, it must be consistent with the legal, regulatory and institutional framework within which it is made, and it must cohere with other judgments in relevant areas. (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.

I raise two objections against Christian List and Peter Menzies' influential account of high-level causation. Improving upon some of Stephen Yablo's earlier work, I develop an alternative theory which evades both objections. The discussion calls into question List and Menzies' main contention, namely, that the exclusion principle, applied to difference-making, is false.

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 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.

This article examines the evolution of the concept of existence in modern visual representation and reasoning, highlighting important milestones. In the late eighteenth century, during the so-called golden age of visual reasoning, nominalism reigned supreme and there was limited scope for existential import or individuals in logic diagrams. By the late nineteenth century, a form of realism had taken hold, whose existential commitments continue to dominate many areas in logic and visual reasoning to this day. Physical, metaphysical, epistemological, and linguistic (...) positions underlie both nominalist and realist views. Since the paradigmatic works on visual reasoning in the 1990s, formal diagram systems have been developed that revive either the nominalist or realist perspectives. Unlike in the nineteenth century, these are not motivated by philosophical views. Nevertheless, they may still have an impact on many areas of philosophy and science outside logic. (shrink)

A theme like “town and science” invites to comparative analysis, and suggests questions like these: Is the urban context a particularly fertile soil for the development of scientific thinking? Or rather the contrary? Is it fertile or barren under specific circumstances? Or does it favour a particular kind of scientific activity?General answers to such questions can hardly be found; still, they may provide case studies with a guiding perspective. Case studies, on the other hand, may lead to better understanding of (...) the implications of the general questions if not to answers. In the following I therefore try to read the emergence of Mesopotamian mathematics into the context of the “urban revolution” and the rise of states (c. 3300 to c. 2300 B.C.).Mesopotamian city states appeared in the late fourth millennium B.C., and were eventually absorbed in larger territorial states a thousand years later. Contemporary with the incipient state formation was the creation of a script and of genuine, coherent mathematics. Both were based on earlier accounting techniques, both were used by Temple officials for administrative purposes, and both were marked decisively by this application. At the same time, both presuppose modes of thought which are not produced directly by their application but only as mediated by a school system.In the mid‐third millennium, an autonomous scribal profession appears for the first time. At the same time emerge the first literary texts and the first “pure” mathematical problems (i.e., problems not directed at or following the pattern of genuine application). It seems as if the scribes, as soon as they were emancipated as a craft, tried out the range of their professional tools.Neither the use of writing for literary purposes nor the possibility to use numbers for “higher” computation were forgotten when the city states were absorbed in larger social systems. Both, however, were subsumed by the interest of the new territorial state, the former as a means to propagate royal ideology, the latter in the royal administration.The final section of the article compares this early Mesopotamian development with other instances of the “urban revolution” and with the development of scientific thought in the Ancient Greek city state and in the context of Medieval city communes. (shrink)

Illusions of personal authorship can arise when causation for an event is ambiguous, but people mentally represent an anticipated outcome and then observe a corresponding match in reality. When people do not maintain such high-level outcome representations and focus instead on low-level behavioral representations of concrete actions, illusions of personal authorship can be reduced. One condition that yields specific action plans and thereby moves focus from high-level outcomes to low-level actions is the generation of counterfactual thoughts. Hence, in the present (...) research we tested whether thinking counterfactually can reduce illusory authorship. In line with predictions, generating behavior-regulating counterfactuals reduced susceptibility to the illusion . Importantly, this only occurred when people expected to re-encounter the situation to which the counterfactuals applied . These findings extend existing research on the boundary conditions of illusory experiences of personal authorship and might hint at a relationship between the illusion and behavior regulation. (shrink)

For Arthur Schopenhauer (1788-1860), logic as a discipline belongs to the human faculty of reason, more precisely to the faculty of language. This discipline of logic breaks down into two areas. Logic or analytics is one side of the coin; dialectic or the art of persuasion is the other. The former investigates rule-oriented and monological language. The latter investigates result-oriented language and persuasive language...

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 a recent article, I criticized Anthony L. Brueckner and John Martin Fischer’s influential argument—appealing to the rationality of our asymmetric attitudes towards past and future pleasures—against the Lucretian claim that death and prenatal non-existence are relevantly similar. Brueckner and Fischer have replied, however, that my critique involves an unjustified shift in temporal perspectives. In this paper, I respond to this charge and also argue that even if it were correct, it would fail to defend Brueckner and Fischer’s proposal against (...) my critique. (shrink)

From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of using (...) geometric diagrams in logic. In this paper, I will trace the historical notes of John Venn and other modern logicians back to the original works published in the Weigel and Weise circles and describe the development of using geometric figures for logical reasoning and representation in that period of time. (shrink)

Derek Parfit famously defends a number of surprising views about "fission." One is that, in such a scenario, it is indeterminate whether I have survived or not. Another is that the fission case shows that it does not matter, in itself, whether I survive or not. Most critics of the first view contend that fission makes me cease to exist. Most opponents of the second view contend that fission does not preserve everything that matters in ordinary survival. In this paper (...) I shall provide a critique that does not rely on either of these contentions. There are other, interrelated reasons to reject Parfit's defense of the two theses. In particular, the availability of the following view creates trouble for Parfit: I determinately survive fission, but it is indeterminate which fission product I am. (shrink)

The digression of Plato’s Theaetetus (172c2–177c2) is as celebrated as it is controversial. A particularly knotty question has been what status we should ascribe to the ideal of philosophy it presents, an ideal centered on the conception that true virtue consists in assimilating oneself as much as possible to god. For the ideal may seem difficult to reconcile with a Socratic conception of philosophy, and several scholars have accordingly suggested that it should be read as ironic and directed only at (...) the dramatic character Theodorus. When interpreted with due attention to its dramatic context, however, the digression reveals that the ideal of godlikeness, while being directed at Theodorus, is essentially Socratic. The function of the passage is to introduce a contemplative aspect of the life of philosophy into the dialogue that contrasts radically with the political-practical orientation characteristic of Protagoras, an aspect Socrates is able to isolate as such precisely because he is conversing with the mathematician Theodorus. (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)

The coronavirus outbreak has led to abrupt changes in people’s daily lives as many state governments have restricted individuals’ movements in order to slow the spread of the virus. We conducted a natural experiment in the United States of America in April 2020, in which we compare responses from states with “stay-at-home orders” and no such orders. We surveyed 458 participants and examined the effects of these government-imposed restrictions on social, mental, physical, and financial well-being as well as the mediating (...) role of resilience. Structural equation modeling reveals that resilience buffers stay-at-home orders’ potential side-effects on well-being. Specifically, individuals living in states with stay-at-home orders report lower functional well-being than individuals living in states without such orders, which negatively relates to resilience. Resilience in turn is associated with higher social, mental, physical, and financial well-being. Thus, resilience can be seen as an effective means of buffering stay-at-home orders’ potential negative effects on the components of well-being. Our results indicate the central role of resilience, which is crucial in dampening the effects of stay-at-home orders on well-being. Following our results, governments and policymakers should focus their efforts on strengthening individuals’ resilience, which is a key predictor of social, mental, financial, and physical well-being. (shrink)

Knowledge on regulatory relations, in for example regulatory pathways in biology, is used widely in experiment design by biomedical researchers and in systems biology. The knowledge has typically either been represented through simple graphs or through very expressive differential equation simulations of smaller sections of a pathway. As an alternative, in this work we suggest a knowledge representation of the most basic relations in regulatory processes regulates, positively regulates and negatively regulates in logics based on a semantic analysis. We discuss (...) the usage of these relations in biology and in artificial intelligence for hypothesis development in drug discovery. (shrink)

In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The family resemblance these diagrams bear in form is often based on a vesica piscis or on a cross: Both logic diagrams and spiritual symbols focus on the intersection or conjunction of two or more entities, e.g. subject and predicate, on the one hand, or god and man, on the other. This paper deals with the development and function (...) of logic diagrams, their analogy to religious art and symbols, and their modern application in artificial intelligence. (shrink)