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)

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)

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)

National Artificial Intelligence (AI) strategies articulate imaginaries of the integration of AI into society and envision the governing of AI research, development and applications accordingly. To integrate these central aspects of national AI strategies under one coherent perspective, this paper presented an analysis of Germany’s strategy ‘AI made in Germany’ through the conceptual lens of ordoliberal political rationality. The first part of the paper analyses how the guiding vision of a human-centric AI not only adheres to ethical and legal principles (...) consistent with Germany’s liberal democratic constitutional system but also addresses the risks and promises inherent to the ordoliberal problematization of freedom. Second, it is scrutinized how the strategy cultivates the fear of not achieving technological sovereignty in the AI sector. Thereby, it frames the global AI race as a race of competing (national) approaches to governing AI and articulates an ordoliberal approach to governing AI (the ‘third way’), according to which government has to operate between the twin dangers of governing too much and not governing enough. Third, the paper analyses how this ordoliberal proportionality of governing structures Germany’s Science Technology & Innovation Policy. It is shown that the corresponding risk-based approach of regulating AI constitutes a security apparatus as it produces an assessment of fears: weighting the fear of the failure to innovate with the fear of the ramifications of innovation. Finally, two lines of critical engagement based on this analysis are conducted. (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)

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 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)

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)

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)

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)

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)

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.

The dramatic events of the crisis have reignited debates on the independence of central banks and the scope of their mandates. In this article, I contribute to the normative understanding of these developments by discussing John Rawls’s position in debates of the 1950s and 1960s on the independence of the US Federal Reserve. Rawls’s account of the central bank in his property-owning democracy, Democratic Central Banking (DCB), assigns authority over monetary policy directly to the government and prioritizes low unemployment over (...) price stability. I contrast DCB with Central Bank Independence (CBI), which requires that the central bank is independent of the government and pursues low inflation. I evaluate DCB by asking whether justice as fairness requires democratic control of the central bank and argue that it does not. Instead, so I argue, the choice between DCB and CBI should be justified in terms of the difference principle. By reflecting on central banking in a property-owning democracy, I cast new light on the Rawlsian realistic utopia of a just capitalist society, while also investigating democratic objections to today’s independent central banks. (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.

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)

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)

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)

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.

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)

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.

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)

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)

This paper critically examines Timothy Williamson’s claim that knowledge figures essentially in explanations of behavior. Since this claim implies that knowledge is causally efficacious in bringing about actions, it plays a key role in Williamson’s case for knowledge being a mental state. I first discuss a central example of Williamson, in which a burglar ransacks a house. I dispute Williamson’s claim that the best explanation of the burglar’s behavior invokes the burglar’s state of knowledge as he enters the house, by (...) arguing that there is a better explanation that only mentions the burglar’s beliefs. Since the reasons that explain the superiority of my proposed explanation generalize, I conclude that one does not have to invoke a subject’s state of knowledge to explain behavior. Nevertheless, Williamson’s explanation is superior to belief-based explanations if one only considers facts that obtain before the action takes place. In the final part of the paper, I argue that this fact does not help Williamson’s case for considering knowledge as a mental state. (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.

In previous research, Schopenhauer is regarded as a consistent representative of a classical picture theory of language. The paper shows, however, that Schopenhauer does not only present a use theory of meaning in his lectures on logic, but also justifies it with the help of the context principle. Furthermore, it is discussed to what extent Schopenhauer's use theory of meaning is similar to the semantic theory of Ludwig Wittgenstein and his successors.

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 criticism of Immanuel Kant’s logic commenced with the advent of the so-called ‘new logic’ in the 20th century. One particular passage from the second preface to the Critique of Pure Reason has been a source of contention, where Kant asserted that logic has not taken a step forward or backward since Aristotle (B VIII). In Kant scholarship, one current strategy to avoid this criticism is to relocate Kant within the domain of philosophy of logic or by segregating his general (...) logic from modern formal systems. In this paper, it will be contended that this strategy is too weak, given that the B-preface has currently been analyzed in a markedly divergent manner by the so-called ‘methodological interpretation’. In his methodology and history of science of the B-preface, Kant means something different by progress and regression than what his 20th-century critics assume he meant. By examining what Kant and his critics considered to be progress and regress in science and logic, good reasons can be put forward for the argument that Kant was correct in his assertion that logic has not gone a step forward or backward. (shrink)

Japanese translation of ""Schopenhauers Gebrauchstheorie der Bedeutung und das Kontextprinzip. Eine Parallele zu Wittgensteins Philosophischen Untersuchungen". In: 97. Schopenhauer-Jahrbuch (2016), S. 29–51" by Tadahiro Oota (太田 匡洋 [訳]).

The counterfactual comparative account of harm (cca) faces well-known problems concerning preemption and omission. In a recent article in this journal, Daniel Immerman proposes a novel variant of cca, which he calls the worse than nothing account (wtna). According to Immerman, wtna nicely handles the preemption and omission problems. We seek to show, however, that wtna is not an acceptable account of harm. In particular, while wtna deals better than cca with some cases that involve preemption and omission, it has (...) implausible implications in other similar cases – cases that, moreover, pose no problems for cca. (shrink)

In light of the problem of logical omniscience, some scholars have argued that belief is question-sensitive: agents don't simply believe propositions but rather believe answers to questions. Hoek (2022) has recently developed a version of this approach on which a belief state is a "web" of questions and answers. Here, we present several challenges to Hoek's question-sensitive account of belief. First, Hoek's account is prone to very similar logical omniscience problems as those he claims to address. Second, the link between (...) belief and action he proposes is too rigid. We close by sketching a generalization of the account that can meet these challenges. (shrink)

Socialism is a large and diverse political tradition, unified by opposition to capitalism. Economically, socialists also typically support common ownership or some form of social, democratic control over the bulk of the means of production. There are various views on whether this requires central planning or is compatible with some form of market economy. Others understand socialism as a set of values, and either way, those who understand socialism in economic terms are often motivated by what they see as the (...) ills of capitalism and the values that can be realized in a socialist society in their pursuit of these economic changes. Socialist values include ending exploitation and alienation and replacing them with human flourishing and self-realization, community, distributive justice, equality, and freedom. Some also see socialism as the way to environmental sustainability, gender equality, and racial justice. The question of socialist strategy—how to achieve socialism—has often been posed as a dichotomy between reform and revolution. This inadequately captures the content of fundamental disagreements among socialists. Instead, the disagreement can be understood as varying views on the use of parliamentary democracy in a capitalist state, the pace of social change, and the nature of the envisioned changes. (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 the year 1714, Johann Christian Lange published a baroque textbook about a logic machine, supposed to simulate human cognitive abilities such as perception, judgement, and reasoning. From today’s perspective, it can be argued that this blueprint is based on an inference engine applied to a strict ontology which serves as a knowledge base. In this paper, I will first introduce Lange’s approach in the period of baroque logic and then present a diagrammatic modernization of Lange’s principles, entitled Calculus CL. (...) Finally, I would like to discuss the possibilities of how to apply CL to modern cases of concern by using an example from epidemiology. (shrink)

In this paper, we critically examine Molly Gardner’s favored solution to what she calls “the problem of justified harm.” We argue that Gardner’s view is false and that her arguments in support of it are unconvincing. Finally, we briefly suggest an alternative solution to the problem which avoids the difficulties that beset Gardner’s proposal.

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.

CL diagrams – the abbreviation of Cubus Logicus – are inspired by J.C. Lange’s logic machine from 1714. In recent times, Lange’s diagrams have been used for extended syllogistics, bitstring semantics, analogical reasoning and many more. The paper presents a method for testing statistical syllogisms (also called proportional syllogisms or inductive syllogisms) by using CL diagrams.

A particularly promising trail on the search for forgotten logic diagrams leads to Upper Lusatia in the 17th century, more precisely to Christian Weise and his students. Samuel Grosser, who later became rector in Görlitz, and Johann Christian Lange, who later became professor of logic at the University of Gießen, are the most prominent to have published remarkable logic diagrams. Even more remarkable, however, is the fact that Lange's interest in these diagrams ultimately gave rise to the idea of building (...) a logic machine. (shrink)

Several attractive principles about prudential concern and moral responsibility seem to speak against animalism. I criticize some animalist responses to this kind of problem, and suggest another answer, which has similarites with the most important argument in favor of animalism: the “thinking animal” argument.

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 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)